Reducing Overcapacity in Chemical Plants by Linear Programming

EUROPEAN JOURNAL

OF OPERATIONAL RESEARCH

ELSEVIER European Joumal of Operational Research 97 (1997) 337-347

Reducing overcapacity in chemical plants by linear programming

Gerd Ox6

Scientific Services Department, Operations Research Group, Ciba Ltd., CH-4002 Basel, Switzerland

Abstract

In 1993 the Operations Research group of CIBA Ltd. Basle was consulted by a company division to help in finding ways to reduce production costs of their crop protection products. A subsequent study of the production and transportation structure showed an opportunity to reduce the number of production lines dramatically and to reassign the products. Furthermore, since transportation proved to cause a significant part of the overall costs, optimal distribution paths had to be found in the same process. When the relevant cost factors were analyzed, the whole problem showed to be very well suited for a linear approach, thus enabling us to use an established and powerful tool for the optimization task, Linear Programming.

After building and refining the linear model, interactive sessions together with the customer resulted in an optimal future European supply chain, reducing annual production costs by approximately 25%.

Keywords: Linear programming; Optimization; Facilities; Transportation; Location

1. Introduction

Before 1995, our customer, the crop protection division of CIBA, was running the production process for their products on many plants scattered all over Europe. Due to segmentation of the overall supply chain costs, local optimization of various supply chain processes took place, causing overall costs to increase. These nonoptimized cost allocations gave rise to challenge the actual European supply chain, with particular focus on the number of production sites (CIBA plus third party locations) and on optimizing product allocations.

1.1. Process structure

A closer look at the situation revealed a complex structure of distributed product processing and transportation (Fig. 1). First of all, one has to distinguish between chemical production of the active ingredi-

ents, and consequent post processing steps, which consist of formulation (a mixing and milling process) and packaging. Since the production of the active ingredients is completely isolated from formulation and packaging, it was not taken into consideration in this project.

The 2-step post processing can either be carried out on combined production lines, or on separate formulation and packaging lines in the same or in different plants. In the latter case, bulk packaging and transportation between production sites is necessary. Finished goods can either be delivered directly to the customers or stored intermediately in central warehouses. The customers are each located in different European countries.

Due to the nature of the products, their need is highly dependent on the season. Two prominent demand peaks can be observed typically during the year (Fig. 3). One is around March, when sales rise to a maximum, and the other one at the end of the

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338 G. Ox / European Journal of Operational Research 97 (1997) 337-347

I xehouse r / / / / /~ [~\ \ \ \~ l

F//I///////////////////r//('////////4 V/////////////////////////////////A

V / / / /A factory A [ tiVelre(lie ~.I [ formulation livery its customer X

ac

kX\ \ \ \ l

== I==1 v/////l ~ packagiDg~//////////A r/////J ~\NXXN combined t \ \ \ \ \ ' l formulatioW

I I factory B

Fig. 1. Some possible production paths (number of factories and customers are much reduced for simplicity).

year, caused by building up stocks due to forecasts. Starting around June, customer deliveries decrease, making supply chain capacity available for presea- sonal distribution.

One of the main requirements in our project was the ability to quickly react on changing demands of the market and therefore realize short throughput times and good logistics. Keeping a base stock of high volume products in central warehouses should enable the plant managers to set up quickly for nonforecasted orders making use of spare capacity available even during high demand periods.

1.2. Goal

The goal of our project was quite simple: to choose an appropriate subset of the existing production plants and lines, and to optimize product allocation, transportation paths and central stock profiles, such that the overall costs are minimal. All this has to be achieved with respect to one basic requirement: delivery must take place within some months (speci- fied for each product) from the order.

2. Problem analysis

2.1. Technologies and subtechnologies

As the different products are numbered by the hundreds, some sort of classification had to be intro-

duced to reduce the effort necessary for data acquisi- tion. There already existed three major product classes, called technologies according to the way of their production, which, after further being subdivided, split up into 18 subtechnologies. All products belonging to a subtechnology need the same equipment for formulation and packaging and thus behave the same in the context of our problem. For the sake of simplicity, we will use the word "technology" instead of subtechnology in the rest of the paper.

2.2. Cost factors

Instead of trying to analyze all cost factors somehow involved in the process, it was decided to focus on so called incremental costs only. These contain all expenditures that can change if choosing another alternative. Cost factors like active ingredients price can be dropped since they remain the same no matter where formulation and packaging is done. Thus it has to be kept in mind that the final optimal value of the objective function (see below) is expressing a relative minimum.

It has to be kept in mind, that the goal of the project was to optimize annual (running) expenses. Investment and deinvestment costs as well as trans- fer prizes to move production of a product to a different plant have not been modeled. Deciding whether a certain scenario makes sense with respect to all these costs requires a lot of knowledge from experts. This is, therefore, dealt with outside the optimization, as discussed in Section 2.3.

In each of the included cost factors, two components of a completely different nature can be distin- guished: production volume independent (PVI) and production volume dependent (PVD) factors (Fig. 2).

PVI's: Take a typical production line, like, for instance, a packaging line for 5 liter jugs. Deprecia- tion of this line does not depend on whether one is using it or not. Another big block of PVI's are general factory overhead costs, whose origin was of no further significance for this project. They were simply distributed to production lines by a measure of the complexity of the corresponding process.

PVD's: Energy and raw materials are typically production volume dependent. Transportation using railroad services depends on volume alone. All these costs increase almost linearly with the produced volume. One of the biggest nonlinear factors were

G. Ox / European Journal of Operational Research 97 (1997) 337-347 339

costs real costs with steps caused by additional shifts

ed costs

Ivolume ~tmaximum capacity independent COSTS

I I I I I 1 I ~ [

VOlUme

Fig. 2. Volume dependent and independent costs.

the wages paid if a second and third work shift has to be called in, which causes small jumps in the volume/cost dependency. Being relatively small compared to the overall sum of costs of a line, they were neglected, though.

Let us discuss the cost factors taken into account in our project in more detail.

2.2.1. Production costs As mentioned above, these are typical examples

of mixed PVD/PVI components, together with an additional small nonlinear cost factor. The stepsize of the latter represents the cost of the smallest additional shift that can be called in, e.g. another shift for one weekday or a complete third shift for the whole week. If a production line is closed in the model, its volume independent costs are of course no longer taken into account. It has to be mentioned that every production line has its own set of cost figures, depending on many, not explicitly modelled, factors like complexity, performance, staff wages and many more. On the other hand, production costs do not differ with the products that can be processed on a certain line.

2.2.2. Transportation costs If one looks at transportation costs in detail, these

can show a very complex structure. Depending on the type of packaging, e.g. bulk or final packaging, one obtains different transportation costs for the same volumes. Furthermore, a vehicle like a truck actually does show also volume independent costs, just think of it travelling half empty. In our case, these problems were of very minor importance.

Firstly, the volumes to be transported between plants or to customers usually are large compared to transportation units like, e.g., trucks. Secondly, we distin- guished between transportation from a production plant to a packaging plant, which is usually done with bulk packaged material, and products delivery to warehouses or to customers.

Duties were taken into consideration as significant factors, too, but since no exact data was available at the time, only guesses of these were added to the transportation PVD costs.

2.2.3. Storage costs These have shown to be the most inaccurate of

the available data and been subject to many discus- sions. Many of the warehouses are shared by several product groups or even different company divisions. This makes it impossible, within the scope of this model, to take the overhead (PVI) costs into consideration or even saving overhead costs by closing warehouses. Furthermore, some warehouses charge handling costs higher than the actual storage costs, while others have a pricing scheme linear with space and storage time. We tried to express these prices with a linear, volume and storage time dependent function, with a different price factor for each warehouse. Handling costs were transformed based on average storage times.

2.3. Alternatives

Finding alternatives to the given situation is an iterative process that shows the close interaction between OR methods and decisions made by production and logistics experts.

1. Choose a subset of plants from the set of existing sites.

2. Test whether there is at least one possible allocation of the production volume onto the lines within these plants. If there is no feasible allocation, goto 1.

3. Allocate the production volume in an optimal way in terms of lowest overall costs, according to Section 2.2.

4. From the resulting load figures, "close down" all unused lines and decide which of the remaining ones can take over production volume of other

340 G. Ox~ / European Journal of Operational Research 97 (1997) 337-347

sparsely used lines in the same plant. Exclude the latter ones as well. All product volume independent costs caused by the excluded units are omit- ted in further optimization steps.

5. Goto 3 until no further lines can be excluded, respecting a minimum required degree of flexibility for future allocation or product changes.

6. Goto 1 to find plant subsets with better optima.

In other words: a subset of the existing lines had to be chosen to obtain a minimal production capacity big enough to satisfy the annual demands with the necessary flexibility and spare capacity, and with the plant locations resulting in lowest possible transportation, production and storage expenses when product allocations are optimized in a next step.

So the degree of freedom for our model consisted of changing the plant subset and of choosing where and when a product will be formulated, packaged and stored. A "clean-up" step consisted of trimming the production capacity in the necessary plants to the minimum required after optimizing by closing down idle formulation and packaging lines. Closing down sparsely used production lines and - - as is necessary in these cases - - moving the products allocated on these to another suitable line is a step that requires a great amount of knowledge about the chemical processes and the equipment and hence could not be automated.

The above scheme is independent of the methods chosen to accomplish each step. Principally, for small problems of this kind, one could use expert knowledge alone as a guide towards the right decisions. As explained in the next section, existing knowledge has been taken advantage of extensively for some of the decision steps, but the complexity of the problem at hand demanded for sophisticated algorithms to be used in steps 2 and 3. This is where Operations Research methods were brought in and have proven to be very powerful for this problem, too.

2.4. Method choice

Since all factors involved can be considered as almost linear and the small nonlinearities were in any case unquantifiable, it appears reasonable to use a linear model. Linear Programming (LP) obviously is the appropriate method to find optimal solutions of

such models. However: the original task consisted of finding the best subset of lines and plants and the most advantageous locations choosing from a set of existing units, which could be considered as an integer programming task with LP optimization of each possible selection. Formally, a mixed integer linear approach should be used to handle problems of this kind, but two reasons kept us from going this way.

Firstly, not every subset makes sense in terms of legal aspects, company culture, and other difficult to model decision factors. At this point, the expertise of the customer had to be brought in. Many considera- tions had been made beforehand and could be used when judging the attractiveness and feasibility of a possible plant subset before optimizing. The whole process of using the model to actually find a "best" solution consisted of many sessions of model runs, together with the customer, who was continuously suggesting new scenarios (possible plant subsets) to be optimized.

Given this, the second reason not to use mixed integer LP should become obvious: efficiency. As one LP run for a given subset takes around 5 min- utes, the interactivity of the model is lost when a whole bunch of scenarios is automatically optimized and compared to each other. Thus one would give away the possibility of influencing the scenario choice by available expertise.

At the very beginning of the project, time has been excluded from the model, as one could easily end up getting lost in detailed production planning instead of keeping the overall optimization task in mind. Furthermore, we feared that an additional dimension could inflate the model to a size no longer manageable. But the prominent seasonality of the market demand (Fig. 3) forced us to drop this simpli- fication and take some account of development over time. A closer look at the available data showed a structure not finer than a month, so the yearly demands could be sliced into 12 monthly demands for each product. This could still be handled easily when building the model.

2.5. Software tools

When it came to choose a suitable software tool, transparency and readability of the linear model and


tons

3000 - demand

amount delivered from warehouse

1000

JAN FEB MAR APFI MAY JUN JUL AUG SEP OCT NOV DEC

Fig. 3. Seasonality of the demand for one product class and delivery from warehouse.

data description were crucial in this project. As mentioned above, the customer's knowledge must somehow be taken into account during the search for an optimal choice of plants. We choose AMPL as the modelling front end together with the CPLEX solver kernel, both running on a SPARC station IPC. For more detailed information on this software see [2] and [3].

3. Mathematical model

3.1. Definitions

First we define the index sets used:

P set of plants T set of technologies (or product classes) FL all formulation lines FLp formulation lines in plant p PL all packaging lines PLp packaging lines in plant p W set of warehouses C set of customers M the 12 months {JAN, FEB ....... DEC}.

M is meant to be a circular ordered set, thus succ(DEC) = JAN and pred(JAN) = DEC.

Each customer has a certain demand of the different technologies every month, given by dctm, with C ~ C, t ~ T, m ~ M. The amount of all products processed during a month is called the line load and written as lt,~, l ~ FLU PL, m ~ M, t ~ T, for both formulation and packaging lines. This notation is also used for warehouse stocks. Transportation between plants or to and from warehouses and cus-

tomers are tsar, ., where s is the source, d the destination, t E T, m E M. s and d can be from index sets of the following combination.

s d FL, FL~, PL, PLp formulation site

to packaging site, PL, PLp W storing into warehouse, PL, PL e C direct delivery, W C delivery from warehouse.

Every production line has a maximum monthly throughput, which does not depend on the type of product processed, and is tagged as usable or unus- able for each technology.

c k capacity of line k, Ult 1 if t can be produced on I, 0 otherwise.

This could as well be merged into one matrix c,, but since u is a binary variable, this way of modelling saves memory and helps AMPL to eliminate trivial (in)equalities where u = 0.

Cost factors are subdivided into two classes, as described in Section 2.2.

PVDz for production volume dependent costs, PVIt for the independent part.

Note that the PVD values are not influenced by the technology produced on a line.

Transportation costs are given for every source/destination pair as shown above. They consist merely of a volume dependent part, which is also true for warehousing.

trs~ costs per ton transported from source s to destination d,

st w costs per ton and month of storage in warehouse w.

3.2. Objective function

Given the above, we are now able to write down the objective: minimize the sum of all incremental costs.

E ( E /mtPVDt + E PVI, m~M,t~T I~FLuPL IEFLUPL

+ ~ lwmtStw + Y'. y ' tij,~trij wEW p~P i~FLp

dEP j~PL a p4=d

342 G. Ox / European Journal of Operational Research 97 (1997) 337-347

+E E pEP iEPLp

wEW

tiwtmtriw + E twc..tr,.,c wEW cEC

+ E E tictmtric) pEP i~PLp

cEC

(1)

with respect to the restrictions described in the following section.

3.3. Constraints

Most important of all requirements is to satisfy the market demand in time. So the amount of products shipped directly from packaging lines or from warehouses to the customers must exactly match their requests for each technology every month.

E E t,c,m + E twc,m =dc,m, pEP IEPL e wEW

VcE C,m ~M,t~ T. (2)

The total amount of all technologies produced on a line during one month may not exceed its monthly maximum capacity.

~Itrm


For simplicity, the effects of combined formulation/ packaging lines have been neglected in this mathematical model description. In the implementation with AMPL, the production line allocations bad to be reduced by the corresponding amount, and transportation had to take account of less products being moved between plants and lines.

4. Model implementation using AMPL

This section describes the realization of the model with the notation of the AMPL frontend tool. For a detailed description of the modelling language see [2] and [3].

4.1. Sets

All variables in the model are indexed and repre- sented by two- or more-dimensional data matrices. The seven index sets are:

1. PLANTS. The 10 existing plants, where formulation and/or packaging can be carried through, labeled as P I , P2 ..... P10 (please notice that, for confidentiality, all item designations have been modified).

2. TECHS. The 18 technologies or product groups. 3. F_LINES {PLANTS}. Formulation lines,

subindexed for each plant; a total of 48 lines were included.

4. P_LINES {PLANTS}. Same for the 69 packaging lines.

5. WAREHOUSES. The 3 central European warehouses to choose from.

6. CUSTOMERS. One representative major sales point for each of the 14 European countries considered.

7. MONTHS. Production allocation has been cut into monthly slices, therefore all variables are indexed with time as well.

4.2. Solution space

One of the most critical modelling steps consisted of choosing a solution space with minimum model redundancy, thus keeping the overall variable count low enough to handle, but still maintaining readabil-

ity and clarity. Two classes of variables were used to describe the allocation of products to lines and trans- portations between sites, warehouses and customers. The variable definitions are shown here in AMPL notation.

1. Product allocated to formulation lines in tons for one month: var f_load {TECHS, p in PLANTS, F_LINES [p], MONTHS}.

2. Product allocated to packaging lines in tons for one month: var p load {TECHS, p in PLANTS, P_LINES [p], MONTHS}.

3. Amount per technology stored in a warehouse for one month: var w load {TECHS, WARE- HOUSES, MONTHS}.

4. Amount per technologies moved from formulation to packaging site: var moved {TECHS, PLANTS, PLANTS, MONTHS}.

5. Amount per technology moved from packaging to warehouse: var stored {TECHS, PLANTS, WAREHOUSES, MONTHS}.

6. Amount shipped directly from packaging to customer: var shipped {TECHS, PLANTS, CUS- TOMERS, MONTHS}.

7. Amount shipped from warehouse to customer: var unstored {TECHS, WAREHOUSES, CUS- TOMERS, MONTHS}.

Notice the use of index sets themselves depending on another index, like "p in PLANTS, FL INES [p]" . This corresponds to our mathematical index set notation FLp and PLt,.

It is clear that the values of some variables could be derived, given the other values, which represents some redundancy. Omitting all dependencies would, however, decrease the model transparency.

4.3. Cost factors

Cost factors have been aggregated into PVI and PVD types, resulting in 4 numbers for each formulation and packaging line, f_x {p in PLANTS, F_LINES [ p]} and p_x {p in PLANTS, P_LINES [p]}, respectively, x meaning one of:

varcost: all linear volume dependent costs per ton and month;

stepwise: stepwise increasing, but linearized costs, e.g. shifts;


GFO: volume independent general factory overhead share;

deprec: depreciation for one month.

Since central warehouses are shared between several company divisions, the expenses of storing a palette of products for one month were calculated from the sum of building depreciation and monthly expenditures, divided by the number of palette places. As one palette always weighs in the order of 500 kilograms regardless which product is packed on it, computing palette spaces from tons is trivial.

Transportation costs were given in costs per ton for each origin/destination pair that can be combined given the 14 customer locations and the union of the sets of packaging sites and central warehouses, and for each formulation/packaging sites combination.

4.4. Parameters

The set of parameters mainly consists of cost factors, as described above, and capacity limits. The maximum throughput of a packaging or formulation line can either be a product independent capacity or 0, if a certain product cannot be processed on this unit. Modelling this has been accomplished by intro- ducing two indexed parameters, one giving the maximum capacity of each line and for each technology, the other simply holding a binary value, indicating whether a certain product can be processed on the unit or not.

The true capacity of a line for any technology can now be given by f_capacity [p, f ] * fusable[ p, f, t], where p means plant, f formulation line and t technology, fcapacity and f__usable being the said parameters c t and u~, for the formulation lines.

4.5. Objective function

Although only volume dependent costs are relevant in the reallocation and rerouting process, the selection of a plant subset results in volume independent factors to be saved. To keep the formulation of the objective function independent of the current scenario, all PVI expenses are included but indexing was performed over the subset of plants only.

4.6. Constraints

Writing down the constraints in AMPL notation following Eqs. (2)-(11) is straightforward and not explicitely shown here. It is to be noted, that the language allows for any (in)equalities of the type "= ", "< " and "> ", arbitrarily intermixed.

Instead of rewriting the model for each scenario, a separate set containing only the used plants was introduced. The constraints are simply indexed over this set instead of all plants, as the following example of a constraint in AMPL notation shows:

subject to f_cap { p in USED_PLANTS,

f in FL INES[ p], m in MONTHS}:

sum{t in TECHS} f_load[1, p, f , m]

< f_capacity[ p, f ];

This example constraint corresponds to inequality (3).

The definition of the plant subset is kept in a separate data file, greatly simplifying the selection of a new scenario:

# plant subset definition set SELECTED_PLANTS "= P2 P4 P6 P7; set SELECTED_WAREHOUSES = W 1 W3;

4.7. Model size

To give an impression of the complexity of the model, one can sum up the number of all variables of the solution space, which gives a total of about 93,000 variables. Most of these were caused by the high degree of freedom for transportation and delivery paths. Variable "shipped", as described in Sec- tion 4.2, can be given as an example: considering the cardinalities listed in Section 4.1, one obtains the size of this 4-dimensional variable as TECHS X PLANTS X CUSTOMERS XMONTHS as 18 X l0 X 14 X 12 = 30240. Please notice that when computing the size of " f_ load" and "p_load", one has to be aware that these are 3-, and not 4-dimensional. The index "p in PLANTS" is merely a subgrouping of the lines given with "F_LINES [p]" and "P_LINES [p]" , respectively.

G. OxE / European Journal of Operational Research 97 (1997) 337-347 345

Similarly, the number of parameters can be obtained as roughly 5,800. This gives an impression about the amount of data needed to run the model. Fortunately, the biggest part of these were the demand figures for each customer, technology and month, which were available in electronic form from forecasts and past year's sales figures.

The number of single constraints is approximately 35,000. More than 70% of these stem from Eq. (4), simply limiting the line loads by their maximum capacity.

These figures, however, may not be interpreted as a direct measure of the number of program variables and constraints really used during the model run. AMPL highly optimizes by eliminating trivial (in)equalities, which results in a significantly smaller LP problem.

5. Practical problem solving

5.1. Using the model

Out of the many possible subsets of plants, only about 20 have been chosen to undergo the optimization process of reallocating the products and rerouting transportation. Many what-if studies have been carried through with these scenarios to get a feeling for their robustness against market demand changes, machine failures, and introduction of new products. As one basic demand was the ability to quickly react upon demand changes, the amount of preproduced goods, that are kept in central warehouses until delivery, has to be limited. A measure of preproduc- tion can be obtained by the ratio of the amount of all products delivered from warehouses, to the total amount of delivered products. The bigger this value, the more products are produced ahead of delivery time. In our approach, it is not possible to retrace the "history" of each delivered order and so the exact production start time cannot be computed.

AMPL provides extensive reporting facilities to extract the data of interest after a model run. Of major interest, in addition to the actual savings in comparison to other alternatives, were the actual product allocations, delivery schemes and warehouse activities. As the way in which each order from a customer can be split up and produced is quite

complicated (Fig. 4), it was necessary to know exactly from which warehouses and packaging sites this order is delivered.

Table 1 shows a typical output after optimizing a scenario. These tables are sorted by plants and lines, each containing the allocation of products (rows) to the line over the months (columns). Line 1 in plant 2, as an example, formulates 183 tons of product P3 in September.

Similar lists can be obtained for warehouse stock profiles, deliveries, transportation and more in any desired level of aggregation or detail.

5.2. Results

An arrangement of 23 formulation lines and 30 packaging lines in 3 plants, and 1 central warehouse gave the best results. Some of the lines in these plants were not used in the optimal allocation scheme, so the independent cost of these can be saved by closing them down. The biggest savings originate from cutting these costs down, consisting mainly of depreciation and general factory overhead. It is difficult to determine exactly for how much of these savings OR methods can take credit, because the model first helped the experts to find feasible scenarios and then took over the fine tuning to reduce production, transportation and storage costs of a given scenario. It can be estimated, though, that the allocation optimization contributed to the overall savings with about 20%.

formula~on site B, forrnulalJon site C, line (]1 line C1

( ~ ~ . 10 tons, ~Februa.=ry ~ packaging site A,

/ 18 tons, April /

/ / 12 tons, April 10 tons, March

\ J ) , , . . _ J (stock is ~ns of ~ / P by end of Apnl)

packaging site B, 30 tons, May 20 tons, May

line B2 ~50~ /

ons of product P by end of May

customer

Fig. 4. The flow of a single order.


Table 1 Part of the monthly allocation scheme for formulation operations

f load[t, 'Plantl ', 'Linel ', m][ * ,* ] : JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC: = P1 83 211 0 0 80 167 84 38 19 12 76 67 P2 998 2456 2415 2 164 1 851 1 412 547 524 503 556 580 2 179 P3 25 0 252 503 16 28 21 17 41 41 86 115 P4 101 0 0 0 117 426 118 506 376 186 428 259

f_load[ t, 'Plant2', 'Linel ', m][* ,* ] : JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC: = P2 0 274 145 292 195 40 204 243 82 0 158 251 P 3 286 0 147 0 80 199 59 0 183 292 130 0 P4 6 18 0 0 17 53 29 49 27 0 4 41

f load[ t, 'Plant2', 'Line2', m][ *,* ] : JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC: = P3 167 167 167 70 167 167 167 17 167 147 111 167 P4 0 0 0 96 0 0 0 150 0 20 0 0 P6 0 0 0 1 0 0 0 0 0 0 0 0

f_load[ t, 'PianO', 'Line 1 ', m][ *, * ] : JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC: = P 12 62 135 333 262 116 84 87 61 66 119 185 139 P13 64 61 0 71 132 249 98 37 15 125 34 12 P14 0 23 0 0 0 0 22 0 252 14 21 8

So both in the feasibility test and in the optimization process, the model made a significant contribu- tion to the final result, saving annual production and transportation costs in the order of 25%.

6. Conclusions

The combination of the customer's expertise and OR methods was the major key to success in this project. It clearly revealed the power of interdisci- plinary work teams when it comes to the application of otherwise academical methodologies to real life. Data quality, the user's engagement in the modelling process and the availability of people from production, logistics and marketing were crucial prerequi- sites to achieve results like the one presented here.

Acknowledgements

I would like to thank Dr. R.W. Lang, head of the PUMA project and customer of the OR study, and

his team, for the invaluable cooperation during data analysis, modelling and optimization phase.

I would also like to thank Prof. Dr. R.W. Schmenner, professor at the School of Business, Indiana University, who acted as a consultant in this project and challenged the use of OR methods a lot.

My appreciations to all who helped me in proof reading this paper and in improving its readability.

References

[1] Charnes, A. and Cooper, W.W. (1961), Management Models and Industrial Applications of Linear Programming, John Wiley and Sons.

[2] Fourer, R., Gay, D.M. and Kemighan, B.W. (1993), AMPL, A Modelling Language for Mathematical Programming, The Scientific Press.

[3] Fourer, R., Gay, D.M., Kemighan, B.W. (1990), AMPL, A modelling language for mathematical programming, Manage- ment Science, 36(5), 519-554.

[4] Lootsma, F.A. (1994), Alternative optimization strategies for large scale production allocation problems, European Journal of Operational Research, 75, 13-40.

G. Ox~ /European Journal of Operational Research 97 (1997) 337-347 347

[5] Martin, C.H., Dent, D.C. and Ec -ldaart, J.C. (1993), Integrated production, distribution, and inventory planning at Libbey- Owens-Ford, Interfaces, 23(3), 68-78.

[6] Mehring, J.S. and Gutterman M.M. (1990), Supply and distribution planning support for Amoco (U.K.) Limited, Inter- faces, 20(4), 95-104.

[7] Schmenner, R.W. (1993), Production~Operations Manage- ment: from the Inside Out, Macmillan Publishing Company.

[8] Van Roy, T.J. (1989), Multilevel production and distribution planning with transportation fleet optimization, Management Science 35(12), 1443-1453.

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Reducing Overcapacity in Chemical Plants by Linear Programming

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