Analysis of the newsboy problem with fuzzy demands and incremental discounts

Analysis of the newsboy problem with fuzzy demands and incremental discounts

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Article ID: iaor20108311
Volume: 129
Issue: 1
Start Page Number: 169
End Page Number: 177
Publication Date: Jan 2011
Journal: International Journal of Production Economics
Authors: ,
Keywords: newsboy problem
Abstract:

This paper proposes an analysis method for the single-period (newsboy) inventory problem with fuzzy demands and incremental quantity discounts. In fuzzy environments, the availability of the quantity discount makes the analysis of the associated model more complex. The proposed analysis method is based on ranking fuzzy number and optimization theory. By applying the Yager ranking method, the fuzzy total cost functions with different unit purchasing costs are transformed into convex piecewise nonlinear functions. To effectively and efficiently find the optimal inventory policy, the proofs of two properties regarding the relative position between the price break and minimums of these nonlinear functions are proposed. The closed-form solutions to the optimal order quantities are also derived. Four cases of a numerical example are solved to demonstrate the validity of the proposed analysis method. It is clear that the proposed methodology is applicable to further cases with different types of quantity discounts and other more complicated cases. More importantly, managerial implications are also provided for decision-makers’ references.

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