Abstract—We consider the capacitated lot sizing problem with multiple items, setup time, stochastic demand and unrelated parallel machines. The problem is formulated as a stochastic mixed-integer linear programming model. The demand will be assumed to be a normal distribution. The stochastic constraints are transformed into equivalent deterministic programming ones by using the chance constrained programming approach and then obtain an optimal solution by deterministic mixed-integer linear programming model. The proposed algorithm is evaluated through a numerical example. Computational experiment demonstrates that the proposed method have good-quality result for the test problem.
Index Terms—Capacitated lot-sizing problem, stochastic demand, chance-constrained programming, parallel machines.
The authors are with the Department of Industrial Engineering Srinakharinwirot University, Ongkharak, 12110, Thailand (e-mail: supatchaya@g.swu.ac.th, punyangarm@gmail.com).
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Cite: S. Chotayakul and V. Punyangarm, "The Chance-Constrained Programming for the Lot-Sizing Problem with Stochastic Demand on Parallel Machines," International Journal of Modeling and Optimization vol. 6, no. 1, pp. 56-60, 2016.
