William R. Stewart

Approximate Traveling Salesman Algorithms

There have been a multitude of heuristic algorithms proposed for the solution of large scale traveling salesman problems. Our intent in this paper is to examine some of these well known heuristics, to introduce some new heuristics, and to compare these approximate techniques on the basis of efficiency and accuracy. We emphasize the strengths and weaknesses of each algorithm tested. One of our major conclusions is that it is not difficult to get within 2–3% of optimality using a composite heuristic which requires on the order of n3 computations where n is the number of nodes in the network.

Efficient market-clearing prices in markets with nonconvexities

This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf [Journal of Economic Perspectives 8(4) (1994) 111].

Stochastic vehicle routing: A comprehensive approach

Abstract A vehicle routing problem is stochastic when the demands at individual delivery (pickup) locations behave as random variables, and the routes must be defined before the values of these random variables become known. This paper presents several formulations and heuristic algorithms for solving this complex problem.

Understanding how market power can arise in network competition: a game theoretic approach

This paper considers competition in electric networks and how the network structure affects the competition. The approach is to examine non-cooperative behavior among producers and calculate a Nash equilibrium under different market specifications. Unlike most other treatments of this problem, which utilize either Cournot or Bertrand models of competition, the model used here examines supply function competition. Two and four node networks are considered. Several results that differ from traditional economic theory are found. In both a two-node and four-node market with imperfect competition among producers, transmission constraints increase their profits (compared to an unconstrained network)—but with little or no change in consumer prices or quantities produced. This is because generators profit primarily at the expense of the owner of transmission rights. The size of the increase in profits depends on the number of firms at each node and the size of the transmission constraint. In the four-node case, an example was found in which decreasing market concentration by breaking up suppliers worsens market efficiency, even if there are no cost diseconomies. In particular, increasing competition at one node increases the consumer price at a second node, and causes an overall decrease in consumer surplus. In general, the cases presented here show that strategic behavior on electric networks may produce results that differ from those predicted by traditional economic theory due to the network structure of the problem.

Dispatchable transmission in RTO markets

We consider transmission owners that bid capacity, under appropriate Regional Transmission Organization (RTO) market rules, at a positive price into forward and spot (dispatch) auctions to derive congestion revenues. This can encompass daily, monthly, or multimonthly auctions, allowing for commitment of transmission to reflect market needs in different time periods, e.g., seasons. We provide two and three node examples and a general formulation of the auction model.

A Lagrangean relaxation heuristic for vehicle routing

Abstract This paper presents a new heuristic algorithm for the vehicle routing problem (VRP) which makes use of Lagrangean relaxation to transform the VRP into a modified m -traveling salesman problem. Application of the proposed algorithm to test problems from the literature has produced new best-known solutions.

Contingent transmission rights in the standard market design

We define transmission rights that are compatible with the Federal Energy Regulatory Commissions proposed standard market design (SMD) and that provide flexibility in the points of receipt or delivery of energy contracts. The contingent transmission rights introduced here provide a viable, flexible method for defining SMD-compatible rights for transmission customers having current (pre-SMD) transmission rights that cover multiple points. These contingent rights can be bought and sold in the transmission rights auctions under SMD.

Why this Book? New Capabilities and New Needs for Unit Commitment Modeling

This book presents recent developments in the functionality of generation unit commitment (UC) models and algorithms for solving those models. These developments, the subject of a September 1999 workshop, are driven by institutional changes that increase the importance of efficient and market responsive operation. We illustrate these developments by demonstrating the use of mixed integer programming (MIP) to solve a UC problem. The dramatically lower solution times of modem MIP software indicates that it is now a practical algorithm for UC. Participants in the workshop also prioritized the features that need to be considered by UC models, along with topics for research and development. Among the highest research priorities are: market simulation; bid selection; reliability and reserve constraints; and fair processes for choosing from alternative near-optimal solutions. The chapter closes with an overview of the contributions of the other chapters.

Environmental factor weighting at the federal energy regulatory commission

Abstract The Federal Energy Regulatory Commission is required to assess the environmental impact of any project under its jurisdiction (e.g. pipeline construction and hydroelectric projects). Normally, this assessment involves preparing a written report that covers the entire project and identifying alternatives that have a lower environmental impact when such alternatives exist. This paper presents an approach based on the Analytic Hierarchy Process (AHP) for measuring environmental impacts on a common scale so that an overall impact index of a project or group of projects can be reported.

Regulatory Evolution, Market Design and Unit Commitment

In the context of competitive wholesale electricity markets, the unit commitment problem has shifted from a firm level optimization problem to a market level problem. Some centralized market designs use it to ensure reliability and determine day-ahead market prices. This chapter reviews the recent history of short-term electricity markets in the United States to evaluate the experience with alternative market designs and the implications for unit commitment modeling. It presents principles for the design of the next generation of unit commitment-based markets.