A note on the knapsack problem with special ordered sets

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Set-valued State Estimation for Nonlinear Systems Using Hybrid Zonotopes

This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation that can efficiently represent nonconvex and disjoint sets. Tight over-approximations of complex nonlinear functions are efficiently produced by leveraging special ordered sets and neural networks, which enable computation of set-valued state estimates that grow linearly in memory complexity with time. A numerical example demonstrates significant reduction of conservatism in the set-valued state estimates using the proposed method as compared to an idealized convex approach

Detecting constraint redundancy in 0-1 linear programming problems

In this paper we present a procedure for obtaining upper bounds on a linear function by means of certain families of packings, coverings and special ordered sets. We also present a new method for detecting redundant constraints in 0-1 linear programming problems based on these bounds that allows consideration of several constraints jointly. Furthermore, we show a redundancy situation which is detected by this new method, but not by the traditional methods, which consider the constraints individually.Keywords: Redundant constraints, packings, coverings, special ordered sets, admissible familiesEn este trabajo se presenta un procedimiento de obtención de cotas superiores para una función lineal a partir de ciertas familias de empaquetamientos, cubrimientos y conjuntos ordenados especiales. Asimismo, s e presenta un nuevo método de detección de restricciones redundantes en problemas de programación lineal 0-1 basado en dichas cotas que permite considerar conjuntamente varias restricciones. Además, se muestra una situación de redundancia que es detectada por este método, pero no por los métodos tradicionales, los cuales consideran las restricciones individualmente.Palabras Clave: Restricciones redundantes, empaquetamientos, recubrimientos, conjuntos ordenados especiales, familias admisibles

A multi-period game-theoretic approach to market fairness in oligopolies

Contemporary process industries are constantly confronted with volatile market conditions that jeopardise their financial sustainability. While mature markets transition to oligopoly structures, the supply chain operation should adapt to a more customer-centric focus. Key issues related to the modelling and impact of the related contractual agreements between firms and customers remain largely unexplored. In the present work, we examine the problem of fair customer allocation in oligopolies under different contractual agreements within a multi-period setting. We consider an ensemble of contract types that vary in terms of pricing mechanisms and duration. The role of fairness is examined following the social welfare and Nash bargaining scheme. In the latter case, the overall problem is formulated as an MINLP. For its efficient solution we employ a piecewise linearisation strategy based on special-ordered sets. The impact of the different fairness schemes on the optimal customer allocation is evaluated via two case studies from the industrial gases market

Energy resource scheduling in a smart microgrid neighbourhood

This project consists of the case study of a smart microgrid district in a spanish town. The smart energy microgrid district consists of several households and a public use building (school) that includes renewable energy sources (photovoltaic), li-ion batteries for electric energy storage, domestic hot water heaters acting as thermal energy storage, a pool for balancing energy consumptions and supplies, and the connection to the electric grid. The problem has been modelled as a non-linear mathematical programming model that is linearly approximated using special ordered sets of type 2. The linear approximation is solved using Gurobi optimization software providing close-to-the-optimum solutions within an interval of 15 minutes that allows near real time operation of the smart energy district. The obtained results allow to advance within the net zero energy neighbourhood concept in all the evaluated scenarios within a daily horizon, and a positive energy balance in wider horizons. Even if these results are obtained in part due to the magnificent insolation conditions of this particular town, they allow to justify that the appropriate use of renewable energy resources, energy storage systems together with balancing mechanism at district level (as the pool in our case study) may lead to nearly net zero energy neighbourhood in other geographical locations too.Universidad de Sevilla. Máster en Organización Industrial y Gestión de Empresa

Reformulations of mathematical programming problems as linear complementarity problems

A family of complementarity problems are defined as extensions of the well known Linear Complementarity Problem (LCP). These are (i.) Second Linear Complementarity Problem (SLCP) which is an LCP extended by introducing further equality restrictions and unrestricted variables, (ii.) Minimum Linear Complementarity Problem (MLCP) which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized, (iii.) Second Minimum Linear Complementarity Problem (SMLCP) which is an MLCP but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. A number of well known mathematical programming problems, namely quadratic programming (convex, nonconvex, pseudoconvex nonconvex), bilinear programming, game theory, zero-one integer programming, the fixed charge problem, absolute value programming, variable separable programming are reformulated as members of this family of four complementarity problems