Fuzzy programming and profit and cost allocation for a production and transportation problem |
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| Institution: | 1. Department of Industrial and Systems Engineering, Faculty of Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima 739-8527, Japan;2. Products Projects Development Department, Juken Sangyou Co. Ltd., 1-1 Mokuzaikou-minami, Hatsukaichi, Hiroshima 738-8502, Japan;1. Centre for Wireless Communications (CWC), P.O. Box 4500, FI-90014 University of Oulu, Finland;2. Department of Computer and Information Science, Linköping University, SE-581 83 LINKÖPING, Sweden;3. SCA Research Lab, ITMO University, St. Petersburg, 197101, Russia;4. Center for Ubiquitous Computing (UBICOMP), P.O. Box 4500, FI-90014 University of Oulu, Finland;1. Faculty of Mathematics, Wroc?aw University of Technology, Wybrze?e Wyspiańskiego 27, 50-370 Wroc?aw, Poland;2. Department of Business Administration, Aichi University, Nagoya Campus, Hiraike 4-60-6, Nakamura, Nagoya, Aichi, 453-8777, Japan;1. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, PR China;2. School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, PR China;1. School of Information Science and Engineering, Central South University, PR China;2. Hunan Engineering Center for Currency Recognition and Self-Service, Changsha, 410083, Hunan, PR China |
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| Abstract: | In this paper, we deal with a real problem on production and transportation in a housing material manufacturer, and consider a production and transportation planning under the assumption that the manufacturer makes multiple products at factories in multiple regions and the products are in demand in each of the regions. First, we formulate mixed zero–one programming problems such that the cost of production and transportation is minimized subject to capacities of factories and demands of regions. Second, to realize stable production and satisfactory supply of the products in fuzzy environments, fuzzy programming for the production and transportation problem is incorporated. Finally, under the optimal planning of production and transportation, we show a profit and cost allocation by applying a solution concept from game theory. Using actual data, we show usefulness of the fuzzy programming and a rational allocation scheme of the profit and cost. |
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