ORIGINAL ARTICLE Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times Purushothaman Damodaran & Mario C. Velez-Gallego Received: 8 September 2009 / Accepted: 19 November 2009 / Published online: 11 December 2009 # Springer-Verlag London Limited 2009 Abstract This research aims at minimizing the makespan of a set of identical batch processing machines arranged in parallel. Each job is defined by its processing time, ready time, and size. Each machine can process several jobs simultaneously as long as the machine capacity is not exceeded. The batch processing and ready times depend upon the batch composition. The batch processing time is equal to the longest processing job in the batch, and the batch ready time is equal to the largest ready time among those jobs in the batch. The problem under study is NP- hard. Consequently, a constructive heuristic is proposed and its performance with respect to solution quality and computational cost is compared against other solution approaches found in the literature. The computational experiments on a set of randomly generated instances show that the performance of the proposed heuristic is competitive with respect to solution quality and requires little computational cost. Keywords Identical parallel machines . Batch processing machines . Unequal ready times . Makespan . Heuristics 1 Introduction A batch processing machine is one that can simultaneously process a set of jobs such that all the jobs in a batch start and complete their processing at the same time. Batch processing machines are commonly used to test electronic assemblies to detect early failures, if any, before using them in the field. The research problem under study was observed at a small electronics manufacturing facility which is responsible for both assembling and testing the printed circuit boards (PCBs). After assembly, the PCBs are grouped into batches and are subjected to thermal cycling on any one of the thermal cycling chambers. The chambers are batch processing machines which can test several PCBs simultaneously. The chambers are expensive and usually the bottleneck. Consequently, the schedulers seek to improve the chamber utilization (i.e., minimize the completion time of the last job or makespan). To remain consistent with the scheduling literature, hereafter, the PCBs will be referred to as jobs and the chambers as batch processing machines. The problem under study is to find a minimum makespan (C max ) schedule for a set of n jobs on m identical batch processing machines arranged in parallel. Job j∈ J is defined by its processing time p j , its ready time r j , and its size s j . Each job has to be assigned to exactly one batch b∈B, and each batch must be formed without violating the capacity (S) of the batch processing machine. The total size of all the jobs in a batch should not exceed S. Two interdependent decisions must be made: (1) batch conformation and (2) batch scheduling. The processing time of batch b is equal to the longest processing job in the batch (i.e., P b ¼ max p j   j 2 b   ). Similarly, the ready time of batch b is R b ¼ max r j   j 2 b   . Once the processing of a batch has begun, no preemption is allowed. Since the processing and ready times of a batch depends upon the composition of the batch, both the batch conformation and scheduling decisions are intertwined and complicates the decision-making process for a scheduler. The problem under study can be represented as Pm|batch, r j |C max using the standard three-field notation. When s j = S for each job, each batch can hold exactly one batch. If r j =0 and s j = S for all the jobs, then the problem under study P. Damodaran (*) Department of Industrial and Systems Engineering, Northern Illinois University, 590 Garden Rd., Dekalb, IL 60115, USA e-mail: pdamodaran@niu.edu M. C. Velez-Gallego Departamento de Ingeniería de Producción, Universidad EAFIT, Carrera 49 #7 sur 50, Medellín, Colombia e-mail: marvelez@eafit.edu.co Int J Adv Manuf Technol (2010) 49:1119–1128 DOI 10.1007/s00170-009-2457-1