Lot-sizing two-echelon assembly systems with random yields and rigid demand |
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| Institution: | 1. Academic College of Tel-Aviv-Yaffo, 29 Melchet, Tel-Aviv 61560, Israel;2. Faculty of Management, Tel Aviv University, Tel-Aviv 69978, Israel;1. Department of Industrial Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-742, South Korea;2. Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC, V6T 1Z2, Canada;3. Department of Industrial and Information Systems Engineering, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul 156-743, South Korea;1. Technical University of Denmark, Department of Mechanical Engineering, Produktionstorvet, 2800 Kgs. Lyngby, Denmark;2. Device R&D, Novo Nordisk A/S, Brennum Park, 3400 Hillerød, Denmark;1. Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China;2. School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005, Australia;3. Southampton Statistical Sciences Research Institute, University of Southampton, SO17 1BJ, United Kingdom;1. Institute of Game Behavior and Operations Management, Nanjing University of Finance and Economics, Nanjing 210046, China;2. School of Management Science and Engineering, Nanjing University, Nanjing 210093, China;3. Business Division, Institute of Textiles and Clothing, Faculty of Applied Science and Textiles, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;4. Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;1. Department of Mathematics, Bengal Institute of Technology, 1. no. Govt. Colony, Kolkata 700150, India;2. Department of Mathematics, University of Kalyani, Kalyani 741235, India;3. Department of Mathematics, Bhangar Mahavidyalaya, Bhangar 743502, India |
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| Abstract: | We consider a two-echelon assembly system producing a single final product for which the demand is known. The first echelon consists of several parallel stages, whereas the second echelon consists of a single assembly stage. We assume that the yield at each stage is random and that demand needs to be satisfied in its entirety; thus, several production runs may be required. A production policy should specify, for each possible configuration of intermediate inventories, on which stage to produce next and the lot size to be processed. The objective is to minimize the expected total of setup and variable production costs.We prove that the expected cost of any production policy can be calculated by solving a finite set of linear equations whose solution is unique. The result is general in that it applies to any yield distribution. We also develop efficient algorithms leading to heuristic solutions with high precision and, as an example, provide numerical results for binomial yields. |
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