Modeling the Effects of Demand Correlation in Location Problems that account for Inventory Pooling

We investigate large-scale facility location models that consider the risk pooling effects of centralizing safety stocks when customer demands are correlated across customer locations. This problem has not been well studied, perhaps because the calculation of safety stock levels with correlated demands requires significant computational effort. The experimental evaluation of any proposed procedure is also difficult, since industrial data is generally unavailable and it is difficult to create a statistically valid correlation matrix of customer demands required to generate random test instances of realistic size. We show that even very low levels of correlation have significant impact on solution cost and structure. This is of practical significance since distribution networks increasingly rely on contracts of relatively short duration, implying low or no fixed facility costs, such that the cost of holding safety stock can represent a large portion of the controllable distribution network costs. We present a method for generating a statistically valid correlation matrix when the correlations between customer demands are inversely proportional to the distance between customer locations. Using a metaheuristic solution procedure, we study a set of test instances that incorporate both safety stock holding costs and outbound transportation costs, illustrating the importance of explicitly considering demand correlation in location models.