Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In  this paper, stochastic dyn...

This study addresses a stochastic structure for generation companies (GenCoʼs) that participate in hydro-thermal self-scheduling with a wind power plant on short-term scheduling for simultaneous reserve energy and energy market. In stochastic scheduling of HTSS with a wind power plant, in addition to various types of uncertainties such as energy price, spinning /non-spinning reserve prices, unc...

Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed-integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for ...

In this section we want to understand what does the notation ∫ t 0 XsdWs mean. 1.1 Stochastic Process Xt Given a probability space {Ω,F,P} and time index set T , a stochastic process (Xs)s∈T is a measurable mapping from Ω×T to some space. In our most interested setting, the value space is R or Rd, while the time index set is T = [0,∞) with Borel σ-algebra. Another common option for T is the int...

In this paper we present a solution method for stochastic integer problems. The method is a Benderstype algorithm that sequentially approximates the nonconvex recourse functions defined by the second stage subproblems. The presented convexification takes into account the domain that is induced by the collection of tender variables. The method is applied to a broad collection of stochastic integ...

Two major approaches to deal with randomness or impression involved in mathematical programming problems have been developed. The one is called stochastic programming, and the other is called fuzzy programming. In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in constraints. Using the concept of simple recourse, such multiobjective st...

in order to implement the cellular manufacturing system in practice, some essential factors should be taken into account. in this paper, a new mathematical model for cellular manufacturing system considering different production factors including alternative process routings and machine reliability with stochastic arrival and service times in a dynamic environment is proposed. also because of t...

The business environment is full of uncertainty. Allocating the wealth among various asset classes may lower the risk of overall portfolio and increase the potential for more benefit over the long term. In this paper, we propose a mixed singlestage R&D projects and multi-stage securities portfolio selection model. Specifically, we present a bi-objective mixed-integer stochastic programming mode...

We present a stochastic model for capacity-expansion planning of electricity distribution networks subject to uncertain demand (CEP). We formulate CEP as a multistage stochastic mixed-integer program with a scenario-tree representation of uncertainty. At each node of the scenario-tree, the model determines capacity-expansions, operating con guration, and power ows. A “super-arc” representation ...

This article deals with distributed control of microgrids composed storages, generators, renewable energy sources, and critical controllable loads. We consider a stochastic formulation the optimal problem associated microgrid that appropriately takes into account unpredictable nature power generated by renewables. The resulting is mixed-integer linear program NP-hard nonconvex. Moreover, peculi...