Achieving an optimal trade-off between revenue and energy peak within a smart grid environment

We consider an energy provider whose goal is to simultaneously set revenue-maximizing prices and meet a peak load constraint. In our bilevel setting, the provider acts as a leader (upper level) that takes into account a smart grid (lower level) that minimizes the sum of users' disutilities. The latter bases its decisions on the hourly prices set by the leader, as well as the schedule preferences set by the users for each task. Considering both the monopolistic and competitive situations, we illustrate numerically the validity of the approach, which achieves an 'optimal' trade-off between three objectives: revenue, user cost, and peak demand

An adverse selection approach to power pricing

We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problems in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an explicit solution for the problem at hand. The optimal contracts are either linear or polynomial with respect to the consumption. Whenever the outside options offered by competitors are not uniform among the different type of consumers, we exhibit situations where the electricity provider should contract with consumers with either low or high appetite for electricity.Comment: 39 pages, 9 figure

Integración de generación distribuida en redes de distribución considerando una formulación matemática binivel

Este proyecto de grado presenta una metodología para solucionar el problema de la ubicación óptima de generadores distribuidos (GD) en sistemas de distribución cuando estos elementos no son propiedad del Operador de Red (OR), considerando un modelo matemático binivel que lleva en cuenta en los niveles superior e inferior los intereses del propietario de los GD y el OR, respectivamente..

Integración de generación distribuida en redes de distribución considerando una formulación matemática binivel

Este proyecto de grado presenta una metodología para solucionar el problema de la ubicación óptima de generadores distribuidos (GD) en sistemas de distribución cuando estos elementos no son propiedad del Operador de Red (OR), considerando un modelo matemático binivel que lleva en cuenta en los niveles superior e inferior los intereses del propietario de los GD y el OR, respectivamente..

Biogeography-Based Optimization for Combinatorial Problems and Complex Systems

Biogeography-based optimization (BBO) is a heuristic evolutionary algorithm that has shown good performance on many problems. In this dissertation, three problem1s 1 are researched for BBO: convergence speed and optimal solution convergence of BBO,1 1BBO application to combinatorial problems, and BBO application to complex systems. The first problem is to analyze BBO from two perspectives: how the components of BBO affect its convergence speed and the reason that BBO converges to the optimal solution. For the first perspective, which is convergence speed, we analyze the two essential components of BBO -- population construction and information sharing. For the second perspective, a mathematical BBO model is built to theoretically prove why BBO is capable of reaching the global optimum for any problem. In the second problem addressed by the dissertation, BBO is applied to combinatorial problems. Our research includes the study of migration, local search, population initialization, and greedy methods for combinatorial problems. We conduct a series of simulations based on four benchmarks, the sizes of which vary from small to extra large. The simulation results indicate that when combined with other techniques, the performance of BBO can be significantly improved. Also, a BBO graphical user interface (GUI) is created for combinatorial problems, which is an intuitive way to experiment with BBO algorithms, including hybrid BBO algorithms. The third and final problem addressed in this dissertation is the optimization of complex systems. We invent a new algorithm for complex system optimization based on BBO, which is called BBO/complex. Four real world problems are used to test BBO/Complex and compare with other complex system optimization algorithms, and we obtain encouraging results from BBO/Complex. Then, a Markov model is created for BBO/Complex. Simulation results are provided to confirm the mode

Fuzzy Bilevel Optimization

In the dissertation the solution approaches for different fuzzy optimization problems are presented. The single-level optimization problem with fuzzy objective is solved by its reformulation into a biobjective optimization problem. A special attention is given to the computation of the membership function of the fuzzy solution of the fuzzy optimization problem in the linear case. Necessary and sufficient optimality conditions of the the convex nonlinear fuzzy optimization problem are derived in differentiable and nondifferentiable cases. A fuzzy optimization problem with both fuzzy objectives and constraints is also investigated in the thesis in the linear case. These solution approaches are applied to fuzzy bilevel optimization problems. In the case of bilevel optimization problem with fuzzy objective functions, two algorithms are presented and compared using an illustrative example. For the case of fuzzy linear bilevel optimization problem with both fuzzy objectives and constraints k-th best algorithm is adopted.:1 Introduction 1 1.1 Why optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fuzziness as a concept . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2 1.3 Bilevel problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Preliminaries 11 2.1 Fuzzy sets and fuzzy numbers . . . . . . . . . . . . . . . . . . . . . 11 2.2 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Fuzzy order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Fuzzy functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 3 Optimization problem with fuzzy objective 19 3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Local optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 Existence of an optimal solution . . . . . . . . . . . . . . . . . . . . 25 4 Linear optimization with fuzzy objective 27 4.1 Main approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 Membership function value . . . . . . . . . . . . . . . . . . . . . . . . 34 4.4.1 Special case of triangular fuzzy numbers . . . . . . . . . . . . 36 4.4.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 5 Optimality conditions 47 5.1 Differentiable fuzzy optimization problem . . . . . . . . . . .. . . . 48 5.1.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.1.2 Necessary optimality conditions . . . . . . . . . . . . . . . . . . .. 49 5.1.3 Suffcient optimality conditions . . . . . . . . . . . . . . . . . . . . . . 49 5.2 Nondifferentiable fuzzy optimization problem . . . . . . . . . . . . 51 5.2.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2.2 Necessary optimality conditions . . . . . . . . . . . . . . . . . . . 52 5.2.3 Suffcient optimality conditions . . . . . . . . . . . . . . . . . . . . . . 54 5.2.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6 Fuzzy linear optimization problem over fuzzy polytope 59 6.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.2 The fuzzy polytope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 6.3 Formulation and solution method . . . . . . . . . . . . . . . . . . .. . 65 6.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7 Bilevel optimization with fuzzy objectives 73 7.1 General formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.2 Solution approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 7.3 Yager index approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4 Algorithm I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.5 Membership function approach . . . . . . . . . . . . . . . . . . . . . . .78 7.6 Algorithm II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80 7.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 8 Linear fuzzy bilevel optimization (with fuzzy objectives and constraints) 87 8.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 8.2 Solution approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 9 Conclusions 95 Bibliography 9

Multi-Echelon Inventory Optimization and Demand-Side Management: Models and Algorithms

Inventory management is a fudamental problem in supply chain management. It is widely used in practice, but it is also intrinsically hard to optimize, even for relatively simple inventory system structures. This challenge has also been heightened under the threat of supply disruptions. Whenever a supply source is disrupted, the inventory system is paralyzed, and tremenduous costs can occur as a consequence. Designing a reliable and robust inventory system that can withstand supply disruptions is vital for an inventory system\u27s performance.First we consider a basic type of inventory network, an assembly system, which produces a single end product from one or several components. A property called long-run balance allows an assembly system to be reduced to a serial system when disruptions are not present. We show that a modified version is still true under disruption risk. Based on this property, we propose a method for reducing the system into a serial system with extra inventory at certain stages that face supply disruptions. We also propose a heuristic for solving the reduced system. A numerical study shows that this heuristic performs very well, yielding significant cost savings when compared with the best-known algorithm.Next we study another basic inventory network structure, a distribution system. We study continuous-review, multi-echelon distribution systems subject to supply disruptions, with Poisson customer demands under a first-come, first-served allocation policy. We develop a recursive optimization heuristic, which applies a bottom-up approach that sequentially approximates the base-stock levels of all the locations. Our numerical study shows that it performs very well.Finally we consider a problem related to smart grids, an area where supply and demand are still decisive factors. Instead of matching supply with demand, as in the first two parts of the dissertation, now we concentrate on the interaction between supply and demand. We consider an electricity service provider that wishes to set prices for a large customer (user or aggregator) with flexible loads so that the resulting load profile matches a predetermined profile as closely as possible. We model the deterministic demand case as a bilevel problem in which the service provider sets price coefficients and the customer responds by shifting loads forward in time. We derive optimality conditions for the lower-level problem to obtain a single-level problem that can be solved efficiently. For the stochastic-demand case, we approximate the consumer\u27s best response function and use this approximation to calculate the service provider\u27s optimal strategy. Our numerical study shows the tractability of the new models for both the deterministic and stochastic cases, and that our pricing scheme is very effective for the service provider to shape consumer demand

Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context: Economic Engineering Modeling of Liberalized Electricity Markets: Approaches, Algorithms, and Applications in a European Context

This dissertation focuses on selected issues in regard to the mathematical modeling of electricity markets. In a first step the interrelations of electric power market modeling are highlighted a crossroad between operations research, applied economics, and engineering. In a second step the development of a large-scale continental European economic engineering model named ELMOD is described and the model is applied to the issue of wind integration. It is concluded that enabling the integration of low-carbon technologies appears feasible for wind energy. In a third step algorithmic work is carried out regarding a game theoretic model. Two approaches in order to solve a discretely-constrained mathematical program with equilibrium constraints using disjunctive constraints are presented. The first one reformulates the problem as a mixed-integer linear program and the second one applies the Benders decomposition technique. Selected numerical results are reported