A new multi-objective optimization formulation for rail-car fleet sizing problems

With potential application to a variety of industries, fleet sizing problems present a prevalent and significant challenge for engineers and managers. This is especially true of applications involving rail cars, where origins and destinations have capacity restrictions. This paper presents a new multi-objective optimization formulation, solution method, and analysis for multi-periodic fleet sizing problems of various sizes. Profit and quality (minimal unmet demands) represent conflicting objectives and are maximized simultaneously. The Pareto optimal set is depicted and is used for trade-off analysis. The solution involves the optimal fleet size as well as the optimal rail-car allocation strategy. The proposed approach is applied to an example problem and is shown to be successful, ultimately providing a new managerial tool for planning and analyzing rail-car fleets more effectively.