The Finite Horizon Economic Lot Scheduling in Flexible Flow Lines

This paper addresses the common cycle multi-product lot-scheduling problem in flexible flow lines (FFL) where the product demands are deterministic and constant over a finite planning horizon. Objective is minimizing the sum of setup costs, work-in-process and final products inventory holding costs per time unite while satisfying the demands without backlogging. 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 of the model. Moreover, the performance of the proposed method is evaluated by some numerical experiments. Two other applicable cases (zero setup costs and Lot streaming) are studied and required modifications in the model formulation and the solution method are described. Finally, a case example in a PCB assembly system is presented to illustrate applicability of the mathematical model and the proposed solution method.