Full‐load route planning for balancing bike sharing systems by logic‐based benders decomposition

Abstract

Public bike sharing systems require some kind of rebalancing to avoid too many rental stations of running empty or entirely full, which would make the system ineffective and annoy customers. Most frequently, a fleet of vehicles with trailers is used for this purpose, moving bikes among the stations. Previous works considered different objectives and modeled the underlying routing problem in different ways, but they all allow an arbitrary number of bikes to be picked up at some stations and delivered to other stations, just limited by the vehicles' capacities. Observations in practice, however, indicate that in larger well-working bike sharing systems drivers almost never pickup or deliver only few bikes, but essentially always approximately full vehicle loads. Many stations even require several visits with full loads. Due to budgetary reasons, typically only just enough drivers and vehicles are employed to achieve a reasonable balance most of the time, but basically never an ideal one where single bikes play a substantial role. Consequently, we investigate here a simplified problem model, in which only full vehicle loads are considered for movement among the rental stations. This restriction appears to have only a minor impact on the achieved quality of the rebalancing in practice but eases the modeling substantially. More specifically, we formulate the rebalancing problem as a selective unit-capacity pickup and delivery problem with time budgets on a bipartite graph and present a compact mixed integer linear programming model, a logic-based Benders decomposition and a variant thereof, namely branch-and-check for it. For the general case, instances with up to 70 stations, and for the single-vehicle case instances with up to 120 stations are solved to proven optimality. A comparison to leading metaheuristic approaches considering flexible vehicle loads indicates that indeed the restriction to full loads has only a very small impact on the finally achieved balance in typical scenarios of Citybike Wien.

Shared mobility systems: an updated survey

“…The problem was solved by means of an enhanced version of a local search metaheuristic called chemical reaction optimization (CRO), which performed better than a truncated version of CPLEX and than the original CRO version. Kloimüllner and Raidl [2017] observed than in large bicycle sharing systems, bicycles are typically picked up in full trucks loads as opposed to partial loads. Making this restriction considerably simplifies the modeling of the problem and has only a marginal effect on solution quality, namely on the case of Citybike Wien.…”

Dynamic Rebalancing Optimization for Bike-Sharing System Using Priority-Based MOEA/D Algorithm

“…After the first stage, due to the reduction of scale of the station in need of rebalancing, the truck with the least inventory quit service in the remaining stages and the other 2 trucks continue the rebalancing work until the end of the horizon. Three initial quantities of truck load when departing from the depot are compared, which includes 60 (fully loaded [54]), 30 (half loaded [26]) and 0 (empty loaded [55]). For each amount of truck load, 20 runs of the optimization using PB-MOEA/D are conducted, and the result is shown in Figure 7.…”

Logic-Based Benders Decomposition for Large-Scale Optimization

“…LBBD has been applied to a variety of additional scheduling and logistics problems. In the transportation logistics domain, they include food distribution [110], bicycle sharing [73,74], lock scheduling [123], and supply chain scheduling [115]. Other applications are project scheduling [70], robust call center scheduling [28], task scheduling for satellites [129], course timetabling [19], wind turbine maintenance scheduling [42], queuing design and control [113,114], service restoration planning for infrastructure networks [50], and sports scheduling [23,94,95,120,121].…”