Mathematical Integer Programming for a One Machine Scheduling Problem

Abstract

This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integer programming formulation, this paper shows how both good-quality lower and upper bounds can be computed. Numerical experiments on Baptiste et al.’s instances are provided, which demonstrate the efficiency of the approach.