• ### Deriving, and Learning About, Spatial Demand Distributions in Location Models

Yigal Gerchak

Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv, 69978, Israel.

Abstract: Location models typically assume that the spatial demand distribution or weights of demand clusters is/are given. However, when a service is new, or considerably altered, such distributions are, in fact, learned gradually as more demands are realized. Recently, location analysts proposed robust optimization models which deal with ranges of weights. We argue that, in principle, uncertain weights can be viewed as mixtures of distributions, and are thus similar to ordinary weights. However, location analysts need a procedure, hopefully a simple one, to revise spatial probability distributions as more information is obtained. We provide a Bayesian model which accomplishes that in a sensible manner. We then show that this theory-based model is, in fact, equivalent to a very simple “physical” mechanism. As the spatial demand distribution evolves with experience, the home bases of servers can be adjusted accordingly, if feasible and desirable.

Keywords: Location, Learning, Bayesian, Robust Optimization.