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Mathematical Problems in Engineering
Volume 2015, Article ID 956158, 6 pages
http://dx.doi.org/10.1155/2015/956158
Research Article

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China

Received 9 February 2015; Revised 11 April 2015; Accepted 12 April 2015

Academic Editor: Chin-Chia Wu

Copyright © 2015 Cuixia Miao and Juan Zou. 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 the parallel-machine scheduling problem in which the machines have availability constraints and the processing time of each job is simple linear increasing function of its starting times. For the makespan minimization problem, which is NP-hard in the strong sense, we discuss the Longest Deteriorating Rate algorithm and List Scheduling algorithm; we also provide a lower bound of any optimal schedule. For the total completion time minimization problem, we analyze the strong NP-hardness, and we present a dynamic programming algorithm and a fully polynomial time approximation scheme for the two-machine problem. Furthermore, we extended the dynamic programming algorithm to the total weighted completion time minimization problem.