Applying Genetic Algorithms for ProductionScheduling and Resource Allocation. SpecialCase: A Small Size Manufacturing Company

A. Ricardo Contreras, C. Virginia Valero, and J.M. Angelica Pinninghoff

Informatics Engineering and Computer Science Department,University of Concepcion, Chile

rcontrer@udec.cl

Abstract. This paper describes a Genetic Algorithm approach to solvea task scheduling problem at a small size manufacturing company. Theoperational solution must fulfill two basic requirements: low cost andusability. The proposal was implemented and results obtained with thesystem lead to better results compared to previous and non-computerizedsolutions.

1 Introduction

Small companies are not generally able to invest in extensive computing resourcesand in these cases planning is typically a non-computerized activity. The coreidea of this work is to model a low cost computer-aided solution keeping in mindthe idea of portability. The hypothesis here is that it is possible to obtain goodresults for small productive companies and that the experience can be replicatedby similar companies. In this work we are operating under the assumption thatpure genetic algorithms can give rise to good solutions, and that those solutionscould be improved later, and because of this we suggest direct constraint handling[2]. Once the genetic algorithm gives a feasible solution, the next step is toimprove this solution by exploring a bounded space through tabu search. Tabusearch is a meta-heuristic that guides a local heuristic search procedure to explorethe solution space beyond local optimality [1]. The local procedure is a searchthat uses an operation called move to define the neighborhood of any givensolution [3], [4].

2 The Problem

In this experiment we have chosen a small foundry. This company does nothandle inventory systems and products are produced on demand for customers.The production line has six stages and there is an expert in charge of dailyproduction planning. The expert is a production chief and decisions he makesare based only on his own experience. In figure 1 we show the production line.

M. Ali and F. Esposito (Eds.): IEA/AIE 2005, LNAI 3533, pp. 547–550, 2005.c© Springer-Verlag Berlin Heidelberg 2005

548 A.R. Contreras, C.V. Valero, and J.M.A. Pinninghoff

A product remains at a given stage a variable time, depending on manyfactors (basically physical features), and operations that are to be accomplishedat each stage depend on human and/or machine resources. The most crucial stageis Fusion, which encompasses Molding and Shoot Blasting. This stage is alwaysdone on site. For other stages it may be possible to outsource if an excessiveworkload occurs.

Fig. 1. Production line

Purchase orders (PO) are the core element of production planning. A pur-chase order contains a key, customer data, product data as well as specifyingthe necessary production processes, costs and delivery dates. Each order couldcontain from one to n products, each product having a variable quantity of com-ponent parts. Planning is focused on obtaining the optimal yield of the criticalresource (alloy) as well as completing the PO in the shortest possible time.

3 The Proposal

The core idea is to generate an optimal production plan for m purchase orders,each one of them having from 1 to n products (with p parts) all of them havingthe same material (alloy). The purchase order specifies the different stages eachproduct must go through and the estimated time to complete each stage. Solutionis represented as a complete population in which manufacturing time is minimal.The population consists of a set of products and the associated resources foreach production stage, having one product as a minimum. This product can beproduced in one production stage (minimum), some of the stages or all of them.

The chromosome is defined as the minimal unit for considering all the prod-ucts, always having the same size, as a means to facilitate crossover, containing kproduction stages; if a particular stage is not required for a specific product, theprocessing time for this stage is zero. Each production stage, is associated witha corresponding resource (i.e. for stage 1 only type 1 resources are considered).

The model was implemented considering the particular constraints the com-pany imposes, trying to obtain a portable solution for applying to similar com-panies. In doing so, a special module was created to configure general parametersas resources, capabilities and so on. Once the genetic algorithm gives a feasiblesolution, the next step is try to improve this solution by exploring a boundedspace through tabu search, in which case, only short term adaptive memoryis used, because we are interested in the neighborhood related to the selectedsolution and not to explore new neighborhoods.

Applying GAs for Production Scheduling and Resource Allocation 549

4 Solution Using Genetic Algorithms

By considering a pure genetic treatment, a simple crossover is accomplishedbased on resources. Mutation is not a valid alternative at this developmentalstage, because a change in a chromosome should lead to a non valid plan.

Initial population generation is created in a deterministic fashion. The num-ber of chromosomes is determined by the quantity of products to be manufac-tured, one chromosome per product.

In general, when working with genetic algorithms we have a population ofindividuals and the objective is to evaluate each one of these individuals to selectthe best of them. In our case, although individual evaluation is important, weneed to evaluate the whole population because it represents company planning.In particular, we are interested in finding the optimal makespan which is definedas the time in which the last product finished its manufacturing process. So,fitness for the population is defined as follows:

Fitness(P (t)) = max{tf (Xt1n), ...tf (Xt

kn)} − min{ti(Xt11), ...ti(X

tk1)}

Where max{tf (Xt1n), ..., tf (Xt

kn)} apply on the ending time for the last pro-ductive stage; min{ti(Xt

11), ...ti(Xtk1)}, apply for the initial time of the first

production stage. In this way we get an integer number representing time units(minutes) allowing us to compare two different populations.

The general parameters are number of generations 2500; roulette wheel is theselection technique, crossover percentage is 75, and mutation doesn’t apply.

Once the genetic algorithm generates a feasible solution, a new heuristic isimplemented to verify if it is possible to obtain an improved result. The selectedheuristic is Tabu Search and the analyzed neighborhood for the solution considersthe following parameters: Move is resource exchange; Tabu list size is 10; numberof neighbors generated is 30% of total products; general depth is 50; partial depthis 50% of General depth; stopping rule is a solution better than the GA solutionis found; and finally, aspiration criteria is: if neighbor fitness is better that actualbest fitness, removes configuration from tabu list.

5 Tests and Results

To analyze the system performance a small family test consisting of 15 productswas considered, with each product having a variable number of component parts(up to 200). The system was able to find, in 50% of considered situations, betterresults than obtained in an experts initial planning.

For different crossover percentages the best value is always reached, but thefrequency of the best value appears to be variable.

By considering tabu search, given a pure genetic algorithm solution, andconsidering only the closer neighborhood, parameters are a general depth varyingfrom 50 to 80 iterations. In general there is no change in results so the generaldepth is arbitrarily set to 50. For partial depth the test considered from 1/3 to2/3 of general depth; as no changes were detected the final value is set to 50

550 A.R. Contreras, C.V. Valero, and J.M.A. Pinninghoff

In each search step, a number of neighbors equivalent to 30% of populationare generated; although the test considered variations from 20% to 50% of popu-lation. A higher value for this parameter is not recommended because of memoryconsiderations.

Performance of the system found improvements in 10% of considered cases.In testing, each parameter set was executed ten times and for each executionthe best ten values (or the average) were considered, distributed in variable sizesets depending on general depth, i.e., for a general depth of 50, the size for eachset is 5, and analyzing the best value and the average of those 5 values.

6 Conclusions

Obtained results are satisfactory because planning obtained represents an im-provement over non-computerized planning. In addition, there were no capitalcosts associated with new equipment as the computer was already in use for gen-eral management tasks. The use of tabu search improves only slightly the puregenetic algorithm solution. The crossover operator results in a large variability.Initial population is deterministically generated by trying to optimize resourceassignment. Evaluation function (fitness) doesn’t consider problem constraintsonce they are handled in a direct way. Classic selection strategy was modified toguarantee that each product is to be selected only once. The roulette wheel waschosen as an adequate mechanism to support the necessary variability.

Acknowledgement

This work has been partially supported by Project DIUC 203.093.008-1.0, Uni-versity of Concepcion, Chile.

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