Two-Stage emergency material scheduling based on benders decomposition considering traffic congestion after a disaster

This study establishes a stochastic mixed integer nonlinear programming model for a two-stage emergency multiclass material scheduling problem considering traffic congestion with a Bureau of Public Roads (BPR) function. The generalized Benders decomposition (GBD) algorithm is used to solve the model on the basis of the characteristics of the decomposable structure and nonlinear convex function. To prove the effectiveness of the GBD algorithm, we set up a 30-node medium-scale case and a 50-node large-scale case for experimental demonstration and compared the GBD algorithm with the simple branch and bound (SBB) and discrete and continuous optimization solvers. Results show that for the medium-scale experiment, the gap between the so-lution results of the GBD algorithm and the ones of SBB or other solvers is less than 0.2%. The solution time of the GBD algorithm is only half of the time of SBB and other solvers. The large-scale case of 50 nodes cannot be solved by the SBB or other solvers, whereas the GBD algorithm can solve it normally, and the results are reasonable. In large-scale cases with more than 50 nodes, the GBD algorithm is more effective and efficient compared with SBB and other solvers. The sensitivity of the correlation coefficient alpha in the BPR function was analyzed. The actual expected total cost increases with the increase in the value of alpha. Its solving results are accurate and reasonable, proving that the results are more practical and applicable after adding the BPR function.