A less-than-truckload carrier collaboration planning problem under dynamic capacities

This paper addresses the deterministic dynamic single carrier collaboration problem for the small- to medium-sized less-than-truckload (LTL) industry. It is formulated as a binary (0–1) multi-commodity minimum cost flow problem and solved using a branch-and-cut algorithm. Its inherent network structure is exploited to generate the lower bounds to the branch-and-cut algorithm using the network simplex method and by relaxing the integrality constraints. Results from numerical experiments indicate inherent trade-offs at the higher degrees of collaboration between waiting for more affordable collaborative capacity and incurring higher holding costs. They also suggest that collaborating LTL carriers experience increased capacity utilization.