An efficient tabu search approach for the two-machine preemptive open shop scheduling problem

Abstract

This article considers the problem of scheduling two-machine preemptive open shops to minimize total tardiness. The problem is known to be NP-hard. An optimal timing algorithm is presented to determine the completion time of each job in a given job completion sequence. Then a tabu search (TS) approach is adopted together with the optimal timing algorithm to generate job completion sequences and final schedules. An efficient heuristic is developed to obtain an initial solution for the TS approach. Diversification and intensification strategies are suggested. Finally, computational experiments are conducted to demonstrate the performance of the proposed approach. The results show that the proposed TS approach finds extremely high-quality solutions within a reasonable amount of time. 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 tardiness open shop scheduling problem with the assumption that the processing of an operation can be arbitrarily preempted. An approximate solution method based on tabu search is proposed. Computational results show that the proposed solution method performs well in terms of both solution quality and computation time.