Coupled Task Scheduling with Time-Dependent Processing Times

Abstract

The single machine coupled task scheduling problem includes a set of jobs, each with two separated tasks and there is an exact delay between the tasks. We investigate the single machine coupled task scheduling problem with the objective of minimizing the makespan under identical processing time for the first task and identical delay period for all jobs, and the time-dependent processing time setting for the second task. We provide optimal solution under certain conditions. In addition, we propose a dynamic program under the condition that the majority of jobs share the same time-dependent characteristic. We develop a heuristic for the general case, and show that the heuristic performs very well.

Keywords: single machine coupled task scheduling, time-dependent processing time, simple linear processing time, dynamic program, heuristic