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Economic Lot Scheduling in Flexible Job Shops

In this paper, we study the common cycle multi-product lot-scheduling problem in a deterministic flexible job shop where all parameters (such as demand rates and setup times) are deterministic and constant over an infinite planning horizon. This production facility involves several work centers (production stages) where each stage has one or more parallel identical machines. A product requires a sequence of operations in different stages based on its unique process route. Moreover, each product must be processed by at most one machine at each stage, but some products may skip some stages. The objective is minimizing the sum of setup and inventory holding costs per time unit without backlogging. This problem involves a combinatorial part (assignment of products to machines at each work center and their sequencing on each machine), and a continuous part (lot-sizing and production starting time for each product at each stage). A new mixed zero-one nonlinear program has been developed whose optimal solution determines simultaneously the optimal assignment of products to machines at each stage, the optimal sequence on each machine, the optimal lot sizes and the optimal beginning times for each production run. In order to reduce computational complexity, instead of solving this MINLP directly, we propose an efficient heuristic method to determine near optimal solution for this model. Two other applicable cases (Zero setup costs and Lot streaming) are also studied and required modifications in the model formulation and the solution procedure are described. Moreover, an example has been presented to illustrate the applicability of the proposed model.