Mathematical modeling and optimization of multi-period fourth-party logistics network design problems with customer satisfaction-sensitive demand

Abstract

In the current customer-driven logistics environment, customer satisfaction has become a critical factor influencing demand. When services differ from expectations, customers often exhibit bounded rational behavior. However, existing research on fourth-party logistics (4PL) network design commonly ignores the impact of customer satisfaction and psychological behaviors on demand, creating a significant gap between current models and customer-centric demands. To address this gap, this work proposes a multi-period 4PL network design problem with demand sensitive to customer satisfaction considering bounded rational behavior. First, a novel mixed integer non-linear programming model is developed to maximize profit under investment budget and service level constraints. Second, due to the NP-hardness and non-convexity, an integration-driven Q-learning based hyper-heuristic algorithm framework is proposed. To prevent reduced diversity and premature convergence resulting from over-exploitation of the global optimum, this algorithm efficiently selects suitable low-level heuristics by integrating both population and individual states with a corresponding adaptive reward function. Finally, the proposed algorithm is compared with eight commonly used algorithms and the exact solver CPLEX using different scale instances. The effectiveness and efficiency are demonstrated by numerical results. Furthermore, managerial insights are provided for investors. Company profit depends not only on investment, costs, and income, but also on customer satisfaction. Increasing the investment budget is more beneficial when the cost-income ratio is around the required service level. Customers with higher required service levels will bring greater profits when the budget is insufficient. Ignoring the impact of customer satisfaction on demand may result in the failure to achieve expected profits.