Informatica

A relevant challenge introduced by decentralized installations of photo-voltaic systems is the mismatch between green energy production and the load curve for domestic use. We advanced an ICT solution that maximizes the self-consumption by an intelligent scheduling of appliances. The predictive approach is complemented with a reactive one to minimize the short term effects due to prediction errors and to unforeseen loads. Using real measures, we demonstrated that such errors can be compensated modulating the usage of continuously running devices such as fridges and heat-pumps. Linear programming is used to dynamically compute in real-time the optimal control of these devices.

The Markowitz model for single period portfolio optimization quantifies the problem by means of only two criteria: the mean, representing the expected outcome, and the risk, a scalar measure of the variability of outcomes. The classical Markowitz model uses the variance as the risk measure, thus resulting in a quadratic optimization problem. Following Sharpe's work on linear approximation to the mean‐variance model, many attempts have been made to linearize the portfolio optimization problem. There were introduced several alternative risk measures which are computationally attractive as (for discrete random variables) they result in solving Linear Programming (LP) problems. The LP solvability is very important for applications to real‐life financial decisions where the constructed portfolios have to meet numerous side constraints and take into account transaction costs. This paper provides a systematic overview of the LP solvable models with a wide discussion of their properties.

It is well known that in linear programming, the optimal values of the dual variables can be interpreted as shadow prices (marginal values) of the right-hand side coefficients. However, this is true only under nondegeneracy assumptions. Since real problems are often degenerate, the output from conventional LP software regarding such marginal information can be misleading. This paper surveys and generalizes known results in this topic and demonstrates how true shadow prices can be computed with or without modification to existing software.

In this research, we develop an algorithm for linear programming problems based on a new interpretation of Karmarkar's representation for this problem. Accordingly, we examine a suitable polytope for which the origin is an exterior point, and in order to determine an optimal solution, we need to ascertain the minimum extent by which this polytope needs to be slid along a one-dimensional axis so that the origin belongs to it. To accomplish this, we employ strongly separating hyperplanes between the origin and the polytope using a closest point routine. The algorithm is further enhanced by the generation of dual solutions which enable us to deform the polytope so that it is favorably positioned with respect to the origin and the axis of sliding motion. The overall scheme is easy to implement, requires a minimal amount of storage, and produces quick good quality lower bounds for the problem in its infinite convergence process. A switchover to the simplex method or an interior point method is also possible, using the current available solution as an advanced start. Preliminary computational results are provided along with implementation guidelines.

In the application of Dantzig–Wolfe decomposition to block-angular linear programming problems with R natural blocks. it is possible to have from 1 to R subproblems structurally while solving all R independent subproblems computationally. Early literature on the topic was inconclusive regarding the relative merits of such formulations. This paper attempts clarification by characterizing the significance of the degree of decomposition as well as presenting extensive empirical results.