Load balance recovery for multi-drop distribution problems: A mixed integer linear programming approach

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Elsa Marília Silva
António Galrão Ramos
José Fernando Oliveira
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In road freight transport, a loaded vehicle with a distribution route and a compliant load balance at the depot can become non-compliant during the route, since the total weight of the cargo and its centre of gravity change with each delivery. Nowadays, vehicles circulating on our roads either undermine safety regulations or lack operational efficiency when these regulations are taken into account and cargo is extensively rearranged after each delivery. This issue has been completely ignored both in the vehicle routing literature and in the container loading literature. The aim of this work is to provide tools capable of ensuring that a cargo arrangement is load balanced along the complete distribution trip. It proposes a multi-drop load balance recovery algorithm (MDLBRA), which seeks to ensure that, when both a complete route and the respective cargo arrangement are provided, the boxes to be removed from the cargo arrangement at the depot and the boxes to be rearranged at each customer are identified, allowing the cargo to remain balanced after every delivery. It is important to notice that a MDLBRA is not a container loading algorithm: a MDLBRA modifies solutions generated by any container loading algorithm so that load balance is guaranteed when the truck leaves the depot and during the entire distribution route. A mixed integer linear programming (MILP) model is proposed to balance the cargo at each customer stop. The MILP model incorporates load distribution diagram constraints in order to determine the feasible domain for the location of the centre of gravity of the cargo arrangement, taking into account the regulatory requirements and the technical characteristics of the vehicle. Extensive computational experiments show that a MDLBRA can be used in practical contexts, as the MILP model was able to find a solution in less than ten minutes in 93% of the unbalanced test instances. © 2018 Elsevier Ltd