This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a multi-stage stochastic linear programming formulation for the problem. The complexity of the proposed algorithms is shown to be within O(N...

This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a multi-stage stochastic linear programming formulation for the problem. The complexity of the proposed algorithms is shown to be within O(N...

This paper proposes a data parallel procedure for randomly generating test problems for two-stage quadratic stochastic programming. Multiple quadratic programs in the second stage are randomly generated in parallel. A solution of the quadratic stochastic program is determined by multiple symmetric linear complementarity problems. The procedure allows the user to specify the size of the problem,...

To solve the multi-stage linear programming problem, one may use a deterministic or a stochastic approach. The drawbacks of the two techniques are well known: the deterministic approach is unrealistic under uncertainty and the stochastic approach suffers from scenario explosion. We introduce a new scheme, whose objective is to overcome both drawbacks. The focus of this new scheme is on events i...

To solve the multi-stage linear programming problem, one may use a deterministic or a stochastic approach. The drawbacks of the two techniques are well known: the deterministic approach is unrealistic under uncertainty and the stochastic approach suffers from scenario explosion. We introduce a new technique, whose objective is to overcome both drawbacks. The focus of this new technique is on ev...

In this study, a new stochastic model is proposed to deal with a multi-product, multi-period, multi-stage, multi-site production and transportation supply chain planning problem under demand uncertainty. A two-stage stochastic linear programming approach is used to maximize the expected profit. Decisions such as the production amount, the inventory level of finished and semi-finished product, t...

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical Programming A, 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem da...

In this study, a two-stage inexact-stochastic programming (TISP) method is developed for planning carbon dioxide (CO2) emission trading under uncertainty. The developed TISP incorporates techniques of interval-parameter programming (IPP) and two-stage stochastic programming (TSP) within a general optimization framework. The TISP can not only tackle uncertainties expressed as probabilistic distr...

Geometric programming is efficient tool for solving a variety of nonlinear optimizationproblems. Geometric programming is generalized for solving engineering design. However,Now Geometric programming is powerful tool for optimization problems where decisionvariables have exponential form.The geometric programming method has been applied with known parameters. However,the observed values of the ...

Abstract: The most important character within the optimization problem is the uncertainty of the future returns. To handle such problems, we utilize probabilistic methods alongside with optimization techniques. We develop single stage and two stage stochastic programming with recourse with the objective is to minimize the maximum downside semi deviation. We use the so-called “Here-and-Now” appr...