Cost allocation for less-than-truckload collaboration among perishable product retailers

We study cost allocation problem arising from less-than-truckload collaboration among perishable product retailers. The relevant costs we consider include fixed transportation cost, variable transportation cost, and decay loss of perishable products. Cooperative game theory is applied to study this cost allocation problem. The corresponding cooperative game, called transportation facility choice game, is established. First, we show that the core of the transportation facility choice game is non-empty. Then, we identify some conditions for concavity and quasi-concavity of the transportation facility choice game with the linear decay and negative exponential decay functions, respectively. Finally, simulation is conducted to analyze how optimal solutions differ under the linear decay and exponential decay functions, and intuitive cost allocation schemes are proposed and compared with the \(\tau \)-value and the Shapley value of the corresponding game. Simulation results show that the optimal solution under linear decay function tends to choose facilities with higher fixed cost than that under exponential decay function. Additionally, among all the cost allocation schemes compared, the simple cost allocation scheme called A-IM, the \(\tau \)-value, and the Shapley value have better performance in terms of the percentage of allocations lying in the core.