Makespan minimization in a job shop with a BPM using simulated annealing

Abstract

A scheduling problem commonly observed in the metal working industry has been studied in this research effort -- A job shop equipped with one batch processing machine (BPM) and several unit-capacity machines has been considered. Given a set of jobs, their process routes,processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized -- The BPM can process a batch of jobs as long as its capacity is not exceeded -- The batch processing time is equal to the longest processing job in the batch -- If no batches were to be formed, the scheduling problem under study reduces to the classicaljob shop problem with makespan objective, which is known to be nondeterministic polynomial time-hard -- A network representation of the problem using disjunctive and conjunctive arcs, and a simulated annealing (SA) algorithm are proposed to solve the problem. The solution quality and run time of SA are compared with CPLEX, a commercial solver used to solve the mathematical formulation and with four dispatching rules -- Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using SA to solve large-scale problems