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The Scientific World Journal
Volume 2014 (2014), Article ID 242107, 7 pages
http://dx.doi.org/10.1155/2014/242107
Research Article

Scheduling Jobs with Variable Job Processing Times on Unrelated Parallel Machines

Faculty of Management and Economics, Dalian University of Technology, Dalian 116024, China

Received 21 March 2014; Accepted 30 April 2014; Published 26 May 2014

Academic Editor: Chin-Chia Wu

Copyright © 2014 Guang-Qian Zhang et al. 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

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waiting) time, the total machine load, the total absolute differences in completion (waiting) times on all machines, and total resource cost. If the number of machines is a given constant number, we propose a polynomial time algorithm to solve the problem.