The common cycle economic lot scheduling in flexible job shops: The finite horizon case

This paper addresses the common cycle multi-product lot-scheduling problem in deterministic flexible job shops where the planning horizon is finite and fixed by management. This problem consists of a combinatorial part (machine assignment and sequencing sub-problems) and a continuous part (lot-sizing and -scheduling sub-problems). To account for these two elements, a new mixed integer nonlinear program (MINLP) is developed which simultaneously determines machine allocation, sequencing, lot-sizing and -scheduling decisions. In order to reduce computational complexity, instead of solving this MINLP directly, we propose an efficient enumeration method to determine optimal solution for this model. The performance of the proposed method is evaluated by some numerical experiments. 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, a numerical example is presented to illustrate applicability of the proposed mathematical model and the solution method.