Centralized Time-Dependent Multiple-Carrier Collaboration Problem for Less-Than-Truckload Carriers

This paper addresses a time-dependent, centralized multiple-carrier collaboration problem (TD-MCCP) for the small to medium-sized less-than-truckload (LTL) industry. The TD-MCCP represents a strategy in which a central entity (such as a third-party logistics firm) seeks to minimize the total system costs of an LTL carrier collaborative that consists of multiple carriers by identifying collaborative opportunities over a shared network under three rate-setting behavioral strategies and a leasing alternative. In contrast to conventional time-dependent network problems that view demand as dynamic, capacities in the proposed LTL multiple-carrier collaborative framework are time-dependent but known a priori, and demand is fixed. The TD-MCCP is modeled as a binary (0–1) multi-commodity minimum cost-flow problem formulation for two rate-setting behavioral cases and solved with a branch-and-cut algorithm. The first case examines the effect of one rate-setting behavioral strategy at a time, and the second case examines the effect of multiple rate-setting behavioral strategies simultaneously. Numerical experiments are conducted to seek insights into the computational performance of the TD-MCCP formulations under various network sizes and numbers of shipments. The results indicate that the attractiveness of the time-dependent multiple-carrier collaboration paradigm increases with a volume-oriented rate-setting strategy. Also, a volume-oriented rate strategy has the potential to increase the capacity utilization of carriers seeking to minimize empty-haul trips. Finally, the leasing alternative can serve as a viable option for a centralized collaborative system, especially when affordable collaborative capacity is scarce.