Introduction

In Chapter 4, different single-machine models were dealt with in detail, and now we extend our expectation-variance (EV) analysis to multimachine environments. In this chapter we focus on a flow shop with unlimited intermediate storage (buffer capacity) where n jobs are waiting to be processed. The flow shop consists of m machines. Our analysis for this environment is identical to that presented by Wilhelm and Ahmadi-Marandi (1982), who studied an assembly system. A flow shop is, in fact, a simpler version of an assembly line, and hence their methodology can be adapted to our case. The EV analysis of a flow shop would act as a stepping stone for undertaking the EV analysis for job-shop and parallel-machine environments. Numerical illustrations indicating the significance and applicability of our work are also presented through example problems. The objective function that we consider is to minimize the makespan. Makespan is an important objective in a flow shop because a lower makespan value implies higher utilization of the machines. Also, we consider permutation flow shops, in which the job sequence does not change across the machines, and the jobs on each machine are also processed according to the first come, first served principle.