Using Simulated Annealing for Open Shop Scheduling with Sum Criteria

Abstract

In this chapter, we consider the open shop scheduling problem which can be described as follows. A set of n jobs J1, J2, . . . , Jn has to be processed on a set of m machines M1,M2, . . . , Mm. The processing of job Ji on machine Mj is denoted as operation (i, j), and the sequence in which the operations of a job are processed on the machines is arbitrary. Moreover, each machine can process at most one job at a time and each job can be processed on at most one machine at a time. Such an open shop environment arises in many industrial applications. For example, consider a large aircraft garage with specialized work-centers. An airplane may require repairs on its engine and electrical circuit system. These two tasks may be carried out in any order but it is not possible to do these tasks on the same plane simultaneously. Further applications of open shop scheduling problems in automobile repair, quality control centers, semiconductor manufacturing, teacher-class assignments, examination scheduling, and satellite communications are described by Kubiak et al. (1991), Liu and Bulfin (1987) and Prins (1994). For each job Ji, i = 1, 2, . . . , n, there may be given a release date ri ≥ 0 which is the earliest possible time when the first operation of this job may start, a weight wi and a due date di ≥ 0 by which the job should be completed. The processing time of operation (i, j) is denoted as tij. It is assumed that the processing times of all operations are assumed to be given in advance. Let Ci be the completion time of job Ji, i.e. the time when the last operation of this job is completed. Traditional optimization criteria are basically partitioned into two types: either