| This paper introduces the development of stochastic programming systematically while summarizing and analyzing the fruits on this field in the past. Based on the study of some researchers, we study stochastic programming systematically, especially on how to solve stochastic programming with recourse with warm-start interior point methods.First of all, we summarily introduce the generations development and current research situations as well as the classification about stochastic programming. And we introduce the models of stochastic programming with recourse systematically. Next, we introduce the interior point method briefly for solving convex optimization problem, especially introducing the path-following primal-dual algorithm in detail. And we summarize the "warm start strategies". We give the warm start interior point methods for solving linear programming and quadratic programming. The algorithm is convergent and it has polynomial-time complexity.Many researchers solve stochastic programming with recourse with specialized decomposition. While, we concentrate on "warm start strategies" and interior point methods. We give a warm start interior point methods for solving multi-stage stochastic linear programming which is extended to solve multi-stage quadratic stochastic programming. Theoretically we have proved that when the discrepancy among scenarios in the event tree is small adequately algorithm 3 is practical completely. The basic idea of our algorithm is as follows: First, we solve the small-scale problem corresponding to the reduced tree. Then we can obtain a starting point for the complete problem from the small-scale problem. Finally we solve the complete problem with long step path-following interior point algorithm.We introduce random variable in the model of stochastic programming with recourse so that our model is in complete accord with reality. Therefore, its application is widespread day by day. We establish a model of two stage stochastic programming for transportation-inventory problem and an example analysis was given. The model has much more value in our real life, especially for the transportation-inventory problem in physical distribution management system with much more uncertainty. |
