A bi-objective cash-in-transit pick-up and delivery problem with risk assessment methodology: a case study

In this paper, the Risk-constrained Cash-In-Transit Vehicle Routing Problem (RCITVRP) is addressed with time windows, pickups, and deliveries. It is crucial for Cash-In-Transit (CIT) companies involved in transporting valuable or hazardous goods to identify risks. Therefore, owing to the high level of risk in CIT operations (e.g., armed robbery or attack), a bi-objective mixed-integer non-linear programming (MINLP) model is used to minimize travel costs and the risks associated with transporting valuables. For risk minimization, a new risk measure is developed, which includes: (i) the level of vulnerability for each vehicle, and (ii) the threat probability on each route. In addition, multiple vehicles are considered with capacity limitations. The epsilon-constraint method, a multi-objective exact solution approach, is implemented to solve the proposed model. Furthermore, several numerical examples are generated to evaluate the model and the solution method, which clearly show the best route with minimum cost and minimum risk (cost value = 112, risk value = 64,600). Eventually, a case study is provided to investigate the applicability of the proposed model.