Balancing fleet size and repositioning costs in LTL trucking

This paper develops an optimization modeling approach for analyzing the trade-off between the cost of a larger fleet of tractors and the cost of repositioning tractors for a trucking company operating a consolidation network, such as a less-than-truckload (LTL) company. Specifically, we analyze the value of using extra tractor repositioning moves (in addition to the ones required to balance resources throughout the network) to reduce the fixed costs of owning or leasing a tractor fleet during a planning horizon. We develop network flow optimization models, some with side constraints and nonlinear objective functions, using event-based, time-expanded networks to determine appropriate fleet sizes and extra repositioning moves under different repositioning strategies, and we compare the optimal costs of the strategies. For repositioning costs, two different cost schemes are explored: one linear and one nonlinear. Computational experiments using real data from a national LTL carrier compare the total system costs obtained with four different strategies and show that extra repositioning may indeed enable fleet size reductions and concomitant cost savings.