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Joint dynamic pricing and investment strategy for perishable foods with price-quality dependent demand. (English) Zbl 1315.90003
Summary: The food quality has always played an important role in the retail process since it has been considered as a direct factor to influence a consumer’s purchase decision. In this paper, we formulate an inventory model for perishable foods, in which the demand depends on the price and quality that decays continuously. The objective is to determine a joint dynamic pricing and preservation technology investment strategy while maximizing the total profit from selling a given initial inventory of foods. We first prove the existence of an optimal solution based on Filippov-Cesari theorem. Then, we obtain all the candidates and provide the conditions that make a certain candidate be an optimal solution according to Pontryagin’s maximum principle. Next, we present an effective algorithm to search for the optimal strategy. Finally, two numerical examples are employed to illustrate the solution procedure and the results, followed by sensitivity analysis and managerial insights.

MSC:
90B05 Inventory, storage, reservoirs
49N90 Applications of optimal control and differential games
91B24 Microeconomic theory (price theory and economic markets)
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