Multi-period fourth-party logistics network design with the temporary outsourcing service under demand uncertainty

In this paper, a novel multi -period fourth party logistics (4PL) network design problem integrating the temporary outsourcing service under demand uncertainty is studied, in which the temporary outsourcing strategy is proposed to accommodate uncertain demand overflows. To address this problem, a two -stage stochastic programming model is formulated. Using the Latin hypercube sampling approach, a mixed integer linear programming reformulation model is provided. To deal with the challenges of sampling in solving efficiency, an improved sample average approximation method is proposed by integrating an improved subgradient algorithm with the dual decomposition and Lagrangian relaxation technique. Computational results of several numerical instances followed by a real -life case clearly support the applicability and effectiveness of the proposed model and algorithm. Comparative analysis shows that integrating temporary outsourcing service into multi -period 4PL network design indeed changes the 4PL network structure and enhances the supply chain performance at a lower overall cost.