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Asian Journal of Applied Sciences
Year: 2008  |  Volume: 1  |  Issue: 2  |  Page No.: 110 - 122

The Multi-Product Multi-Constraint Newsboy Problem with Incremental Discount and Batch Order

Ata Allah Taleizadeh, Seyed Taghi Akhavan Niaki and Seyed Vahid Hosseini    

Abstract: This study points out the real-world prevalence of the multiple-product multiple-constraint Newsboy problem, i.e., the Newsstand problem, in which not only there are incremental discounts on the purchasing prices, but also the orders are placed in batch forms. The constraints are the service levels and warehouse capacity. Moreover, the quantities of the orders are integer multiples of packets, each containing more than one product. The objective of this problem is to find the order quantities such that the expected sum of the shortage, holding and purchasing costs is minimized. We assume that the holding and shortage costs occur at the end of the period; they are modeled by a quadratic function and that the decision variables are integer. We present a formulation to the problem and show that it is a integer nonlinear programming model. Finally, we provide an efficient algorithm to solve the new problem and illustrate the results with a numerical example.

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