Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Production Management I- Lecture 5 -
Methods and Tools for Materials Management
Contact:Dipl.-Ing. Tim Hö[email protected] R. 208Tel.: 80-27391
Objectives of the Lecture:
• To calculate requirements using appropriate materials management tools.
• To present the most common methods and tools used in materials management.
• To explain the selection, application and limitations of the methods and tools presented.
• To provide an overview of the options of IT support in materials management.
L5 Page I
Lecture 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
Structure of the Lecture:
5.1 References L5 page III
5.2 Summary of Lecture L5 page 1
5.3 Introduction and Problem L5 page 2
5.4 Deterministic Calculation of Requirements L5 page 5
5.5 Stochastic Calculation of Requirements L5 page 11
5.6 Defining Emergency Stock Level L5 page 15
5.7 Determining Lot Size L5 page 19
5.8 Questions on the Lecture L5 page 23
5.9 Exercise: Methods of Calculating Requirements and Lot Sizes E5 page 1
5.10 Calculation Exercise E5 page 9
5.11 Calculating Requirements Using the Gozintograph A5 page 1
5.12 Derivation of the Andler Formula A5 page 3
5.13 Exponential smoothing of second order A5 page 5
L5 Page II
Lecture 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
5.1 References Lecture 5:
/1/ Wiendahl, H.P. Betriebsorganisation für Ingenieure, Hanser-Verlag,München, 1997
/2/ Grochla, E. Grundlagen der Materialwirtschaft, Gabler Verlag,Wiesbaden, 1992
/3/ REFA Methodenlehre der Planung und Steuerung,Hanser-Verlag, München, 1991
/4/ Hackstein, R. Einführung in die technische Ablauforganisation,Hanser-Verlag, München, 1998
/5/ Hartmann, H. Materialwirtschaft: Organisation, Planung, Durchführung undKontrolle, Deutscher Betriebswirte Verlag, Gernsbach, 1993
/6/ Hahn, D. /Produktionswirtschaft; Controlling industrieller ProduktionLassmann, G. Bd. 1, Physica-Verlag Heidelberg, Wien, 1986
/7/ Hackstein, R. Produktionsplanung und -steuerung (PPS), VDI-Verlag, Düsseldorf, 1989
/8/ Oeldorf, G. / Olfert, K. Materialwirtschaft, Ludwigshafen. Kiehl Verlag, Ludwigshafen (Rhein), 1998
/9/ Eversheim, W. / Betriebshütte, Produktion und Management, Neu bearb.Schuh, G. (Hrsg.) Auflage. Springer-Verlag, Berlin, Heidelberg, New York, 1996
/10/ Dangelmaier, W. Modell der Fertigungssteuerung, Beuth-Verlag, Berlin, 1993
/11/ VDMA Integrierte Materialwirtschaft, Maschinenbau-VerlagFrankfurt, 1990
/12/ Eversheim, W. Organisation in der Produktionstechnik. Band 1: Grundlagen.3. Auflage. VDI-Verlag, Düsseldorf, 1996
/13/ Günther, H.-O. / Produktion und Logistik, 5. Auflage, Tempelmeier, H. Springer-Verlag, Berlin, 2002
/14/ Tempelmeier, H. Material-Logistik; Modelle und Algorithmen für die Produktionsplanung und –steuerung und das Supply Chain
Management, 5. Auflage, Springer-Verlag, Berlin, 2002
L5 Page III
Lecture 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
5.2 Summary of the Lecture:
The large range of parts used in many companies makes the deployment of suitable management tools in the field of materials management essential. The purpose of the tools is to meet what can, in some cases, be contradictory requirements for:
- Higher levels of material availability
- Lower storage space and capital commitment
- Greater flexibility
- More favourable purchase prices.
In research and practice, there is a wide range of methods and tools geared to materials management. There is an extensive range of methods and tools in research and practice. The diversity of their characteristics makes it essential to analyse the function for which they are required precisely before selecting the most suitable one. It is possible, for example, that several different methods, e.g. a deterministic calculation of A and B parts, can exist along with a stochastic calculation of the requirement for C parts.
In addition to the functional characteristics, it is important to consider the work and time required to enter and calculate information. When the task is relatively straightforward, a rule of thumb may well be the most suitable solution. When the problems are more complex and the calculation methods more time consuming, it is advisable to use IT-assisted tools. However, it is important to remember that even the calculating techniques, concealed behind the coloured masks on the monitors, must be suitable for the task in hand and that it is vital to make the optimum selection from what is usually a wide range of parameters, if the result is to be satisfactory.
Lecture 5
L5 Page 1
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Problems in materials management
Target conflicts
Lot size StockLow capital commitmentLow requirement for spaceRational manufactureHigh availability
... ... ...
Requirements Effects
Problem of quantity
- Number of parts
- Number of procurement operations
- Number of suppliers
Uncertain material requirement
Time
Req
uire
men
t
Part 4711old
Part 4712new
techn. modification
Problems in Materials Management
Notes on Figure 1:
5.3 Introduction and problem
The problems facing materials management are characterised particularly by the contradictory requirements for availability of ready materials on one hand, and low stock levels on the other hand. Because of the number of steps involved in the procurement process, it has become essential to use appropriate IT tools..
Lecture 5
L5 Page 2
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Quantity-Related Problems illustrated by Examples from Industrial Practice
Automobile manufacturer
Machine toolmanufacturer
No. of product types:
∅ no. Of parts per product:
Total no. of parts:
No. of orders per week:
No. of suppliers:
~ 20 600
16.000
10
700
5.000 10.000
140.000
10.000
1.050
Anmerkungen zu Bild 2:
Die Anforderungen an die Materialwirtschaft hängen stark vom jeweiligen Produkt- und Unternehmenstyp ab. Eine manuelle Beherrschung der Teilevielfalt ist bei komplexeren, variantenreichen Produkten sowie in der Einzel- und Kleinserienproduktion kaum noch möglich.
Vorlesung 5
V5 Seite 3
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Focus of the Lectures Materials Planning I and IIIntroduction
Methods
Materials procurement planning
Static lot sizes calculationStatic lot sizes calculation
Dynamic lot sizes calculation
Dynamic lot sizes calculation
Materials requirement planning
Stochastic requirement calculation
Stochastic requirement calculation
Deterministic requirement calculation
Deterministic requirement calculation
Materials stock planning
Definition of emergency stock levels
Definition of emergency stock levels
LogisticsLogistics
Legend: = Lecture 4 = Lecture 5
Area of conflict with emergency stock levelArea of conflict with
emergency stock level
Functions and concepts of material storagesFunctions and concepts of material storages
Tasks and objective of materials planningTasks and objective of materials planning
Planning of material sourcingPlanning of material sourcing
Notes on Figure 3:There is already a wide range of methods and tools, some of which are IT-supported for the groups of functions in the areas of material requirement, stock and procurement planning.
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Lecture 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
According to: Wiendahl
Gross requirementAdditional requirement+
Total requirement=
Stock level-
-
No. earmarked (Reservations)
+
Emergency level+
Net requirement=
- Scrap- Spare parts- Test purposes- etc.
Order inventory(When products are externally manufactured)
- Workshop stock(When products are manufactured in-company)
Available stock
Net Requirement
Notes on Figure 4:
According to REFA, the gross requirement is the period-oriented requirement of material disregarding the inventory. The net requirement is calculated by the difference of gross requirement and the available stock at a certain date. Material requirement planning is based on the net requirement.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Source: Olfert
Production step method
Production step method
Deterministic calculation of requirements
Deterministic calculation of requirements
Analytical method
Analytical method
Synthetic method
Synthetic method
Re-netting methodRe-netting method
Gozinto methodGozinto method
Disposition step method
Disposition step method
Where-used reportWhere-used report
Deterministic calculation of requirements entails precise determination of material requirements in terms of quantity and date required.
Deterministic calculation of requirements entails precise determination of material requirements in terms of quantity and date required.
Methods of Deterministic Calculation of Requirements
Notes on Figure 5:
5.4 Deterministic calculation of requirements
The deterministic calculation of requirements is based on the planned requirement for products or product components (primary requirement). The exact requirement for assemblies, single parts and raw materials (secondary requirement) is determined over all levels of the product structure in an analytical process by breaking down the product step-by-step on the basis of the parts list. In contrast to this, the synthetic method is based not on the whole product but on single components, examined in isolation. In this case the where-used report is used as a tool.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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According to: Wiendahl
Structuring Products According to Production and Planning Steps
R 1
T 3 T 4
Production steps technique Disposition steps techniqueStep
0
1
2
3
4Exact determination of requirement datesDecomposition of the components on several structural levelsStraightforward products without repeated use of components
Decomposition of requirement on only one structural level eachMore difficult to determine exact requirement datesComplex products
+-
+-
E 1
R 2
R 1 T 2
T 3
G 2
T 4
G 1
T 1T 2G 2
T 1
R 1
R 1
E 1
R 2 R 1 T 2
T 3
G 2
T 4
R 1
G 1
T 1T 2G 2
T 3 T 4
T 1
R 1R 1
Legend: E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part(Teil); R = Raw material (Rohmaterial)
Notes on Figure 6:
The production steps method is based on a product structure broken down into the chronological sequence. In contrast to this, the components which are used in a number of several applications are combined on the lowest structural level in the disposition step method. This eliminates the need for multiple breakdowns.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Calculating date required
W 26
- 3 W
= W 23
Date higher order components requiredLead time
Date required
Calculating net requirement
85
x 3= 255- 110
= 145
Net requirement of higher order componentsUse
Gross requirementAvailable stock
Net requirement
G1Engine
1001585
T2Cog wheel
255110145
G2Transm.17060
110
2 33 W
W 26
G1
G2 T2
Example of How to Calculate Net Requirements
Legend: W = Week; G = Assembly Part (German: Gruppe); T = Single part (Teil)
Notes on Figure 7:
The requirement deadline for a component is calculated on the basis of the requirement deadline for the higher-ranking components minus lead time. In the disposition step method, the requirement dates calculated are sometimes too early. However, more time-consuming calculation operations permit the actual data of requirement to be calculated accurately.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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1 11
32 1
1 2 21
1 1 1 1
Compo-nents
Available stock
Net Re-quirement
Require-ment date
E1 --- 100 W 34
G1 15 85 W 26
G2 60 210 W 23
T1 25 160 W 23
T2 110 145 W 23
T3 210 100 W 21
T4 160 260 W 21
R1 --- 260 W 19
R2 100 160 W 19
2 W
2 W
3 W
8 W
Lead time
Total requirementComponentGross requirementAvailable stockNet requirementUse
16010010060------40---------60---2001001006060---R2R1R1R1R2R1
20010060---------160110
200100220110T4T3T4T3
10010060145110------2511060
10010085255170G2T1T1T2G2
8515100G1
100---
100E1
Using the Disposition Step Method to Determine Net Requirements
Legend: W = Week; E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part (Teil); R = Raw material (Rohmaterial)
11
Notes on Figure 8:
The information needed to structure the products is contained in the parts lists. The gross requirement for a component is calculated by multiplying the net requirement for the higher-ranking components by the number of times it is used (see Fig. 7). The net requirement is obtained by subtracting the available stock. In the disposition step method, the available stock is allocated to each component on only one structural level. This avoids errors.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Alternative Presentation of Product Structure Using Gozinto-Graph
Product, assembly part, single part, raw materialRequirement
Gozinto-Graph
Straightforward mathematical requirement
Unclear presentation, takes time to get used to
+
-
E1100
G1-
G220
T4-
T1-
R1-
T2-
T3-
R2-
1 1
1 2 2
31 1
1
1
Legend: E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part (Teil); R = Raw material (Rohmaterial)
1
Notes on Figure 9:
Alternatively, the composition of a product can be shown by a Gozinto-Graph. Since this presents each component only once, this form of presentation permits the requirement to be worked out on the basis of a very straightforward algorithmic resolution. This form of categorising products is therefore used by many IT systems to organise the material needed for internal data structures.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Consumption Models as Basis for Stochastic Determination of Requirement
Con
sum
ptio
n
Time
Con
sum
ptio
n
Time
Con
sum
ptio
n
Time
Consumption model
Without trend With trend
Con
sum
ptio
n
Time
Pure constant model
Seasonal constant model
Pure trend model
Seasonal trend model
Without seasonal fluctuation
With seasonal fluctuation
Without seasonal fluctuation
With seasonal fluctuation
Source: REFA
Notes on Figure 10:
5.5 Stochastic Calculation of Requirements
The stochastic calculation of requirements differs from the deterministic mode in that it is based on historical data, which is extrapolated for the future using stochastic methods and which therefore carries a degree of statistical uncertainty. The consumption pattern must first be interpreted before a suitable technique can be selected. The consumption models suggested by REFA /3/, for example, are useful in this context.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Common Techniques of Stochastic Determination of Requirement
According to: REFA/ Zeigermann/Tempelmeier
Exponential smoothing of first order
Timet t+1
V1V-V1
V1 = Exp. smoothed value 1st order
α = Smoothing factor
( )VVVVP ttttt
1
1
1
1
1
1 −−+−+== α
Exponential smoothing with trend correction at
1 = corrected estimate value of the trends‘ axis intercept
bt1 = exponential smoothed value of the
trends‘ gradient
baP ttt
11
1 +=+
Con
sum
ptio
n V
Timea
)1(*1 ++=+
tbaPt
Pt+1 = Forecast valuea = Axis interceptb = Gradient
Regression analysis
Floating mean valueVi = Requirement in period i
Time
n ∑−+=
+=
t
ntiit VP n 1
1
1
Ver
brau
ch
Perioden05
1015202530354045
7 8 9 10
V
V1
Pt+1
VV1
Pt+1
Con
sum
ptio
n V
Con
sum
ptio
n V
Con
sum
ptio
n V
Time
Notes on Figure 11:
While the regression analysis for a given set of value couples determines a mean straight line, the other operations shown in the figure adapt the forecast value flexibly to the changes in consumption. The characteristics of the forecasting method can be influenced by changing the parameters (number of periods considered “n”, smoothing factor “α”).
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Comparison of Forecasting Methods
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10Period t
Req
uire
men
t
Actual RequirementFloating mean Value (n = 5)Exp. smoothing of f irst orderExp. smoothing w ith trend correctionRegression analysis for period 7
Notes on Figure 12:
The floating mean value is very suitable for pure constant models, since its reaction is sluggish, particularly when the number of periods taken into account “n” is high. The sensitivity of the technique must be increased when trend models are required. However, when this is done, the operation reacts very strongly to any random peaks in requirement. Similar considerations apply to the exponential smoothing method in relation to the definition of the α-factor. When the α-factor is high, the operation reacts very swiftly to any changes in requirement, causing the current requirement values to be heavily weighted when they are included in the forecast. In contrast, when the α-factor is low, the predicted value reacts slowly.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Suitability of Forecasting Methods for Various Consumption Models
Regression analysis
Exponentional floating of the first orderExponentional floating with trend correction
Exponential smoothing given seasonal demand *
Multiple regression *
Floating mean value
Pur
e co
nsta
nt
mod
el
Pur
e tre
nd
mod
el
Sea
sona
l co
nsta
nt
mod
el
Sea
sona
l tre
nd
mod
el
Method
Consumption model
Suitable Suitable in some cases Suitable in principle, but not always useful
Source: Dangelmaier * Not further explained in this lecture
Notes on Figure 13:
The methods used in order to take explicit account of seasonal influences are based on the values recorded in the same period of the previous year. When seasonal trend models are used, a further component which reflects the trend can be added to this technique. These techniques are explained in greater detail in literature /6/.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Reasons for Storing Emergency Stocks
Time
Sto
ck le
vel
Stock emergency level
Actual requirement
Requirement forecast
Time
Stock emergency level
Target delivery dateActual delivery date
Time
Stock emergency level
Stock level assumed
Actual stock level
Source: FIR
Sto
ck le
vel
Sto
ck le
vel
Uncertainties in procurement
Uncertainties in determining stock level
Uncertainties in determining requirements
Notes on Figure 14:
5.6 Defining Emergency Stock Level
The purpose of emergency stocks is to avoid bottlenecks in the material supply from occurring when the requirements and stock levels differ from those planned. However, there are conflicting aims even in defining the emergency stock levels. Any increase in the emergency stock level, in an attempt to improve the capacity to supply, is at the expense of increasing storage and stock costs (see Fig. 15).
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Impact of Emergency Stock on Cost
Source: Wiendahl
FMK = Cost incurred as a result of incorrect quantities (German: Fehlmengenkosten)
SBK = Cost of emergency stock (German: Sicherheitsbestands-kosten)
Level of service = x 100%No. of requests satisfied immediately
Total no. of requests
FMK + SBK
SBK
80% 100%
FMK
Level of service
minimale Kapitalbindung
Minimum storagecosts
Maximum readiness to supply
Objectives
Notes on Figure 15:
The progressive course of emergency stock costs is the result of the additional costs (e.g. for renting or building additional warehouses) when the available storage capacity is exceeded and from the steep increase in handling, transport, and administrative expenditure incurred when a warehouse is filled to capacity. The excess quantity costs result, for example, from loss of production caused by incorrect parts.
Lecture 5
L5 Page 16
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Techniques of Determining Emergency Stock Levels
According to: Riggs
Ultra-conservative method
Ultra-conservative method
Percentage methodPercentage method
Heuristic functionHeuristic function
Emergency stock
Maximum daily con-sumptionto date
Maximum poss.
procurement time in days
Emergency level
∅removal
from stock
∅procure-
menttime
Factor(25-
40%)
Emergency level
- ∅ removal from stock- Standard deviation- Replacement procurement time- etc.
f
=
=
x
x x
=
Notes on Figure 16:
The “ultra-conservative method” of defining the emergency stock level estimates the “worst case” scenario. This normally results in unnecessarily high stock levels. The percentage method, which uses average values for stock removal and for procurement time as well as a factor which can be set individually, is usually more suitable for determining useful emergency stock levels. The heuristic method explained in Fig. 17 is outstanding in that it provides the option of specifying a required service level.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Heuristic Method of Determining Emergency Stock Level
According to: REFA
Emergency stock level: BS = b x s = 4,3 x 10,29 = 44,25 units
(Given 99% level of service)
Emergency stock level: BS = b x s = 4,3 x 10,29 = 44,25 units
(Given 99% level of service)
Quantity removed from stock Determining factor “b”87654321n
10294105127104116100109Removal
[units]
Replacement procurement time
∅ removal from stock:
Standard deviation:
unitsxn i 1,1071x =∑=
( )units
xn
xn
s ii
29,10
11
1 22
=
⎥⎦⎤
⎢⎣⎡ −
−= ∑ ∑
(Probability of correctness 95%)
Factor „b“
Number of removals n
1
2
3
4
5
6
7
5 10 20 50 100 200 400
4,3
8
Level of service:99%95%90%
Notes on Figure 17:
This method is explained in greater detail in REFA /3/.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Conventional Techniques of Determining Lot Size
Source: Wiendahl
Techniques of determining lot size
Techniques of determining lot size
DeterministicDeterministic StochasticStochastic
Static(constant lot size)
Static(constant lot size)
Dynamic(variable lot size)
Dynamic(variable lot size)
Basic model (according to Andler)
Extended basic models
Floating economic lot size
Part period technique
WAGNER-WITHIN technique
SILVER-MEAL technique
Order point technique
Order rhythm technique
Notes on Figure 18:
5.7 Determining Lot Sizes
The deterministic methods of determining lot sizes strive to reduce lot size-dependent costs to an arithmetic minimum. The static methods assume a constant removal rate from the stores whilst the dynamic methods are based on the planned variable requirement values. The stochastic methods were explained in Lecture 4.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Determining the Optimum Lot Size according to Andler
Source: REFA
Total cost
Storage costManufacturing cost
Cos
t
Quantityxopt
Quantity
Cos
ts
Quantity
- Order processing cost
- Set-up cost- Material cost- Additional cost with unfavourable manufacturing quantity
- Order processing cost
- Set-up cost- Material cost- Additional cost with unfavourable manufacturing quantity
- Storage cost- capital commitment
- interest cost(external capital)
- Opportunity cost(equity capital)
- Storage cost- capital commitment
- interest cost(external capital)
- Opportunity cost(equity capital)
Legend:xopt = Optimum lot size [units]iL = Storage cost rate [%]xkes = Total requirement per
period [units]KR = Set-up cost [€]Kh = Manufacturing cost per unit
of quantity [€/Unit]
„Andler Formula“„Andler Formula“
Cos
tsLh
gesRopt iK
xKx
⋅⋅⋅
=%200
Notes on Figure 19:
The cost-optimised lot size according to Andler is given by the sum of all fixed costs per lot (set-up efforts, etc.) and variable costs per lot (storage). The original Andler formula assumes an infinite production speed, i.e. stock levels in the production area are not taken into account. However, when the Andler formula is expanded, the production phase can also be included on the basis of the throughput time involved. A derivative of the Andler formula is given in the Appendix (Chapter 5.12).
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Calculating Floating Economically Efficient Lot Size
Period1 2 3
Kges, n = Unit cost (for n periods)A = Fixed lot costKL = Storage costs per unit and periodBmi = mean stock level in period “i”xges,n = cumulated lot size (n periods)
Formula
• Single product manufacturing
• Production speed infinitely high
• Stock removal rate variable (actual requirement for period)
Boundary conditions
Summary of the requirement per period up to minimisation of costs per unit.
Summary of the requirement per period up to minimisation of costs per unit.
Stock level
170
3060
n=2
n=1
n=3
1
2
3
4
60
30
80
50
n=2
n=1
n=3
Lot size 170Lot size 90Lot size 60
Requirement[units]
Period
4,17
3,38
3,41
Unit cost [€]
nges
n
imiL
nges x
BKAK
,
1,
∑=
⋅+=
Notes on Figure 20:
In this method, the planned requirements for future periods are condensed until the sum of the lot and storage costs per unit are reduced to a minimum. When the requirement fluctuates substantially, this method has considerable advantages over the Andler formula.
Lecture 5
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Additional Factors which Impact on the Determination of Lot Size
Source: REFA
General Outsourcing• Available storage space• Liquidity• Storage life of the products
In-company manufacture• Capacity use of manufacturing facilities
• Flexibility required of manufacturing facilities
• Manufacturing sequence (throughput times, set-up times)
• Supply capability of supplier
• Pricing• Transport facilities/ packaging units
Uni
t cos
ts
xopt½ xopt 2 xopt
Advisable spread
• Better utilisation of capacity
• Lower prices
• Capacity use of transport facilities
• Better utilisation of capacity
• Lower prices
• Capacity use of transport facilities
• Higher flexibility
• Less requirement for space
• Shorter throughput time
• Higher flexibility
• Less requirement for space
• Shorter throughput time
Lot size
Additional relevant criteria in determining lot size
Notes on Figure 21:
In addition to the methods previously discussed, in practice, there are diverse additional criteria which are used to determine lot size. When, for example, the machining time for a lot is long in relation to the available capacity, bottlenecks can occur, which lead to delays in processing subsequent orders. Since the overall cost curve is generally very flat in the area around the minimum, permissible tolerance limits can be given for the optimum lot size, without causing the unit costs to rise too steeply.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
5.8 Questions on the Lecture
1. How do the analytical techniques differ from the synthetic techniques in deterministic calculations of requirements?
2. Explain the difference between the production step method and the disposition step method.
3. List a suitable forecasting technique for each of the four consumption models (in accordance with REFA) and explain under what circumstances each of the techniques is suitable.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
4. Explain briefly some reasons for keeping emergency stocks.
5. Explain the impact of the emergency stock on cost.
6. Discuss briefly the advantages and disadvantages of the techniques of defining the emergency stock levels.
Lecture 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
7. List the boundary conditions which apply to the application of the Andler technique.
8. Explain briefly the advantage of the technique of the floating economic lot size over the Andler technique.
9. List relevant criteria used to determine lot sizes in addition to the cost variables used in the Andler formula.
Lecture 5
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Methods and Tools for Materials Management
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Appendix-Lecture 5-
Methods and Tools for Materials Management
Appendix 5
A5 Page I
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
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Presentation of Product Structure in a Gozinto-Graph
E1
100
G1
-
G2
20
T4
-
T1
-
R1
-
T2
-T3
-
R2
-
1 1
1 2 2
3
1 1
1
1
Product, assembly, part, raw material
Requirement
Legend: E = Product (German: Erzeugnis); G = Assembly Part (Gruppe); T = Single part (Teil); R = Raw material (Rohmaterial)
Notes on Figure A-1:
5.11 Calculating Requirements Using the Gozinto-Graph
The principle of calculating gross requirement using the Gozinto technique is explained in greater detail in the following, on the basis of the product structure shown in the so-called Gozinto-Graph (Fig. A-1).
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Appendix 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Gozinto-Graph Calculation Plan
Z Quantity Z Quantity Z Quantity Z Quantity1 E1 0 100 1002 G1 1 0 100 1003 G2 2 1 100+20 0 200 3204 T1 2 1 100 0 100 2005 T2 1 0 300 3006 T3 1 0 320 3207 T4 1 0 640 6408 R1 2 1 200 0 320 5209 R2 1 0 640 640
Run 3 Gross requirement
Product, assembly, single part
Arithmetic step
Run 0 Run 1 Run 2
z = Arrow counter
(According to: Hahn, Laßmann)
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Notes on Figure A-2:
The stop criterion in this type of gross requirement calculation is the number of arrows starting from one nodal point, which describe the use of a part or of an assembly within a product. The secondary requirements of the assemblies, single parts, etc. are determined in the individual runs on the basis of the elements, whose arrow numerator is a “z” or an “o”. In the case of the assembly G2, account must also be taken of the primary requirement. Fig. A-2 shows the arithmetic development of the Gozinto technique /8/.
Appendix 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Determining the Optimum Order Quantity according to Andler
Optimum order quantity when products are manufactured externally
Gives the optimum procurement quantity.
Legend:x = Order quantityxges = Total quantity per periodxopt = Optimum procurement quantityKB = Order cost per order KB,ges = Order cost per periodKB,zus,ges = Additional cost per periodKx = Additional cost per unit of quantityKL = Storage cost per orderKE = Cost per unit of quantity when products are
manufactured externallyiL = Interest rate for storage [%]
Order cost:
Additional cost:
Storage cost:
Total cost:
Bges
gesB Kx
xK ⋅=,
gesxgeszusB xKK ⋅=,,
LfL iKxK ⋅⋅=200
LfgesxBges
LgeszusBgesB
iKxxKKx
xKKKK
⋅⋅+⋅+⋅=
++=
200
,,,
0)( =xK I
Lf
Bgesopt iK
Kxx
⋅⋅⋅
=200
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Notes on Figure A-3:
5.12 Derivation of the Andler Formula
ANDLER derives the economic lot size or order quantity both for in-company manufacture and for external manufacture. Only the cost categories which vary with the procurement quantity need to be considered, since these are the only ones which influence the decision in favour of one or the other alternative. The sum of all costs which influence the order quantity or the lot size is minimised. Fig. A-3 shows the calculation of the optimum order quantity when the products are purchased externally and the cost categories which must be taken into account /3/.
Appendix 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
WZL©
Economic lot size when goods are manufactured in-company
Determining Economic Lot Size When Goods Are Manufactured In-Company
Gives the economically efficient lot size.
Legend:x = Order quantity xges = Total quantity per periodxopt = Optimum procurement quantityKR = Setting up costs per order KB,ges = Setting up costs per periodKA = Order processing costKL = Storage cost per orderKh = Manufacturing cost per unit of quantity iL = Interest rate for storage [%]
Order processing costs:
(Operations planning/ administration etc.)
Setting up costs:
Storage cost:
Total cost:
Rges
gesR Kx
xK ⋅=,
.constK A =
LhL iKxK ⋅⋅=200
LhARges
LAgesR
iKxKKx
x
KKKK
⋅⋅++⋅=
++=
200
,
0)( =xK I
Lh
Rgesopt iK
Kxx
⋅
⋅⋅=
200
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Notes on Figure A-4:
The most economically efficient lot size when the products are manufactured in-company can be calculated in the same way (Fig. A-4).
The calculation of the optimum procurement quantity, when other cost factors (such as staggered discounts and tax considerations) or restrictions (such as delivery periods, minimum stock levels, etc.) are involved, is considerably more complex. The cost progressions are then uneven and can no longer be shown by a straightforward equation.
Appendix 5
Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
5.13 Exponential smoothing of second order
Initial point: Fluctuation of the time series about a linear trend
tbaVt ⋅+= for t = 1...T
Forecast equation with exponential smoothing of second order:
rbarbtbarbVP ttttrt ⋅+⋅+⋅+=⋅+= =+ )(
Objective: Determining and with the information available at time point t at bt
If a straight line (a+b*t) is smoothed with exponential smoothing of first order, then it is
displaced by the absolute value of .
describes the average age of the considered values:αα−
⋅1b
t=−αα1
αα
ααα
αα
αααα
αα
−⋅−⋅+=
−⋅⋅−⋅⋅+⋅=
−⋅⋅⋅−−⋅⋅+⋅=
−⋅+⋅−⋅=
∑∑
∑∞
=
∞
=
∞
=
1)(
11)(
)1()1()(
))(()1(
2
00
0
btba
btba
rbtba
rtba
r
r
r
r
r
r)(1 1tbaV t ⋅+=
With the consumption smoothed with exponential smoothing of first and second order:
VVV ttt1
11 )1( −⋅−+⋅= αα
VVV ttt2
112 )1( −⋅−+⋅= αα
there is the correlation:
tbVtbtbatbaV tt ⋅−=⋅−⋅+=⋅+= )()( 11
tbVtbtbatbtbatbaV tt ⋅⋅−=⋅⋅−⋅+=⋅−⋅+=⋅+= 22)()()( 122
tbVV tt ⋅=−⇒ 21
which is put into graphs in fig. 1.
Appendix 5
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Production Management I (Prof. Schuh)
Methods and Tools for Materials Management
and can be determined with the smoothing factor α and the value of the exponential smoothed time series of second order :
Period
Vt
Vt
t
αα−1
Fig. 1
at bt
VVVVVbVa
VVVVb
tttttttt
tttt
t
212111
2121
211
)(1
1)(1
−⋅=−
⋅−
⋅−+=−
⋅+=
−⋅−=
−−
=
αα
αα
αα
αα
αα
V t2
Vt1
Vt2
rVVVVrbaP ttttttrt ⋅−⋅−
+−⋅=⋅+=+ )(1
2 2121
αα
Appendix 5
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