In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex N-fold integer minimization problems and to convex 2-stage stoch...

In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models studied in mathematical finance for several decades have attracted attention in stochastic programming. We consider Conditional Value-at-Risk as risk measure in the framework of two-stage stochastic integer programming. The paper addresses structure, stability, and algori...

T disjunctive decomposition (D2) algorithm has emerged as a powerful tool to solve stochastic integer programs. In this paper, we consider two-stage stochastic integer programs with binary first-stage and mixedbinary second-stage decisions and present several computational enhancements to D2. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which ...

We formulate and solve a new stochastic integer programming model for dynamic sequencing and scheduling of appointments to a single stochastic server. We assume that service durations and the number of customers to be served on a particular day are uncertain. Customers are sequenced and scheduled dynamically (on-line) one at a time as they request appointments. We present a two-stage stochastic...

In this paper, impacts of various uncertainties such as random outages of generating units and transmission lines, forecasting errors of load demand and wind power, in the presence of Demand response (DR) programs on power generation scheduling are studied. The problem is modelled in the form of a two-stage stochastic unit commitment (UC) which by solving it, the optimal solutions of UC as well...

This paper presents a mathematical model for designing cellular manufacturing systems (CMSs) solved by genetic algorithms. This model assumes a dynamic production, a stochastic demand, routing flexibility, and machine flexibility. CMS is an application of group technology (GT) for clustering parts and machines by means of their operational and / or apparent form similarity in different aspects ...

Combinatorial optimisation problems often contain uncertainty that has to be taken into account to produce realistic solutions. However, existing modelling systems either do not support uncertainty, or do not support combinatorial features, such as integer variables and non-linear constraints. This paper presents an extension of the MINIZINC modelling language that supports uncertainty. Stochas...

We propose a new approach to risk modeling in power optimization employing the concept of stochastic dominance. This leads to new classes of large-scale block-structured mixed-integer linear programs for which we present decomposition algorithms. The new methodology is applied to stochastic optimization problems related to operation and investment planning in a power system with dispersed gener...

and Applied Analysis 3 with initial data x 0 x0, where f :R ×Rn → R, g:R ×Rn → Rn×d, x0 is a vector, and · denotes the greatest-integer function. By the definition of stochastic differential, this equation is equivalent to the following stochastic integral equation:

We present a new algorithm that uses both local branching and Monte Carlo sampling in a multi-descent search strategy for solving 0-1 integer stochastic programming problems. This procedure is applied to the single vehicle routing problem with stochastic demands. Computational results show the usefulness of this new approach to solve hard instances of the problem.