Mathematical programs with equilibrium constraints: automatic reformulation and solution via constrained optimization

Constrained optimization has been extensively used to solve many large scale deterministic problems arising in economics, including, for example, square systems of equations and nonlinear programs. A separate set of models have been generated more recently, using complementarity to model various phenomenon, particularly in general equilibria. The unifying framework of mathematical programs with equilibrium constraints (MPEC) has been postulated for problems that combine facets of optimization and complementarity. This paper briefly reviews some methods available to solve these problems and described a new suite of tools for working with MPEC models. Computational results demonstrating the potential of this tool are given that automatically construct and solve a variety of different nonlinear programming reformulations of MPEC problems.\ud \ud This material is based on research partially supported by the National Science Foundation Grant CCR-9972372, the Air Force Office of Scientific Research Grant F49620-01-1-0040, Microsoft Corporation and the Guggenheim Foundation

How restricting carbon dioxide and methane emissions would affect the Indian economy

India and China contain about 40 percent of the earth's people. They are at an early stage of economic development, and their increasingly massive energy requirements will depend heavily on coal, a potent source of carbon dioxide, a powerful and long-lasting greenhouse gas. India also has important sources and uses of hydroelectric and nuclear power, petroleum, and natural gas. Agriculture still produces about 30 percent of its gross domestic product, and about 72 percent of the population lives in rural areas - with their large animal populations and substantial forest acreage. India has vast cities and an industrial sector that is large in absolute terms, although it represents only 30 percent of the economy. The model developed to analyze the economic effects of constraints on greenhouse gas emissions is a multisectoral, intertemporal linear programming model, driven by the optimization of the welfare of a representative consumer. A comprehensive model was built not to project the future at a single stroke but to begin to answer questions of a"What if?"form. The results strongly suggest that the economic effects on India of such constraints would be profound. The implications of different forms of emissions restrictions - annual, cumulative, and radiative forcing - deserve more attention. Cumulative restrictions - or better still, restrictions on radiative forcing - are closely related to public policy on greenhouse effects. Such restrictions also provide significant additional degrees of freedom for the economic adjustments required. They do this, in part, by allowing the postponement of emissions restrictions, which is not permitted by annual constraints. Of course, the question arises whether a country, having benefited from postponing a required reduction in emissions, would then be willing to face the consequences in economic losses. Might there be a genuine preference - albeit an irrational one - for taking the losses annually? Would compliance with international agreements for emissions restrictions be more likely if they required annual, rather than cumulative, reductions? Monitoring requirements would be the same in either case; if effective monitoring were carried out, it would detect departures from cumulative or radiative forcing constraints just as easily as departures from annualconstraints.Environmental Economics&Policies,Carbon Policy and Trading,Montreal Protocol,Transport and Environment,Energy and Environment

Growth and welfare losses from carbon emissions restrictions : a general equilibrium analysis for Egypt

The authors assess the economic effects in Egypt, under various conditions, of restricting carbon dioxide emissions. They use their model to assess the sensitivity of these effects to alternative specifications: changes in the level or timing of restrictions, changes in the rate of discount of future welfare, and the presence or absence of alternative technologies for generating power. They also analyze a constraint on accumulated emissions of carbon dioxide. Their time model has a time horizon of 100 years, with detailed accounting for every five years, so they can be specific about differences between short- and long-run effects and their implications. However, the results reported here cover only a 60-year period - and are intended only to compare the results of generic,"what if?"questions, not as forecasts. In that 60-year period, the model economy substantially depletes its hydrocarbon reserves, which are the only non produced resource. The authors find that welfare losses due to the imposition of annual restrictions on the rate of carbon dioxide emissions are substantial - ranging from 4.5 percent for a 20 percent reduction in annual carbon dioxide emissions to 22 percent for a 40 percent reduction. The effects of the annual emissions restrictions are relatively nonlinear. The timing of the restrictions is significant. Postponing them provides a longer period for adjustment and makes it possible to continue delivering consumption goodsin a relatively unconstrained manner. The form of emissions restrictions is also important. Welfare losses are much higher when constraints are imposed on annual emissions rates rather than on total additions to the accumulation of greenhouse gases. Conventional backstop technologies for maintaining output and consumption - cogeneration, nuclear power, and gas-powered transport - are more significant than unconventional"renewable"technologies, which cannot compete for cost.Environmental Economics&Policies,Energy and Environment,Carbon Policy and Trading,Montreal Protocol,Climate Change

Term-End Exam Scheduling at United States Military Academy/West Point

Scheduling term-end exams (TEE) at the United States Military Academy in West Point is unlike any other exam timetabling problem we know of. Exam timetabling normally produces a conflict-free timetable covering a reasonably long exam period, where every exam is scheduled exactly once for all the students enrolled in the corresponding class. The situation is quite different at West Point. There are hundreds of exams to schedule over such a short time period that there is simply no feasible solution. The challenge is then to allow something that is not even considered elsewhere, that is, creating multiple sessions of some exams, scheduled at different times within the exam period, to allow each student to take all exams he/she must take. The overall objective is to find a feasible exam schedule with a minimum number of such duplicate exams. The paper describes a system that has been developed at GAMS Development Corp. in close cooperation with the scheduling staff at West Point, and that has been used successfully since 2001. It uses mathematical optimization in several modules, and some of the techniques proposed are new. It is fast and flexible, and allows for human interaction, such as adding initially unexpected constraints, coming for instance from instructors’ preferences and dislikes, as well as their hierarchical rankings. It is robust and can be used by people familiar with the organization at West Point, without the need for them to be technically-trained. Overall, using the course and student information databases, it is an effective decision support system that calls optimization tools in an unobtrusive way

Computing Wardropian Equilibria

This note considers alternative methods for computingWadropian (traffic network) equilibria using a multicommodity formulation in nonlinear program and complementarity formats. These methods compute exact equilibria, they are efficient and they can be implemented with standard modeling software