A two-stage flexible flowshop problem with deterioration

Abstract

We study a scheduling problem under considering deterioration on a two-stage flexible flowshop of particular structure (parallel machines in the first stage and a single batching machine in the second stage). The deterioration of a job means that its processing time on the batching machine is dependent on its waiting time, i.e., the time between the completion of the job in the first stage and the start of the job in the second stage. The objective is to minimize the makespan plus the total penalty cost of batching-machine utilization ratio. First, we prove the problem is strongly NP-hard. An efficient heuristic algorithm for the general problem is constructed and its worst-case bound is analyzed. Computational experiments show that the heuristic algorithm performs well on randomly generated problem instances. © 2008 Springer-Verlag Berlin Heidelberg.