Regression approximation for a partially centralized inventory system considering transportation costs

Inventory centralization for multiple stores with stochastic demands reduces costs by establishing and maintaining a central ordering/distribution point. However the inventory centralization may increase the transportation costs since either the customer must travel more to reach the product, or the central warehouse must ship the product over longer distance to reach the customer. In this paper, we study a partially centralized inventory system where multiple central warehouses exist and a central warehouse fulfills the aggregated demand of stores. We want to determine the number, the location of central warehouses and an assignment of central warehouses and a set of stores. The objective is the minimization of the sum of warehouse costs and transportation cost. With the help of the regression approximation of cost function, we transform the original problem to more manageable facility location problems. Regression analysis shows that the approximated cost function is close to the original one for normally distributed demands.