Mathematical Modeling And Algorithms For Two Kinds Of Stochastic Optimization Problems In Supply Chain Under Uncertainty

Recently,the research on supply chain operation and coordination under un-certain environment is increasingly con concerned by the academic community and business community.A supply chain planning is a network of suppliers,man-ufacturing plants,warehouses,and distribution channels organized to acquire raw materials,convert these raw materials into specified final products,and distribute these products to customers.In the optimized process of supply chain,the biggest challenge stems from the existence of some random factors in the system.How to coordinate the interests of various participants in the supply chain,and to the maximum extent to match the supply in upstream and demand in downstream,has always been the key research field for the supply chain planning.In this paper,we mainly focus on two types of supply chain stochastic opti-mization problems,which respectively based on uncertainty of demand and both the demand and capacity uncertainties.The specific content would be included the following two aspects:First,for the case of demand uncertainty,we construct a new two-stage s-tochastic optimization model of supply chain with multiple factories and distribu-tors for perishable product.By introducing a second-order stochastic dominance constraint,we can describe the preference consistency of the risk taker while min-imizing the expected cost of company.To solve this problem,we convert it into a one-stage stochastic model equivalently;then we use sample average approx-imation method to approximate the expected values of the underlying random functions.A smoothing penalty function approach is proposed with which we can get the global solution and avoid introducing new variables and constraints.Meanwhile,we investigate the convergence of an optimal value from solving the transformed model and show that,with probability approaching one at expo-nential rate,the optimal value converges to its counterpart as the sample size increases.Numerical results show the effectiveness of the proposed algorithm and analysis.Second,for the uncertain capacity and demand,we establish a multi-source supply chain stochastic optimization model with decisions truncated by random variables,which is more suitable the actual situation.The model is a non-convex problem because the decisions truncated by the random capacity in the objec-tive function.To solving such non-convex optimization problems,we use a novel transformation technique to convert non-convex problems into a equivalent con-vex optimization problems.Similarly,we apply the sample average approxima-tion method to approximate the expected value function,and also deal with the un-smoothness of the plus function in the model by constructing a smoothing function,which can be differentiable and maintain global convergence of the o-riginal problem.Then the model is converted into a general non-linear integer programming problem eventually.The numerical tests are performed to show the effectiveness of the multi-source supply chain optimization model with random variables truncation and algorithm.