CON/SLK due date assignment and scheduling on a single machine with two agents |
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| Authors: | Yunqiang Yin Du‐Juan Wang Chin‐Chia Wu T.C.E. Cheng |
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| Affiliation: | 1. Faculty of Science, Kunming University of Science and Technology, Kunming, China;2. Transportation Management College, Dalian Maritime University, Dalian, China;3. Department of Statistics, Feng Chia University, Taichung, Taiwan;4. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
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| Abstract: | We consider scheduling problems involving two agents (agents A and B), each having a set of jobs that compete for the use of a common machine to process their respective jobs. The due dates of the A‐jobs are decision variables, which are determined by using the common (CON) or slack (SLK) due date assignment methods. Each agent wants to minimize a certain performance criterion depending on the completion times of its jobs only. Under each due date assignment method, the criterion of agent A is always the same, namely an integrated criterion consisting of the due date assignment cost and the weighted number of tardy jobs. Several different criteria are considered for agent B, including the maxima of regular functions (associated with each job), the total (weighted) completion time, and the weighted number of tardy jobs. The overall objective is to minimize the performance criterion of agent A, while keeping the objective value of agent B no greater than a given limit. We analyze the computational complexity, and devise polynomial or pseudo‐polynomial dynamic programming algorithms for the considered problems. We also convert, if viable, any of the devised pseudopolynomial dynamic programming algorithms into a fully polynomial‐time approximation scheme. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 416–429, 2016 |
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| Keywords: | scheduling two agents due date assignment |
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