Two Formulations for Minimizing Weight-Distance Objective in Single Vehicle Routing Problem with Quadratic, Cubic Objective Function and its Linearization

Here we consider a single vehicle routing problem (of unlimited capacity and capacity constraint can be easily included) that visits different dealers. As it visits the first dealer, it offloads the demand of first dealer and moves on to second dealer ‘lighter’, and so on. Fuel consumption depends on both weight carried and distance travelled. In this context we seek to minimize weight-distance travelled by the vehicle for the entire tour. We give two formulations of the above problem that has received very little or no attention in literature. It results in a ‘cubic’ and ‘quadratic’ terms in the objective function with negative cost coefficients in one formulation and positive cost coefficients (of ‘cubic’ and ‘quadratic’ terms) in other formulation. We give two linearization schemes for the two formulations. One linearization has less number of constraints and is expected to be more efficient CPU time wise.