ANALYZING AND MANAGING FLEXIBILITY IN ENGINEERING SYSTEMS DESIGN BASED ON DECISION RULES AND STOCHASTIC PROGRAMMING: APPLICATIONS IN WASTE-TO-ENERGY SYSTEMS

Ph.DDOCTOR OF PHILOSOPH

Risk trading in capacity equilibrium models

We present a set of power investment models, the class of risky capacity equilibrium problems, reflecting different assumptions of perfect and imperfect markets. The models are structured in a unified stochastic Nash game framework. Each model is the concatenation of a model of the short-term market operations (perfect competition or Cournot), with a long-term model of investment behavior (risk neutral and risk averse behavior under different assumptions of risk trading). The models can all be formulated as complementarity problems, some of them having an optimization equivalent. We prove existence of solutions and report numerical results to illustrate the relevance of market imperfections on welfare and investment behavior. The models are constructed and discussed as two stage problems but we show that the extension to multistage is achieved by a change of notation and a standard assumption on multistage risk functions. We also treat a large multistage industrial model to illustrate the computational feasibility of the approach

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework

On modelling planning under uncertainty in manufacturing

We present a modelling framework for two-stage and multi-stage mixed 0-1 problems under uncertainty for strategic Supply Chain Management, tactical production planning and operations assignment and scheduling. A scenario tree based scheme is used to represent the uncertainty. We present the Deterministic Equivalent Model of the stochastic mixed 0-1 programs with complete recourse that we study. The constraints are modelled by compact and splitting variable representations via scenarios

Real options "in" projects and systems design : identification of options and solutions for path dependency

Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2005.Includes bibliographical references (p. 289-298).This research develops a comprehensive approach to identify and deal with real options in" projects, that is, those real options (flexibility) that are integral parts of the technical design. It represents a first attempt to specify analytically the design parameters that provide good opportunities for flexibility for any specific engineering system. It proposes a two-stage integrated process: options identification followed by options analysis. Options identification includes a screening and a simulation model. Options analysis develops a stochastic mixed-integer programming model to value options. This approach decreases the complexity and size of the models at each stage and thus permits efficient computation even though traditionally fixed design parameters are allowed to vary stochastically. The options identification stage discovers the design elements most likely to provide worthwhile flexibility. As there are often too many possible options for systems designers to consider, they need a way to identify the most valuable options for further consideration, that is, a screening model. This is a simplified, conceptual, low-fidelity model for the system that conceptualizes its most important issues. As it can be easily run many times, it is used to test extensively designs under dynamic conditions for robustness and reliability; and to validate and improve the details of the preliminary design and set of possible options. The options valuation stage uses stochastic mixed integer programming to analyze how preliminary designs identified by the options identification stage should evolve over time as uncertainties get resolved. Complex interdependencies among options are specified in the constraints.(cont.) This formulation enables designers to analyze complex and problem-specific interdependencies that have been beyond the reach of standard tools for options analysis, to develop explicit plans for the execution of projects according to the contingencies that arise. The framework developed is generally applicable to engineering systems. The dissertation explores two cases in river basin development and satellite communications. The framework successfully attacks these cases, and shows significant value of real options "in" projects, in the form of increased expected net benefit and/or lowered downside risk.by Tao Wang.Ph.D

Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems

We take advantage of the interpretation of stochastic capacity expansion problems as stochastic equilibrium models for assessing the risk exposure of new equipment in a competitive electricity economy. We develop our analysis on a standard multistage generation capacity expansion problem. We focus on the formulation with nonanticipativity constraints and show that their dual variables can be interpreted as the net margin accruing to plants in the different states of the world. We then propose a procedure to estimate the distribution of the Lagrange multipliers of the nonanticipativity constraints associated with first stage decisions; this gives us the distribution of the discounted cash flow of profitable plants in that stage

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal