A supply chain design model with replenishment frequency and solution approach considering economies of scale in cost of depot and transportation

In this study, a three-layer supply chain design model consisting of one supplier, many depots and many retailers is discussed. The problem is to determine the number and capacity of the depots to open, which retailer to be assigned to which opened depot, and the replenishment frequencies for each depot and retailer are decided. While making these decisions, the model aims to minimize the total system costs, which include the cost of opening and operating depots, inventory costs in depots and retailers, and transportation costs both from supplier to depots and from depots to retailers. It is taken into account that there is quantity reduction in transportation costs calculated between all stages and economies of scale in depot costs. To achieve a near-optimal solution, a periodic inventory control policy with a power of 2 replenishment frequency policy is used in depots and retailers to facilitate cross-docking between inbound and outbound parties in depots. The distinguishing feature of the proposed model is that facility location decisions as the strategic decision is integrated with the tactical decisions of depot-retailer assignment and replenishment frequency determination. While making these decisions, the effects of cross-docking in depots on inventory and transportation costs are explicitly modelled, and the quantity dependence in transportation cost and depot opening and operating costs are considered. The problem is formulated as a nonlinear mixed integer programming model and a heuristic search-based approach is proposed for its solution. The superiority of the proposed approach over the solution to be found without considering the supply frequencies has been demonstrated in the numerical analysis.