This paper studies the winner determination problem under disruption and demand uncertainty from the perspective of fourth-party logistics platform. To hedge risks brought by double uncertainty, a hybrid mitigation strategy that integrates temporary outsourcing strategy and fortification strategy is developed. With the objective of minimizing total cost, a new two-stage stochastic winner determination model under double uncertainty is constructed, which is further transformed into mixed-integer linear programming model by using an improved sample average approximation algorithm based on the chi-square test and the Latin hypercube sampling method. To address the challenges brought by numerous demand and disruption scenarios in model solving, combining dual decomposition Lagrangian relaxation algorithm and scenario reduction approach, a sampling-based heuristic algorithm is proposed. To validate the effectiveness of our model and algorithm, a real case and several numerical examples including cases generated by using the Combinatorial Auction Test Suite are provided. The results of numerical examples and real case indicate that the proposed algorithm has superior performance to CPLEX, validating the effectiveness of model and methods. Sensitivity analysis results show that demand fluctuations and the magnitude of disruption probability have significant impacts on the selection of risk response strategies.