A Scheduling Problem with One Producer and the Bargaining Counterpart with Two Producers
First this paper considers a Common Due Window (CDW) scheduling problem of n jobs on a single machine to minimize the sum of common weighted earliness and weighted number of tardy jobs when only one manufacturer processes these jobs. Two dynamic algorithms are designed for two cases respectively and each case is proved to be ordinary NP-hard. Successively the scenario, where two manufacturers jointly process these jobs due to the insufficient production facilities or techniques of each party, is investigated. A novel dynamic programming algorithm is proposed to obtain an existing reasonable set of processing utility distributions on the bi-partition of these jobs.
KeywordsSchedule Problem Optimal Schedule Dynamic Programming Algorithm Bargaining Solution Total Processing Time
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- 1.Anger, F.D., Lee, C.-Y., Martin-Vega, L.A.: Single Machine Scheduling with Tight Windows. Research Report, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FloridaTransportation Science, pp. 86–16 (1986)Google Scholar
- 2.Kramer, F.-J., Lee, C.-Y.: Common Due Window Scheduling. Production and Operations Management 6, 262–275 (1997)Google Scholar
- 3.Lee, C.-Y.: Earliness-Tardiness Scheduling Problems with Constant Size of Due Date Window. Research Report, Department of Industrial and System Engineering, University of Florida, Gainesville, Florida, pp. 91–17 (1991)Google Scholar
- 15.Lawler, E.L.: Fast Approximation Algorithms for Knapsack Problems. In: Proc. 18th Annual Symposium on Foundation of Computer Science, pp. 206–213. IEEE Computer Society, Long Beach, CA (1977)Google Scholar
- 17.Muthoo, A.: Bargaining Theory with Application. Cambridge University Press, Cambridge (1999)Google Scholar
- 18.Zhang, D.: A logical Model of Nash Bargaining Solution. In: Proceeding of IJCAI, pp. 983–990 (2005)Google Scholar
- 22.Touati, C., Altman, E., Galtier, J.: Generalized Nash Bargaining Solution for Bandwidth Allocation. Computer Networks (in press)Google Scholar
- 26.Chen, Q.-L.: A New Discrete Bargaining Model on Job Partition Between Two Manufacturers. PhD Dissertation, The Chinese University of Hongkong (2006)Google Scholar