Fulfillment Center Location and Network Design in Dual-Channel Retailing

With the emergence of e-commerce and the growing trend for online shopping, many retailers are adding online sales channel to their traditional brick-and-mortar stores. In this paper, we study the problem of fulfillment center location and network design for a retailer that seeks to integrate online sales channel into its traditional brick-and-mortar retail channel. The proposed analytical model seeks to locate fulfillment centers, select stores for online demand fulfillment, assign stores to fulfillment centers, and allocate safety stocks at fulfillment centers and stores to deal with variability in demand and lead time at minimum total cost. The problem is modelled as a mixed-integer nonlinear program, which is then reformulated as a mixed-integer second-order conic program. We present an exact branch-and-cut algorithm for the reformulated problem, in which extended polymatroid inequalities are separated to improve the convergence of the algorithm. Extensive computations under different cost scenarios and parameter settings confirm the efficiency of our exact algorithm. Through computational experiments, we showed that our algorithm reduces computation time, provides lower optimality gap, and outperforms the state-of-the art commercial solver on large instances. We conduct sensitivity analyses to understand the impact of variation in cost and model parameters and present managerial insights. The model also determines if the safety stock inventory should be pooled at the distribution centers (i.e. centralized inventory) and/or held at the stores (i.e. decentralized inventory). Using the model, we show the benefits of integrating fulfillment centers in the dual-channel network to serve in-store demand as well as online demand and its impact on facility location and network design decisions.