Behavioral pricing of energy swing options by stochastic bilevel optimization

Holders of energy swing options are free to specify the amounts of energy to be delivered on short notice, paying a fixed price per unit delivered. Due to the complexity of potential demand patterns, risk elimination by replication of these contract at energy exchange markets is not possible. As a consequence, when selling delivery contracts, the energy producer has to explicitly consider the risk emanating from fluctuations in supply cost. The impact of these risk factors can be mitigated by the contract seller, who is an energy producer, to a certain extent: Supply cost fluctuations can be absorbed by the own generation portfolio whereas demand uncertainties can be influenced by the choice of the strike price, implicitly changing the buyer's behavior. Considering this, the determination of the optimal strike price can be formulated a a stochastic bilevel problem where the optimal decision of upper level player (price setting and production) depends on the optimal decision of a lower level player (demand depending on the price). We present a solution algorithm tailored to the resulting specific stochastic bilevel problem. We illstrate the effects of the behavioral pricing approach by studying behavioral price setting for natural gas swing options, highlighting in particulr the influence of the seller's production and contract portfolio as well as of the market liquidity on optimal exercise prices

Bilevel programming and applications

A great amount of new applied problems in the area of energy networks has recently arisen that can be efficiently solved only as mixed-integer bilevel programs. Among them are the natural gas cash-out problem, the deregulated electricity market equilibrium problem, biofuel problems, a problem of designing coupled energy carrier networks, and so forth, if we mention only part of such applications. Bilevel models to describe migration processes are also in the list of the most popular new themes of bilevel programming, as well as allocation, information protection, and cybersecurity problems. This survey provides a comprehensive review of some of the above-mentioned new areas including both theoretical and applied results

Three essays on multi-level optimization models and applications

The general form of a multi-level mathematical programming problem is a set of nested optimization problems, in which each level controls a series of decision variables independently. However, the value of decision variables may also impact the objective function of other levels. A two-level model is called a bilevel model and can be considered as a Stackelberg game with a leader and a follower. The leader anticipates the response of the follower and optimizes its objective function, and then the follower reacts to the leader\u27s action. The multi-level decision-making model has many real-world applications such as government decisions, energy policies, market economy, network design, etc. However, there is a lack of capable algorithms to solve medium and large scale these types of problems. The dissertation is devoted to both theoretical research and applications of multi-level mathematical programming models, which consists of three parts, each in a paper format. The first part studies the renewable energy portfolio under two major renewable energy policies. The potential competition for biomass for the growth of the renewable energy portfolio in the United States and other interactions between two policies over the next twenty years are investigated. This problem mainly has two levels of decision makers: the government/policy makers and biofuel producers/electricity generators/farmers. We focus on the lower-level problem to predict the amount of capacity expansions, fuel production, and power generation. In the second part, we address uncertainty over demand and lead time in a multi-stage mathematical programming problem. We propose a two-stage tri-level optimization model in the concept of rolling horizon approach to reducing the dimensionality of the multi-stage problem. In the third part of the dissertation, we introduce a new branch and bound algorithm to solve bilevel linear programming problems. The total time is reduced by solving a smaller relaxation problem in each node and decreasing the number of iterations. Computational experiments show that the proposed algorithm is faster than the existing ones

Applications of Optimization Under Uncertainty Methods on Power System Planning Problems

This dissertation consists of two published journal paper, both on transmission expansion planning, and a report on distribution network hardening. We first discuss our studies of two optimization criteria for the transmission planning problem with a simplified representation of load and the forecast generation investment additions within the robust optimization paradigm. The objective is to determine either the minimum of the maximum investment requirement or the maximum regret with all sources of uncertainty explicitly represented. In this way, transmission planners can determine optimal planning decisions that are robust against all sources of uncertainty. We use a two layer algorithm to solve the resulting trilevel optimization problems. We also construct a new robust transmission planning model that considers generation investment more realistically to improve the quantification and visualization of uncertainty and the impacts of environmental policies. With this model, we can explore the effect of uncertainty in both the size and the location of candidate generation additions. The corresponding algorithm we develop takes advantage of the structural characteristics of the model so as to obtain a computationally efficient methodology. The two robust optimization tools provide new capabilities to transmission planners for the development of strategies that explicitly account for various sources of uncertainty. We illustrate the application of the two optimization models and solution schemes on a set of representative case studies. These studies give a good idea of the usefulness of these tools and show their practical worth in the assessment of ``what if\u27\u27 cases. We compare the performance of the minimax cost approach and the minimax regret approach under different characterizations of uncertain parameters. In addition, we also present extensive numerical studies on an IEEE 118-bus test system and the WECC 240-bus system to illustrate the effectiveness of the proposed decision support methods. The case study results are particularly useful to understand the impacts of each individual investment plan on the power system\u27s overall transmission adequacy in meeting the demand of the trade with the power output units without violation of the physical limits of the grid. In the report on distribution network hardening, a two-stage stochastic optimization model is proposed. Transmission and distribution networks are essential infrastructures to modern society. In the United States alone, there are there are more than 200,000 miles of high voltage transmission lines and numerous distribution lines. The power network spans the whole country. Such vast networks are vulnerable to disruptions caused by natural disasters. Hardening of distribution lines could significantly reduce the impact of natural disasters on the operation of power systems. However, due to the limited budget, it is impossible to upgrade the whole power network. Thus, intelligent allocation of resources is crucial. Optimal allocation of limited budget between different hardening methods on different distribution lines is explored

Optimization approaches for energy infrastructure network design

This dissertation focuses on applying operations research techniques to problems arising in the energy sector. The work presented attempts to push the existing frontiers in energy optimization by adding to an existing open-source framework in electricity infrastructure optimization and applying bilevel programming to relatively unexplored applications in natural gas market modeling. This dissertation consists of five chapters. Chapter 1 provides an introduction encompassing a brief description and motivation for the dissertation’s work. The future development of the U.S. electricity sector will be shaped by technological, economic, and policy drivers whose trajectories are highly uncertain. Chapter 2 describes an optimization model for the integrated generation and transmission system in the continental U.S., which is used to explore electricity infrastructure pathways from the present through 2050. By comparing and contrasting results from numerous scenarios and sensitivity settings, we ultimately affirm five key policy-relevant insights. (1) U.S. electricity can be substantially decarbonized at a modest cost, but complete decarbonization is very costly. (2) Significant expansion of solar PV and wind to combine for at least 40% of the generation mix by 2050 is fairly certain. However, solar PV and battery storage are more affected by economic and policy assumptions than wind. (3) Investments in long-distance transmission are minimal, while investments in battery storage are much more significant under a wide range of assumptions. (4) Optimal solutions include large investments in natural gas capacity, but gas capacity utilization rates decline steadily and significantly. (5) Cost structures shift away from operating expenditures and toward capital expenditures, especially under climate policy. We conclude our article by discussing the policy implications of these findings. Chapter 3 presents a bilevel programming model to aid decision-making in natural gas markets where multiple autonomous agents interact strategically, possibly with conflicting interests. In the proposed model, a liquefied natural gas (LNG) operator is the leader, and a natural gas (NG) producer is the follower. The LNG operator attempts to optimally locate LNG export terminals, purchase gas from the NG producer, and export it as LNG. The NG producer aims to optimize production, pipeline investments, and sales to domestic consumers and the LNG operator. To solve the bilevel problem, we first reformulate it as a single-level problem by exploiting the lower-level problem’s convexity. Then, we use disjunctive reformulations of complementarity constraints and piecewise linear approximations of objective function terms to convert the problem into a convex quadratic mixed-integer program (QMIP). Computational experiments confirm that the QMIP is tractable and can be solved efficiently. We apply our bilevel framework to a case study of the Gulf-Southwest region of the United States and evaluate several decision-making scenarios. The scenario results emphasize the importance of using the bilevel methodology to anticipate the effects of new LNG export facilities on NG prices across the domestic gas network. Adding these large gas-consuming facilities at specific locations puts upward pressure on domestic gas prices, although this is somewhat mitigated by the NG producer’s optimal production response to the increased demand. Chapter 4 presents a risk-based integer bilevel programming model that considers two players in a leader-follower setting, where each tries to maximize their individual profits. The leader or manufacturer makes decisions pertaining to facility location and the amount of raw material to buy from the supplier. The supplier or follower decides how much raw material to produce. Both players face demand uncertainty in their respective markets while making investment, production, and sales decisions. We develop models for optimal decision-making under risk-neutral and risk-averse objectives and explore the effects of different risk attitudes on the problem and its optimal solution. These problems are hard to solve as the number of scenarios increase, and solving them generally involves developing customized algorithms. To find feasible solutions to the resulting stochastic bilevel problem, an algorithm is developed that iteratively solves a restricted version of the problem to obtain feasible solutions to the original problem. Extensive computational experiments are performed to evaluate algorithmic tractability and solution quality. The proposed algorithm is able to find high-quality feasible solutions to the bilevel problem in a very reasonable amount of time, and the attained solutions are found to be close to the optimal solution. The methodology is demonstrated with an example that addresses strategic issues in the natural gas market. The model considers two players, the liquefied natural gas (LNG) operator or leader and the natural gas (NG) producer or follower acting in a leader-follower setting. The LNG operator makes decisions pertaining to the locations of LNG facilities and the amount of gas to buy from the producer. The follower decides how much gas to produce. Both players face demand uncertainty in their respective markets and make investments, production, and sales decisions. The case study explores the Gulf-Southwest region of the United States and demonstrates the impact of the risk-averse decision-making approach on investment and operational decisions. Chapter 5 concludes this dissertation by summarizing the most important findings from each study and outlining valuable directions for future research.Operations Research and Industrial Engineerin

Exact Algorithms for Mixed-Integer Multilevel Programming Problems

We examine multistage optimization problems, in which one or more decision makers solve a sequence of interdependent optimization problems. In each stage the corresponding decision maker determines values for a set of variables, which in turn parameterizes the subsequent problem by modifying its constraints and objective function. The optimization literature has covered multistage optimization problems in the form of bilevel programs, interdiction problems, robust optimization, and two-stage stochastic programming. One of the main differences among these research areas lies in the relationship between the decision makers. We analyze the case in which the decision makers are self-interested agents seeking to optimize their own objective function (bilevel programming), the case in which the decision makers are opponents working against each other, playing a zero-sum game (interdiction), and the case in which the decision makers are cooperative agents working towards a common goal (two-stage stochastic programming). Traditional exact approaches for solving multistage optimization problems often rely on strong duality either for the purpose of achieving single-level reformulations of the original multistage problems, or for the development of cutting-plane approaches similar to Benders\u27 decomposition. As a result, existing solution approaches usually assume that the last-stage problems are linear or convex, and fail to solve problems for which the last-stage is nonconvex (e.g., because of the presence of discrete variables). We contribute exact finite algorithms for bilevel mixed-integer programs, three-stage defender-attacker-defender problems, and two-stage stochastic programs. Moreover, we do not assume linearity or convexity for the last-stage problem and allow the existence of discrete variables. We demonstrate how our proposed algorithms significantly outperform existing state-of-the-art algorithms. Additionally, we solve for the first time a class of interdiction and fortification problems in which the third-stage problem is NP-hard, opening a venue for new research and applications in the field of (network) interdiction

Multilevel decision-making: A survey

© 2016 Elsevier Inc. All rights reserved. Multilevel decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a multiple level hierarchy. Significant efforts have been devoted to understanding the fundamental concepts and developing diverse solution algorithms associated with multilevel decision-making by researchers in areas of both mathematics/computer science and business areas. Researchers have emphasized the importance of developing a range of multilevel decision-making techniques to handle a wide variety of management and optimization problems in real-world applications, and have successfully gained experience in this area. It is thus vital that a high quality, instructive review of current trends should be conducted, not only of the theoretical research results but also the practical developments in multilevel decision-making in business. This paper systematically reviews up-to-date multilevel decision-making techniques and clusters related technique developments into four main categories: bi-level decision-making (including multi-objective and multi-follower situations), tri-level decision-making, fuzzy multilevel decision-making, and the applications of these techniques in different domains. By providing state-of-the-art knowledge, this survey will directly support researchers and practical professionals in their understanding of developments in theoretical research results and applications in relation to multilevel decision-making techniques

Three essays on bilevel optimization algorithms and applications

This thesis consists of three journal papers I have worked on during the past three years of my PhD studies. In the first paper, we presented a multi-objective integer programming model for the gene stacking problem. Although the gene stacking problem is proved to be NP-hard, we have been able to obtain Pareto frontiers for smaller sized instances within one minute using the state-of-the-art commercial computer solvers in our computational experiments. In the second paper, we presented an exact algorithm for the bilevel mixed integer linear programming (BMILP) problem under three simplifying assumptions. Compared to these existing ones, our new algorithm relies on weaker assumptions, explicitly considers infinite optimal, infeasible, and unbounded cases, and is proved to terminate infinitely with the correct output. We report results of our computational experiments on a small library of BMILP test instances, which we have created and made publicly available online. In the third paper, we presented the watermelon algorithm for the bilevel integer linear programming (BILP) problem. To our best knowledge, it is the first exact algorithm which promises to solve all possible BILPs, including finitely optimal, infeasible, and unbounded cases. What is more, our algorithm does not rely on any simplifying condition, allowing even the case of unboundedness for the high point problem. We prove that the watermelon algorithm must finitely terminate with the correct output. Computational experiments are also reported showing the efficiency of our algorithm