The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty

The robust capacitated vehicle routing problem (CVRP) under demand uncertainty is studied to address the minimum cost delivery of a product to geographically dispersed customers using capacity-constrained vehicles. Contrary to the deterministic CVRP, which postulates that the customer demands for the product are deterministic and known, the robust CVRP models the customer demands as random variables, and it determines a minimum cost delivery plan that is feasible for all anticipated demand realizations. Robust optimization counterparts of several deterministic CVRP formulations are derived and compared numerically. Robust rounded capacity inequalities are developed, and it is shown how they can be separated efficiently for two broad classes of demand supports. Finally, it is analyzed how the robust CVRP relates to the chance-constrained CVRP, which allows a controlled degree of supply shortfall to decrease delivery costs.