Maximum Lateness Scheduling on Two-Person Cooperative Games with Variable Processing Times and Common Due Date. (6th April 2017)

• Record Type: Journal Article
• Authors: Liu, Peng; Wang, Xiaoli
• Other Names: Gaudioso Manlio Academic Editor.
• Is Part Of: Journal of optimization. Volume 2017(2017)
• Publication Date: 2017-04-06
• Subjects: Mathematical optimization -- Periodicals; Structural optimization -- Periodicals; Mathematical optimization; Structural optimization; Periodicals; Electronic journals; 519.6
• DOI: 10.1155/2017/7150637
• Languages: English
• ISSNs: 2356-752X

Abstract

Abstract : 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.