Production planning and pricing policy in a make-to-stock system with uncertain demand subject to machine breakdowns |
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Authors: | Xiutian Shi Houcai Shen Ting Wu T.C.E. Cheng |
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Affiliation: | 1. International Center of Management Science and Engineering, School of Management and Engineering, Nanjing University, Nanjing, China;2. School of Business and Department of Mathematics, Nanjing University, Nanjing, China;3. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China |
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Abstract: | We consider a make-to-stock system served by an unreliable machine that produces one type of product, which is sold to customers at one of two possible prices depending on the inventory level at the time when a customer arrives (i.e., the decision point). The system manager must determine the production level and selling price at each decision point. We first show that the optimal production and pricing policy is a threshold control, which is characterized by three threshold parameters under both the long-run discounted profit and long-run average profit criteria. We then establish the structural relationships among the three threshold parameters that production is off when inventory is above the threshold, and that the optimal selling price should be low when inventory is above the threshold under the scenario where the machine is down or up. Finally we provide some numerical examples to illustrate the analytical results and gain additional insights. |
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Keywords: | Production planning Dynamic pricing Machine breakdown Uncertain demand Inventory control |
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