Contract design for the fourth party logistics considering tardiness risk

Nowadays, tardiness has become a significant risk in the logistics industry. To address this problem, we introduce the tardiness risk index to quantify both the magnitude of the tardiness risk and the maximum probability of tardiness occurring. In this paper, we investigate the contract design problem with the tardiness risk index to mitigate the tardiness risk when a fourth-party logistics company (4PL) delegates the delivery task of a client to a third-party logistics company (3PL). Specifically, the contracts are designed in a decentralized system with information symmetry and information asymmetry when 3PL is risk neutral and risk averse. Furthermore, the incentive problems demonstrated that the 3PL is encouraged to make the optimal effort for delivery and the 4PL determines the optimal fixed payment and penalty coefficient. Through analyzing the experimental simulation results, we can find that the contract can effectively mitigate the tardiness risk and the maximum probability of risk occurrence.