Sequencing, lot sizing and scheduling of several products in job shops: The common cycle approach

This paper deals with the multi-product, finite horizon, static demand, sequencing, lot sizing and scheduling problem in a job shop environment where the objective is to minimize the sum of setup and inventory holding costs while satisfying the demand with no backlogging. To solve this problem, we assume a common cycle for all products and divide the planning horizon into an integer number of identical production cycles. The problem is formulated as a mixed non-linear program which simultaneously determines sequencing, lot sizing and scheduling decisions. Unfortunately, for medium or large problems, the solution of this model may require an excessive amount of computational time. To solve such problems, we propose an adaptation of the simulated annealing algorithm and a tabu search algorithm. Within these two methods, a neighbouring solution is obtained by altering the production sequence of one of the machines. The modified set of sequences is then used as an input to another mixed non-linear program to determine lot sizes and starting dates. Some computational results are given to help assess the performance of the proposed heuristics.