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Stochastic Programming Model for Discrete Lotsizing and Scheduling Problem on Parallel Machines

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Author(s): Kensuke Ishiwata | Jun Imaizumi | Takayuki Shiina | Susumu Morito

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 02;
Issue: 03;
Start page: 374;
Date: 2012;
Original page

Keywords: Stochastic Programming | Lotsizing and Scheduling | Parallel Machines | Scenario Aggregation Method

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.

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