A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times |
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| Authors: | Dujuan Wang Yunqiang Yin T.C.E. Cheng |
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| Affiliation: | 1. Transportation Management College, Dalian Maritime University, Dalian, People's Republic of China;2. School of Management Science and Engineering, Dalian University of Technology, Dalian, People's Republic of China;3. School of Management, University of Science and Technology of China, Hefei, People's Republic of China;4. Data Science Research Center, Kunming University of Science and Technology, Kunming, People's Republic of China;5. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China |
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| Abstract: | We investigate a single‐machine scheduling problem for which both the job processing times and due windows are decision variables to be determined by the decision maker. The job processing times are controllable as a linear or convex function of the amount of a common continuously divisible resource allocated to the jobs, where the resource allocated to the jobs can be used in discrete or continuous quantities. We use the common flow allowances due window assignment method to assign due windows to the jobs. We consider two performance criteria: (i) the total weighted number of early and tardy jobs plus the weighted due window assignment cost, and (ii) the resource consumption cost. For each resource consumption function, the objective is to minimize the first criterion, while keeping the value of the second criterion no greater than a given limit. We analyze the computational complexity, devise pseudo‐polynomial dynamic programming solution algorithms, and provide fully polynomial‐time approximation schemes and an enhanced volume algorithm to find high‐quality solutions quickly for the considered problems. We conduct extensive numerical studies to assess the performance of the algorithms. The computational results show that the proposed algorithms are very efficient in finding optimal or near‐optimal solutions. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 41–63, 2017 |
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| Keywords: | scheduling due window assignment controllable processing times resource allocation FPTAS |
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