The urban transport planning with uncertainty in demand and travel time: a comparison of two defuzzification methods

Nowadays the traffic congestion is being a common problem in major cities, every time the travel time is increasing and also the number of private cars. It is urgent to take actions to solve this problem. The urban transport is becoming into the best way to fight against congestion; but to make it more attractive to users it has to be more efficient (less travel time, less waiting time, low fare). The urban transport process has four main activities: Network design, Timetabling, Vehicle scheduling and Crew scheduling. The problem presented here is about the integration of the frequency and departure time scheduled both are subactivities of the timetable construction, besides it includes multiple periods planning and multiperiod synchronization, also the authors consider uncertainty in demand and travel time using fuzzy numbers. The planners faced this problem everyday. The authors created a mathematical model including the characteristics previously mentioned, the objectives of this model are to minimize the total operation cost, to maximize the number of multiperiod synchronization between routes, and to minimize the total waiting time for passengers. The SAugmecon method is used to solve the problem, 32 instances were randomly generated based on real data, and the comparison of two defuzzification methods (k-preference and second index of Yager) is presented. Also, the comparison of the problem with uncertainty on demand and uncertainty on demand and travel time is presented.