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Mathematical Problems in Engineering
Volume 2015, Article ID 437403, 6 pages
Research Article

Shapley Value for Parallel Machine Sequencing Situation without Initial Order

Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received 27 July 2014; Accepted 5 October 2014

Academic Editor: Dongdong Ge

Copyright © 2015 Shanshan Liu and Zhaohui Liu. 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.


We consider the parallel identical machine sequencing situation without initial schedule. For the situation with identical job processing time, we design a cost allocation rule which gives the Shapley value of the related sequencing game in polynomial time. For the game with identical job weight, we also present a polynomial time procedure to compute the Shapley value.