Bi-objective optimization for customers’ satisfaction improvement in a Public Bicycle Sharing System

In recent years, the popularity of the Public Bicycle Sharing System (PBSS) for urban transportation is increasing. The fleet size of the system and the capacity of its stations are some key factors in establishing a successful sharing system. These factors affect the number of rejected demands and the lack of free docks for returning bicycles because of demand variation at stations. This paper presents a bi-objective optimization solution for PBSS in which the first objective function minimizes the mean number of rejected requests for renting bikes and free docks for returning bikes per each satisfied demand. In other words, this function tries to minimize the mean number of dissatisfied users per each replied demand for renting. The second objective function minimizes the total number of bicycles and docks of the system. The goal is to minimize users’ dissatisfaction with the least possible fleet size considering capacity constraints. The model is discussed under Jackson Network and the Mean Value Analysis (MVA). Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to solve and examine the efficiency of the proposed model via different numerical examples.