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 identif