Multi-period fourth-party logistics network design with promised service time and regret behavior

Promised service time and regret behavior arising from deviations between promised and actual performance significantly influence fourth-party logistics (4PL) network design. This paper proposes a novel multi-period 4PL network design problem incorporating the promised service time decision and decision-makers’ regret behavior. First, promised service time ranges are determined by predicting transportation times of third-party logistics providers, enabling cost-effective promises to customers. A mixed integer non-linear programming model is formulated to maximize profit by characterizing the decision-makers’ regret behavior through regret theory. Second, an equivalent reformulation model is developed and solved using the exact solver CPLEX, efficiently addressing small and medium-scale regional networks. Moreover, a Q-learning based collaborative hyper-heuristic with global and local-spaces classification (QLCHH-GLSC) algorithm framework is proposed, ensuring suitability for larger-scale networks. Specifically, local search spaces are dynamically classified based on the solution obtained from the construction heuristic selected by global-driven Q-learning. Subsequently, local-driven Q-learning is designed to select the most suitable perturbation heuristic for each individual within these spaces. Finally, the effectiveness and efficiency of the proposed algorithm are demonstrated through numerical results compared to CPLEX and commonly used methods. Furthermore, some managerial insights are provided for 4PL managers. Strategically deciding on promised service time while considering regret behavior can enhance both service punctuality and profitability. Interestingly, in markets with a low impact from service deviations, regret-averse decisions driven by high-level regret ensure service quality and long-term profitability, while in high-impact markets, excessive conservatism will lead to profit losses without significantly improving punctuality.