Logic-based benders decomposition for two-stage flexible flow shop scheduling with unrelated parallel machines

Abstract

We study a two-stage flexible flow shop scheduling problem (FFSP) with the objective of makespan minimization. There is a single machine in stage 1 and unrelated parallel machines in stage 2. We propose a logic-based Benders decomposition (LBBD) algorithm, which decomposes this problem into a mixed-integer programming (MIP) master problem that sequences jobs on stage 1 and assigns jobs to machines on stage 2, and a set of constraint programming sub-problems that aim to find a feasible schedule on stage 2. Extensive computational results show that LBBD outperforms the best-known MIP model for this problem in terms of both computational time and ability to prove optimality over the majority of test instances. Additional experiments show that the superiority of LBBD over the monolithic MIP model holds regardless of whether algorithm tuning features are applied.