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Journal of Optimization
Volume 2017 (2017), Article ID 7150637, 7 pages
Research Article

Maximum Lateness Scheduling on Two-Person Cooperative Games with Variable Processing Times and Common Due Date

School of Management, Shenyang University of Technology, Shenyang 110870, China

Correspondence should be addressed to Peng Liu

Received 22 December 2016; Accepted 28 March 2017; Published 6 April 2017

Academic Editor: Manlio Gaudioso

Copyright © 2017 Peng Liu and Xiaoli Wang. 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.


A new maximum lateness scheduling model in which both cooperative games and variable processing times exist simultaneously is considered in this paper. The job variable processing time is described by an increasing or a decreasing function dependent on the position of a job in the sequence. Two persons have to cooperate in order to process a set of jobs. Each of them has a single machine and their processing cost is defined as the minimum value of maximum lateness. All jobs have a common due date. The objective is to maximize the multiplication of their rational positive cooperative profits. A division of those jobs should be negotiated to yield a reasonable cooperative profit allocation scheme acceptable to them. We propose the sufficient and necessary conditions for the problems to have positive integer solution.