| Single-period Two-product Inventory Model with Reorder and Substitution |
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| 引用本文： | LI Xiao-shen,GAO Ke-quan (Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China, Department of Mathematics Physics,Henan University of Science Technology,Luoyang 471000,China). Single-period Two-product Inventory Model with Reorder and Substitution[J]. 数学季刊, 2006, 21(1): 148-158 |
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| 作者姓名： | LI Xiao-shen GAO Ke-quan (Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Department of Mathematics Physics Henan University of Science Technology Luoyang 471000 China) |
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| 作者单位： | Department of Applied Mathematics，Dalian University of Technology，Dalian 116024，China; Department of Mathematics Physics，Henan University of Science Technology，Luoyang 471000，China |
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| 摘 要： | In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer's substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi's, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level.
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| 关 键 词： | 存量 最佳有序量 代入法 最大值模型 运筹学 |
Single-period Two-product Inventory Model with Reorder and Substitution |
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| LI Xiao-shen GAO Ke-quan. Single-period Two-product Inventory Model with Reorder and Substitution[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(1): 148-158 |
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| Authors: | LI Xiao-shen GAO Ke-quan |
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| Affiliation: | [1]Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China [2]Department of Mathematics Physics, Henan University of Science Technology, Luoyang 471000,China |
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| Abstract: | In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer's substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi's, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level. |
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| Keywords: | inventory optimal order quantity substitution reorder |
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