A bankruptcy approach to solve the fixed cost allocation problem in transport systems

In this paper, we study the allocation of a fixed cost among different cities involved in a line-shape transport system like a tram line or a railway. The central characteristic of the problem is that the intended cost is not depending on the infrastructure length or the use intensity. Estañ et al. (Ann Oper Res 301(1):81–105, https://doi.org/10.1007/s10479-020-03645-1 , 2021) originally introduced the problem and axiomatically studied it. Based on the well-known bankruptcy problem and game, we analyze it by applying two other approaches. First, adding a parameter, we take into account the municipalities revenues in the determination of cost shares. That enables one to transform a fixed cost allocation problem (FCAP) into a well-known bankruptcy one. We propose two bankruptcy problems for FCAP and use the proportional, adjusted proportional, constrained equal awards, constrained equal losses, and Talmud rules to solve it. Then, we define two bankruptcy games corresponding to FCAP and use the Shapley value for cost allocation. The characteristic functions have attractive interpretations; one considers the agents’ minimum desire to contribute to the cost, and the other does their minimum expectation from the overall profit. We investigate presented solutions if they meet some fairness and stability properties. Finally, we apply the suggested approaches to a practical problem.