A multiple objective stochastic approach to vehicle routing problem

Abstract

This research incorporates the concept of chance-constrained programming and multiple objective goal programming in the area of vehicle routing problem. The research led to the development of the model of the goal programming (GP) stochastic vehicle routing problem (SVRP) that allows decision-makers’ involvement in the solution process of problem for obtaining satisfactory solutions. Due to the complexity of the SVRP, a set of stations to be visited by a fleet of vehicles needs to be partitioned into feasible sets of routes, one for each vehicle enabling the application of the multiple objectives GP technique to each of the vehicle routes. The multiple objectives SVRP then consisted of the following two major stages: (1) route construction stage (RCS) and (2) route improvement stage (RIS). The RCS of the problem consists of the problem formulation and partitioning a set of stations into feasible sets of vehicle routes. Due to the complexity of the problem, only heuristic methods for solving SVRP are considered in this stage. On the other hand, the RIS of the problem consists of (1) problem formulation in which goals and probabilistic constraints are identified, (2) transformation of problem in (1) into an equivalent deterministic form, and (3) GP formulation of RIS in which priorities of various goals are identified. To solve the problems stated in the RCS and RIS of the problem, two interactive computer programs coded in Fortran computer language are developed. To test and validate the algorithm proposed in this research, two test problems, usually employed by other researchers, were took into consideration. A modification of the Clarke and Write algorithm is developed to determine the most favorable vehicle routes of the SVRP for the “E”-type problem. Additionally, two heuristic algorithms which are the modification of the Clarke and Wright “savings” approach are developed for solving the “F”-type problem. The E- and F-type problems are the name given to the equivalent deterministic form of the probabilistic cost minimization problem and total loading and unloading time minimization problem, respectively.