Metaheuristics for the risk-constrained cash-in-transit vehicle routing problem

This paper proposes a variant of the well-known capacitated vehicle routing problem that models the problem of routing vehicles in the cash-in-transit industry by introducing a risk constraint. In this problem, which is called the risk-constrained cash-in-transit vehicle routing problem (rctvrp), the risk associated with a robbery, which is assumed to be proportional both to the amount of cash being carried and the time or the distance covered by the vehicle carrying the cash, is limited by a certain risk threshold. A library containing three sets of instances for the rctvrp, some with known optimal solution, is generated based on VRP instances from the literature. A mathematical formulation is developed and small instances of the problem are solved using ibm cplex. Four constructive heuristics as well as a local search block composed of six different local search operators are developed and combined using two different metaheuristic structures: a multi-start structure and a perturb-and-improve structure. In a statistical experiment, the best parameter settings for each component are determined, and the resulting heuristic congurations are compared in their best possible setting. The resulting methods are able to obtain solutions of excellent quality in very limited computing times.