Mixed Integer Linear Programming Model for Vehicle Routing Problem for Hazardous Materials Transportation

Abstract

This paper presents a mathematical model to solve the Heterogeneous Vehicle Routing Problem (HVRP) in the context of hazardous materials (HazMat) transportation. To evaluate the model a linear approximation of the total routing risk is used as objective function. In the first stage a routing risk measure is proposed as a nonlinear function of the truck load. This function is approximated by means of two different piecewise linear functions (PLF). A genetic algorithm is employed to estimate the interval limits of PLF. These two functions are utilized to approximate the total routing risk for the best known solution for the benchmark instances of HVRP with fixed costs and unlimited fleet, both approaches are compared with the nonlinear risk function value. In the second stage the best piecewise linear approximation of the routing risk is integrated to a mixed integer linear programming (MILP) model for solving the risk optimization problem. The final model is tested on HVRP instances with 20 nodes. Results show that total cost minimization and total risk minimization appear to be conflicting objectives.