A scheduling problem with one producer and the bargaining counterpart with two producers

Authors:
Xiaobing Gan;Yanhong Gu;George L. Vairaktarakis;Xiaoqiang Cai;Quanle Chen
Affiliations:
Department of Information and System Management, Shenzhen University, Shenzhen, China;Department of Applied Mathematics, Shenzhen University, Shenzhen, China;Department of Operations, Case Western Reserve University, Cleveland, OH;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, HK;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, HK
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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Abstract

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.