Use of a fuzzy theory technique for grouping of trips in the vehicle routing and scheduling problem

A technique of grouping trips on the basis of their similarity is presented. It is to be used in conjunction with any of the existing routing and scheduling models of demand responsive transportation (DRT) vehicles. The proposed approach treats the similarity of two trips as a fuzzy relation. For a given trip pair, the level of similarity is defined by the membership grade of the fuzzy relation for different attributes of the trips. The composite similarity of the trip pair is then computed by a fuzzy integral. Based on the matrix of the composite similarity, trip groups are identified by connecting trip pairs whose membership grade is greater than a given value. The technique allows grouping of trips when the total number of trips is very large, without losing the flexibility of the manual grouping process. It permits the selection of different similarity criteria, different values of weights among the criteria and the cut-off point of similarity grade depending on the requirements of the day. This is possible by expressing the similarity as a fuzzy relation. The technique can be used as part of pre-screening of the original set of trips before any of the existing scheduling algorithms is applied.