Provide an Optimal Transportation Model for Urban Travelers with a Risk-Based Approach

In this research, the risks that can influence the development of an optimal transportation model were taken into account to present an optimal public transport model that considers risks. This is an applied desk and field research. GAMS were used for modeling and solving the model. The mathematical model is a combination of passengers and means of transportation and involves risk planning associated with the means of transportation in the system which should be used by travelers who are in known geographical locations and each require a specific service. At the same time, a time limit for service and a certain late payment are defined for each customer. The means of transportation in the system are different in terms of speed of transportation, cost per time unit, and their ability to travel to the customers' locations. At any time, each mean of transportation can transport one passenger and must return to the origin for the exchange of passengers. The objective function of the proposed model includes the optimal allocation of cost and risk minimization of passengers, as well as determination of the optimal routes for each vehicle, and is aimed at minimizing the costs of transportation, service and latency. An applied example is presented at the end.