A fast heuristic to minimize number of tardy jobs in preemptive open shops

Abstract

This article considers the problem of scheduling preemptive open shops to minimize the number of tardy jobs. A mixed integer program is presented for solving small-sized problems. An efficient heuristic is constructed for solving large-sized problems. This heuristic can be viewed as a generalization of the well-known Moore’s algorithm for the single machine non-preemptive scheduling problem to the preemptive open shop scheduling problem. A lower bound based on assignment problem is proposed for performance evaluation of the heuristic for large-sized problems. Computational results for randomly generated problems are reported. For small-sized problems, the solution obtained by the heuristic has an average deviation of about 4.02% from the optimal value. The lower bound has an average deviation of about 21.03% from the optimal value. For large-sized problems, the solution obtained by the heuristic has an average deviation of less than 54% from the lower bound.