Squeezing Branch and Bound Algorithm for Machine-fixed, Machining-Assembly Flowshop Scheduling Problems

Abstract

This paper considers minimizing makespan in a machine-fixed, machining-assembly flowshop scheduling problem (MAFS) with M-parallel machines at the machining stage and one robot at the assembly stage. M-parts of each job are machined on prespecified machines at the machining stage and these parts are assembled at the assembly stage after all component parts for each job have been machined. Since this problem has been proved strongly NP-complete, we propose a branch and bound based heuristic algorithm, called the "squeezing branch and bound (squeezing B&B)" algorithm which searches for a prespecified number of promising nodes in parallel at each branching level and terminates the search without backtracking. For increasing the effectiveness of the squeezing B&B, a new lower bound is proposed and a dominance rule is incorporated into the branching process of the proposed method. The results of numerical experiments show that the proposed method can efficiently obtain an optimal (or best) schedule for almost all instances of the machine-fixed MAFS with two, three and five machines at the machining stage.