University of Nigeria Research Publications
NWANKWOJIKE, Bethrand Nduka
Aut
hor
PG/MENG/02/33067
Title
Application of Optimization Technique To
Maximize the Revenue of Palm Oil Mills( A Case study of Nigerian Institute for Oil Palm
Research (NIFOR) Oil Mill.
Facu
lty
Engineering
Dep
artm
ent
Mechanical Engineering
Dat
e March, 2004
Sign
atur
e
APPLICATION OF OPTIMIZATION
.._ TECHNIQUE TO MAXIMIZE THE
REVENUE OF PALM OIL MILLS
A CASE STUDY 0 F NlGERIAN INSTlTUTE FOR OIL
PALM RESEARCH (NIFOR) OIL MILL
'..
NWANKWOJKE BETHRAND NDUKA PG/M. ENG/O2/33 06 7
I l.
DEPARTMENT OF MECHANTCAL ENGINEERING
... UNIVERSITY OF N1G ElUA NSUKKA
MARCH 2004
CERTIFICATION PAGE
This is to certifL that the research project was carried out by
1 NWANKWOJIKE, BETHRAND 'NDUKA (PG/M,ENG/02/33067) of
depai-tifient of Mechanical Engineering, University of Nigeria Nsukka, under
the supervision of Dr. 0. Onuba and is hereby admitted as having partially
satisfied the requirements for the award of Masters degree in Mechanical
Engineering (industrial Engineering and management) of the university
I-IEAD OF DEPARTMENT ,
I ............................. EXTERNAL EXAMINER
I
DEDICATION PAGE
To God be the glory.
This work is dedicated tomy'rnother late' Mrs. Roseline Uzoagbala
Nwankwojike (1955-1994) whose heart desire is fulfilled in this work
ACKNOWLEDGEMENT
I shall always be gratefbl and indebted to my project supervisor Dr. 0.
Onuba for his invaluable guidance, helping hands and ever willing at any
time and place to give necessary encouragement and useful advice that made
this work very successfi.d.
I am also grateful to Engr. S.A. Ugwu (Head of Department of
Mechanical Engineering), Dr. S.O. Enibe, Mr. S.C. Nwanya, Miss Justina
Chidimma Eze, Miss. Endurance Ogboso, Miss. Njideka Sara Orjiene and
I.
many who have helped at various stages in the investigation and writing of
this project.
My gratitude goes to my dear father Mr. Romanus Nwakwojike, my
brothers Friday, Amobi, Chidiebere and Anayo for their concern towards my
academic pursuit.
My thanks are due ;o all the staff of NIFOR oil mill Division of
Nigeria Institute for Oil Palm Research Benin City and the management of
other factories visited during data collection.
Lastly 'l wish to thank everyone who contributed in any way towards
my academic progress and is only Almighty God that can reward them to
their own satisfaction.
TABLE OF, CONTENTS
Con tents Page
Chapter One: Introduction
Chapter Two: Literature Review
Chapter Three: Methodology i
Chapter four: Data Presentatioii and Analysis
4.1 Experimental milling of the oil palm h i t bunches----------------- 73
4.2 orm mu la ti on of linear optimization model for palm oil mills------78
4.3 Analysis of the opinions of palm oil mill factory workers on
perceived needs for effective output of the palm oil mill venture-88
..+.
Chapter Five: Summary, C o ~ l c l ~ r s i o ~ ~ and Recon~mendation
vii
Table 2.1 'The contents of durable fire bricks used in palm oil mill factory------- 6 6
Table 4.1 Records of: experimental mil ling of oil palm fruits----------------- 73
. 'Table 4.2 Percentage analysis of dura records-------------------------------- 74
Table 4.3 Percentage analysis of tenera records------------------------------- 75
t #
Table 4.4 Percentage a~lalysis of pisifera records------------------------------ 76
Table 4.5 ]'rice of oil pallll products---------------- ----' ........................ 77
Table 4.6 Revenue per unit mass of dura and tenrera bunches milled------77
Table 4.7 Llescription of the various item questions of the interview--- 88
Table 4.8 Percentage analysis of palm oil mill worl<ers opinions to the
..._ item questions of the interview according to their levels of need-92
'Table 4.9 Perceiltage analysis of the palm oil inills idle time effects
F I G . 4. I : Vcl-y I I ~ L I C ~ I nwtled proli le plok ol'thc entirc palm oil mill
ABSTRACT
'I'he study applied linear programming technique and other decision
malting tools such measures of central tendency and dispersion, graph and so
: on to tind out what the entrepreneurs of palin oil mills require to n~aximize
revenue and minimize cost of production in their palm oil mill factories. 111
this study, data was collected by mealls of experimental processing of a
given mass of each of the fruit types, direct observation of the operation of
the mill unitslmacl~ines and interview conducted for selected palm oil inills
factory s tdf and customers of the venture. The secondary data source,
which includes the past production records, the daily nlaintenance
recordslhistory ol'the plants units and the mill plants manual were used to
confirm the accuracy of the experimental data. The data generated were '": processed using average, percentile, tables, chart, and graphs. The processed
data were analyzed using linear programming technique with the fruit types,
the dura, tenera and pisifera forming the clecision variables. The ratio of .
2:3:0 for dura, tenerq ancl pisil'esa respectively was found in this stydy as the
combining ratio of the thrce oil palm fiuit types in a processing fi-uit
aggregate (mixture of dura, tcnera and pisifera fr~iits) for optimum revenue
derivation froni the use of palm oil i l ~ i l l in the processing of oil palm fruits. I. The study also provides sufficient process parameters, and cxplanation
(obtained liom the mill factory praclical experience) on various unit
"- operations and maintenance of the mill units. I n addition the work
1-econ~mencls an altermtive source of fuel for operating the mills steam boiler
from the palm wastes such as shell, fibre and empty fruit bunches to
substitute the use of fire wood and diesel which cause high cost of
production in this sector.
CHAPTER ONE
INTRODUCTION
1.1 GENERAL DESCRIPTlON OF THE STUDY
Prior to mid eighties, Nigeria was the world's largest producer and
exporter of palm products such as palm oil and palm lternel. This was
possible through the active participation of farmers, who were encouraged
by the favourable prospects of the sector.
I-Iowcver i n recent time the output and exportation rate of palm
psoclucts in Nigeria is dwinclling. The decreasing rate of oil palm products
output in the country is caused by increased domestic coi~suinption due to
rapid population growthand limited investments in large scale processing of
oil palm fruits . 'rhe direct eSf'ect of this limited investment in large scale
processing of oil pa1111 fruits is the excessive waste of unprocessed raw fruits
due to inadequate processing facilities to process them.
.According to Hartley ( 1 977), investors are scarecl away from this processing
sector due to s l o ~ i rate of the sectors returns thereby talting longtime for the
scctor to break even, when compared with other production and co~n~nercial
sectors.
Processing involves the conversion of raw products to other acceptable
forms of' procluctssince many raw products cannot be used effectively if
they are not proccssed. This is true of palm fiuits, wl~ich cannot be put to
use effectively unless they were processed to other inox useful products
such as palm oil and palm lternel. 'l'he Iternel yields palm lternel oil (P.K.0)
and palm lter~lel cake (P.1C.C). I'rocessing improves the use of raw products
and enhances the sales of the I-csulting products i n large scale (Bor 1990).
'I'lm-elixe the processing of palm fruits is very important in the marketing of
the resulting products, because an efficient and efrective processing
technique will increase thc quantity and improve the quality of the palm
products available [or both consumption and export at a reduced price.
Altho~igh studies on oil palm fruits processing methods are not new in
Nigeria, most ol'thc previoi~s work3 limit their Focus on the efficiency of the '. .
three major methocls of processing palm fruits. The methods are
(i) 1 ,ocal or 1.nanua1 i~~ethod.
. .,(ii) I-land press neth hod.
(iii) Lmge-scale Factory mill method.
'l'he previous studies established that the use of factory mill method is more
efficient lor the li-uit processing tlian others, because the other two methods
are laboriow and time consu~ning.
varying nnt~lre of the three palm fruit varieties and the varying effects of the
mill units on thein was observed to affect the quality of the products derived
t.om them. The fruits are dura, tenera and pisifera. Pisifera gives low grade
of palm oil and no kernel when processed because its shelless kernel are
crushed on pressing giving a mixture of kernel oil and palm oil that cannot
be separated. This ugly phenomenon is less when dura and tenera are
processed. T~ILIS, empirical data from ihe mill effects on various fruit types
is required when seeltillg for solution to the problem of poor product quality
that characterised the recent mills
'i;urthermore, thc propertics of the various palm fruits types showed that dura
has high Iternel and sliell content, while tenera has high inesocarp (palm oil
and fibres) contents. Because of this varying quantities of palm oil and
kernel output of the palin fruit types and the need for the shell and fibre for
operating the mills steam boilers, the operators of the mill ventures face the
problem of choosing the h i t typc to be processed in order to obtain
optimum.pn)lit when tlic prod~lcts are sold. The fruit type to be processed I
(Or ~oinbiiiation 01. them) must give enough palm wastes (shells and fibre
for the steam boikr without excess.
In addition the oil extraction rate of the recent mills was found to ,be, les
than the designed rate of 98% due to high libre content that characterisc
most of the fsuits processed in them recently. According to Gebr. Strock
(1 990), fibre content of any fioit aggregate ondergoing processing in the mill
ii inversely proportional to the rate of oil extraction of the mill. Also the nut
content oS a palm Sruits mixture affects the life of the digester arms and the
entire mills performance.
'I'hc mqjor intention of this project work is to investigate all the
relevant constraints militating against the performance of the palm oil inills
and determination of the en~pirical data based on the constraints. This will
enable the use ol' an appropriate optimization technique (linear prograinining '.. .
tccliniques) to cleter~nine tllc ratio or each h i t type (dura, tenera and
pisifera) that is required in any processing aggregate (mixture of the fruit
types) to obtain an optimum revenue from the use of the palm oil mill. Also
thc work will provide sufficient practical data on various units of operations
of the ~nill and i t? maintei~ance covered from the factory point of view, to
serve as guides Tor mill engineers and managers to prevent frequent
bseakdown that characterisecl the recent mills in Nigeria. This will increase
tire overall profit margin of thc mill enterprise, which will in turn encourage
investment in the large scale palm fruit processing sector.
1.2 PROBLEM ANALYSIS
The major problems facing the operators of large scale palm oil mill
in Nigeria include the following;
i. High cost of the mill equipment, which makes it difficult for the
operators to purchase new parts for the replacement of damaged and
ineffective ones (old units). This also limits their ability to procure
new mill plants that would have helped in the task of processing the
abundant raw palm fruits in this country. The high cost of the mill
plant is due to surplus (unused) capacities in some mill units' design.
. . 11. Poor qualities of products processed from the mill. This leads to low
price of these products which cause, inability of the mills returns to
justifL its high cost. The low grade of mill output is caused by
inadequate maintenance of the plant units to their specific process
parameters as a result of inadequate practical data and lay down
procedures and parameters covered' from the factory point of view for
both corrective and preventive maintenance of the mill plant.
iii. High daily cost of operating the mill leading to high production cost
of the mill products when compared with the cost of products
processed using other methods, making it difficult for the mill
products to compete favourably in the market with the products of the
other methods. The excessive use of firewood as the sole source of
fuel for operating the mills steam boiler which constitutes over 80%
percent of the daily mill expenditure is one of the major cause of the
high production cost of the mill products.
iv. The varying properties of the three different types of palm fruits, (the
dura, tenera and pisifera) namely, the varying mesocarp and kernel
content of each of the fruit type, varying quality of the products
obtained when each type is processed individually, the varying effect
of the fruit types on the life of the mill units and on the oil extraction
efficiency of the mill. In addition to the different prices of unit
quantity of palm oil and palm kernel. The above factors have
imposed the task of choosing the palm fruits type (s) or a combination
of them that will give optimum benefit when processed. The task is
whether to engage in the processing of high kernel content fruits or
high palm oil content ones or both.
This work applied linear programming method, guided by other
decision making techniques and practical experience on the mill
process to formulate and solve a palm oil mill model whose solution
8
: r ~ t l o~licr rclntctl tlata will of'f'cr satisfying s01~1tio1i to the above ~nc~itioned
of. hctory ~nanagcmcnt and could I x anticipated. 'I'licrcforc, the operators of
I . 1ktcrrni1l:ltiw o f c~npiric.:ll tlat:l lx~scd on the co~~straints limiting the
pcrli~~*~n,i~lcc of' tlic pal111 oil ~liills md tlic cvali~ati~n of the revenue
ot~tlxlt of' tlic systc~ll in rcl:itio~i to the tlmc different palm fruit typks.
. . I . I;or~iit~lntio~l ant1 solvirlg ol' a lillcar 131-ogra~nrning model ol' the palm
oil ~ i~ i l l s rising tlic cliipirical h t n tlctcr~uincd.
iii. Determination of practical parameters for future modification of the
mill design and for establishing future palm plantations.
v. Provision of sufficient explanation to process parameters of the
various units of the mill and their maintenance requirements to guide
the mill engineers in the prevention of the mill breakdown, poor
quality of the mills output and in the evaluation of the plants
performance.
vi. To establish an alternate source of he1 for the systems steam boiler to
substitute the use of firewood in mills.
vii. To encourage investment in the oil palm enterprise and the use of
large scale palm oil mills for the processing of palm fruits to reduce
excessive waste of unprocessed fruits in Nigeria .
1.4 RELEVENT RESEARCH QUESTIONS
Some research questions are very pertinent to this study, knowing
fully well that every production system has an objective and sequence of
operation. One will be interested in asking the following questions.
i. What type of palm fruits is the mill designed to process (pisifera,
tenera or dura)?
I . . 11. If the mill is designed to process all the fruit types. How do properties
of each fruit type affects the mill units, the quality and quantity of the
products as well as the revenue derived from the sale of the mill
outputs?
iii. Which of the identified effects (in number (ii)) above requires
encouragement relative to the fruit types?
iv. which of the fruit type will give the maximum benefit when
v. Can the mill give good quality of products that can compete favorably
with products of other methods?
vi. How does good maintecance culture helps to improve the mill
performance. ?
vii. Can we use any other economical fuel source in the mill other than
firewood? I
Others such as the effects of good management policies, workers
motivation and supervision, raw material supply and product demands
on the entire systems performance are minor questions.
1.5. SIGNIFICANCE OF THE STUDY
This work will encourage investment in large scale processing of oil
palm fruits using a mechanized palm oil mill as well as investment in
the palm business through the provision of sufficient data and
explanations to various process parameters covered from practical
mill experience which will be useful to mill engineers and managers
in minimizing the effects of various factors that militate against the
smooth operation of the palm oil mill plant. The data will also be
useful for design modification of future mills so as to reduce their
cost, which will enhance easy procurement of the mill equipment at a
reduced price in future. They will also be important for the planning
of the oil palm species contents of the future oil palm plantations in
other to comply with the fruit types to be recommended for optimum
I
benefit in the sector, and'also enhance reduction in the production cost
of mill products as well as increasing the profit margin of the venture
(mill plant). The increase in the number of palm oil mills in this
country will increase the quantities of palm oil and palm kernel
products available in this country for both consumption and export,
since there will be enough facilities to process the abundant palm
fruits in this nation without excessive wastes
1.6 THE SCOPE OF THE STUDY I
This work covered all areas of operation in NIFOR oil mill division of
Nigeria Institute for Oil Palm Research (MFOR), Benin City in Edo
State of Nigeria. Also related informatioddata obtained from the
Production and Research Engineering Divisions of the same institute
on the MFOR Small Scale Processing Equipment (SSPE) and other
Palm oil mill factories visited during the study were also considered in
the work to diversify the study. , , I.
1.7 LIMITATIONS OF THE STUDY
This research project would have been better than as it is now, but
lack of reading materials militated against this work because only few of the
reading materials required for this work, in almost all the libraries visited
during the initial period of data collection could be obtained.
1.8 DEFINITION OF T E ~ S
I 1. Revenue: Income derived from the'sale of the mill products
2. F.F.B: Fresh fruit bunches that is palm heads or stalk of palm head
containing riped fruits
3. Palm Nut: A depericarped palm fruits
4. Palm Kernels: The seed inside the palm nut (This is soft and edible)
5. P.K.0: Palm kernel oil-oil extracted from palm kernel
P.K.C: Palm kernel cake:- A chaff remains after oil has been
extracted from the kernel
NIFOR: Nigerian Institutes for Oil Palm Research
- - Equal to
> - Greater than or equal to
< - Less than or equal to
Si : Slack or surplus variable
Shell : A hard covering of the kernel seed
Model: An assembly of linear programming equations
Datalparameter: Characteristic or determined features or facts that
are certain from which solutions are drawn.
Oil Palm: The palm tree, which yields the fruits
Mesocarp: The outer most edible covering of the palm fruit which
contains the dil cells and fibre
Optimum: Maximum.
Aggregate: Mixture of dura, tenera and pisifera fiuits or any two of
'them being processed in the palm oil mill
Respondent:- For the purpose of research, it means all the members
of target population of the study interviewed
WorkshopISeminar: Short courses organised for workers to help them
update their skill
cbl'licicl~t alltl c~co~~olllic:~l \\:I\ lilt. tlic ~ i l a x i ~ ~ l r ~ n l Imi~Iit of ~ll;iill~i~l~l. ' 1 ' 1 1 ~
c~l~gi~lcc~.s rises \ ; I I ' ~ O ~ I S sys~eiililt'ic l i l \ \ i ~ i111tl thcorics developed by the
scicrltists to li~ltl boliitio~is to p;~rtic~il;rr prol~lcm(s). 1'1lginecrs approach to
~ ~ ~ * o b l c ~ ~ ~ - s o l i ~ t i o i ~ Iws atl\~a~lc.ccl to tllc cxtci~t that succcss often depend on
tllcir ahil i (\: to tlcal ~ v i t l ~ Ix)tll cco~~o~li ic aid physical i'actors of the problem
co~lcc~mxl. I ~ C ~ ; I I W 111;111~ cvlyii~c~cring ~JI-OC'CSSCS 01' rccclit tinic requircs
.c;c)rl~plc~x tlccisioi~s i l l ~ l lci l (Icsiyi, co~is~~.rietio~~, opc1-;1tiot1 and maintenance.
( l l c l ~ R C I I I I I I ~ ;111d OII\\II~\;I IOOS). 111 I';ICI to CIIOOSC a111ong alternative uses
of ~.cso~i~.cc~. s~il'licicnt ~cbcll~~ic;rl ;111t1 cco11o111ic linowlcdgc 01' thc project to
\vl~icll tllc I-csorll-ccs arc lo he allocalctl i s very essential. Ikgineers select
I 0 1 ' i I I ~ I I : i I i c i o ~ i I I I o r s i i i o ~ i . This makes
I 0 7 ) . I 1g\\,t1 S.A.(2003) said Illat i l l 1.ccc11t practice the technique is
incar
used
I IlCill'
profit. They are usually represented by symbols such as alphabetical
letters.
(c). Constraints: These are limitations placed on the achievement of the
objective. In selecting values for the decision variables the decision-
maker is faced with certain restrictions or limits which cannot be
violated or altered. These may involve limits on resources such as
raw materials, labour time, machine time, storage time, legal or
constitutional requirements such asproduct standards, supply terms,
work period and ' safety standard. Other limitation includes
technological requirements such as components, product size,
machine rest periods, materiaYproduct idle periods and others based
on forecasts policies such as customers orders, materials safety stock
and product safety stock. I
(d). Parameters: They are fixed values attached to the decision variables
that speci@ the impact each unit of the decision variable will have on
the objective function as well as on any constraint in which they
appear.
(e) Linear Relationship: This speaks of the impact of each decision
variable on the objective function and on each constraints in which it
appear and requires that it must be linear.
(f). Divisibility: This concerns potential values, which may be decimals
but could be rounded off to the closest number.
(g). Certainty: This involves the parameters (Numerical values) stated in
both the objective function and constraint, which must remain the way
they are stated.
(h). Non-Negativity Requirements: This is to say that only positive
values and zero are' allowed for variables. The negative values are
unrealistic and therefore are not considered in the determination
profit , resources or cost.
2.2-2 CHARACTERISTICS OF LINEAR OPTIMIZATION PROBLEMS I
A linear optimization problem can be an allocation problem, a
transport problem or an assignment problem. Generally all linear
programming problems go with the following characteristics:
(a). The problem must be limited or constrained and these constraints are
capable of being expressed in quantitative terms.
(b). There must be choices or variation in the magnitude of parameters
used.
(c). Variables must be related to constraints in a linear manner
(d). There must be an objective function required to be optimized, which
must be related to the variables in a linear manner.
cli l'li.rctlt \ i i l t ~ c s o I' t lic. tlccisio~i variables on thc objective, which may
li~rict ion a11d tlic C O I I S ~ r;~i~lts i l l :I standard lincar programming [ormat.
I I ~ S I i I . AIloc:~liori 171-oblc'rils can bc solved by graphical
;~~lal!w:s ol' tlic ~iloclcls solr~lio~l \ \ , Iwi clcsir-ccl. Iri firidi~ig solution to linear
( i i ) . 'I'llc r i ~ l l t Il:lnd side of' a n cqu:ltio~l can always bc lnadc non-negative
Oy ~ilrrltiplyirlg both sitlcs hy -I . 'I'llat is to say that the right side of
(iv) . Also tllc clircction ol 'm i11cc.luaiity is rcvcrscd wllcn it is niultiplied by - -
cocf'ficicnf 01' tllc c y a t imls 01' t l ~ 1llodc1 (ill stiiildd hrm) will be formed.
'I'llis first or initial matrix is d a ~ ~ e t ~ Iirst or initial fcasible tableau. This
rcsulti~lg matrix is solvctl using C;ni~ssi;tn elimination iterative method until
all llic i~idcx ~iu~ilbcrs (!lot i~lclutlcd in tlic co~~stant column) are zcro or
~lcpl ivc. At this point ,111 opli~iial solution or the lnodel is obtaincd and the
tlw 1rst11t i~ig opt i t ~ i a l 111:itrix. 'I'llc sclisitivity analysis of tllc nod el solution
G I I I also be cilr~ictl out algebraically by this ~nctliod if desired.
I
2.3 THE OIL PALM
Oil palm is an indigenous forest trees of West African Origin. The
plant is ubiquitous as a natural grove and belongs to the family of palmae
(C.W.S. Hartley 1967). In its natural grove the tree attains a height of 15
metres to 18 metres, although improved species are shorter.
Rain requirement of 150cm to 200cin per annuin, temperature of not
less than 25' C, good sunshine and a loamy to light clay soil are factors I
necessary for the plant growth and good production (Onwubuya 1997)
Nearly all the parts of the plant have some applications, the root is
medicinal, and the bunk is good for housing, bridge construction, fuel
(firewood) and the juice tapped from it constitute the palm wine. The leaves
are used for roofing and broom making while the fruits constitutes the main
source of the three basic commercial products derived from the plant. The
i palm oil and palm kernel oil forms the 'basic raw materials for industries
such as soap, detergent making, margarine, candle, cosmetic, pharmaceutical
industries and so on. The palm oil also constitutes a basic part of our foods
and diets while the kernel cake is used for livestock feed production.
2.3-1 TYPES OF PALM FRUITS AND THEIR CHARACTERISTICS
The oil palm tree (plant) bears fruits on maturity. The fiuits may be
red in colour with brown caps, green with black caps or red with black caps.
The individual fruit is a drupe, Its mesocarp (covered by thin layered
epicarp) contains oil cells which produce the palm oil. Under the mesocarp
lies a hard-shelled nut fiom which kernel is obtained on processing. The
kernel gives the palm kernel oil and cake on hrther process. The mesocarp
and kernel content of any palm fruit depends on its type. We have three
distinct types of oil palm fruits. There are dura, tenera and pisifera. There
are produced by the three species of oil palm plants.
(a) Dura: A dura fiuit is between 2cm .to 3.5cm in length with an average
weight of 4g and shell thickness range of 2mm to 8mrn. The fiuit
posses little or no fibre rings, low mesocarp and high kernel content
than tenera and pisifera. The fruits palm oil output is low when
compared with the other two species because its low mesocarp
content.
(b) Tenera: A typical tenera is about 3cm or less in length with average
weight of 2.5g and over 80 percent mesocarp content. They posses
about 0.5mm to 1.5mm shell thickness with fibre rings. This fruit
yields high quantity of palm oil and less kernel when processed.
(c). Pisifera: Pisifera is a shelless fruit with little or no kernel in it. Its
length is less than 2cm with high mesocarp content and fibre rings.
i s 1 - 1 1 i t ( I . \ 1 1 0 7 ' . Alicr harvesting, processing of i1 lo other
Processing and marketing of palm product is not new in Nigeria,
historical evidence proves the existence of it over a century ago. According
to Hartley (1997) a missionary hope waddle wrote about the main port of
Bonny in River State which was their main sect of palm oil and kernel trade
in 1846. I
The search for an effective and efficient method of processing fruit of
oil palm took a significant turn in Nigeria around 1830 when British colonial
government recognised that palm oil was a dependable raw material for soap
production in United Kingdom.
The processing of the raw palm fruits involves cooking or sterilization
of the fresh fruits, stripping of the fruits from their stalk or bunch, digestion
I o r pounding of the cooked fruits, extraction of crude palm oil from the
digested products, separation of kernel nuts and fibres, cracking of the kernel
nut and separation of shell and kernel. Other processes include the
clarification of the extracted crude oil to a more acceptable products and the
storage of the products. Presently we have three different methods of
processing palm fiuits.
There are traditional or local method, Hand press method and large scale
factory mill method. Each differs from one another in the sequence of the
processing operations due to different nature of facilities involved and the
extraction efficiency of them. The traditional or local method of processing
raw palm h i t s is laborious because all the processing operations are done
by manual means. Also the extraction efficiency of the method in very low.
The products obtained from processing of palm fruits locally usually retain
1 most of their natural qualities since they are never subjected to a serious
thermal operation. Over 65 percent of farmers in this country use this
method. The hand press method was later developed to reduce the crude
nature of the manual method. This method includes both hydraulic and crub
presses. The device used in this are constructed in a way that the cooked
fruits are placed in a cylinder of hot water under the action of beaters, the oil
and water subsequently run off through the sieves at the side and bottom of
I
the system and later separated, before clarification as in manual methods.
Although the extraction rate of the method ranked up to 65 percent it is still
characterised by some manuai operations of the local method.
The factory method is a large scale method of processing palm fruits
using palm oil mills which involves mechanical milling of the fruits from its
bunches to palm oil and kernel with little or no human interference because
the milling is a continuous flow process. The method can mill between 3
tones to 30 tones of fresh fruit bunches O;'.F.B) per hour depending on the
millrcapacity. The system has over 98 percent extraction rate and provides
over 95 percent of our industrial and domestic needs. Because of the heavy
capital involved in procuring palm oil mills, only' about 13 percent of our
farmers use it. Since the factory mill method is recommended for used
because of its efficiency, this work will use the linear programming tools to
make policies that will be adopted to enhance maximum output of the mills
to justifL their cost. The NIFOR Oil mill division of Nigeria Institute for Oil
Palm Research uses a palm oil mill plant of six (6) tons of FFB per hour I
milling capacity for the processing of the harvested palm fruits bunches from
the Institutes plantations
2.4 THE NIFOR OIL MILL
The Nigerian Institute for Oil Palm Research (NIFOR) formerly
known as WAIFOR was established in 1930 with conducting findings on oil
palm plants (crops) and its products as her major area of operation.
Presently the institutes responsibility has been extended to research on other
palms such .as Raphia palm, Dead palm, Coconut palm and other ornamental
palm species. In addition NIFOR also conducts research on design and
fabrication of small scale palin fruit processing machines
The Institute is divided into departments that were subdivided into
divisions for effective management. The divisions include Account, Audit,
Agronomy, Agricultural economics and extension, Administrative,
. ,
Computer and Statistic, Chemistry, . Health, Maintenance Engineering,
Production and Oil mill divisions. . .
A director assisted by a deputy director and other assistant director's
heads the institute.
The Oil Mill division is under the production and sales department. Areas of
operation of this division includes processing of the harvested fresh fruit
bunches (FFB) of oil palm fruits, black soap and ash making, maintenance
of the mill machines and marketing of the processed product of the mill.
, The division forms the base for the experimental testing and evaluation of
research findings in the Institute using its mill plant and its accessories.
The Oil mill division is headed by a Production Engineer with overall
employment size of 15 professional and 35 non-professional staff. The
division is further subdivided into sections for effective supervision in the
mill factory. The sections include welding, mechanical, Electrical,
Administrative, quality control, store keepingRecording and sales. . ,
The NIFOR Palm Oil mill and other equipment/tools used for
maintenance quality control and soap production constitutes the major
resources of the division in addition to her human resources.
The palm oil mill plant is a continuous factory flow process that process
palm fruit bunches (FFB) to palm oil and kernel. The shell, fibre and empty
bunches are direct by-products of the process. The milling process occurs
with little human control as illustrated in the material (FFB) transformation
flow diagram of the palm oil mills below. Others such as the layout plan of
the mill plant and the schematic flow diagram of the palm oil inill shown in
Appendices A1 and A2 respectively will aid your understanding of the
' various units of operation of the NIFOR oil mill factory described below.
F I G - 2 - 2 : : RAW MA'I'EIUAL, (FFI$) TRANSFORMATION IN PALM
I I..oaling Resip > Calyx Lcaves and Dirt
Ash > Fruit (Secondary Product)
-1
Oil
Crr~dc Oil 1 1 IVcss cakc (Nut and Fibres) r 1
\(/~crccncd Oil , I ,~e t nuts V
Silo Drycr Walcr
--
'I Nut Cracker
Sludgc Crackcd Mixture
Ccnlri fugc M rackcd niixture M
Sludgc Optiotiiil Vibrating screen 1 \ /
Oil Rccovcrcd Polids 1 (scc. l'roducl)
1 Iigli tirade Oil (I'si~~~ary
'k Slrttlpc to drain or I;rtitl disposal
$hell/~ibre (fuel)
Kcrncl (I'ri~w~ry l'roduct) 1'0 Boiler
2.4-1 WEIGHING AND LOADING STATION
The raw materials (FFB) from the farm or plantation are received at
the weighing bridge station at the entrance of the factory premises where the
quantity of the input supplied can be measured. After measuring and
recording of the quantity of the raw material (FFB) supplied, it is then taken
to the loading ramplplatform. This ramp enables easy loading of the
bunches into the cages used for conveying the bunches to the sterilizer.
The highly treated cages for the fruit bunches are perforated all over
their bodies for easy penetration of steam into the fruit bunches contained in I
it during sterilization. The cages are supported on steel chassis in which
bogie rollers are attached for easy movement of the cages on the rail, which
extended from the ramps to the sterilizer. The motion of the cages from the
loading station in and out of the sterilizer vessel is effected by the use of an
1
electric motor driven gear and pulley system called capstan equipment with
the aid of nylon or marine rope and hooks. The weighing bridge is also used
for measuring quantities of mill products when sales are made in large scale.
Determination of the difference between the weight of raw materials or the
products plus its container and the weight of the empty container form the
base at which this weighing bridge operates. The FFB cage in NlFOR mill
is capable of containing 1.5 tones of fresh fruit bunches.
The following is the routine and corrective maintenance activities
required in keeping the facilities of loading and weighing station;
i. Regular and adequate lubrication of the cage bogie rollers, the rails
and the capstan gearbox with the manufacturers recommended
lubricants or its equivalent. This will assist in preventing excessive
wear of these facilities , ,
I
ii. Daily checking of the weighing bridge reliability using standard
weights.
iii. Protection of electric motors and other electrical cables in this section
from excessive water bath
iv. Welding of broken rails and thermal straightening of the bend ones as
well as replacing any one whose damage is beyond repair forms the
1 major corrective maintenance in this section. Others include recoiling s
of bui-nt electric motor coils and replacement. of others with new one if
their damage goes beyond repair and also replacement of burnt
electric cables.
2.4-2 STERILIZATION STATION
Sterilization is the process of cooking the fresh fruit (FFB) using a
continuous steam flow or by water bath. This forms the first stage of the
I process in the milling of fresh h i t bunches of oil palm using palm oil mill.
'I'llis is clone witlg a prcssrwc vcsscl callccl stcrilizer. The raw fruits bunches
(1;1;13) arc sterilized i l l ortlcr to
- Stop aciclification o f oil (F.17.A rcduccd).
- 17acilitatc thc scparatiotl and loosening of the fruits from their
b~~ticlics.
- I'rccondition tllc l i t l i t pcricarp for subsequent processing
operations (oil cxtractio~l).
- Obtain good cracking condition.
- I'recondition t l~c kcrnel nuts to minimize kernel breakage
during pressing.
'I'hcrcTorc inatlccpatc sterilization affccts the whole subseq~lent milling
proccsscs advcrscly.
'I'hc stcrilizer co~nn~only uscd in moticri~ factories is thc horizontal sterilizer
. because vertical sterilizers are laborious. The l~orizontal sterilizers used in
NI170R Oil mill division are provided with a pair of internal rails each to
ctial~lc casy motion of thc F1713 cages in and out of the container. Its
~ I . C S S I I ~ C rating is 3kgf/cm3 and operatcs satisfactorily at about 40 psi gauge
prcssurc (2.7~kgflcn1~) and at temperature range of 100°c to 120°c
maxilnuni. Tkwll of thc two sterilizers used has a capacity of containing
tlirce (3) cages ol' fruit bunches. The stcri lization period for normal bunches
1. Exhaust pipinghalve
2. Steam inlet pipinghalve. 2b. As valve for discharging condenses I.
along steam inlet pipe . . .
3. Pressure gauge
4. Steam valve for directing steam to the doors rubber seal to enable it
gum
5. Adjustable sterilizer door
Spreader sheet for even distribution of steam
Continuation of Boogies rail
Wedge
Condensate valve
By-pass valve
Cement coating
Wire gauze for reinforcement of cement coat
Grass wool (wool that can withstand high temps)
14. The steel metal vessel
15. Steam rubber seal in the door
16. Gaskets.
Capacity = 3 cages = 4500kg (4.5 tomes) of FFB, Holding capacity
(Cooking Time) = 50 min. - 7Omin. depending on the hardness of the bunch.
The sterilizer vessel is insulated to prevent excessive loss of heat during the I
cooking. This is done using a coating of grass wool followed by a net of
metal gauze reinforced cement (or ceramics) coating. The gaskets used in
the sterilizer vessels are abettor cods. The vessel is an alloy of steel that can
withstand high pressure.
The grass wool and the abettors packing used for insulating and prevention
of steam leaking in the sterilizer respectively are materials that can withstand
I high temperature (heat) without burning. '
The pipinglvalve arrangements of a horizontal sterilizer is relatively simple
consisting of one inlet, exhaust, condensate and a by-pass valve.
- The steam from the boiler are admitted into the sterilizer vessel
through the inlet valve via a reducing valve distributor or from the
exhaust of the steam alternator set.
- Spreader plate which runs practically across the sterilizer length under . ,
I
the inlet pipe spreads the steam evenly throughout the vessels to
prevent over cooking of bunches immediately under the aperture and
undue local erosion. I . - The exhaust pipinglvalve system is used for discharging of steam out
of the vessel when required and after sterilization
- The condensate valve is used to drain condensed water out of the
vessels bottom as a result of temperature reduction of steam particle
during the process for the prevention of uneven contraction of the
bottom part of the vessel resulting from relative condensation of steam
during the cooking. I
- The By-pass valve is usually partially open for most of the
sterilization period to allow continuous bleeding of
air/stearn/condensate mixture out of the vessel. This condition is
required for satisfactory sterilization result. 1
- The wedge at the end of the rail in the sterilizer is to prevent excess
motion of the loaded cages to in the vessel cover.
- The gauge is a safety,device that indicates pressure of the steam in the 1.
vessel at any time of the process.
Mode of Operating the Sterilizer
i. Drain all the condensed water at the bottom of the vessel.
ii. Lock all the valves.
iii. Load the vessel with the maximum number of cages it can hold.
iv. Close the vessels door and bleed . out , condensed water along the inlet
pipe using the small valves along the inlet pipe.
v. Unlock the inlet valve and bleed the air in the sterilizer by downward
displacement by opening the condensate and by-pass valves for about
30 seconds.
vi. After bleeding, lock the condensate and By-pass valves partially and
allow bunches to cook under continuous steam supply.
vii. Whenever the pressure increases above the rated value, open or
unlock the exhaust valve for excess steam release or lock the inlet
valve and then, unlock it again whenever the pressure restores to
normal. After Cooking:
viii. Lock.the inlet valve and the steam valve that supply steam to the v
sterilizer door to allow the vessels pressure to drop gradually for about
10 minutes.
I ix. Unlock the exhaust valve for about five minutes to bleed out excess
steam before unlocking the condensate and By-pass valve hlly for
draining of excess condensates. Note that opening of the last two
valves before the exhaust valves and allowing the vessels pressure to
build above the specified working pressure is severely dangerous.
x. Make sure that gauge indicates zero reading and that condensates
I are hlly drained before opening the vessels door for the cages
dispatching .
xi. Drain condensed water at the bottom of the vessel after use and
whenever it is not in used regularly, to avoid excessive corrosion of
the sterilizer. Servicing of valves and regular replacement of burnt
gasket in the vessel to avoid leaking of steam constitutes the common
routine maintenance activities in this unit. Others include welding of
broken rails and pipes, and the doubling of the sterilizers vessel
whenever its thickness reduces by more than 20mm to avoid accident.
2.4-3 STRIPPING
Stripping (or threshing) is the separation of the sterilized fruits
(together with associated calyx leaves) from the sterilized bunches stalks.
After which the fruits are conveyed to the oil extraction unit while the empty
stalk or bunch refuse are conveyed to the incinerator via the refuse bunch I
elevator.
Before stripping process, the sterilized fruit bunches (FFB) are
transported in their container (cages) using capstan equipment and an over
head crane which lifts the cages to a height above the sterilized bunch hopper
head crane which lifts the cages to a height above the sterilized bunch hopper
and empties the cages by tipping into the hopper while the cages are still
suspended from the hoist.
The threshing machine set up in the NIFOR Oil mill consist of a timed
beater arm stripper, a long cylindrical rotary drum stripper and a bottom
worm or screw feeder. The beater arm stripper is placed in between the
bunch hopper and the drum stripper to pre thresh the sterilized bunches
before feeding them to the drum stripper.
The beater arm stripper consists of a rotating shaft with curved
projections set at a fixed angel to the shaft and equidistantly spaced from one
another. The design and the position of this stripper enables it to perform its
pre-threshing function of dislodging the fruits in the sterilized bunches
passing across it from the bunch hopper to the main drum thresher
The horizontal cylindrical1 drum stripper (6.0m length and 2.lm
diameter) is made of a central shaft carrying spike bars to which the
cylindrical cage is attached The two ends of the shaft are supported on
bearing. The cylindrical cage of this device is made up of tee bars (T-bars)
running parallel to the axis of the cylinder. The bars are spaced to permit the
1 escape of the fmit nuts and close enough to prevent stalks from passing
between the space. The partially stripped bunches by the beater arm stripper
are fed continuously at the other end as the stripped while the empty stalk
passes out continuously at the other end as stripped fruits drops through the
drum spaces to the screw feeder at the bottom of the stripper.
The rate of the rotation of the drum is such to ensure that bunches of
normal size are lifted by the centrifugal force (assisted by the bars inside the
cage) to dislodged the fruits out of the stalks. The cycle is repeated for
many times leading to the removal of all fruits as the stalk gradually move
towards the end of the cage into the refuse bunch conveyor. This feeds them
into the inclined conveyor that finally transports them to the incinerator for
burning. The dislodged fiuits pass out through the cage spaces into the
screw or worm conveyor, which feeds the bucket elevator (fruit elevator).
The fiuit elevator transports the stripped fruits to the digester for digestion.
The rows of irregular spaced steel plates teeth at the outlets end of the cage
drum is to ensure that fiuits which escape removal from the bunch up to this
point are dislodged in the same manner as in the beater arm before disposal
of the empty Gunch.
Routine maintenance activities in this section include regular and
adequate lubrication of the gears and bearings with specified lubricants and
subsequent replacement of them when worm. Others include regular
reconditioning of the feeder worm to dimension for effective fruit removal,
replacement of weak pins and fasteners of the bucket-elevator and regular
removal of fibre-cake accumulated on the drum cage and other parts of the
stripper.
2.4-4 DIGESTION
After stripping of bunches, the sterilized h i t s together with
accompanying calyx leaves must be reheated and the pericarp of the fruits
removed from the nuts and prepared for pressing. This is done using a steam
kettle provided with stirring arms called digester. The stirring arm of the
digester is also called digester am.
The Palm oil mill digester is a steam-jacket vessel in which the stripped
fruits is stirred and reheated to make them suitable for pressing. The
digester has a vertical rotating shaft to which the stirring arms are attached.
They stir and rub the fruits to seperate the pericarp from the nuts and at the
same time opens as much oil cells as possible. The digester is always kept
full as the digested fruit is drawn out continuously or intermittently fiom the
bottom of the vessel by continuous flow of freshly stripped fruit at equal rate
fiom the fruit elevator conveyor into the kettle. This is essential for good
digestion of the fruits, since it helps to ensure maximum holding time and I
maximum stirring 1 rubbing (depericarping) effect per revolution of the
I rotating arms on the fruits. Inadequate digestion increases oil loss to fibre
and can be noticed if the press cake contains undigested pericarps and when
some undigested pericarps are found attached to uncracked nuts. The four
pairs of long stirring arms of the digester and its smooth sleeved wall
prevent the accumulation of dry fibres on the wall of the digester. This
maintains the rate of heat transfer to the digester contents from the vessels
steam jacket I
The digester arms are set at fixed angles to the horizontal to give
individual fruit an up and, down movement as the arms sweeps by, causing
the rubbing of the fruits against one another as the digested fruits moves
downward to the bottom of the digester. The normal speed of rotation of the
digester arm is approximately 26 r.p.m.
Sufficient heat must be supplied in the form of steam to raise the
temperature of the digested &its close to 100°C at the bottom outlet for I
effective oil instruction and to minimise breaking of nuts during pressing by
increasing the elasticity of the nuts. Bottom perforation of the vessel helps
to drain oils f o h e d during digestion to increase the rubbing friction during
the process.. This increases the efficiency of the digestion process.
The digester used in this factory has a holding capacity of 60 minutes.
It has a diameter of 1.2m and height of 2.7m. When the space
occupied by the shaft and stirring arms is considered the volume of fruits the
vessel can contain will remain about 2550 litres (2.52m3) out of the total
volume of 2.75 cubic metre of the vessel. This vessel holds a maximum of
4.2 tons of digested fruits. In practice the digestion time is less than 60
minutes.
I Lubrication of the gearbox, i d bearings regularly with the
manufacturers specified lubricants and regular replacement o f damaged
digester sleeves and arms are common maintenance activities in the digester.
Others include reconditioning of worn digester arms and shafi using a hard
facing manganese-silicon electrode and cleaning of the digester shoots
regularly for easy flow of materials into the vessel. The diagram of the
digester described above is shown below.
F I G . 2 . 4 : . A DIAGItAM OF I)lGKS'I'E1Ul'l~ESS FEEDER
Cicnr box
I llleclric ro to r drive
Steam Jacket
Digesters sllaft
Digesters arm
2.4-5 OIL EXTRACTION AND CLARIFICATION
The extraction of crude palm oil fiom the digested palm h i t s in the
NIFOR mill is by pressing using a mechanical driven semi-continuous
hydraulic press machine. Clarification is a process by which the extracted
crude oil is cooked or refined to remove impurities and water in it. This will
make the product suitable for storage and use. I
The Press Machine
The continuous feeding of digested h i t s fiom the digester to the
press machine is by the means of a vertical chute connecting the digested
fruits hopper and the digester.
In the hydraulic press, the digested h i t is pressed in a press cage by
the means of a hydraulic ram of diameter 250mm. The press cage diameter
is 540rnm with thickness of 4Omm and a perforated body through which the
crude oil is expelled during p;essing. Each of the perforations is 2mm in
diameter for one quarter of the cage thickness and 4mrn in diameter for the
outer three-quarters of their remaining cage thickness. They are drilled in
lines with 12.5mm spacing between adjacent holes. To ensure that the press
cake formed during pressing is divided into convenient portions for easy
handling by the press machine, five steel dividing plates are usually
positioned in between the cages during pressing. During the pressing, the
digested cake flows into the press cage td fill its volume whenever the press
ram does not obstruct its passage. In this process the ram descends from the
above as the press cone closed the cages bottom to subject the fruits in the
press cage to pressure (70kgf7cm2) to expel the crude oil out of the digested
cake. The ram continues its downward movement as this cake breaker cone
descends inward to force out part of the pressed cake. The ram ascends to its
starting position automatically, once it reaches its lowest downward point to
allow more digested fruits into the press cage. The cone at the same time
moves outward to expel the whole pressed cake of the cycle. The pressed oil
oozes out to the crude oil tank through the cage perforations and the crude
oil funnel. The crude oil is stored temporally in the crude oil tank before
pumping to the clarification room for further process.
Lubrication of the press gearbox with the manufacturers specified t
gear oil or its equivalent, regular changing of slacked belts and regular
gauging of hydraulic systems oil form the routine maintenance activities in
the press machine. Others such as welding of broken shafts or their
replacement with new shafts when damaged beyond repair and the
reconditioning of press worm and cages constitutes the common corrective
maintenance in this unit
<--- Extracted crudc Oil to Crr~tlc Oil 'l'n~ik
Ilytlranlic or Oil A 2
Ilydraulic or Oil
FIG-2.6: . II~CONDITIONING l'AIIAMICr'TEHS O F SCREW
WORMS,
Mi11 tliti~ct~sion 5mm
(61)) PRESS WORMS AND CAGES Mi11 Din~~ieter 4ma1
I O I ~ I I I I Max, 12intn
52
I
Note that the conditioning of worms is done when the dimension of the
screw is reduced to the indicated minimum dimension (in figures above)
using any hard facing electrode. While the whole worm and cages are
changed (or replaced) when their body thickness reduce to minimum
dimensions indicated in the diagrams above. This will prevent excessive
leaking of nuts and fibres to the crude oil tank.
I The Clarifier
Clarification, which involves cleaning and drying of crude palm oil to a
suitable clean product, is performed using a continuous settling flow tank or
clarifier and a vacuum dehydrator.
The impurities and large portion of water present in the crude oil are
removed in the clarifier. This involves settling out of solid particles and
water (sludge) at the bottom of the vessel with the less dense clear oil
I forming the upper layer. The speed of settling of these particle in a clarifier
is proportional to
- Square of the particles diameter
- The difference between the densities of the settling particles and the
- medium through which they are settling (oil) and also inversely
proportional to the viscosity of the medium (Gebre Stroke 1991).
Since the viscosity of a medium reduces with temperature increase,
the speed of settling increases with temperature. Therefore a high
temperature range of 85OC to 100°C is required for effective performance of
the clarifier and good clarification results. In the continuous settling clarifier
used in this factory, the seperation of the diluted crude oil into clean oil and
sludge is automatic and continuous. The dilution of crude oil is usually 100
percent (with water) or more. The diluted crude oil enters the clarification
tank through a pipe at the top, which is lowered approximately half way
down the tank. An over flow pipe near the top of the tank is used to drain
the seperated oil out of the tank. Also the sludge pipe is used for continuous *
draining of the seperated sludge out of the vessels through its bottom. After
clarification, the separated oil containing over 0.5 percent of water are dried
to around 0.08 percent moisture content using vacuum dehydrator to make it I
suitable for storage.
Note that the clarifier is a steam jacket vessel. This enables the
continuous supply of steam to the system and also for uniform. heat
distribution to all parts of the tank to ensure uniform cooking of the oil in the
vessel. The diagram of the clarifier and its steam circulation network is
shown below.
FIG. 2 . 7 ( a ) LONGITUDINAL SECI'lON OF A CL,AlillW!X
r-------- I ! Crudcoil
From lllc press
The conlir~uous < Sclllirrg lank
Cl ude Oil - Iloppcr
The major maintenance required in the clarification station include repair1
replacement of damaged valves and pumps in the unit and regular
adjustment of the relative height of the sludge take off and clean palm oil
overflow pipes to avoid high oil content of the discharged sludge.
2.4-6 NUTIFIBRE SEPERATION
I When digested h i t is pressed to extract oil, a cake made up of nuts
and fibre is produced. The composition of this cake varies considerably,
depending on the type of fruit processed. This cake fiom the press machine
is a compacted wet mass that must be broken before separation of the fibre
and the nut is possible. The complete separation of fibre and nut is achieved
using a cake breaker conveyor and a nut/fibre separator
Cake breaker Conveyor:
The loosing and pre-drying of the compacted wet cake fiom the press I
machine is achieved using a cake breaker conveyor. This system is also
used to dry the cake, (particularly the fibre) before feeding it to the nut/fibre
separator. The conveyor is a steam jacket trough type with a rotating shaft
fitted with paddles; at an angle to the horizontal for slow forward movement
of the cake in the trough and to provide uniform distribution of heat required
for effective drying of the cake. The diameter of the conveyor trough used in I
the NIFOR mill is 60cm and the speed of rotation of the paddle is 75 r.p.m.
' The movement of the paddle breaks the compacted fibre-nut cake and
provides a forward movement that feeds the loosed cake to the NutIFibre
separator.
NutfFibre Separator:
The NutLFibre separator used is a vertical column type. The top of the
column is connected to the fibre cyclone via a duct. Inserted at the close
bend end of the duct is a fan, which sucks air through the open end of the . ,
1.
column and blows it along the duct to the fibre cyclone. The fibre is
seperated from the nut by. this air sucking process. The fan provides an air
sucking velocity of 7.1 metres per second in the column.
The fibre passes through the sucking fan to the cyclone while the nuts
falls through the bottom of the separating column directly into a screw
conveyor. The separated nuts are conveyed through a rotating screen to
remove dusts, small stone and'broken kernels before transporting them to the
nut silo where the nuts will be reheated before cracking.
Protection of the fan blades from excessive wear by depositing runs of
hard welding electrode metal on the blades and replacement of old fan
blades and casing constitutes the maintenance works in this unit.
2.4-7 KERNEL EXTRACTION
After separation of fibres and nuts, the fibres finds their way to the I
steam boilers fbmace, while the nuts are conveyed to the nut silos where
they are conditioned for cracking. The nut conditioning, cracking, removal
and recycling of uncracked nuts and the separation of the shell from the
kernel constitutes the kernel extraction process. Others include drying and
bagging of the extracted kernel.
(a) Nut Conditioning (Nut Silo):
This involves drying of the nut sufficiently to loose the kernels from j
the shell and then cool them before cracking of them. This is achieved using
a steam jacket nut silo. The nuts are fed continuously into the silo at the top
and removed continuously from the bottom at the same rate so that the level
of nuts remains fairly constant in the vessel throughout the milling process.
The capacity of nut silo used ~ ~ ' M F O R mill is 30 tons of palm nuts per day
(1250 tons per hour).
(b) Nut Cracking (Cracker):
The cracking of the nut is facilitated using vertical throw nutcracker. The
rotor of this cracker is attached to a horizontal shaft, which rotates at a speed
of 1300 r.p.m. The stator ring has a diameter of 71cm and lies in a vertical
plane. The feeding of the nuts in the cracker is directed at the centre of the
rotor via a chute and pass out along four channels in the rotor. They strike
the stator at points round the circumference but due to the method of feed 1
the striking tends to concentrate at one point. ,The cracker used has a
capacity of cracking one ton of nuts per hour with efficiency of 96 percent.
Separation of uncracked nuts from the cracked mixture is achieved using
cracked mixture screen. The separated nuts (uncracked) are later recycled to
the cracker.
(c) Kernellshell Separation (Hydrocyclone):
I The seperation of wet kernel from its shell in a cracked mixture is by
the use of Hydrocyclone separator.
A hydrocyclone is a cylindrical cone bottomed vessel with a critical
size aparture at its bottom. The upper part of the cylinder is closed by a
horizontal plate, through which a short length of pipe known as the
adjustable height overflow tube passed. The cylinder extends upwards above
this plate and this section of it is closed by a piece of plate. Below the two
horizontal plates is an inlet pipe that enters the cylinder tangentially. Also an
exist pipe situated near the top of the cylinder forms part of the system. The
hydrocyclone imparts circular motion to the fluid by means of a tangential
centrifugal force and after a helical racing, the fluid find its way out through
the bottom of the cyclone. The fluid used in the hydrocyclone is water.
During the kernellshell seperation, the mixture of shell and kernel is placed
in a bath of water connected to a pump. This is to enable the water charged I
with shell and kernel to be pumped into the cyclone causing downward
movement of the shell pieces (being denser than kernels) to the bottom of
the cyclone. The larger part of the water together with most of the kernels
after taking part in an initial downward circular movement gradually move
upward towards the center of the cylinder and leaves the hydrocyclone via
the over flow tube and exist pipe. The shape of the kernel also contributes to
its upward movement in the cyclone. After this the shell fraction passing
downward is again pumped by another pump to a second cyclone called
shell cyclone to distinguish it from the first one which is called kernel
cyclone. The two cyclones are adjacent with a perforated partition between
them to allow equal water level in them. The shell passes out of the shell
cyclone through its coned bottom aparture. It is then discarded or used as
the boiler he1 after dewatering of it over a screen. Maintenance requirement . ,
of the Hydrocyclone includes;
1. Regular adjustment of the overflow tube heights to compensate for the '
effects of wears in the cone outlets and the pump rotor.
2. Reconditioning (or replacement where necessary) of the perforations
in the perforated partition between the cyclones regularly to prevent
kernels passage through it to the shell fraction in shell cyclone
(d) Kernel drying (Silo Dryer):
Apart from external moisture on t'he surface of kernel seperated in the
hydrocyclone, there is internal moisture amounting up to 20% of the
kernel weight inside them. This moisture is difficult to remove, as it
must first diffuse outwards to the surface before it can evaporate. This
drying is done using a continuous kernel silo dryer. In this dryer, the
wet kernel from the hydrocyclone is fed continuously at the top while
dried kernels are removed similarly fkom the bottom at the same rate.
Drying is achieved by continuous blowing of warm air current
through the kernels in the silo using in fan. Drying of kernels to 7% .
moisture content is necessary for good storage condition of the kernel
to avoid mucor growth within the kernel when stored and this silo
provides this service in the mill.
The detail arrangement of the kernel processing machines described
above in a palm oil mill is shown below.
I 2 . : l A l A 1 A l A A N M N ' OF KERNEL
ICX'I I<AC"l' ION 1'1 , A N T I
L Wcl nuls livnr lhe tihrc/n~~t scpxator
- --- -- - -
N l I I ( ' o n d i ~ i o ~ ~ i ~ y (Nut Silo)
-- -- - -- - - I_- 1
l illcracked Nut
--
I<cl.nc.l I )I.) illy (Kclncl Silo)
2.4-8 ENERGY GENERATION IN THE MILL
The milling of oil palm fruits process requires energy in the form of
heat for the extraction process and also i~ the form of electrical energy for
operating the mill machines in the mill factory. The steam boiler
generates this energy using the process wastes. The boiler produces steam
which is used for operating the steam alternator set and for the milling
processing.
The fuel used by the boiler is supposed to be palm waste such as fibre
and shell with little quantity of firewood to initiate combustion process in its
' furnace, but recently the used of firewood dominate. The boiler used in the
NIFOR mill has a capacity of producing 2500kg of steam per hour with a
working temperature of 20S°C and pressure of 1 8 0 ~ 1 c m ~ . *
The boiler consists of a furnace for combustion of fuel to produce heat
needed for the steam production. The furnace is made up of firebricks,
which withstands high temperature without excessive dilapidation and the
fire rods, which separates the burning he1 (palm wastes or firewood) and the . ,
I
burnt ash. The adjustable furnace doors in the roof and front of the furnace
is used for feeding fuel to the furnace and for removing of the ash from the
furnace respectively.
Another essential part of the boiler is the pressure vessel. 'I'he vesscl
is insulated with grass wool coated with ccranlics to prevcnt exccssive loss
of heat from thc system. It is nlacle up of flame or boilcr tubes, which
extends from the furnace through tllc vessel to tllc smoke box. The mode
heat transl'er from the furnace through thc tubes to thc watcr contained in the
vcsscl is by conductio~l and convection. 'I'hc safety provisions in the boiler
vessel are the pressure gauge a~ld thcr~nometers for pressure and temperature
regulation in thc unit respectively and the black alarm which indicates
excessive loss of water below fire levcl in vessel. Others include the safety
valvc that regulates the pressure of the steam in the vessel and the manhole
door entrance into the boiler during inspection and maintenance. The blind
flange is a provision reserved for connecting the system to any other unit
where steam may be needed outside thc mill or to any othcr unit that cannot
be fcccl through the main steam valve.. The condcnsatc valve is for draining , ,
condensed water out of the vessel to avoid cxcessive corrosion and
un~lecessary reduction on the system te~nperature during operation. The
smoke produced in the system is handled with the aid of the smoke box and
1'01- ( I r ~ r r i l ~ i I i ty ol' h i let- t lie olwntors or firemen 111ust observe the
. . I I'risurc that tlic \vatc'~- Ic\:c'l i n tlic \lcsscl did riot fall below the fire
I c \ ~ l i~iclic;~tc.d i l l tlic r i l l i t I)! ~-cgr~lar gauging of' \vater in the vessel.
l'liis is to prcvciit corrosiori ol'tlic' slccl vessel and the flame tubes.
iv. 'I'lle Ii~.chricIts liw covcri~ig tlic li~rnacc roof must be a durable type to
~lio~~i(lctl li.0111 aggregate ratio tlisplaycil in tablc 2.1 below have been
tcstcil autl c :o~ li I-liictl to' I,c cl~~r:~l,lc and ccononi ical. Thus, the
/
~ m ~ w s s , tlll-or~gl~ I,iolocgical cligcstion ol'tllc slidgc extracts using an efficient (.
1. Furnace door. 21. Blind flange.
1
2. Fire rods.
3. Fire bricks.
4. Boiler tubes.
5. The check valve.
6. Black alarm
7. Steam outlet valve.
8. Manhole door.
9. Safetyvalve.
10. Feeding valve (water inlets).
1 1. Smoke box.
12. Chimney.
1 3. Manhole door of the chimney.
14. Drain valve.
1 5. Belasting load support.
16. Furnace.
17. Cement coating.
1 8. Wire gauze.
19. Grass wool.
20. Steel (Pressure) Vessel.
CHAPTER . THREE ,
METHODOLOGY
3.0. PREAMBLE The intention of this chapter is to discuss the procedures used for data
collection and analysis in this study. This will be discussed in detail under
the following headings:
1. Research Instruments.
ii. Methods of data analysis.
3.1. RESEARCH INSTRUMENTS:
The research instruments used for data collection in this study comes
under two major groups. There are Primary and Secondary Instruments.
(a). Primary Instruments:
This involves all the primary sources of data, which include the following
i. Experimental milling of the oil palm h i t bunches (FFB).
. . 11. The opinion of the palm oil mill workers on the various item questions
of the interview conducted for them on the perceived needs for
effective performance of both human and material resources in the
palm oil mill factory.
The experimental milling test involves the processing of given
quantities of each of the three oil palm fruits types from bunch to palm oil,
kernel, shell, fibre and empty bunch using MFOR oil mill factory. After
each process, each of the products obtained were measured and recorded . .
I _
according to the fruit types. -. . * - - .
In addition, data obtained from the milling of the combined fruit
aggregate and the interview conducted for the factory workers were used to
confirm the precision of the test result.
(b). Secondary Instruments: I
The Secondary source of data includes the following:
i. Production records of the NIFOR oil mill factory.
. . 11. The palm oil mill plant manual.
The data deduced from the production records of NIFOR oil mill and
the factory plant manual were also used to confirm the certainty of the data
obtained from the milling experiment and the workers response to the
I .interview questions.
3.2 METHODS OF DATA'ANALYSIS
The data gathered were analysed using the following
i. Averages.
. . 1 1 . Percentages.
iii. Tables.
iv. GraphsJCharts.
v. Linear programming technique.
The percentage of the products obtained fiom the experimental
milling relative to the processed fresh h i t s bunches (FFB) and their average
percentage ratios for each fruit type were computed fiom the experimental
data. Also determined from the experimental data is the products' ratio . 8 ' .relative to unit quantity of the fruit bunches. This was used along with the
data on the selling price of the mill products to construct palm oil mill linear
programming model. This optimization model was evaluated by simplex
method using a computer aided program written by the researcher in q-basic
language which he also used for sensitivity analysis of the model and for
testing of the result in other palm oil mills. The choice of the language used
in the program is because q-basic is users fiiendly and the most commonly
used computer language in Nigeria.
Tables and graphs were also used extensively to display the 1
f
percentage profiles of the mill workers opinion on the item questions of the
interview conducted for them according to their perceived levels of need.
Although fifty-one (51) workers were sampled only twenty (20) were
allowed to respond to each item question because no worker can express
opinions to all the twenty-six (26) item questions of the study due to
educational qualification, experience, areas of specialization, age and sex
barriers.
'I'l~c data ohtaincti li-om tllc cxpcri~llcntal milling of tlic fresh fruit
;~c.cortIi~ig to tlic f r i ~ i t typcs ant1 a~lalyzcd usi~ig average, pcrcentnges and
clucstions of' t l~c intcrvic~v co~ltl~~ctctl for somc of tlicm were also
annlyzcd nccordi~lg to thc ~wccivcd lcvcls of' nced usi~ig percentages
displayctl on a table mid plots on gl-apl~s. Othcr seconclnl-y data such as tlie
~llnrkc~ pricc o S palm products, tllc procluction constraint records of
NII;OI< oil mill fiilctory \vcrc eqt~a'lly a~lalyzcd and displayed in this
cllaplcl~.
111 adtlitio~~, a li~icar ~ m g r a ~ ~ i ~ i i i n g ~iiodcl for Palm oil mills rcvenue
~llaximizatio~i was constrktcd ming the ratios cletermincd from the data
collcctctl as ~llajor pramctcrs, wllilc tlic h i i t types (dura and tenera)
1i)rmcd tlic niajor clecision val-iablc tlsccl in li)r~nulation of tlie model.
'I'lic s'olutiol~ ol'tllc ~llodcl was oht~lilicd itsi~ig il co~iipi~ter program
\vrittc~l by tllc rcsexcllcr i l l q-basic Intiguagc. 'I'hc program, its flowchart
:wcl tllc algoritlial of l-iuini~g i t W C ~ C d ~ t i \ i l ~ d in Appendix B to enhance
t I ~ ~ t r s t a c l i n 0[' any intot-cstctl rcadcr.
74
'I'A131,lC 4.2: '1'1115 PI5I~<'EN'l'A(';li ANA1,YSIS OF IIATA OI31'IANED FROM THE
- . -. - - -. -.
Milling I<cs~rli (KG) Aver;lge Percentage
TABLE 4.4: PERCENTAGE ANALYSIS OF DATA
OBTIANED FROM THE EXPERIMENTAL MILLING
OF PISIFERA BUNCHES.
From table .4.4, it is clear that processing of pisifera is not
- ecoi~omical because an average pisifera bunch contains 75% empty
bunch, which has little or econoinic value. In addition the palm oil
obtained from the milling of pisifera fiuit is a low grade palm oil called
Technical Palin oil (T.P.O.) because pisifera lternel are crushed during
pressing giving a mixture of Palm oil and lternel oil which cannot be
scpnratccl i n tllc pt.occss. 111 aclclition. attwipts to process Pisifera bunches
Ily otlicr ~ i i c t l ~ I s (Ma~lua l a ~ d I land ~wcss) yield similar results showing
that ion o f lllc p~-cscnt r l ~ ~ t l ~ o d s call p.occss the f'ruit succcssf~~lly. Again
TA131,K 4.5: T 1 1 1 5 S151,l,IN(; I'I<ICk: OF IJNlrl' MASS OF PALM 0 1 I,
A N D l<EItNF,l,.
4.2 CONSTRUCTION OF THE LINEAR PROGRAMMING
MODEL OF PALM OIL MILLS.
Since the growing and processing of pisifera fixits is not economical, the
I researcher considered dura and tenera as his major decision variables in
the construction of the linear programming model for the revenue
maximization in the palm oil mills. The detail of the procedure followed
in construction of the model is presented below.
4.2-1 DEFINITION OF DECISION VARIABLES
The decision variables are:
XI = The quantity (in kilogram) of Fresh fruit bunches of dura
processed per hour.
X2 = The quantity (in kilogram) of Fresh fruit bunches of tenera
processed per hour.
4.2-2 DEFINITION OF TUE OBJECTIVE FUNCTION I
The objective function is revenue maximization. From table 7 above the
revenue derived from lkg of dura and tenera bunches are N37.36 and
S38.38 respectively. Therefore the objective hnction Z = 3736x1 +
38.38X2 .Thus it is stated as,
Maximize Z = 37.36X1 + 38.38X2
4.2-3 DEFINITION OF THE CONSTRAINTS
The objective function defined above is subjected to the following
constraints. Note that the constraint inequalities and equation presented
hclow i s constr~~c(ccl using cl;, ta li.oln tahlcs K q and otl~crs stated against
. a .
W. '1'1 I E ItlClWSIC UUNCI I CONVKYOII. (Inclined
1Slcvn tor)
'I'hc c:~pacily of' ctnpty l)unch or ~vfiisc clcvator is 1.8tons(1800kg) of
'1;1:13 pcr I m w . Wc arc awrw li-om trlblcs in section 4.1 that dura \yields
vii. 'I'll I< C'AKIC l ~ l < l ~ A l < l ~ l < CONVICYOI<
'I'liis systcni Iias a capacity 0 1 ' C ~ I I V C Y ~ I I ~ (or flow rntc 00 2400kg of
'I'llc capacity or this separator is 20001cg of dried prcssed cake per hour. It
i s also k I I O W I ~ that t lie cake I~t~caltcr, conveyor rctiuces the pressed cake
111ass by 10% ;~l'ter pre-dryitig. l ' l~cre~orc the constraints is stated as
'I'hc n u t silo Iii~s a I~o ld i~~g capacity of 30000kg (301otis) of nuts per day
( 12501<g/I1ou1.) a d durn yields 39.3% 0 1 ' nuts wliilc tenera givcs 13.2% of
I
tlic nuts \vlicli ~~~occssccl scparatcly. 'l'lic constraints is then statcd as
'k cracltcrs cajjxity is 1 toti (1000kg) or dried liuts per hour. The nuts
li-otii tllc nut silo arc dricd to 9% of weight before feeding it on the
cracltcr liw ~naxiliiuni cracking cfficict~cy. 'I'hus thc constraints is stated
'I'l~c Iloltling or flow ratc ol'tllc silo clrycr is 500kg of dried kernels per
Ilor11- mtl the Itcrtlcl is ~.ccli~cccl by 13% of' its wight after drying
'l'llc capacity oftllc clnrilicr is 350Okg ofcr~t fc oil per hour. 'I'he crude oil .
'l'lltis tllc constrainfs is stalccf:
0.489X 1- 0.602X2 5 3500
... M I L VACrlJllM I)ItYI<I<'S CAI'ACITY CONS?'ltAIN'I'
'l'liis unit has a capacity of drying, I tons (1000kg) 01'relincd palm oil per
Ilour. 'l'lnrs the clcan oil flow ralc constraillt in this unit is stated below.
'I'his ~,unlp has a capacity of putnpirig 2500kg of sludge per hour. Tllus
tllc constraint is sl:\tcci;
0.298X 1 -1- 0.367X2 _< 2500
xv. 1SN ICI<C;Y C; 1CNICI<A'I'ION AND LI'I'ILISA'I'ION IN 'TI-IE MILL
It was statcd carlicr tltat tllc c~~crgy required for thc milling process and
li,r operating tllc mill ~nachii~cs (Electrical cnergy) is required to be
I generated in the mill through its boiler which produces the steam used for
operating the alternators as well as other milling process.
The steam boiler is capable of producing 2500kg of steam per hour
with energy requirement of 8.35 x lo6 kJ per hour. Having known that
this energy should be generated using palm waste, which includes the
empty bunch, the fibre and the shell. The limitation on the milling process
due to energy requirement and its generation in the factory is as follows,
given the specific heat content of shell, fibre and empty bunches as
2 l9OOKJ / kg, 20900 KJIkg and 21 000 KJIkg respectively.
Thus the constraint is stated as
The equality sign indicates that the means of producing the energy (fibre,
shell and empty bunches) are all wastes which has little or no commercial
value and therefore exciss of them are not required. Also any quantity
less than the above will lead to shortage of the fuel required which in turn
will cause reduction in the energy output of the system that is equally
undesirable.
4.2-4 THE SUMM-ARY OF THE PALM OIL MILLS REVENUE
MAXIMIZATION MODEL.
The summary statements of the linear optimization model of the palm oil
mill assembled in a linear programming format is as follows:
Maximize Z = 37.36X1 + 38.38 X2
Subject to:
XI+ X2 < 6000 , ,
-
1.15X1+ 1.15X2 ,<go00
0.35X1 + 0.4X2 5 1800
0.65X1 + 0.6X2 14200
0.72X1 + 0.66X2 5 4200
0.318X1 + 0.391X2 5 1800
0.459X1 + 0365x2 5 2400
4.2-5 SOLUTION AND INTERPRETATION OF THE PALM OIL
MILL LINEAR PROGRAMMING MODEL
(a). THE MODEL IN A CANONICAL (STANDARD) FORM
Maximize Z - 37.36X1 + 38.38 x2+ OS1 + OS2+ oS3+ OS4+ OSs+ OS6+ OS7+ OSs+ OSg+ Oslo+ OSll + OS12+ OS13+ oS14 =0.000
Subject to:
Note: Si (i = l,2---- 14) = slack variables.
(b). INITIAL SIMPLEX TABLEAU OF THE MODEL(Basic solution)
1.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.000 0.000 0,000 0.000 6000
1.150 1.150 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 WOO
0.350 0.4000.0000.000 1.000 0.000 0.0000.0000.0000.0000.000 0.000 0.000 0.000 0.000 0.000 1800
0,650 0.600 0,000 0,000 0,000 1.000 0.000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 4200
(c) . FIRST ITERATIVE SIMPLEX TABLEAU OF THE MODEL (Second
feasible solution)
(d). THE OPTIMAL SIMPLEX TABLEAU OF THJ? MODEL
(Optimal solution)
(e). INTERPRETATION OF THE MODELS OPTIMAL SOLUTION . ,
This optimal solution indicated that l903.163kg of dura fruits bunches
And 2867.88kg tenera bunches are required in an oil palm fruit aggregate
for optimal revenue of N173699.50 to be derived from the use of palm
oil mill in the processing of the fruit. In other words the dura and tenera
must be combined or mixed in the ratio of 1903.163 : 2867.880 (which is
approximately a ratio 2 : 3) in all oil palm fruits proccssed using palm oil
mill in order to achieve maximum revenue and minimum running cost in
the palm oil mill factory.
, , I h is is t lol lc ~ i s i ~ i g l~ ,c~.cc~ i ( ; igc~, displayct l i n a table and graphs to enable
I I I I \ i c to~- i rs ro1icc1.11111g ot l lcr ~-cquircnlents for o p t i m u m
I)ocs I':11111 Oil klill 111anag~I"s ; I C ; I ~ C I ~ ~ C ' 1)ackgrounct and modes of
cflcclivc control a id ~ ~ ~ n a g c t l l c ~ l t O K tllc mill I'actory.
'1'0 obtain any pcrlnissioii from high autlioritics in the factory before
making use of tools and other facilities in the factory.
!;I-c.c Ilanils i l l thc controlling and rlsi~ig of resources in the factory for
lbr cfTectivc tiiaintcnaticc atid opcration ofthe mill.
ill-scrvicc Iraining to upclate your skill and tliat of other workers.
- - - - - -- - - - - a - - --
Atlcq~inlc i~icclilivcs like pro~iiotio~is and increase in allowance.
'1'0 bc arlncd with llic rcclrrircd safely ltils for your effective performance
;11iiI to avoid ilcci(lc11t.
- - - - - - - --- - - - - - - - - -- - -- -. - - - -.
'1'0 I,c ilisurcd agaillst factory Iiazartls.
- . - -- - - - - - -- - - - - ---- -. -- - - - -- - --
11'11tl i111l):lct of file :~tloptctl r~~:~ir~fcrl:incc policy on tlic rcvcnuc profilc
liw cf'fcctivc rcp:~ir nncl servicing of tlic mill units wlien h e .
ant1 ccrtairl misco~lccptions t h a t arisc fiom tlic work and on the possiblc
caliscs of'thc fault to avoid fi~lurc occiwrcncc wlwe possible.
'1'0 I x C I I C O I I I . ; I ~ C C ~ to rcatl plant manuals and otllcr handbooks on thc
any c~~~crgct icy when hclp is not im~ncdiatcly available.
I~nportcd mill parts to locally f'ah~.icntcd ones for the replacement of worr
A wcll cqi~ippcd spare parts storc in your factory, which will contair
The ordering and delivery of spare parts for maintenance in the mills to
be when needed to prevent excess inventory cost.
Impact of other factors on the mills output profile.
DO YOU PREFERNEED-:
Diesel generating set to steam operating gen. set (in cooperated in the
mill during installation) for generating electrical energy used in the mill
factory.
Fresh h i t bunches harvested from wild palm plants or plantation that are
not adequately maintained.
Processing of dura tc tenera bunches or vices versa.
More trucks for conveying h i t s bunches form the farm to the mill to
avoid delay and scarcity of the mill input (FFB).
Firewood as the only reliable fuel for operating the steam boiler to palm
wastes (such as empty bunches, shell and fibres).
Additional mills or increase in the capacity of your present mill to enable
your process all your h i t s when due.
I n addition, 100% of' tlic scsponrtents agreed that the use of
iircwootl aid gci)csatitig sets (WII~CII use dicscl or petrol) in the mills are
not ticcclcd at all bccnusc of'tticir advcrse eficct on the expected returns
fsom h e tiiills. 'l'iiis equally applied to thc use or wild fruit bunches from
all uiltiiai~itairictl plaiitatioil. Vinally 50% of t l~c rcspondents are in very
1i111cli llced or incrcasc iti tlic capacity of tlwir mills where possible or
atltlitior~ai iiiills to mcct up with cffcctive proccssiiig of the raw fruits
4.3-1 MAJOR CAUSES OF DOWN TIME IN THE PALM OIL MILL FACTORY During the interview conducted for the workers in the palm oil mill
' I ' l~c data is on inajor causcs of idlc time and ef'fect in hourly down
tinic of' tile pdrll oil mill. Accolvlirig to t.cspondents the ~iiajor causes of
itllc hoirss oi' llrrriim atid mill scsoul-ces in thc palm oil mill factories
In this study the idle hours of NIFOR Oil Mill in the year 2000 was
organised and used as a specimen to show the effect these factors
mentioned above i.13 the palm oil mill factory. The data are analysed
below according to the above listed causes using percentages, table and a
graph for easy survey of the effects (idle time in hours) of these factors at
glance by the reader.
TABLE 4.9:NIFOR OIL MILL IDLE TIME IN THE YEAR 2000
RIAIN'I'ENANC:
E (HOURS)
LACK OF
(1-IOlJ IIS) (HOlJRS)
LACK
0 li
WA'I'ER
(1101JIIS)
JAN -
FEB. 3 2
APRIL.
MAY
J U N E (72--
DRC.
3TAL
CAUSES OF DOWN TIME
, ,
1 i. . 1
I It is quite clear from table I0 and graph 4 Ihnt lack of fiesh fruit bunches causes , . .
the highcst idle tiinc of 53.57% ill t l~c pahn oi! mill factory. According to the I 1
respondents this is caused by limited nurnbcr of trucks available for conveying
the raw material (FFR) frpm . . the plantation to the mill premises. Thus provision
of marc truclts for transportaiion of the fruit bunches to the mill is required.
'Time consumed during maintenancc cspccinlly shut down maintenance caused
37.2% ol' tllc rnills anw;ll idle time. 'I'his suggcstcd that provision of
atlcquatc rnaintcn;~~icc Iilcilitics and rcgr11:ir preventive nlaintenance
sllould bc atloptccl i n (llc mill factory to reducc this cffect.
I ,;~clc of liretvood a t ~ l tlicscl sllowcd a sum total of 6.58% of mill
tlow~l liilic. Sillcc the usc ol' thcsc co~i~niotlitics in tlic ~iiillitig process is
not ~lcctlcd at d l , it slic~~ltl bc avoidcd to rcduce down time in the inill
I;lctol.y.
1,aclc of watcr cmscrl 2.67% of total idlc tirnc, the respondents to
illis said that sourcc ol'walcr is 11ot likely tllc major probleni of the mills
Iwt tllc li-cq~rcnt failurc of jmnps, pipcs and other means of conveying the
water to tllc mill.
4.4 IIISCIIISSION
'I'l~c :)in1 of this scctiou is to discuss and interpret the results
ol)t:liricd lion1 thc data ~ l c l o t lw ill Sort nation collected and clnalysed in
tlic ~ r c v i o ~ s scctioi\s ofillis project.
I t i s clcady scc11 liwn t l~c ctitir-c investigation that for the derivation
of optini~tnl h c f i t s (cost t i~ i~~i~niza t io~i atld 11rol3 maximization) from
tllc rlsc ol'palm oil mill in thc pl-occssing of oil palrii fruit, that the fruit
:~ggrcgatc proccssctl should contain the dwa, teticra and pisifera bunches
(fiuit) in illc ratio of 2:3:O. 111 addition to this, adequate maintenance of
tllc mill n d l i ~ l c s and olllcr ~~roccssing acccssorics, rcgular and adequate
plai~laliorl ~l~:~in~cnailce, changc from the usc of firewood to palm wastes
as fuel in the mill and effective motivation of the factory workers through
incentives are equally required. These and others form the major sub
headings of our discussion in this section.
i. The Ratio of the Oil Fruit Types in a Fruit Aggregate to be
processed in palm oil mill for optimum benefit
The result obtained fiom the optimal solution of the palm oil
factory mill model indicated that dura and tenera h i t s should be mixed
(combined) in the ratio of 2:3 for maximum revenue (and cost
minimization) derivation fiom the use of palm oil mills. This ratio
indicated that pisifera is not needed in any processing fruit aggregate
because fiom our investigation the fruit can not be processed and any
attempt to include it in a ratio causes low grade of products extracted
fiom such a ratio. This agreed with our earlier information that pisifera
fruit kernel are crushed during the milling process giving a mixture of ,
kernel oil and palm oil which cannot be separated by simple method.
When h i t s of dura and tenera are processed in this ratio, it brings
the fibre and nut content of the digested and pressed cake to equilibrium.
This helps to achieve high oil extraction rate of over 98% and minimum
kernel breakage of less than 2% in the mill. The effective recovery of
kernel and palm oil in this process increaset the revenue derived since the
two constitutes the major commercial products of this venture.
Anotlicr good sidc of tllis ratio is that it provides enough palm
\vastcs (lvitll l i t 1 lc cxccss) fi)r tlic operation of tlic mills steams boiler.
'I'llis crlablcs unintcrruptctl productio~l 01' stcam for both processing and
h r opcratillg of tllc clcctric gcnct-ating sct i n the mill factory. The use of
~ ~ i i l ~ l l wastcs climi~latcs tlw (IO\VII lime a110 ovcr 80% C X C C S S ~ V ~ mill
cxpc~itlitul-c associated witli lllc usc of lirctvood atld dicscl. ?'his demands
111:it rut111.c pla~itation slioi~ltl Ix plil~mcd to contain tlic dura and tenera
I plants in thc ratio of 2:3. Whilc pisifera should be for brceding purpose
only bccarrsc any plantation \vllicIi contain up to 5% of pisifera plant is
uneconomical since over 98% of the plant populace are sterile.
ii. Adequatc Mainteriaucc of tlic mill
' I Iic I T S L I I I ol '1l1~ i~ivcsligatio~l slio\vccl tllat C V ~ ~ C I ~ tllc mill rnnchincs
ar-c. atlctli~atcl y ~ll:ii~i~:ii~lccl (1)otli ~ I T V C H ~ ~ V C and col-rcctive) in accordance
\vitli tllc ~li:inrrhctrlrcrs rcco~lilllclltlatioli and guided by other
1>a1.;unctc1-/i1lIi)r111atic111 prbvided i l l section 2.4 of this work that the
wccssivc l>~~caI<~lo\v~i wliicli clwactcriscd tllc prcscnt mills will bc a thing
of tlic past. 'I'llis will sctli~cc thc idlc ti~ilc in tlic mill factory as well as
cxccssivc wnstc of p~wlucts i l l tllc system. 111 addition this cnsures good
qrl:iJity of' proclr~ct ~~soccssccl in tlic mill bccausc the cffccts of the inill
r~liits on tllc li.uits will 1101 dcviatcs fionl tlic cxpectetl effect.
iii. Adequate Maintenance of the Oil Palm Plantation
Since total quality control starts from the inputs, the need for
adequate maintenance of the oil palm plantation should not be over
looked when the issue of maximum performance of the venture is raised
because poor quality of input will always leads to poor output irrespective
of the condition of the mill used. Adequate maintenance of the plantation
which include regular fertilization,
and other agricultural measures are
weeding, proper drainage, irrigation
required for good health and growth
of the oil palm plants and regular supply of good quality of their bunches
to the mill. This reduces the deviation of the individual fruit bunch from
their species properties. For instance inadequate plantations maintenance
has leads to duras of low kernel content and negligible mesocarp and
teneras of little mesocarp and kernel content which adversely affect the
output profile expected from such a fruit. f
iv. Workers Motivation
The investigation indicated that all the workers in the palm oil mill
factories are in very much need of seminars, workshops and in-service
training to up date their skill for better performance in the factory. In
most of the factories visited, the plant manual and other hand books on
the mill systems are not available to the workers and those workers who
are very old in the job do not find the use some modern tools easy. This
is the. main reason while the workers need the development of such
essential skill necessary for the improvement of their strategies and
tactics for quick and effective maintenance of the plant to reduce idle
time in the factory. The workers opinions shows that they require
increase in their allowance promotion, insurance policy against the
factory hazards and other cash bonus from their to employer to perform
their duty effectively.
v. Technical-Oriented mill managers
The uncooperative attitude of some mill managers militates against
the effective performance of palm oil mill factories and their human
resources. Of course 58.30% of the workers who participated in this
interview indicated that mill manager who are not science/technically
oriented do not cooperate well with the technicians in the factory. This
set of managers will even want the technicians to always obtain
permissions from the mill authorities before making use of the factories
workshop, spare parts and so on. However 80% of the respondents
indicated that they do not have any need for such permission. Therefore
technicians in palm oil mill factories need free hands in the controlling
and using of the mill facilities for effective and timely performance of
their duty to avoid excessive down time in the factory.
4.4-1 FINDINGS
During the course of this study the following findings were- made: -
iv.
vi.
vii.
viii.
In the entire palm oil mill factories visited the use of firewood as
the major fuel for operating the palm oil mills steam boiler
dominates the use of palm wastes.
All the palm oil mills visited uses diesel generating sets for the
generating electrical energy used for operating the factories
machines instead of the in built steam turbine driving generating
set in the mills.
Effluent treatment station for effective microbiological digestion of
sludge (produced in the milling process) to biogas (fuel) is absent
in all the mills visited.
Incinerator where the empty bunch(s) is discarded (wasted) by
burning them to ash without any use of the heat energy produced
during the burning constitutes part of the mills visited (Waste of
useful heat energy). ,
Inadequate motivation of palm oil mill factory workers was also
observed and this reduces their effective performance in their job.
The use of inexperienced causal workers is highly pronounced in
all the mills visited.
Non-technical oriented managers head more than 80% of palm
oil mill factories visited during study.
Inadequate maintenance of palm plantations and the mill plant
characterised all the industries visited. This was identified as the
major cause of low grade of the products produced in the palm oil
mills.
4.4-2 IMPLICATION
The implication of the results of this study include the following
1. The palm oil mills need the provision of raw fruit input which
should contain dura and tenera. fruits in the ratio of 2:3 and most of
the mills visited operate with high tenera content fruits while others
process high dura content input. This adversely effects the
extraction rate of the mills, volume of palm wastes available for
operating the steam boiler and life of the digester unit. Therefore
government, communities and individual should endeavour to
establish future oil palm plantations that will contain dura and
tenera plants in the ratio of 2:3.
2. The allowance paid to palm oil mill factory workers should be re-
examined and increased to make the workers affected happy to
perform their work diligently and effectively.
3. Since mill managers who are technically inclined (preferable
engineers) cooperate with workers more than those who are not
inclined in this area, authorities concerned should gradually change
to making those who read technical sciences managers of the mill
factories, otherwise, the federal governments effort in pursuit of
increased palm products output of the nation will be fruitless.
4. The use of inexperienced causal workers for operating and
maintaining the mill machines are undesirable since this discourage
specialization, which in turn increases the rate of accident and
breakdown in the palm oil mill, factories.
5 . ,The excessive use of firewood and diesel generator in the mill
factory cause high cost of production in the venture and therefore
should be avoided.
6. The burning of the empty bunches in the incinerator is not
desirable in the mills since the heat energy produced is lost and is
never use for other purpose in and outside the mill. Therefore for
.effective utilisation of this waste, it should be conveyed to the
boiler furnace so that the energy produced will be effectively used t
in the boiler for steam making.
7. Again the absent of efficient sludge treatment station in all the
mills causes loss of energy which should have been generated from
sludge and harmful disposal of this waste to the environment.
Thus the development of this sector in the palm oil mills should be
encouraged to increase the energy potential of the mill system.
CHAPTER FIVE , ,
SUMMARY, CONCLUSION AND RECOMMENDATION
5.1 SUMMARY
The study is an application of optimization technique to maximize the
revenue of palm oil mills using NIFOR oil mill as a case study. The work
identified limited number of investor in the large scale processing of palm
fruits using palm oil mills as the major cause of the decreasing rate of
Nigeria's palm products output recently. This is because of inadequate
processing mills to process the abundant raw oil palm fruits in this country
which causes excessive loss of unprocessed fruits annually in this nation. It
was further identified that investors are scared away from this large scale
processing sector due to slow rate of returns of the sector, thereby taking
long-time for the sector to break even. This was as a result of some factors ,
that hinders the smooth operation of the mills. The study identified the
factor as high cost of production in the mill as a result of high daily cost of /
operating the mill system, poor quality of oil and kernel processed in the i mill, high cost of maintenance in the venture due to insufficient explanation
of the process and maintenance parameter to the operators of the mills and
high cost of procuring the mill and its accessories. In the cause of this work.
It was observed that over eighty percent (80%) of the daily expenses in the
I palm oil mill factory is spent for procuring firewood (fuel) for the operation
of the mills steam boiler. Inadequate maintenance of the plant machines
which causes deviation from the expected effect of the mill units on the
fruits was also identified as a major cause of poor quality of the mill
products. Others factors which militate against maximum profit output of
the venture include low oil extraction rate of the recent mills due to improper
mixture of the fruit aggregates processed in them, lack of maintenance of the
plantation, inadequate motivation of workers and so on. Although NIFOR
oil mill was used as the projects case study, related information obtained
from other factories such as Okomu palm Plc, Risom palm limited and
Adapalm limited were used to confirm the precision of the experimental data
obtained from NIFOR mill and to diversity the study.
In this work data were collected by two major means which include
the primary instrument and secondary instruments. The primary source of
data involves the experimental processing of given mass of each of the fiuit
types, direct participation in the milling of the combined fruits types and the I workers opinion to various item questions of the interview conducted for
them during the study on the perceived needs for effective performance of
the mill venture. The secondary data sources include previous production
records, maintenance history records and the mill plant manual. The
secondary data collected were mainly used to confirm the precision of the
primary data. The data generated was analyzed using averages, percentiles,
tables, graphs, charts, linear programming method and a computer program
(writing .in q-basic language). The h i t types dura, tenera and pisifera
formed the major decision variables. A linear optimization model for palm
oil mills generated was solved by simplex method while the computer , 5
program is used to test sensitivity of the model (optimal solution). In t'he
literature, various milling processes were explained, sufficient and practical
parameters for the operation and maintenance of the units were also
provided as a guide for the operators of the mill machines for effective
prevention of excessive idle time and accidents in the mill factory.
The result of the study indicated that for optimum profit (minimum
cost maximum revenue) derivation from the use of palm oil mills in the large , a
1
scale processing of the oil palm fruits that the dura and tenera bunches
should be combined in a ratio of 2:3 respectively. This will enable us to
achieve the necessary equilibrium content of the fibre and nut in the digester
and press volume for effective operation of the units and for high oil
extraction rate. In addition, this ratio will help to provide enough shell, fibre
and empty bunches without much excess for the operation of the mills steam
boiler, in order to eliminate the use ofsfirewood and diesel in the mill which
cause over 80% of the mills expenditure. The study also indicated that
pisifera is not needed in the fruit ratio since the presence of the fruit in a
processing ratio causes low quality of oil output because the pisifera kernels
are crushed during pressing giving a mixture of palm oil and kernel oil
I which can not be separated by simple method. Also indicated is adequate
preventive maintenance culture in the mill factory to reduce idle time and
high cost associated with excessive shutdown maintenance that characterised
the sector. Adequate care of oil palm plantations through regular
fertilization, weeding and other important agriculture measures to ensure
good quality and regular supply of the inputs (FFB) to the mill and effective
motivation of workers through incentives, provision of safety devices, , ,
insurance against factory harzard and cash bonus were also required for
effective revenue output of palm oil mills. Provision of credit facilities, I
input subsidiary and tax alleviation to the oil palm farmers by government
was also indicated to encourage participation in the sector
It is established from the results of this work that for maximum , ,
revenue derivation from the use of palm oil mills in the processing of oil
palm fruits that the fruit aggregate processed should contain the dura and
tenera fruits in the ratio of 2:3 without pisifera because the presence of the
pisifera in a processed aggregate causes low grade of oil output. Also
advocated is the establishment of future plantations that will contain dura
I and tenera plant species in the same'ratio while pisifera should be used for
cross breeding purpose only since over 98% ofthe entire pisifera plants are
sterile and any plantation which contains up to 5% of the plant species is
uneconomical.
Also established in the study is a good and regular preventive and
maintenance policies to reduce high cost of maintenance and idle time
associated with excessive breakdown of machines that characterised palm oil
mills recently. In addition adequate care of the oil palm plantation though
effective fertilization, weeding and other agricultural practices is also
required to ensure regular supply of good quality of the fresh fruit bunches
. (FFB) input to the mill.
Furthermore, the use of palm wastes (which includes the shell, the
fibre and the empty bunches) as fuel in the mills to ensure uninterrupted
production of steam is very much needed to eliminate the use of firewood 1
and diesel in the palm oil mill factory. This will reduce the cost of
production in this sector by eighty percent (80%).
i The work equally showed that adequate
112
motivation of workers
increases their effective performance in the factory. Again the investigation
indicated that technical-oriented managers cooperate well with palm oil mill
workers than managers traiqed in other areas, and also this encourages the
performance of the workers which in turn improves the efficiency and life of
the mill system and its output.
The study also advocated for the exclusion of incinerator in the mill f
design because the heat energy produced by burning empty bunches in it is
never used anywhere both in and outside the mill., This waste of energy is
undesirable in modem technology.
5.3 RECOMMENDATION !- . ,
The research work is on the application of optimization technique to . . .
maximize revenue of palm oil mills and also to minimize relative cost of
production in this sector. Based on the results of data collected and analysed
and other findings in this study. The following are recommended
1. It is quite clear now and well established that all processing palm
fruits aggregate ,must contain dura and tenera fruits in the ratio of 2:3
for optimum benefits from the use of palm oil mills. .
2. Also recommended is the establishment of future oil palm plantations
that will contain 40% and 60% of dura and tenera plant species
t
respectively. This will ensure fwture supply of fiuits input to the mill
that will reflect the milling ratio of 2:3 for dura and tenera fruits
. , I mentioned above.
3. The researcher strongly advocates that pisifera plant species should be
cultivated for breeding purpose only.
4. In addition, adequate and regular preventive maintenance of the mill
facilities is equally recoininended to reduce high cost and excessive
idle time associated with shut down maintenance in the mill factories.
5. Adequate maintenance of oil palm plantations through regular . ,
fertilization, weeding and other agricultural measures is very much
needed to ensure regular supply of high quality fiuits to palin oil
mills.
6. Effective utilization of 2alm wastes such as empty bunches, shells and
fibre is strongly reconimended as fuel for steam production in other to
reduce high cost of production associated with the use of firewood
and diesel in the mill factory. . , i', 7. Exclusion of the incinerator in the mill design and the introduction of
a conveyor into the system for transporting the empty bunches fiom
the stripping unit to the boiler where the energy produced by burning
them will be effectively used for steam making is very much needed
in the mills.
8. The researcher also advocates for the development of effluent (sludge)
treatment station in all palm oil mills. This will facilitate effective
digestion of the sludge waste to biogas (fuel) and enable unharmful
disposal of the waste to the environment.
9. Furthermore, the study recommends that all palm oil mill managers
should be university graduates whose academic background are
technical-biased. This is because those managers who are not
technical inclined are always very jealous of the factory workers and
also suppresses them to the extent that these technicians live in
perpetual fear of them.
10. Adequate incentives like increase in allowance paid to the workers in
the palm oil mill factory, promotions and insurance against factory
hazards from the employers is also advocated for effective
performance the mill workers.
I 1 1 . Also the work recommends strohgly that government should facilitate
investment in the large scale processing of palm fruits using palm oil
mills through provision of credits facilities, input subsidiary and tax
alleviation to investors in the oil palm business to enable then1
establish more palm oil mills in this nation. This will enable effective
processing of the nations abundant oil palm fruits, thereby creating
employment for the nations populace and diversifying the nations
economy.
5.4 SUGGESTIONS FOR FURTHER RESEARCH
with regards to the results and limitations of this project the
researcher wished to suggest similar studies into the following areas.
1 . An investigation into the efficiency of palm oil mill factories in 1 .
Nigeria. This will be an eye opener to palm oil mill entrepreneurs on
the effects of idle time in the venture.
2. A study on the effective utilization of the organic fraction of palm oil
mill sludge wastes for he1 and other purposes.
3. An investigation into the applications of palm kernel shell distillates.
. ,
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APPENDICES
CONTENTS PAGE
APPENDIX A
A 1. The layout diagram of palm oil mill factory---------------------------- 123
A2. The schematic flow diagram of palm oil mill factory----------------- 124
A3. The layout diagram of the recommended palm oil mill model------ 125
A4. List of palm oil mill factories visited during the study--------------- 126
A5. Distribution of worker sampled according to their qualifications--- 127
APPENDIX B . .
B 1. The algorithm of the computer program-------------------------------- 128
B2. The programs flowchart--------------------------------------------------- 130
B3. The palm oil mills revenue maximization program-------------- 131-142
FFB
LO
AD
ING
PL
AT
FOR
M
AP
PE
ND
IX A
\
FA
CT
OR
Y.
C E
NT
RA
NC
E
GA
TE
I FR
UIT
I
I BUNCH
I
INC
INER
ATO
R
PRO
CE
SSING
PIT
1
I----- I
I SHE
LL
I
HO
PPER 1
STE
EL
PER
FOR
AT
ED
FFB ST
ER
ILISE
R
// I
n
CL
AR
IFICA
TIO
N
EN
GIN
E R
OO
M
BO
ILE
R H
OU
SE I I1
WA
TER TO
WER
WITH T
AN
K
OIL PU
MPE
D TO-
SAL
ES T
AN
K
I W
aste Water
AP
PE
ND
IX A
3. T
HE
LA
YO
UT
DIA
GR
AM
OF
TH
E R
EC
OM
ME
ND
ED
PA
LM
-
OIL
MIL
L M
OD
EL
FA
CT
OR
Y (Incinerator excluded)
FRU
IT
BU
NC
H
HO
PPER
PIT
TRESH
ING
ST
AT
ION
- - - - - - - -
OIL
EXTR
AC
TION
ST
AT
ION
(Press and digester) --------
KER
NEL
PRO
CESSIN
G
STA
TIO
N
I----- I
I SHELL
I H
OPPER
I I [----A
I----- I
SHELL
I 1 H
OPPER
I [----A
CLA
RIFIC
ATIO
N
WA
TER PU
MP
OIL PU
MPE
D T
F
1
SAL
ES TA
NK
BOILER
HO
USE
3
OU
TSID
E
THE L
c
I PR
EMISES
II , w
astk Water
L R
EFU
G
BU
NC
H (T
ransporting the stripped C
ON
VE
YO
R
bunches to the boiler furnace)
WA
TER TO
WER
W
ITH TANK
APPENDIX A4. LIST OF PALM OIL MILL FACTORIES SAMPLEDNISITED DURING THE STUDY
1. NIFOR OIL MILL FACTORY:- - - - - The case study Oil Mill Division, Nigerian Institute for Oil Palm Research (NIFOR) Benin City Edo State. Nigeria
2. NIFOR SMALL SCALE PROCESSING EQUIPMENT WORKSHOP (A Mini Palm Oil Mill Factory for Testing of Small scale Processing Equipment(SSPE) fabricated in NIFOR) Production and Research Engineering Division Nigeria Institute for Oil Palm Research Benin City Edo State. Nigeria
3. RISOM PALM MILL Risoin Palm Nigeria Limited Ubima River State Nigeria
4. ADAPALM MILL Adapalm Nigeria Limited Ohaji Imo State Nigeria ,
5 . OKOMU PALM OIL MILL FACTORY I Okomu palm PIC
Okomu Edo State Nigeria
6. PALM KERNEL PROCESSING MILL Brother Ken Ago-allied Industries Limited Owerri Imo State Nigeria.
APPENDIX A5. DISTRIBUTION OF WORKERS SAMPLED ACCORDING TO THEIR QUALIFICATIONS
QUALIFICATION , ,
B.Sc, B. Eng and equivalent
NUMBER OF WORKERS
M.Sc, M.Eng. and equivalent 5
S.S.C.E & TCII and equivalent 7
H.N.D.
Craft men (SSCE with Trade test ,Certificate)
3
1 CraFt men (FSLC with Trade test Certificate)
Total , , 51
APPENDIX B1. THE ALGORITHM OF THE PROGRAM
The algorithm steps are as follows:
Step 1. Start the program in Q-basic
Describe the number of decision variable in the equation
Write the number of constraints in the equation.
Add slack variables.
Express the equation in canonical form.
Develop the basic variables
Make the heading variables in the simplex tableaux
Input the objective function, max Z =. . . .
Enter the coefficient of the variables.
Enter the rhs after the slack variables
Enter the ratio after rhs .
Are all inputs correct at this point? If yes
Develop the simplex tableaux else go to step 2
Develop the slack variable coefficient
~ i s i l a ~ the simplex tableaux on the screen
Is the optimal solution positive? if yes
Stop and end if
Else
18. Find the entering and leaving variables in the Simplex
Tableaux.
19. Develop the another simplex tableaux on the screen . ,
I. 20. If optimal solution reached
21. Stop
22. Else go to step 19
23. Print rhs
end
[APPWDIXI TIIE CO~PUTER PRO CRAM^ 131
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l j l . : ( . ' l ARR SUB INTl lO ( ) I ' l < ( ' I A i E SUB 0NEE:N'I'RY ( ) IjKC'l AliK SU13 TENTItY ( ) r)l:cI.neri SUB THRENTKY ( ) I 'I,:c'J d1UZ TREENrl'12Y ( ) IIb:CtA[?E SUB DISTABLEAUX ( ) i?l~;ClJAI7i;: S U R MIVALUE ( ) I~ lKl ,ARI< S I l R WORKINGSIMPLEX ( ) D I ~ ~ C I ~ A R E SUt3 S IMDISPLAY ( ) I?l.:M "TIIT!; PROGRAM WAS DEVELOPEII T O M A X I M I Z E A REVENUE O F PALM O I L MILLBS" l<!::M "WRI' ITEN BY NWANKWOJIKE BETHRAND NDUKA" I<RM " H E G . N O . P G / M . E N G / 0 2 / 3 3 0 6 7 'I
I:l.:M " COU!lS E 'T ITLE MASTER DEGREE PROJECT" IO.:M "COURSE CODE ME 6 0 0 RrW "GUPDI<VISOR DR. 0 . ONURA" I:l*:M " DEPAItCLMEN1' MECHANlCAL ENGINEERING ( I N D U S T R I A L ENGINEERING AND MANAGEMENT) l i lW "UIT!VEHSTTY: U N I V E R S I T Y O F N I G E R I A NSUKKA" 'COMMON SHARED CON, BV, DEC, ACROS, E T , ENTRY, LEAVING, P I V O T , I N T R 0 , T O P E Q r ' l ,S >;I'IU.;L:,;N 9 1 NI?!I'1' "ENTER TlIE NUMBER OF D E C I S I O N V A R I A B L E S " , DEC i NI'UI', "ENTER 'rHE NUMBER O F CONSTRIANTS IN ,.SYSTEM O F EQUA'I'ION" , CON VV - 'CON i 1: ACROS = 1 + DEC + CON I<k:L>lM, SHARED DECV$ ( D E C ) , BASV$ ( B V ) , HEAD$ (ACROS) , MAT1 (DEC) , MAT1 (CON, DEC) I l l ~ I l 1 M SIIARED IIIIS ( I ) , RHS2 ( B V ) , TABLEAUX ( B V , ACROS) , S I M P L E X ( B V , ACROS) RIzD114 SHARED P S (ACROS) , R A T I O (BV - 1 ) , RAC (BV - 1 ) , T O P E C (ACROS) ' I)EVET,OP,SNG THE D E C I S I O N VAHIABLjES l.'Ol< '1 = 3. '1'0 DEC p~ .. U X I I .t S T R S ( I ) nr,:cv$ (I) = L E F T S ( P $ , 1) + R I G H T S ( P $ , 1 ) w x ' l ' I ' l~k:Vl~IIO1"ING THE B A S I C VARIABLES I~A!;V$ ( I ) = " Z " 1.'(?1< T = 2 T O BV p + 8, x !I I- S 'SR$(DEC + T - 1 )
I!ASV$ ( I ) = L E F T $ ( P S , I . ) + RIGH'S$ ( P $ , 1 ) NKX'I' J
' I)EVEL,OPING TlIE T O P HEADING VARIABLES I N T H E S I M P L E X TABLEAUX I I E A D S ( 1 ) =: " Z " . ,
FQR I = 1 T O DEC I I E A I . I $ ( I .i- 1) = D E C V $ ( I ) NPXT I : FOR J = 1 T O CON: HEAD$ ( D E C -1. 1 + J) = BASV$ ( 1 + R ) : NEX'I' J
Yl.:%Y . CL,S (:OLIOIZ 11: P R I N T : P R I N T : P R I N T "THE O B J E C T I V E FUNCTTON MAXIMISE Z =I'
, K$ = "ENTER THE C O E F F I C I E N T o!? THE V A R I A B L E f 1 : F = L E N ( K $ ) : J = 2 COLOR 1 3 : FOR I = 1 TO DEC LOCATE 5 + J, 6 : P R I N T K$; lo l1 ; DECV$ ( I ) ; " I N THE O B J . FUNCTION: "
J = J + 2 NEXT I COLOR 1 0 : J = 2 1.'011 I = 1 'ro DEC
LOCA'rE J + 5 , 1: -I 3 2 : I N P U T MAT1 J = J + 2
NEXT I [1)YL1%: CLS : SCREEN 0.
COL,OI7 1 4 , 0 : LOCATE 2 , 1 0 : P R I N T " T H I S AREA DEALS WI'I'H THE CONSTRIANTS" 1,OCATE 4 , 15 : P R I N T "THE FORMAT X l + X 2 + S l + S 2 . . . + S N <= RHS" TI,$ = S T R I N G S ( 3 , C H R $ ( 3 ) ) + " " + S T R I N G S ( 3 , C H R S ( 2 1 9 ) ) D$ = "ENTER C O E F F I C I E N T O F THE VARIABLE"
V l I8:W PRIM'T G 'YO 2 4 132 i2C)1< 1 = 1 '1'0 CON: C L S : COLOR 1 0 : LOCATE 6 , 25 : P R I N T "CONSTRIANT" ; I ),'OR &'I = 1 1'0 UEC
COLOR 1 2 : LOCATE 7 -1. K, 8 : P R I N T D$; DECV$ (J) Nl?X'I ' J 1:OR I< = 1 1'0 DEC
COLOR 1 0 : LOCATE 7 + IC, 4 6 : I N P U T . MXT2 ( I , K) ,I<KXrl ' K
COLOR 11: LOCATE 7 + DEC + 1, 8 : P R I N T "ENTER T H E R H S VALUE A F T E R < = " COLOlZ 1.3 : LOCATE 7 t DEC + 1 , 38 : I N P U T Rl IS
NEX'l' I COLCII? 1 5 : P R I N T : P R I N T : I N P U T " I S A L L CORRECT AT T H I S P O I N T ? ( Y / N ) " , 13s - U C A S E $ ( D $ ) .IF D$ = " Y " THEN G O T 0 DYE2 V.[EW P R I N T : G O T 0 I D Y E Z
i )YE:% : ' DIXVELoOPING THE S I l d P L E X MATRIX TABLEAUX S I M L ' I j E X ( l . , 1.) = I lWR I = 2 T O DEC + 1 : S l M P L E X ( 1 , I ) = - (MAT1 ( I - 1 ) ) : NEXT I r m x I = 2 TO B V : FOR ,J = 2 TO DEC -1. 1 : : l i ~ l l ' l , l ~ ~ X ( I , ,J) = P l A ' I 2 ( 1 - 1, J - 1) N1,;XT ,J : NKXr1' I
' r)I~:VI~:IOF'II\IG THE SLACK VARIABLE C O E F F I C I E N T , I i 1 1.'01: I = 1 T O AV: S I M P L E X ( I , DBC + 1 F J) = 1 , I =: J + 1: NEX'I' 1
,.'JTPIL)ISPI.rAY M IVALUE
W ( I R K [NCSIMPLEX 1)l S'L'ADLEAUX L: 1 ,s
':I J I < IU; ~wirr I JJ !'I< ! N'I' : P R I N T TAB ( 7 5 ) ; " F P R THE SIMPLEX MAXIMIZATION PROBLEM W I T H O B J . FUNCTION"
J = 1 5 r'i.lLOR lo: P R I N T TAB ( 2 ) ; "MAXIMISE %=" ; t.'OI( I = 1 TO LIEC COLOR 1 5 : T R S = S T R $ (MAT1 ( I ) ) + DECV$ ( I ) 11.' 1 = DEC THEN P R I N T ' I ' A B ( J ) ; TR$; T A R ( J + 7 ) ; : GOTO P I K R E I'RiN?' TAL3(J ) ; T R S ; T A B ( J + 7 ) ; " + " ; d = ,J + 9 NEXT I
I?I KRE: COLOIZ 1.4 : P R I N T : P R I N T TAB (10) ; " Z " ; Rk1S2 (1) COI,01? 1 5 : P R I N T : P R I N T " PR0I)UCE : 'I P l l l N T : k'OR T = I T O DEC: FOR J = 2 T O RV L r: nEcv$ ( I ) = BASVS ( J) THEN L'1!1 b!'r ' r A n (10) ; DOCV$ ( I ) ; TAB (29) ; R1192 (J) ; " P R O F I T U N I T S " l,:Nl) I F iNI<;<'l' ,-I : l\IKX'T I l < N ) SUL?
SUI3 ONEEN'I'RY " l ' l i IS PROGRAM F I N D S TIiE ENTRY VARIARLE AND THE LEAVING VARIAFTAF: ' 11,' Tl lE MATRIX HAS ONLY ONE ENTRY
LCN'L'RY = P S ( 1 )
1,'OIi I ' = 2 'To R V : l i A l ' I O ( 1 - 1) = RIIS ( 1 ) / S I M P L E X ( I , ENTRY) R . h C ( J - I) = RATIO(I - 1 ) : NEXT 1
1:OR I = I. T O BV - 2 : FOR J = I + 1 TO BV - 1 1 F RAC: ( I ) c = RAC (J) TIIEN GOT0 PE:NFOLD
I ~ E M F U I ~ D : NEXT J : NEXT I FOI< I = 2 T O BV
Lr: I < A C ( l ) = R A T I O ( ] : - 1) TIiEN UEAVlNG = 1 l3ii:;VS (1) = IIEADS (EN'SRY) I,:NIl I I;' : NEXT :I : P l V O T = SIMPTIEX (TAEAVING, ENTRY)
l,:PJI) :.;lJH
SU!3 TKNTRY 1 Jb 'TI! [ S S U R I'INDS 'THE EN'I'RY AND 1'HE L E A V l N G V A R I A B L E S WITH. T H E I R C O R E S P O N D I N G P iil.:I)IM RA'1'102 ( B V - 1 ) , I W C 2 ( B V - 1 )
!Wl< 1 - 2 T O B V : R A T I O ( 1 - 1 ) = R H S ( 1 ) / , S I M P L E X ( I , P S ( 1 ) ) I - 1) = IIATIO(I - 1)
iO\ ' I ' l t j2 (1 - I ) = R H S (I) / S I M P L , G X ( I , PS (2.)) : RAC2 ( I - 1 ) = R A T 1 0 2 ( I - 1 ) : N E X T \.:OR I = 1 7 '0 DV - 2 : F O R J = I + 1 T O '13V - 1 I v RAC ( r ) < = mca ( J ) THEN GOTO PENOLDY SWAP RAC (1) , RAC (J)
Y : X F R A C 2 (I) <= R A C 2 ( J ) T H E N G O T 0 P E N F O L D Y S W A P R A C 2 ( I ) , R A C 2 ( J )
I'i~:PII'OI,DY: NISXT J : NEXT I Pi l l41 = R A C ( 1 ) : M I N 2 = R A C 2 ( 1 ) 11: i d l N 1 c M I N 2 ?'HEN
1::N'I'RY -; P S ( 1 ) !.'OR '1 - 2 T O BV
I I > R A c ( ~ ) = K A T I O ( 1 - 1 ) THEM L,l.:I\VING = 1 I\ti\%VS (1 ' ) = I jEADS (ENTRT) I,3N1) T I ' : NEX'I' 1 l.:Nl) 11;'
11: M1M2 < M I N I . 'I'llEN EEI'I'RY 2: P S ( 2 )
' 1;OR I = 2 T O B V I F R A C 2 ( 1 ) = R ~ T % 0 2 ( 1 - 1) T H E N ' '
' 1 , E A V I N G = 1 I3ASV$ ( :t ) = I-IEADS ( E N T R Y END TF: NEXT I E N D 1 F
I ) r V O T = S I M P L E X ( L , E A V I N C , E N T R Y ) i<+ll,l SUli
. ' :I 1 1 3 'l'l Il?I<N'I'RY 1 31 ' I ' l l 1'; I'AI(?' 'I 'IIIES 'I'O FIND TtIE ENTRY AND LEAVIMG POSI'I'ION 1N TIlE SIMPLEX TALILEA i<lll)lM Ib'iTIO2 (BV - I ) , RAC2 (BV - 1) , R A ~ 1 d 3 (BV - I ) , RAC3 (RV - 1 ) . 517<(1j,~ . 1,'i)R I1 = 2 TO EV: R A T I O ( I - 1) = R I I S ( 1 ) / s I M P L E x ( I , P S ( 1 ) )
I < A V ( I - 1) = R R T I O ( 1 - 1) I<A' ImlO% ( I - 1 ) = R l l S ( 1 ) / S I M P L E X ( 1 , P S ( 2 ) ).: RAC2 ( I - I ) = RATIO^ ( 1 - 1) I Z A ' I ' J . ~ ~ ( S - I ) - RI-IS(1) / S I M P L E X ( 1 , P S ( 3 ) ) : K A C 3 ( I - 1 ) = R A T I O ~ ( S - 1 ) 14 I;:XT I
I;OI? 1 - 1 TO RV - 2 : FOR J = I TO RV - 1 I 17 rmc: ( r ) C = RAC ( J ) THEN GOTO PENTY SWAP IIAC ( I ) , RAC ( J )
PIWI'Y : I F RAC2 ( I ) c = RAC2 ( J ) THEN GOT0 PGFOLDTY SWAP KAC2 ( I ) , KAC2 ( J )
L I W I ' ' Y : I F RAC3 ( I ) <= RAC3 ( J ) TIlliN GOT0 .'rRECK I SWAP RAC3 ( I ) , RAC3 (J)
rmrxx : NEXT J : NEXT I M I N l = R A C ( 1 ) : MIN2 = R A C 2 ( 1 ) : MIN3 = RAC3 (1)
J l K ( 1 ) = MTN1: J I K ( 2 ) = M I N 2 : J I K ( 3 ) = MIN3 l.'OIZ 1. = I TO 2 : FOR J = I + 1 TO 3 11,' J T l < ( I ) < = J I K ( J ) THEN GOT0 T A S S I T ' '
SWAP J I K ( I ) , J I K ( J ) ' I : N E X T J : N E X T I : M I N = J I K 9 1 0 .
I P 'MIN - M I N l THEN ' r<NmsKY 2 P S (I.)
FOR I - 2 'I'O BV TF R A C ( L ) = R A ? ' I O ( I - 1 ) THEN LEAVING = I RASVS ( I ) = HEADS (EN'PRY) END I F : NEXT I I:ND T F
1 I: I41 N = RAC2 ( 1.) THEN !<PITRY = P S ( 2 ) . ,
~ , ' O R I = 2 TO nv I F KAC2 ( I . ) = RATIO2 ( I - I ) TIIEN LEAVING = I BASVS ( I ) = HEADS (ENTRY) END I F : NEXT I E:ND I F
I F MTN = R A C 3 ( 1 ) THEN ENTRY = P S ( 3 ) . ,
I FOR I = 2 TO BV . ,
' I F KAC3 (1) = RATIO3 (I - 1) THEN LEAVING = I BASVS ( I ) = FIEADS (ENTRY) END I F : NEXT I END 11.' q
P I V o T = SIMPLEX (LEAVING, ENTRY) l,:NI) S U U
c;Ul< 'I'I?,L<EN'I'RY 138 "I'II 1 S PART 1'KIlCS 'l'0 F I N D 'SHE ENTRY AND LEAVlMG P O S I T I O N 1 M 'I'IIE S I M P L E X ~ ' A ~ ~ I J E A I(RI)I M R A T I O 2 (BV - 1.) , RAC2 (BV - 1 ) , R A T I O 3 (BV - 1 ) , RAC3 (RV - 1 ) , J I K !? \ IWI? r - 2 TO B V : RATIO( I - 1 ) = K H S ( I : ) / S I M P L E X ( I , P S ( I . ) )
I:,\.(:(I - I.) = t w r r . o ( x - 1 ) l l r , ' l . l ~ j 2 ( 1 - . I . ) = R I I S ( 1 ) / S I M P L G X ( 1 , P S ( 2 ) ) : K A C 2 ( I - 1 ) = R A T I O 2 ( 1 - 1 ) l : / ~ ? ' J 0 3 ( 1 - I ) = I < H S ( I ) / S I M P L E X ( 1 , L'S(3)) : I I A C 3 ( I - 1) = R A T I O ~ ( I - 1 ) N1':XrI' I'
I.'OI( I - 1 'SO 13V - 2 : I'OR J = I '1'0 UV - I. l 1: JlAc: ( 1 ) c. = IU\C ( J ) 'I'IIGN GOTO PKNY
;b?r\L1 I ? A C ( I ) , R A C ( J ) I'J4:NY : i F I<AC2 ( I ) <= RAC2 ( J ) I'HEN G O T 0 PI$FOLDY
SWAP RAC2 ( I ) , RAC2 ( J ) l : , l Y : 1F RAC3 ( I ) < = 1 m C 3 (J) THEN G O T 0 RECK
SWAP RAC3 ( I ) , I W C 3 (J) I<KrK ; NEXT J : NEXT I
M I N l = R A C ( 1 ) : M I N 2 = RAC2 (1) : M I N 3 = RAC3 ( 1 ) < l , T I < ( 1 ) = M I N I : J I K ( 2 ) = M I N 2 : J I R ( 3 ) =. M I N 3 k ' 0 R .L = 1 TO 2 : FOR J = I + 1 'SO 3 IF' JTK(1) <= J I K ( J ) THEN G O T 0 A S S I T :;NAP J L I < ( I ) , J I K ( J )
I'~$;Y r 'l ' : NEXT J : NKXT I : M I N = J I K 9 1 0 '
11.1 M l I J - M.CN1 TlIAPJ EN'I'RY = PS ( 1 )
l,'(lI< I - 2 T O BV I17 KAC(1) = R A ' r I O ( I - 1) THEN
1,EAV'INC: = I BASV$ ( I ) = HEADS (ENTRY)
I END, I F : NEXT I END I F . .
I F M I N = RAC2 ( 1 ) THEN ra:ru"Y - PS ( 2 )
L:OI< I = 2 T O BV 1F R A C 2 ( 1 ) = R A T I O Z ( 1 - 1 ) THEN 1,GAVING = I liASV$ ( I ) = HEADS (ENTRY) EN11 I F : NEXT I KNLI I F
I F MIN = RAC3 ( 1 ) THEN ENTRY = P S ( 3 )
I FOR I = 2 T O BV CF R A C 3 ( 1 ) = R A T I O ~ ( I - 1 ) THEN L,EAVING = I i3ASVS ( I ) = HEAD$ (ENTRY) L,:NT) I F : NEXT I EN11 1F
, r1vo.r. = SIMPLEX (LEAVING, E N T ~ Y ) I,:NT) SUB . .
I A'I' '1'11 IS P O I N T OPTIMAL SOLUTION IS CHECKED FOI< I - 1 'TO ACROS 'I'OPI<C ( 1 ) = TABLEAUX (1, I ) : NEXT I ~ ' 0 1 1 E = 1 T O ACROS - 1: FOR J = I -+ 1 T O ACROS TF T O P E C ( 1 ) c= T O P E C ( J ) THEN G O T 0 IPREDDY
. . SWAP TOPEC ( I ) , T O P E C ( J ) I F ' I I I ~ > ~ ~ Y : NEXT J : NEXT I
I ) - SGN (TOPEC ( I ) ) 11' 1) - - I THEN C'01.,01? 1 % : P1;INT : P R I N T TAB ( 1 0 ) ; "OPTIMAL SOLU'I'ION NOT YET ATTAINED" (?OLL)K 1 1 : P R I N T TAB ( 7 ) ; "DO YOU WISH TO CONTINUE SOLVING FOR OP'I'IMAL SOL!IJ'I'J
('OI,Oi< 1 5 : PI11N'I' : P R I N T I' . . . . . . . . . . . . . . P R E S S ANY KEY TO CONTINUE" l)AX$ = 1'NPUrI'$ ( I ) . ,
I I<IL'- ? l ~ ~ ' ~ ~ ~ ~ ~ ~ ~ ~ G 'I'l-IE TABLEAUX VALUES A S S I M P L E X VALUES. I*.'OIZ T - 1 T O R V 1.'01l J = I T O ACROS S LMPLEX ( I , J ) = TABLEAUX ( I , J ) NEXT J R l i S ( T . ) = R H S Z ( 1 ) NI*:Xrl' T
K I ,Sl< c'cj1,OR 1.2 : P R I N T : P R I N T TAB ( 2 0 ) ; "OPTIMAL SOLUTION IS W T A I N E D . "
l<E PORrl' , l<Idl) , ,
l*:Nl) I P' 11;' Il'rtj = " Y " 'l'tlEN END
PI I VALUE bJORKINGSIMPLEX 111 STAR LEAUX
I 1,' I I ' l ' $ = " N" TIiEN I::I\JD I F l < ~ l N ( . I ,:: ICNI) !.;[ID
' : I ) ] ! CllVALtUE 140 "I'IILS PART O F TI IE PROGRAM F I N D S THE ENI'RY AND LEAVING V A R I A B L E S I N TI IE S I M P L E X
FOR I = 1 '1'0 ACROS 'I'OPEC (I) - S I M P L E X (1, I ) : NEXT I [.'OR I = 1 '1'0 ACROS - 1: FOR J = I + 1 T O ACROS .I F TOPEC ( I ) <= TOPEC (J) THEN G O T 0 FREDDY SWAP 'I'OPEC ( I ) , TOPEC ( J )
I,'I<I.:l)DY: NICX'Y J : NEXT I ]*:'I -: 0 : FOR 1 = 1 T O ACKOS [I7 .':'lblPI,EX (1, I ) = TOI 'EC(1) TI-IEN
y 1 ' - . I.:#J* .+ 1 . ,
ps (']<'l') .=- 1 I.:NII r r: NLXT I 1 1 : b.;'lS = 1 THEN ONEICNTRY r~~l,sl~,;.rI~ 12'T = 2 rl'I-lr<N 'l'I<Nrl'RY EILJL.:I F E'I' = 3 'r1lEtrl T I l l < I ~ ~ N ~ I ' I ~ Y l.:I ,sE C I ,S
.';CRE:E:N 9 (:OI,OR 1 5 , 8 COLOR 10 : LOCATE 1 0 , 1 6 : P R I N T "PROGRAM D E S I N G E D FOR A MAXIMUM OF THREE EN COLOR 1 5 : LOCATE 1 2 , 1 9 : P R I N T "ENTRY V A R I A B L E S ARE MORE THAN THREE(^) I '
COLOR 14 : LOCAl'E 1 4 , 2 3 : P R I N T "THEREFORE PROGRAM I S SUSPENDED" COI,OR 15 END I F
::!Ill I.iOI.:l(lN(;SIMPL,lCX ' '1'11 1 !< /\RAE SOLVES 1'1IE S I M P L E X TABLEAUX
I J I < l N'S : P R I N T l,'Ol< .I = 1 TO BV YOi? J = 1 TO ACROS I F ' 1 = LEAVING THEN G O T 0 BEN I'f\I?L,EAUX ( I , .I) = S I M P L E X ( I , J ) - ( S I M P L E X ( L E A V I N G , J ) * S I M P L E X ( I , ENTRY) ) / I'OL,OR 1 2 : PIX I N T "TABLEAUX ( " ; I ; " , " ; IT ; " ) " ; " = " , . S I M P L G X ( I , J); " II
C'OI.OR 1 0 : L'KINT "= " , . TABLIZAUX ( I , J) : GO'l10 YUZ LI1:N :
'SABI,E7\rJX ( I , J ) = S I M P L E X ( I , J ) / P I V O T , J; l l ) l l . " = I t . C'Ol,Oli 1 :.' : P R I N T "TABLEAUX ( " ; I ; " , " . , S I M P L E X ( 1 , J ) ; " / " ; P I V O T CO1,OR 1 0 : P R I N T " = ' ; T A R L E A U X ( I , J ) "
YUZ: NKX'I' J 1 1 4 ' 1 - IJEAVIMG THEN
!<!I>;:? (I) = RHS (1) / P I V O T ( ' 0 1 ,O?R 1 5 : P R I N T " R H S 2 ( 'I ; I ; 'I) =" , . R I I S ( 1 ) ; "/'I; P I V O T ('01,OK 14 : P R I N T " = " ; R H S 2 (I) (;0'1'0 NETY I~'N1) IF l<F lS2 (1 ) = RIIS(T) - ( R I I S ( L E A V 1 N G ) * S I M P L E X ( 1 , ENTRY) / ( P I V O T ) )
, RIIS ( I ) ; " - ( " ; RHS ( L E A V I N G ) ; I' * " ; S I M P L E X ( L (:Ol,OR 1 5 : P R I N T " R I l S 2 ( " ; I ; ")='I. C'OLUR 7 4 : P R I N T "="; R H S 2 ( I )
N I X " : SLEEI' 1 : NEXT I 1?1\71) SUU
. . . SUB S I M I I l S P L A Y 142
.. . , ? ,:..
, .., ' D I S P L A Y I N G TiIE SIHPLI:X 'I'ADLEAIJX I .
C L S SCREEN 9 COL017 14, 0 i.,l:NI% (190, 3 0 ) - ( 4 4 5 , 3 0 ) , 13