| Determining the optimal size of a fleet, in general, involves decisions from three levels of hierarchy: strategic, tactical, and operational. While decisions based on each level have traditionally been examined separately, they are economically interdependent and must be analyzed simultaneously to minimize total costs over the planning horizon. This research addresses a rental fleet sizing problem (RFS) in the context of the truck rental industry, subject to uncertain customer travel time, and non-stationary customer demand that is dependent on geographical location, time, and the economic cycle of the industry. We integrate tactical (asset purchases and sales) and operational (empty truck movement and vehicle assignment) decisions, with the explicit incorporation of an asset age factor, to achieve lower cost solutions. The unique model has led to a Two-Phase algorithm solution approach to deal with large-scale RFS problems—Phase I Benders decomposition with the development of the demand-shifting feasibility algorithm allocates customer demand efficiently among available assets by asset type and age. Different initial demand allocation schemes and the benefits of the derived inequalities are discussed in regards to solution quality and computational performance. By taking advantage of the initial bounds and dual variables from the Benders procedure, Phase II Lagrangean relaxation further improves the solution convergence as well as reduces the computational expense. To apply subgradient optimization, a network flow sub-problem can be solved to convert Lagrangean lower bound solution as well as to update the upper bound. For practical large-sized problems, spatial aggregation is studied through p-median location analysis; also end-of-horizon effects are also examined on a numerical basis. Comprehensive computational studies are presented to show the good quality and efficiency of the algorithm, as well as scenario-based analysis to provide insights into the truck rental business. The solutions to this research consist of asset movement decisions for both loaded and empty trucks, and asset procurement/disposal decisions over time and location. Altogether, it provides rental transportation industry with an effective tactical/operational decision support tool. |
