A Continuous Approximation approach for the Integrated Facility Location-Inventory Allocation Problem

In today’s business many companies have a complex distribution network with several national and regional distribution centers. In this paper, we study an integrated facility location and inventory allocation problem for designing a distribution network with multiple national distribution centers (NDCs) and retailers. The key decisions are where to locate the regional distribution centers (RDCs), how to assign retail stores to RDCs and what should be the inventory policy at the different locations such that the total network cost is minimized. We model our problem using a Type-I (probability of stock-outs) service level measure. This paper presents a continuous approximation (CA) model for solving the problem described above. The model takes a nonlinear form and solution techniques are developed using the theory of nonlinear programming. The main contribution of this work lies in developing a refined CA modeling technique when the discrete data cannot be modeled by a continuous function. Our methodology is illustrated on a real life application of a leading US retailer. Numerical analysis suggests that the total network cost is significantly lower in the case of the integrated model as compared with the non-integrated model. It also shows that the regular CA approach leads to a solution which is inferior to the solution obtained by the modified CA approach.