Transportation cost allocation on a fixed route

• Five fairness criteria are analyzed based on comprehensive practical consideration.
• Allocation models and algorithms are developed to satisfy multiple fairness axioms.
• Allocation method has stable performance for both optimal and non-optimal routes.
• Computational studies validate the advantages by comparison with multiple methods.

A fundamental problem for determining the service cost in logistics is to allocate the transportation cost on a given route. Our real application usually has 5–20 customers per route, and the routing to all customers or any subsets of customers may not be optimal with respect to total distance travelled. To identify the objective and evaluate different cost allocation methods, five fairness criteria are introduced. We investigate a number of popular allocation mechanisms to identify their properties on fairness and feasibility for implementation. A contribution constrained packing model is proposed to consider these multiple fairness criteria for cost allocation. To determine the proper parameters in our model for different routes, a modified Nelder–Mead algorithm with a simplex enlargement operation is introduced. Two approximation methods for computing excess rate, an important measure of a fair allocation, are analyzed and the original routing sequence approximation is recommended for application. Through a computational study, we demonstrate that our method satisfies an important set of fairness axioms and improves cost allocation from the existing allocation schemes within acceptable time requirements.