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...

This paper presents a general mathematical formulation for the simultaneous design and scheduling of multipurpose plants. The formulation is based on the Resource Task Network process representation, uses a periodic, uniform time grid, continuous-time representation and originates mixed integer nonlinear programs (MINLPs) or mixed integer linear programs (MILPs), depending on the type of tasks ...

This paper provides a survey of recent progress and software for solving convex mixed integer nonlinear programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in recent years. By exploiting analogies to well-known techniques for solving ...

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

The development of optimization models for planning and scheduling is one of the most useful tools for improving productivity of a large number of manufacturing companies. This paper presents a mixed-integer programming model for scheduling steelmaking-continuous casting production. We first review the recent works in continuous casting planning. We focus on a model inspired from an application...

We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such...

This paper presents a method in expansion planning of transmission systems using the AC optimal power flow (AC-OPF). The AC-OPF provides a more accurate picture of power flow in the network compared to the DC optimal power flow (DC-OPF) that is usually considered in the literature for transmission expansion planning (TEP). While the AC-OPF-based TEP is a mixed-integer nonlinear programming prob...