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The static bike rebalancing problem (SBRP) concerns the task of repositioningbikes among stations in self-service bike-sharing systems. This problem can beseen as a variant of the one-commodity pickup and delivery vehicle routingproblem, 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 maytemporarily 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 indefault. Both cases require further visits in order to meet the actual demandsof such station. This paper deals with a particular case of the SBRP, in whichonly a single vehicle is available and the objective is to find a least-costroute 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 should beappropriately determined in order to respect such constraints. We propose aniterated local search (ILS) based heuristic to solve the problem. The ILSalgorithm was tested on 980 benchmark instances from the literature and theresults obtained are quite competitive when compared to other existing methods.Moreover, our heuristic was capable of finding most of the known optimalsolutions and also of improving the results on a number of open instances.

A heuristic algorithm for a single vehicle static bike sharing rebalancing problem