Single-Machine Scheduling with Job Rejection, Deteriorating Effects, and Deteriorating Maintenance Activities

Abstract

This paper addresses the single-machine scheduling problems with simultaneous considerations of job rejection, deterioration effects, and deteriorating multimaintenance activities. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the single machine. Three deterioration effect models are investigated, and it is assumed that each machine may be subject to several maintenance activities over the scheduling horizon, and the duration of the maintenance depends on its running time. Moreover, due to the restriction of the budget of maintenance, the upper bound of the total maintenance frequencies on the machine is assumed to be known in advance. The objective is to find jointly the optimal accepted job set, the optimal maintenance frequencies, the optimal maintenance positions, and the optimal accepted job sequence such that the cost function based on the total completion time and rejection penalty is minimized. It is shown that all the versions of the problem under study are polynomial time solutions.

An Optimal Algorithm for Scheduling with Variable Job Processing Times and Rejection

“…A extensive survey of different scheduling models and problems involving rejection can be found in Shabtay et al [8]. More recent papers which have considered scheduling with rejection include Nian and Mao [9], Shabtay [10], and Ou et al [11].…”

Scheduling Jobs with Variable Job Processing Times on Unrelated Parallel Machines

“…A recent survey of the scheduling problems with controllable processing times was given by Shabtay and Steiner [ 5 ]. More recent papers that have considered scheduling problems with deterioration effects and/or learning effects and/or controllable processing times include Bai et al [ 6 , 7 ], Cheng et al [ 8 ], Gorczyca and Janiak [ 9 ], Hsu and Yang [ 10 ], Huang and Wang [ 11 ], Lee et al [ 12 ], Leyvand et al [ 13 ], Nian and Mao [ 14 ], Shabtay and Steiner [ 15 ], Wang et al [ 16 ], J. B. Wang and M. Z. Wang [ 17 ], J.…”