Scheduling Demand‐Responsive Transportation Vehicles using Fuzzy‐Set Theory

A scheduling algorithm for the time‐window‐based, many‐to‐many, dial‐a‐ride problem is presented. The algorithm is based on two steps: developing the initial route and inserting leftover trips. These two steps are applied to the scheduling of one vehicle at a time. The paper introduces fuzziness in the values of two basic input parameters, travel time and the desired time of vehicle stop, and applies fuzzy‐arithmetic rules and logic to develop the schedules. Since travel time is fuzzy, the possibility of inserting a stop between two existing stops is evaluated by fuzzy grade. Further, the degree that the arrival time of the vehicle satisfies the desired time of the passenger is evaluated by the intersection of two fuzzy sets: arrival time and desired time of vehicle arrival. Thus, the feasibility of inserting a stop between two existing stops is evaluated by two criteria: (1) The feasibility of stopping at the stop; and (2) user satisfaction. Threshold values that specify the minimum acceptable level of stopping possibility and passenger satisfaction are introduced to evaluate the acceptability of the schedule. The proposed approach allows the dispatcher to develop different sets of schedules based on his judgment of the balance between supply and demand. The schedules may vary from a conservative (reliable) schedule requiring a large number of vehicles to a “risky” (unreliable) schedule requiring a small number of vehicles. The method should be useful for making schedules when travel time is not certain and has a large variation, such as the scheduling of vehicles in an urban area.