A game theoretic/network equilibrium solution for the railroad freight car management problem

The paper presents the development and solution procedures of a mathematical model of the management of a fleet of cars shared by autonomous profit maximizing managers faced with time-varying demands requiring shared service responsibility. Motivation for the model development arises from the freight car management problem, in which many railroads independently manage an interchangeable fleet of cars that serve customers with time-dependent origin-destination patterns; this often requires the cooperative service of more than one railroad. The problem is formulated as an N-person, noncooperative game played on a temporal-spatial network. An iterative sequential procedure is developed for which car management decisions for each railroad over a specified time horizon are based on the previously calculated optimized decisions of car management decisions for all other railroads. Several realistic test case problems are reported that exhibit rapid convergence to an equilibrium solution. It is proposed that this modeling procedure be used as a basis for evaluating (and possibly generating optimal) interrailroad agreements for the exchange of empty freight cars.