Abstract
We consider an extension of the standard newsvendor problem by allowing for multiple classes of customers. The product is first sold to customers with the highest priority, and the remaining units (if any) are sold at a discounted price to customers in decreasing order of priority until all classes of customers have been served, limited only by the available stock. Unsold items, if any, have a salvage value. The demands of different priority customers are independent random variables with known probability distributions. The problem is to find the purchase quantity that maximizes the expected profit. We show that this problem actually reduces to the standard newsvendor problem with the demand distribution being a mixture of the input demand distributions. Since this mixture of distributions is typically hard to handle analytically, we propose a simple general heuristic which can be implemented using different types of distributions. Some of these implementations produce near optimal solutions. We tested these implementations for the case of two demand classes of customers and found that they outperform previously published heuristics in almost all instances. We suggest applications for this model in the Chinese pharmaceutical industry, apparel industry, and perishable goods among others. We also propose an extension involving shortage cost.
Highlights
Arrow et al [1] and Morse and Kimball [2] were the first who formulated and solved the single-period, single-How to cite this paper: Li, B., Sundararaghavan, P. and Nandkeolyar, U. (2015) A Newsvendor with Priority Classes and Shortage Cost
The main theoretical result of this paper is that the newsvendor problem with multiple demand classes characterized by decreasing prices reduces to the standard newsvendor problem with the demand distribution being a mixture of the input distributions, the selling price p1, the unit cost c, and the salvage value s
We demonstrate that some implementations of this general heuristic produce near optimal solutions, and they significantly outperform the heuristics reported in the literature
Summary
Arrow et al [1] and Morse and Kimball [2] were the first who formulated and solved the single-period, single-. The main theoretical result of this paper is that the newsvendor problem with multiple demand classes characterized by decreasing prices reduces to the standard newsvendor problem with the demand distribution being a mixture of the input distributions, the selling price p1 , the unit cost c, and the salvage value s. Since typically this mixture distribution does not have a closed analytical form, we propose a general heuristic that replaces it by a more tractable distribution with the same first two moments.
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