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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 756251, 6 pages
http://dx.doi.org/10.1155/2013/756251
Research Article

Single-Machine Scheduling with Upper Bounded Maintenance Time under the Deteriorating Effect

School of Economics and Management, Southeast University, Nanjing 210096, China

Received 14 January 2013; Revised 15 April 2013; Accepted 17 April 2013

Academic Editor: Mustapha Ait Rami

Copyright © 2013 Pengfei Xue and Yulin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a single-machine scheduling problem with upper bounded actual processing time and upper bounded maintenance time under deteriorating effect. The actual processing time of a job is a position-dependent power function. If the actual processing time of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance should also be paid. The maintenance duration studied in the paper is a position-dependent exponential function. The objective is to find jointly the optimal maintenance frequency and the optimal job sequence to minimize the total cost, which is a linear function of the makespan and the total tardiness. We show that the studied scheduling problem can be transformed as a classic assignment problem to solve. There is also shown that a special case of the scheduling problem can be optimally solved by a lower order algorithm.