Maximum latency scheduling problem on two-person cooperative games

  • Authors:

  • Yanhong Gu;Jing Fan;Guochun Tang;Jiaofei Zhong

  • Affiliations:

  • Department of Applied Mathematics, Shenzhen University, Shenzhen, China 518060;Science Faulty, Shanghai Second Polytechnic University, Shanghai, China 201209;Institute of Management Engineering, Shanghai Second Polytechnic University, Shanghai, China 201209;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75080

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2013

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Abstract

This paper studies a two-person cooperative game in which a set of jobs has to be processed jointly by two people. Each of them has a single machine and his processing cost is defined as the minimum value of the maximum latency of his negotiably assigned jobs. The objective is to maximize the multiplication of their rational positive cooperative profits. In the case where all jobs have the same processing time, if they have a common due date, the problem is polynomial-time solvable; if due dates can be different, there exits an optimal schedule in which the jobs assigned to each person are scheduled in Earlier Due Date first (EDD) order and a polynomial-time dynamic programming is further proposed. In the case where processing times can be different, the NP-completeness of this problem is proved, and a pseudo-polynomial-time dynamic programming algorithm is developed.