Solving a New Multi-Period Mathematical Model of the Rail-Car Fleet Size and Car Utilization by Simulated Annealing

Abstract

There is a significant interaction between sizing a fleet of rail cars and its utilization. This paper presents a new multi-period mathematical model and a solution procedure to optimize the rail-car fleet size and freight car allocation, wherein car demands, and travel times, are assumed to be deterministic, and unmet demands are backordered. This problem is considered NP-complete. In other words, the traditional exact optimization approaches cannot solve a real-life size problem of this kind in a reasonable time. To tackle this problem, an efficient meta-heuristic algorithm based on simulated annealing (SA) is proposed. This algorithm works efficiently on a neighborhood search within solution space and probable acceptance of inferior solutions to escape from being trapped in local optima. A number of numerical examples are solved to check for efficiency and validity of the proposed SA algorithm. We conclude that the proposed model and algorithm are useful to identify good strategies for the sizing of rail car fleets and allocation of related cars.