A String of Disjoint Job Block with Processing Time Associated with Probability in Two-Stage Weighted Open Shop Model

Abstract

Open-shop scheduling problem (OSSP) is a well-known topic with wide industrial applications which belongs to one of the vital issues in the field of engineering. This paper deals with a two-stage open shop scheduling problem in which the processing time of jobs is allied with probabilities. The concept of a string of two job blocks which are disjoint in nature is considered so that the first block covers the jobs with a fixed route and the second block covers the jobs with an arbitrary path. Further, the weights of jobs are also introduced due to their applicability and relative importance in the real world. The objective of this study is to propose a heuristic which on execution, provides an optimal or near-optimal schedule to diminish the makespan. Several numerical illustrations are produced in MATLAB 2018a to demonstrate the effectiveness of the proposed approach, and to confirm the performance, the results are compared with the existing methods developed by Johnson and Palmer.