A multiple type bike repositioning problem

This paper investigates a new static bicycle repositioning problem in which multiple types of bikes are considered. Some types of bikes that are in short supply at a station can be substituted by other types, whereas some types of bikes can occupy the spaces of other types in the vehicle during repositioning. These activities provide two new strategies, substitution and occupancy, which are examined in this paper. The problem is formulated as a mixed-integer linear programming problem to minimize the total cost, which consists of the route travel cost, penalties due to unmet demand, and penalties associated with the substitution and occupancy strategies. A combined hybrid genetic algorithm is proposed to solve this problem. This solution algorithm consists of (i) a modified version of a hybrid genetic search with adaptive diversity control to determine routing decisions and (ii) a proposed greedy heuristic to determine the loading and unloading instructions at each visited station and the substitution and occupancy strategies. The results show that the proposed method can provide high-quality solutions with short computing times. Using small examples, this paper also reveals problem properties and repositioning strategies in bike sharing systems with multiple types of bikes.published_or_final_versio

A Study of the Static Bicycle Reposition Problem with a Single Vehicle

The Bicycle Sharing System (BSS), a public service system operated by the government or a private company, provides the convenient use of a bicycle as a temporary method of transportation. More specifically, this system allows people to rent a bike from one location, use it for a short time period and then return it to either to the same or a different location for an inexpensive fee. With the development of IT technology in the 1990s, it became possible to balance the bicycle inventory among the various destinations. In fact, a critical aspect to maintaining a satisfactory BSS is effectively rebalancing bicycle inventory across the various stations. In this research, we focus on the static bicycle repositioning problem with a single vehicle which is abstracted from the operation issue in the bicycle sharing system. The mathematical model for the static bicycle reposition problem had been created and several variations had been analyzed. This research starts to solve the problem from a very restrictive and constrained model and relaxes the constraints step by step to approach the real world case scenario. Several realistic assumptions have been considered in our research, such as a limited working time horizon, multiple visit limitation for the same station, multiple trips used for the vehicle, etc. In this research, we use the variable neighborhood search heuristic algorithm as the basic structure to find the solution for the static bicycle reposition problem. The numeric results indicate that our algorithms can provide good quality result within short solving time. By solving such a problem well, in comparison to benchmark algorithms, this research provides a starting place for dynamic bicycle repositioning and multiple vehicle repositioning