A Hybrid Metaheuristic to Solve the Resource Allocation Problem in Bike Sharing Systems

Abstract

Bike sharing systems have recently enabled sustainable means of shared mobility through automated rental stations. Spatio-temporal variation of bike rentals, however, leads to imbalances in the distribution of bikes causing full or empty stations. The resource allocation problem tackles imbalances at a tactical planning level by means of bike allocation and relocation. We propose a MIP formulation of an extended dynamic service network design model. The objective is to determine optimal fill levels at stations while minimizing the expected costs of relocation for the typical bike demand. The MIP formulation is hard to solve due to a large number of binary variables for relocations (stations times stations times periods). Thus, we present a hybrid metaheuristic integrating a large neighborhood search with exact solution methods provided by a solver. The large neighborhood search iteratively improves the solution with the help of limiting and controlling possible relocation regimes by a fix-and-optimize strategy, i.e. a small subset of “free” binary relocation variables. The majority of remaining binary variables are tentatively fixed to zero leading to a fast solvable truncated MIP of the resource allocation problem. Therefore, a commercial solver can provide a local optimal value based on the defined neighborhood, in a reasonable time. Results obtained indicate that the hybrid metaheuristic outperforms CPLEX for data from Vienna’s bike sharing system “Citybike Wien”.