Optimising a mathematical model for a multi-sized public bicycle sharing system considering built-in control centres under fuzzy demand, a case study

A public bicycle sharing system makes bikes available for users to travel from one station to another in a city. Bicycles are repaired after getting used by users at the control centres if needed and then returned to their source bike station. There are very essential decision criteria to build a bicycle sharing system, the most important of which are the exact number and location of bike stations and control centres, the number of bicycles, and the number of docks in each station. This paper presents a single-objective nonlinear mathematical model for the bicycle sharing problem to minimise the system's total cost considering built-in control centres. Subjective distance is mentioned in this article so that distance-dependent costs become closer to real urban conditions. In this article, two exact and - heuristic methods are considered for solving the problem. Also, the applicability of the proposed model is examined through a real case study. After validating the model in a small dimension, the model is solved by a grasshopper optimisation algorithm in a large scale, and different numerical tests are developed.