Polynomial Size Formulations for the Distance and Capacity Constrained Vehicle Routing Problem

Imdat KARA, Tusan DERYA, Theodore E. Simos, George Psihoyios, Ch. Tsitouras, Zacharias Anastassi
The Distance and Capacity Constrained Vehicle Routing Problem (DCVRP) is an extension of the well known Traveling Salesman Problem (TSP). DCVRP arises in distribution and logistics problems. It would be beneficial to construct new formulations, which is the main motivation and contribution of this paper. We focused on two indexed integer programming formulations for DCVRP. One node based and one arc (flow) based formulation for DCVRP are presented. Both formulations have O(n 2 ) binary
more » ... 2 ) binary variables and O(n 2 ) constraints, i.e., the number of the decision variables and constraints grows with a polynomial function of the nodes of the underlying graph. It is shown that proposed arc based formulation produces better lower bound than the existing one (this refers to the Water's formulation in the paper). Finally, various problems from literature are solved with the node based and arc based formulations by using CPLEX 8.0. Preliminary computational analysis shows that, arc based formulation outperforms the node based formulation in terms of linear programming relaxation.
doi:10.1063/1.3636940 fatcat:likgmwdjbnfatf4rltems5gwwm