Stochastic Shop Scheduling: A Survey

Abstract

In this paper a survey is made of some of the recent results in stochastic shop scheduling. The models dealt with include: Job shDps. Two objectivr: functions are considered: Minimization of the expected iz-,i-on time of the last job, the so-called makespan and cini-:iztoime of the sum of the expected completion times of all jobs, the so-called flow time. The decision-maker is not allowed to preempt. The shop models with two machines and exponentially distributed processing times usually turn out to have a very nice structure. Shop models with more than two machines are consideraIy harder..-_ INTRODUCTION AND SUkQ4AYIn this paper an attempt is made to survey the recent results in stochastic shop scheduling. Four shop models are considered; a short description of. these follows. (i)Open Shops. We have n jobs and m machines. A job requires an execution on each machine. The order in which a job passes through the machines is immaterial.(ii)Flow Shops with Infinite Intermnediate Storage. We have n jobs and m machines. The order of processing on the different machines is the same for all jobs; also the sequence in which the I. I jobs go through the first machine has to be the same as the sequence in which the jobs go through any subsequent machine, i.e. one job may not pass another while waiting for a machine. A flow shop with these restrictions is often referred to as a permutation flow shop. (iii) Flow Shops with Zero Intermediate Storage and Blocking. This shop model is similar to the previous one. The only difference is that now there is no storage space in between two successive machines. This may cause the following to happen: Job j after finishing its processing on machine i cannot leave machine i when the preceding job (job j-l) still is being processed on the next machine (machine i+l); this prevents job j+l from starting its processing on machine i. This phenomenon is called blocking. 1* (iv)Job S;;os. We have n jobs and m machines. Each job has its own machide order specified.Throughout this paper will be assumed that the decisionmaker is not allowed to preempt, i.e. interrupt the processing of a job on a machine. For results where the decision-maker is allowed to preempt, the reader should consult the references. In this paper two objectives will be considered, namely (i) minimization off the expected completion time of the last job (the so-called mak espan) and (ii) minimization of the sum of the expected comp=i ion times of all jobs (the so-called flow time).This survey is organized as follows: In Section 2 we give a short d'escription of the most important results in deterministic shz scheduling (without proofs). The purpose of this section is r: enable the reader to compare the results for the stochas-:_I versions of the different models, presented in Section 3, wiz their deterministic counterparts. For the stochastic models iz Section 3 we will not present any rigorous proofs either. However, we will provide for each model heuristic arguments that -ay rmake the results seem more intuitive. In...

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