Integrated planning of inbound and outbound logistics with a Rich Vehicle Routing Problem with backhauls

Abstract

This paper addresses the integration of the planning decisions concerning inbound logistics in an industrial setting (from the suppliers to the mill) and outbound logistics (from the mill to customers). The goal is to find the minimum cost routing plan, which includes the cost-effective outbound and inbound daily routes (OIRs), consisting of a sequence of deliveries of customer orders, pickup of a full truck-load at a supplier, and its delivery to the mill. This study distinguishes between three planning strategies: opportunistic backhauling planning (OBP), integrated inbound and outbound planning (IIOP) and decoupled planning (DIOP), the latter being the commonly used, particularly in the case of the wood-based panel industry under study. From the point of view of process integration, OBP can be considered as an intermediate stage from DIOP to IIOP. The problem is modelled as a Vehicle Routing Problem with Backhauls, enriched with case-specific rules for visiting the backhaul, split deliveries to customers and the use of a heterogeneous fleet. A new fix-and-optimise matheuristic is proposed for this problem, seeking to obtain good quality solutions within a reasonable computational time. The results from its application to the wood-based panel industry in Portugal show that IIOP can help to reduce total costs in about 2.7%, when compared with DIOP, due to better use of the delivery truck and a reduction of the number of dedicated inbound routes. Regarding OBP, fostering the use of OIRs does not necessarily lead to better routing plans than DIOP, as it depends upon a favourable geographical configuration of the set of customers to be visited in a day, specifically, the relative distance between a linehaul that can be visited last in a route, a neighboring backhaul, and a mill. The paper further provides valuable managerial insights on how the routing plan is impacted by the values of business-related model parameters which are set by the planner with some degree of uncertainty. Results suggest that increasing the maximum length of the route will likely have the largest impact in reducing transportation costs. Moreover, increasing the value of a reward paid for visiting a backhaul can foster the percentage of OIR in the optimal routing plan.