Batch scheduling in the no-wait two-machine flowshop to minimize the makespan

Abstract

We consider a scheduling problem where a set of jobs are simultaneously available for processing in a no-wait two-machine flowshop. The objective is to minimize the makespan, i.e. the maximum completion time of the jobs. The operations of all jobs are processed on both machines in batches. A constant setup time is incurred whenever a batch is formed on the machines. The processing time of a batch is defined as the setup time plus the sum of all processing times of the jobs it contains. The completion time of a job is defined as the time at which the batch containing it is completely processed on machine two. The no-wait scheduling problem in the two-machine flowshop without batching is known as polynomially solvable. We show that several restricted versions of the problem under study in this paper are strongly NP -hard, which imply that the general problem is also strongly NP -hard. We then establish some interesting properties and exploit them to design solution methods for two special cases. Scope and purpose In this paper, we consider scheduling a set of jobs in a two-machine no-wait flowshop, which is a typical manufacturing setup for steel and plastic production. The jobs are sequentially processed on the machines in batches. A constant setup time is incurred whenever a batch is formed on any of the machines. Our goal is to finish all jobs in the earliest possible time. We first give NP -hardness proofs for three special cases. These results suggest that it is very unlikely to devise an efficient method to find an optimal schedule for the problem under study. We also design solution procedures for two further restricted cases, in which the jobs share some specific characteristics. This paper initiates research into scheduling with batching in the no-wait flowshop environment.