Improving Branch-and-Price for Parallel Machine Scheduling

Abstract

In this paper we present a hybrid exact-heuristic method to improve a branch-and-price algorithm to solve the unrelated parallel machines with sequence-dependent setup times scheduling problem. As most of the computational time in the column generation (CG) process is spent in subproblems, two new heuristics to solve the subproblems are embedded in the branch-and-price (BP) framework with the aim to improve the efficiency of the process in obtaining optimal solutions. Computational results show that the proposed method improves a state-of-the-art BP algorithm from the literature, providing optimal solutions for large instances (e.g. 50 machines and 180 jobs) of the parallel machine scheduling problem with sequence dependent setup times, in significantly less time. One of the proposed approaches reduces, in average, to a half the time spent in the root of the branch-and-price tree and to a quarter the time spent in the full branch-and-price algorithm.