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On the unimodality of METRIC Approximation subject to normally distributed demands

Thibaut Barthelemy (thibaut.barthelemy***at***univie.ac.at)

Abstract: METRIC Approximation is a popular model for supply chain management. We prove that it has a unimodal objective function when the demands of the n retailers are normally distributed. That allows us to solve it with a convergent sequence. This optimization method leads us to a closed-form equation of computational complexity O(n). Its solutions are at most 0.001% above the optimum for all our instances. Our proof relies on a generic analytical rule that we introduce to prove unimodality, so quasi-concavity or quasi-convexity, of univariate functions.

Keywords: supply chain management ; METRIC ; normal distribution ; unimodality ; quasi-convexity

Category 1: Applications -- OR and Management Sciences (Supply Chain Management )

Category 2: Convex and Nonsmooth Optimization

Category 3: Nonlinear Optimization (Unconstrained Optimization )

Citation: University of Vienna, Department of Business Administration, Austria

Download: [PDF]

Entry Submitted: 07/13/2015
Entry Accepted: 07/13/2015
Entry Last Modified: 07/28/2015

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