Rescheduling Rework Jobs on Single Machine locked by initial loads

Abstract

In this paper, the problem of Rescheduling Rework Jobs on Single Machine (RRJSM) is investigated. Suppose that a single machine has a set of the initial loads locked for some desired purposes. The objective of RRJSM is to minimize the maximum waiting time of rework jobs by scheduling or inserting them into the locked initial loads. Firstly, the RRJSM problem is formulated and proved to be NP-hard as for computational complexity. Secondly, two properties of RRJSM problem are addressed. Furthermore, a heuristic algorithm is designed basing on the properties and its complexity is given as well. Finally, the optimality condition of the algorithm and the judgment of optimal solution are given and proved respectively.