Integrated Forward and Reverse Cross-Docking with Vehicle Routing and Scheduling Under the Uncertainty of Inspection Results: A Genetic-Mathematic Algorithm

Despite the recognized advantages of cross-docking in forward logistics, very few studies have investigated reverse cross-docking, and these studies do not consider the operational uncertainties of returned products in the reverse flow, which is required in practice. This paper introduces a vehicle routing and scheduling problem for the integration of forward and reverse logistics, in which the cross-docking facility is employed as (i) the distribution center in forward flow and (ii) the collection and dispatching center of returned products in reverse flow. We present two modes based on the inspection point: (i) retailer site or (ii) cross-dock. A deterministic mixed integer linear programming model is presented for the retailer-site inspection mode to minimize the total operational costs. For the second mode, a robust optimization counterpart of the modified deterministic model is formulated to account for the uncertainties arising from the inspection results revealed at the cross-dock. A genetic-mathematic algorithm is proposed to solve the large-sized instances. Through numerical studies, we evaluated the performance of the algorithm and demonstrated cost reductions and truck utilization improvements as benefits of integration. Moreover, in sensitivity analyses using a quasi-real case of a personal electronic device supply chain, and employing simulation, the price of robustness of the second model was evaluated by considering various budget sets, which justified the full robustness and application of the cross-dock as the inspection point in the closed-loop supply chain.