This work concerns the formulation and solution of a multi-period security-constrained optimal power flow problem for real-time electricity market operations. The solution of the proposed problem is intended to be part of the core pricing procedure for electricity trading in open markets where...

Recent environmental trends, including (1) an expansion of existing command and control directives, (2) the introduction of market-based policy instruments, and (3) the adoption of extended producer responsibility, have created a need for new tools to help managerial decision-making. To address...

In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called potential-driven network models. When operators of these networks face increasing demand or the need to...

Tolerancing conducted by design engineers to meet customers' needs is a prerequisite for producing highquality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not something new, engineers often use known distributions, including the...

Purpose The main purpose is to minimize the total inventory cost of chain, whereas the stochastic constraints are satisfied. In other words, the goal is to find optimum agreed stockpiles and period length for products to minimize the total inventory cost of the chain while the stochastic...

Purpose The purpose of this paper is to propose a procedure to construct the membership functions for a one-unit repairable system, which has both active and standby redundancy. The coverage factor is the same for the operating and standby unit failure. Design/methodology/approach The α -cut...

In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints...

In this paper the issue of mathematical programming and optimization has being revisited. The theory of optimization deals with the development of models and methods that determine optimal solutions to mathematical problems defined. Mathematical model must be some function of any solution that...