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.
University of Vienna, Department of Business Administration, Austria