Evaluation of three collaboration and profit sharing methods for carriers in pickup-and-delivery problems

This study examines three methods of collaboration and profit-sharing for less-than-truckload (LTL) carriers. The collaboration methods are evaluated under the scenario that all participating carriers share some or all of their pickup and delivery jobs with a central authority who will assign jobs to carriers and determine optimal vehicle routes to maximize profit. The novelty of this work is that it allows carriers to retain some of their jobs. Collaboration Method 1 is a two-step approach where the first step involves the central authority determining the job allocation for the shared jobs and the vehicle routes for each carrier that includes their retained and allocated jobs to maximize total profit. The second step involves dividing the total profit among the carriers using a contribution-based profit-sharing model. Collaboration Method 2 is a one-step approach where the central authority simultaneously determines the job allocation and vehicle routes, and at the same time allocates profit to the carriers with fairness constraints included in the model. Collaboration Method 3 is also a two-step approach similar to Method 1, except that in the first step, the central authority determines the job allocation and vehicle routes for only the shared jobs (not including retained jobs). Mathematical models and solution algorithms based on large neighborhood search (LNS) are proposed for all three methods. The numerical experiments are conducted using hypothetical networks with up to 30 jobs and 3 carriers. Results indicate that on an average the total profit from Method 1 is 5.3% higher than that of Method 2 and 11.88% higher than that of Method 3. The total profit from Method 2 is 6.60% higher than that of Method 3.