Abstract
The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station must be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances.
Highlights
The task of repositioning a commodity from one location to another is a well-known problem arising in different contexts such as logistics, transportation, and various disciplines, notably industrial engineering and operations management
The aggregate average results for instances containing 20, 30, 40, 50, and 60 stations are reported in Tables 2 and 3, where Instance group denotes the set of 10 instances of a particular group; UB1 Gap (%), UB2 Gap (%), and Gap (%) correspond to the gap between UB1, UB2, and the upper bound found by Erdogan et al (2015), respectively, and the lower bound reported in Erdogan et al (2015); Time (s), UB1 Time (s), and UB2 Time (s) indicate, respectively, the CPU time in seconds spent by Erdogan et al (2015), TS1, and TS2, where the last two are scaled to our processor as mentioned above; Avg
Time (s) is the average CPU time in seconds spent by ILSSBRP to completion over the 10 runs; Avg
Summary
The task of repositioning a commodity from one location to another is a well-known problem arising in different contexts such as logistics, transportation, and various disciplines, notably industrial engineering and operations management. A practical application arises in self-service bike sharing systems (BSS), which are becoming increasingly popular in recent years. Users rent bikes and return them at stations distributed over a region. A vehicle with limited load capacity periodically collects and delivers bikes across different stations so as to rebalance the system. Alternatives to the street traffic are important because of its impact in urban congestion, and in the environment, commuting, and so on. Up to 2009, there were about 120 bike sharing programs around the world and, according to DeMaio (2009), they have a favorable impact on: decreasing traffic congestion, improving public health, and helping reducing the Working Paper level of CO2 emissions. One of the most famous systems is the Velib’ system in Paris, with 1800 stations and more than 20,000 bikes
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