Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove, under some moderate conditions, that optimal solutions and stationary points obta...

In order to maintain the stability and security of the power system, the uncertainty and intermittency of wind power must be taken into account in economic dispatch (ED) problems. In this paper, a dynamic economic dispatch (DED) model based on chance constrained programming is presented and an improved particle swarm optimization (PSO) approach is proposed to solve the problem. Wind power is re...

* Correspondence: [email protected] Department of Medical Education, Faculty of Medicine, 06490, Bahçelievler, Ankara, Turkey Full list of author information is available at the end of the article Abstract In this article, a method is developed to transform the chance-constrained programming problem into a deterministic problem. We have considered a chance-constrained programming problem u...

Optimally combining frequency control with selfconsumption can increase revenues from battery storage systems installed behind-the-meter. This work presents an optimized control strategy that allows a battery to be used simultaneously for self-consumption and primary frequency control. Therein, it addresses two stochastic problems: the delivery of primary frequency control with a battery and th...

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space ...

In this paper, a chance-constraint joint single vendor, single buyer supply chain problem with stochastic demand and fuzzy lead-time is investigated. The lead-time is lot size dependent; and delay times such as moving, waiting and setting time are fuzzy. The shortage costs result from backorder and/or lost sale, and the uncertain demand follows a uniform distribution. The buyer’s cost function ...

The paper determines the optimum qualities and prices of two substitute products for a manufacturer cum retailer in an imperfect production process over a random planning horizon for maximum profit. In this Economic Production Lot-size (EPL) process, items are produced simultaneously, defective production commences during the out-of-control state after the passage of some time from the commence...

A multi-objective chance-constrained programming integrated with Genetic Algorithm and robustness evaluation methods was proposed to weigh the conflict between system investment against risk for watershed load reduction, which was firstly applied to nutrient load reduction in the Lake Qilu watershed of the Yunnan Plateau, China. Eight sets of Pareto solutions were acceptable for both system inv...

Existing approaches to constrained dynamic programming are limited to formulations where the constraints share the same additive structure of the objective function (that is, they can be represented as an expectation of the summation of one-stage costs). As such, these formulations cannot handle joint probabilistic (chance) constraints, whose structure is not additive. To bridge this gap, this ...

In this article, we present an efficient algorithm for solving a class of chance-constrained optimization under nonparametric uncertainty. Our is built on the possibility representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use foundation to formulate one minimizing distance between desired distribution and constraint RKHS. provide systematic way cons...