Frederic H. Murphy

A mathematical programming approach for determining oligopolistic market equilibrium

During the past several years it has become increasingly common to use mathematical programming methods for deriving economic equilibria of supply and demand. Well-defined approaches exist for the case of a single firm (monopoly) and for the case of many firms (perfect competition). In this paper a certain family of convex programs is formulated to determine equilibria for the case of a few firms (oligopoly). Solutions to this family of convex programs are shown to be Nash equilibria in the formal sense ofN person games. This equivalence leads to a mathematical programming-based algorithm for determining an oligopolistic market equilibrium.

Generation Capacity Expansion in Imperfectly Competitive Restructured Electricity Markets

We consider three models of investments in generation capacity in restructured electricity systems that differ with respect to their underlying economic assumptions. The first model assumes a perfect, competitive equilibrium. It is very similar to the traditional capacity expansion models even if its economic interpretation is different. The second model (open-loop Cournot game) extends the Cournot model to include investments in new generation capacities. This model can be interpreted as describing investments in an oligopolistic market where capacity is simultaneously built and sold in long-term contracts when there is no spot market. The third model (closed-loop Cournot game) separates the investment and sales decision with investment in the first stage and sales in the second stage-that is, a spot market. This two-stage game corresponds to investments in merchant plants where the first-stage equilibrium problem is solved subject to equilibrium constraints. We show that despite some important differences, the open- and closed-loop games share many properties. One of the important results is that the prices and quantities produced in the closed-loop game, when the solution exists, fall between the prices and quantities in the open-loop game and the competitive equilibrium.

Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations

A rotor for exchangers in which the thermodynamic characteristics of two gas currents are transferred from one current to the other while they are being passed through the exchanger insert in zones separated from one another, said rotor being formed with sector spaces defined by the outer surface of an inner hub, an outer envelope and radial spokes interconnecting said hub with said envelope, which sector spaces are filled with a moisture and/or heat transferring insert formed as prefabricated units having the shape of the sector spaces.

Electric Utility Capacity Expansion Planning with Uncertain Load Forecasts

Abstract This paper is concerned with the role and impact of uncertainty in the forecast of electricity demand. In particular, the emphasis is upon how uncertainty about future demand affects current choices and strategies of capacity expansion. The uncertainty in demand is incorporated into both a stochastic linear program with recourse and an ordinary linear program. In the latter case only the “expected value” of demand is considered. The main result of this paper is that under fairly general conditions an ordinary linear program provides the same optimal solution as the more complex stochastic linear program.

A graphics interface for linear programming

We describe the interface to a software system that assists users in the process of formulating linear programming models. The main idea is to introduce a new representation that allows modelers to depict their problems in a graphical rather than mathematical form. This representation is described in detail together with a number of other interface design principles that we believe will aid modelers—including hierarchical decomposition, multiple model representations, alternative formulation approaches, the use of model templates, and database and model management facilities. These features are illustrated using the output of a prototype system formulating a realistic LP problem.

Compensating for non-homogeneity in decision-making units in data envelopment analysis

Abstract Data envelopment analysis (DEA) assumes homogeneity among the decision-making units (DMU) in terms of the nature of the operations they perform, the measures of their efficiency, and the conditions under which they operate. When the DMU are not homogeneous, the efficiency scores may reflect the underlying differences in environments rather than any inefficiencies. One strategy to overcome this is to separate DMU into homogeneous groups. However, one needs large numbers of DMU to do this. Another strategy is to adjust for non-homogeneity. This paper presents three adjustment techniques along with the basic Charnes, Cooper, and Rhodes (CCR) model. We do two simulation experiments where we know the underlying efficiencies of the DMU and the parameters of the non-homogeneities. We also compare the four models using actual data from a DEA evaluation of municipal reverse logistics channels. The results show none of the adjustment mechanisms are clearly superior to the unadjusted CCR model. Consequently, what makes a good adjustment mechanism is open at this time.

Approaches to Diagnosing Infeasible Linear Programs

This paper addresses the problem of diagnosing an infeasible linear program. In practice, there are several approaches one may take, most generally using the Phase I dual variables as an initial guide. Other approaches, however, have emerged to complement the traditional ones. These and new approaches are presented here with the aim of building a toolkit for automatic reasoning when an LP expert is not available. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Modeling and Forecasting Energy Markets with the Intermediate Future Forecasting System

This paper describes the Intermediate Future Forecasting System IFFS, which is the model used to forecast integrated energy markets by the U.S. Energy Information Administration. The model contains representations of supply and demand for all of the major fuels consumed in the United States, and is a partial equilibrium model containing a large number of equations and inequalities. We discuss methods for solving the models, as well as the convergence properties of the solution procedure. We also present issues associated with managing large models.

Computing Market Equilibria with Price Regulations Using Mathematical Programming

One approach to modeling and solving for economic equilibria relies on mathematical programming. These models solve for competitive equilibria. However, policy analysis often requires measuring the impacts of government price regulations that differ from the competitive equilibrium. In this paper we provide a unified framework for computing market equilibrium in mathematical programming models in the presence of government price regulations. The iterative procedure that we use is essentially a Gauss-Seidel algorithmic strategy. The paper concludes by showing how to represent tax/rebate programs, average-cost pricing, and price ceilings.

Views of mathematical programming models and their instances

Large-scale mathematical models are built, managed and applied by people with different cognitive skills. This poses a challenge for the design of a multi-view architecture of a system that accommodates these differences. A primary objective of mathematical modeling is providing insights into problem behavior, and there are many constituencies who require different views for different questions. One constituency is composed of modellers who have different views of basic model components. Another constituency is composed of problem owners for whom models are built. These two constituencies, which are not exhaustive, have significantly different needs and skills. This paper addresses this issue of multiview architecture by presenting a formal framework for the design of a view creation and management system. Specific views we consider include algebraic, block schematic, graphic, and textual. Both form and content are relevant to view creation, and the merits of views are determined by their value in aiding comprehension and insight. The need for a central, formal structure to create and manage views is demonstrated by the inadequacy of direct mappings from any of the popular systems that are typically designed to support only one view of linear programming models and their instances.