Models and Heuristics for the Flow-Refuelling Location Problem

Purpose of this paper: Firstly, the paper serves as an overview of the emerging field of flow-refuelling location, which mainly occurs in the context of locating alternative-fuel (hydrogen, electric, liquefied natural gas and hybrid) vehicle refuelling stations. We aim to review and explain models and solution approaches, with a particular focus on mathematical programming formulations. Secondly, we propose a new heuristic for this problem and investigate its performance.

Design/methodology/approach: The subject scope of this paper is the flow-refuelling location model (FRLM). While in most location problems demand arises at customer locations, in so-called flow-capturing models it is associated with journeys (origin-destination pairs). What makes the FRLM even more challenging is that due to the limited driving range of alternative-fuel vehicles, more than one facility may be required to satisfy the demand of a journey. There are currently very few such refuelling stations, but ambitious plans exist for massive development – making this an especially ripe time for researchers to investigate this problem. There already exists a body of work on this problem; however different authors make different model assumptions, making comparison difficult. For example, in some models facilities must lie on the shortest route from origin to destination, while in others detours are allowed. We aim to highlight difference in models in our review. Our proposed methodology is built on the idea of solving the relaxation of the mixed-integer linear programming formulation of the problem, identifying promising variables, fixing their values and solving the resulting (so-called restricted) problems optimally. It is somewhat similar to Kernel Search which has recently gained popularity. We also use a parallel computing strategy to simultaneously solve a number of restricted problems with less computation effort for large-sized instances.

Findings: Our experimental results show that the proposed heuristic can find optimal solutions in a reasonable amount of time, outperforming other heuristics from the literature.

Value: We believe the paper is of value to both academics and practitioners. The review should help researchers new to this field to orient themselves in the maze of different problem versions, while helping practitioners identify models and approaches applicable to their particular problem. The heuristic proposed can be directly used by practitioners; we hope it will spark further works on this area of logistics but also on other optimisation problems where Kernel Search type methods can be applied.

Research limitations: This being the first paper applying a restricted-subproblem approach to this problem it is necessarily limited in scope. Applying a traditional Kernel Search method would be an interesting next step. The proposed heuristic should also be extended to cover for more than just one FRLM model: certainly the capacitated FRLM, the FRLM with deviation, the fixed-charge FRLM and the multi-period FRLM should be investigated.

Practical implications: Our work adds to a body of research that can inform decisionmakers

at governmental or international level on strategic decisions relating to the establishment or development of alternative-fuel refuelling station networks.