Abstract
In recent years, it has been difficult for manufactures and suppliers to forecast demand from a market for a given product precisely. Therefore, it has become important for them to cope with fluctuations in demand. From this viewpoint, the problem of planning or scheduling in production systems can be regarded as a mathematical problem with stochastic elements. However, in many previous studies, such problems are formulated without stochastic factors, treating stochastic elements as deterministic variables or parameters. Stochastic programming incorporates such factors into the mathematical formulation. In the present paper, we consider a multi-product, discrete, lotsizing and scheduling problem on parallel machines with stochastic demands. Under certain assumptions, this problem can be formulated as a stochastic integer programming problem. We attempt to solve this problem by a scenario aggregation method proposed by Rockafellar and Wets. The results from computational experiments suggest that our approach is able to solve large-scale problems, and that, under the condition of uncertainty, incorporating stochastic elements into the model gives better results than formulating the problem as a deterministic model.
Highlights
In the manufacturing and supply chain industries in recent times, one of the most important challenges has been to determine how best to deal with the significant fluctuations in demand
This stems from the fact that the main focus in production planning is on determination of lot sizes, which corresponds to tacticallevel decision-making, and determination of scheduling, which corresponds to operational-level decision-making, where the goal is to optimize both of these factors concurrently
We investigate the advantages of the stochastic programming model by numerical simulation to first compare the results obtained when following a deterministic programming model with the results obtained when the problem is considered in terms of a stochastic programming model, and we assess the performance of the procedure
Summary
In the manufacturing and supply chain industries in recent times, one of the most important challenges has been to determine how best to deal with the significant fluctuations in demand. Even if one is able to treat the most recent demand with certainty, it is quite likely that when decisions are made at a point in time later, uncertain elements will come into the mix In such a situation, it becomes necessary to develop a plan which takes into account those uncertain elements. Compared with a deterministic programming model that does not incorporate probabilistic factors, the stochastic programming model poses a large-scale problem for which it is often extremely difficult to find a solution. With this in mind, we felt it would be possible to obtain a solution by devising an approximate solution method based on the scenario aggregation method proposed by Rockafellar and Wets [4]. We discuss the accuracy of the approximate solution and the computation time, and demonstrate the effectiveness of the solution method we developed
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