Common due-date assignment and scheduling on a single machine with sequence-dependent setups and discretely controllable processing times

Abstract

This study addresses the common due-date assignment and scheduling problem on a single machine in which job-processing times are not given, but controllable. The problem is to determine the common due-date, the processing times and the sequence of the jobs to be processed on the single machine. The controllable processing times are considered in the discrete form in that the processing time of a job is determined by selecting one of its discretely available ones with different processing costs. In particular, sequence-dependent setups, in which setup times depend on the type of job just completed and the job to be processed, are also considered. A mixed integer-programming model is proposed for the problem that minimizes the sum of earliness, tardiness, due-date assignment and job processing costs. Then, due to the problem complexity, two-stage heuristic algorithms are proposed in which an initial solution is obtained by the positional weights, and it is improved by the pairwise interchange method together with determining job-processing times. Computational experiments were done on a number of random instances, and the results are reported.