Fourth-party logistics network design under uncertainty environment

A novel fourth-party logistics (4PL) network design problem under uncertainty environment is studied in the current work. Demand uncertainty and two types of disruptions, facility and third-party logistics (3PL) disruptions, are simultaneously considered. To minimize the total cost, a two-stage stochastic programming model is presented, which is further approximated as a mixed-integer linear programming model using the sample average approximation (SAA) method. As a large number of disruption and demand scenarios generated in the approximation process lead to challenges in model solving, the scenario reduction (SR), SAA, dual decomposition and Lagrangian relaxation (DDLR) approaches are integrated to present an SR-DDLRSAA algorithm. The effectiveness of our model and algorithm is illustrated by adopting numerical instances and real-life cases. A comparative analysis indicates that the impact of disruptions on the 4PL network is closely related to the values of the disruption probability and the fluctuation degree of uncertain demand. Furthermore, we extend the proposed basic model by considering demand uncertainty and three types of disruptions, namely supply, facility, and 3PL disruptions, and analyze the impact of supply disruption on the 4PL network.