A Variable Neighborhood Search Approach to a Multi Order Fulfillment and Consolidation Problem.

This study focuses on the problem of multi-order fulfillment and consolidation in e-Commerce retail (MOFCP). We examine a retailer that operates an online channel and a network of stores or warehouses. In this context, the term” store” is broadly used to refer to an individual physical store or a local warehouse. Customers can place orders containing multiple items through on-line platforms. The goal is to find the locations that fulfill each order and a consolidation point of each order such that the total transportation costs are minimized. To capture the economy of scale of the transportation costs, we model the transportation costs through piece-wise linear cost functions. We propose an integer programming IP formulation enhanced by valid inequalities, as well as a nested Variable Neighborhood Search heuristic. Through preliminary numerical experiments, we show that the heuristic has 1.58% and 2.98% overall average increase in costs compared to the MILP for the case of tight inventory to demand ratio (𝑘𝑘 = 1) and suplus inventory to demand (𝑘𝑘 = 1.5) respectively. The overall average running time is about 2 times faster for tight inventory and about 5 times slower than the IP when inventory is surplus. [ABSTRACT FROM AUTHOR]