Two-stage Stochastic Optimization Problem Under Feasibility Chance-constrained

Two-stage stochastic optimization problem under feasibility chance-constrained has a wide range of applications in industrial production,logistics transportation,planning location and other fields.Many scholars are very concerned about modeling and solving algorithms.Two-stage stochastic optimization problem under feasibility chance-constrained is a typical stochastic optimization problem,which can be transformed into a large-scale mixed integer programming problem under some assumptions.Based on the model structure,it is crutical to construct a fast and effective decomposition algorithm to solve such problems.From the perspective of model analysis and decomposition algorithm construction,this paper studies two types of two-stage stochastic optimization problem under feasibility chance-constrained: Two-stage stochastic mixed 0-1 optimization problem based on the chance constraint and Two-stage stochastic lot-sizing problem based on the chance constraint.For two-stage stochastic mixed 0-1 optimization problem with the chance constraint,this paper considers a two-stage model with only 0-1 variables in the first stage and mixed 0-1 variables in the second stage.By introducing 0-1variables and using a bilinear transformation strategy to deal with the chance constraint,combined with the branch and bound algorithm and the bilinear Benders decomposition algorithm,we propose a type of branch-bilinear Benders cutting plane algorithm,where the ‘‘no–good” cut and strengthen liftingand-project cut are used to deal with the infeasible solution of master problem and the convex hull of the approximating scenario subproblem,respectively.In order to test the effectiveness of the model and algorithm,we conducted numerical experiments on the server location problem to verify the effectiveness of the algorithm proposed in this paper.For the two-stage stochastic lot-sizing problem with the chance constraint,this paper uses the simple recourse property of the problem,the bilinear model is equivalently transformed into a linear new model that is easier to solve.According to the structure and information of the constraints,two types of valid inequalities are applied to the new model.Numerical experiments verify that the proposed new model and basic mixing inequality are effective for solving this problem.