This paper studies the planning problem of hydro-thermal system with annual water consumption constraints, which are motivated by the practical system in the Yellow River Basin of China. This problem is formulated as one multistage stochastic optimization problem. The high-dimensional, dynamic, nonlinear and stochastic characteristics of hydro-thermal systems are considered. Since we can hardly...

In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution. The cost coefficients of the objective functions are multi-choice types. At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach. Further, a general tran...

We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a selfconcordant family with respect to the barrier parameter. We also show that the complexity value of the first stage problem increases additively with the number of stages and scenarios. We use these results to propose a proto...

Multistage stochastic programs bring computational complexity which may increase exponentially in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal solution are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic pr...

The stochastic uncapacitated lot-sizing problems with incremental quantity discount have been studied in this paper. First, a multistage stochastic mixed integer model is established by the scenario analysis approach and an equivalent reformulation is obtained through proper relaxation under the decreasing unit order price assumption. The proposed reformulation allows us to extend the productio...

Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method produce solutions that are immunized against uncertainty. The main focus in discrete been on analysis and solution of one- or two-stage problems, where decision maker limited options reacting additional knowledge gained after parts have fixed. Due it...

in this research, we address the application of uncertaintyprogramming to design a multi-site, multi-product, multi-period,closed-loop supply chain (clsc) network. in order to make theresults of this article more realistic, a clsc for a case study inthe iron and steel industry has been explored. the presentedsupply chain covers three objective functions: maximization ofprofit, minimization of n...

In this paper, we propose a successive approximation heuristic which solves large stochastic mixed-integer programming problem with complete fixed recourse. We refer to this method as the scenario updating method, since it solves the problem by considering only a subset of scenarios which is updated at each iteration. Only those scenarios which imply a significant change in the objective functi...