An integrated model and solution approach for fleet sizing with heterogeneous assets

This paper addresses a fleet-sizing problem in the context of the truck-rental industry. Specifically, trucks that vary in capacity and age are utilized over space and time to meet customer demand. Operational decisions (including demand allocation and empty truck repositioning) and tactical decisions (including asset procurements and sales) are explicitly examined in a linear programming model to determine the optimal fleet size and mix. The method uses a time–space network, common to fleet-management problems, but also includes capital cost decisions, wherein assets of different ages carry different costs, as is common to replacement analysis problems. A two-phase solution approach is developed to solve large-scale instances of the problem. Phase I allocates customer demand among assets through Benders decomposition with a demand-shifting algorithm assuring feasibility in each subproblem. Phase II uses the initial bounds and dual variables from Phase I and further improves the solution convergence without increasing computer memory requirements through the use of Lagrangian relaxation. Computational studies are presented to show the effectiveness of the approach for solving large problems within reasonable solution gaps.