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An Inventory Model for Weibull Deterioration with Stock and Price Dependent Demand

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Abstract

Customer purchasing needs are generally affected by factors such as selling price and inventory level and not only by demand. Demand is considered either to be a constant or a function of a single variable in most of the cases, which is not always feasible. Consequently, in the present study, demand rate as a function of stock level and selling price. The deterioration rate has been considered here to be Weibull two parameters, shortages are partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. In this model, first show that for any given selling price, optimal replenishment schedule exists and unique. Then, the total profit is a concave function of price with respect to time. Next, present a simple algorithm to find the optimal solution. Finally, in this paper solve a numerical example to illustrate the solution procedure and the algorithm.

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Acknowledgments

The author would like to express his gratitude to the editors and anonymous referees for their constructive suggestions to enhance the clarity of the present article.

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Authors and Affiliations

  1. Faculty of Science and Technology, ICFAI University, Tripura, Kamalghat, Sadar, West Tripura, 799210, India

    Umakanta Mishra

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  1. Umakanta Mishra
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Mishra, U. An Inventory Model for Weibull Deterioration with Stock and Price Dependent Demand. Int. J. Appl. Comput. Math 3, 1951–1967 (2017). https://doi.org/10.1007/s40819-016-0217-0

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