Scheduling two-machine preemptive open shops to minimize total completion time

Abstract

This paper deals with the problem of scheduling two-machine preemptive open shops to minimize total completion time. The un-weighted version of this problem is known to be NP-hard in the ordinary sense, while the weighted version of this problem is known to be NP-hard in the strong sense. Based on the analysis of problem characteristics, several fundamental properties are presented. A dynamic programming (DP) algorithm is developed to optimally solve both the un-weighted and weighted versions of the problem. Also, an efficient heuristic is proposed for solving large-sized problems. Computational results show that the proposed DP algorithm can handle problems with up to 30 jobs within a reasonable amount of time, and that the proposed heuristic has an average percentage deviation of less than 0.5% from the optimal solution value for problems with up to 30 jobs. Scope and purpose Shop scheduling problems, such as flow, job and open shop problems, are widely used in the modeling of industrial production processes and are receiving an increasing amount of attention from researchers. In an open shop scheduling problem, the order of processing the operations of a job on different machines is immaterial. Examples of open shop scheduling include teacher-class assignment, examination scheduling, and testing/repair operation scheduling. The purpose of this paper is to examine the two-machine total completion time open shop scheduling problem with the assumption that the processing of an operation can be arbitrarily preempted. An exact solution method based on dynamic programming is proposed for solving small sized problems, while a heuristic procedure is proposed for efficiently solving large sized problems.