The Solution of Vehicle Scheduling Problems with Multiple Objectives in a Probabilistic Environment

Vehicle Scheduling Problem (VSP) is a generic name given to a whole class of problems involving the visiting of "stations" by "vehicles," where a time is associated with each activity. The studies performed to date have the common feature of a single objective while satisfying a set of restrictions and known customer supplies or demands. However, VSPs may involve relevant multiple objectives and probabilistic supplies or demands at stations, creating multicriteria stochastic VSPs. This paper proposes a heuristic algorithm based on goal programming approach to schedule the most satisfactory vehicle routes of a bicriteria VSP with probabilistic supplies at stations. The two relevant objectives are the minimization of the expected travel distance of vehicles and the minimization of the due time violation for collection service at stations by vehicles. The algorithm developed consists of three major stages. In the first stage, an artificial capacity of vehicle is determined, on the basis of decision maker's subjective estimates. The second one clusters a set of stations into subsets by applying an efficient cluster method developed. In the third one, the stations in each subset are scheduled by applying an iterative goal programming heuristic procedure to each cluster.