A VNS approach for a joint fulfillment and consolidation problem in e-commerce

Recent advances in supply chain and logistics illustrate that consolidation of orders can considerably reduce transportation costs and CO2 emissions. In this paper, we study the impact of consolidation on order fulfillment in e-Commerce. We consider a retailer with an online platform and network of physical stores, who must decide the optimal locations from which to fulfill a set of multi-item orders, as well as the optimal consolidation points for each order. To model the economy of scale obtained by consolidating orders, we consider piecewise-linear concave transportation costs. Our model extends the existing literature by considering multiple orders at a time and stores with limited inventory. We formulate the problem as an MILP and propose a Variable Neighborhood Search (VNS) to find good quality solutions in a short time. We tested the performance of the proposed algorithm on different scenarios, where stores have a varying percentage of overlapping items. Via numerical experiment, we observed a 0.22% average relative increase in cost using VNS for instances with large overlap in items among stores and a 2.36% average relative increase for the other scenarios. On average, the VNS is 16 times faster than the MILP formulation.