Transmission Expansion Planning Using an AC Model: Formulations and Possible Relaxations

Transmission expansion planning (TEP) is a rather complicated process which requires extensive studies to determine when, where and how many transmission facilities are needed. A well planned power system will not only enhance the system reliability, but also tend to contribute positively to the overall system operating efficiency. Starting with two mixed-integer nonlinear programming (MINLP) … Read more

On the impact of symmetry-breaking constraints on spatial Branch-and-Bound for circle packing in a square

We study the problem of packing equal circles in a square from the mathematical programming point of view. We discuss different formulations, we analyse formulation symmetries, we propose some symmetry breaking constraints and show that not only do they tighten the convex relaxation bound, but they also ease the task of local NLP solution algorithms … Read more

On convex relaxations of quadrilinear terms

The best known method to find exact or at least epsilon-approximate solutions to polynomial programming problems is the spatial Branch-and-Bound algorithm, which rests on computing lower bounds to the value of the objective function to be minimized on each region that it explores. These lower bounds are often computed by solving convex relaxations of the … Read more

Reformulating Linear Programs with Transportation Constraints — with Applications to Workforce Scheduling

We study linear programming models that contain transportation constraints in their formulation. Typically, these models have a multi-stage nature and the transportation constraints together with the associated flow variables are used to achieve consistency between consecutive stages. We describe how to reformulate these models by projecting out the flow variables. The reformulation can be more … Read more

A Multi-stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation … Read more