An MIP-Based Heuristic Approach to Determine Production Lot Size for Capacitated Single-Stage Production Processes with Stochastic Demand on Parallel Machines

This paper deals with the capacitated single-stage production lot sizing and scheduling problem with multiple items, setup time, stochastic demand and unrelated parallel machines. A stochastic mixed-integer linear programming model is proposed to formulate the problem. Based on the uncertain constraints, the chance constrained programming approach is used to transform them into equivalent deterministic constraints and then obtain an optimal solution by deterministic mixed-integer linear programming model. Due to the complexity of problem, the mixed-integer programming (MIP) of the equivalence deterministic model of the capacitated single-stage production lot sizing problem with multiple items, setup time, stochastic demand and unrelated parallel machines is reformulated as a shortest path reformulation problem. The proposed algorithm is evaluated through a numerical example. Computational results show that the proposed method gives optimal or near optimal solution and have good-quality result for the test problem.