Edward J. Anderson

Optimal Offer Construction in Electricity Markets

In this paper we study strategies for generators making offers into electricity markets in circumstances where both the demand for electricity and the behaviour of competing generators is unknown but can be represented by a probability distribution. Given this probability distribution, we derive necessary optimality conditions for a broad class of supply offer curves. We show how these conditions can be used to construct an optimal solution for a simple example. We also consider the case in which a generator is restricted in the number of prices at which power can be offered.

On-line scheduling of a single machine to minimize total weighted completion time

This paper considers the on-line scheduling of a single machine in which jobs arrive over time, and preemption is not allowed. The goal is to minimize the total weighted completion time. We show that a simple modification of the shortest weighted processing time rule has a competitive ratio of 2. This result is established using a new proof technique which does not rely explicitly on a lower bound on the optimal objective function value. Since it is known that no on-line algorithm can have a competitive ratio of less than 2, we have resolved the open issue of determining the minimum competitive ratio for this problem.

Using Supply Functions for Offering Generation into an Electricity Market

In this paper, we study strategies for generators making offers into electricity markets in circumstances where demand is unknown in advance. We concentrate on a model with smooth supply functions and derive conditions under which a single supply function can represent an optimal response to the offers of the other market participants over a range of demands. In order to apply this approach in practice, it may be necessary to approximate the supply functions of other players. We derive bounds on the loss in revenue that occurs in comparison with the exact supply function response, when a generator uses an approximation both for its own supply function and for the supply functions of other players. We also demonstrate the existence of symmetric supply-function equilibria.

Price competition with integrated and decentralized supply chains

We consider price competition with a linear demand function and compare two cases. In the first case each distribution channel is vertically integrated, while in the second, decentralised, case the manufacturers and retailers act independently. We explore the effect of varying the level of price competition on the profits of the industry participants and demonstrate the important role played by the spread of underlying market shares. The coefficient of variation of these market shares determines whether decentralised supply chains can outperform integrated supply chains with an appropriate level of competition.

Two Dimensional Rendezvous Search

We consider rendezvous problems in which two players move on the plane and wish to cooperate to minimise their first meeting time. We begin by considering the case where both players are placed such that the vector difference is chosen equiprobably from a finite set. We also consider a situation in which they know they are a distanced apart, but they do not know the direction of the other player. Finally, we give some results for the case in which player 1 knows the initial position of player 2, while player 2 is given information only on the initial distance of player 1.

Rendezvous Search on the Line with Indistinguishable Players

Alpern introduced a problem in which two players are placed on the real line at a distance drawn from a bounded distribution

Asymmetric rendezvous on the plane

F

A Class of Continuous Network Flow Problems

known to both. They can move at maximum velocity one and wish to meet as soon as possible. Neither knows the direction of the other, nor do they have a common notion of a positive direction on the line. It is required to find the symmetric rendezvous value

A co-evolutionary approach to modelling the behaviour of participants in competitive electricity markets

R^{s}(F)

A Contract and Balancing Mechanism for Sharing Capacity in a Communication Network

, which is the minimum expected meeting time achievable by players using the same mixed strategy. This corresponds to the case where the players are indistinguishable they both take directions from a controller who does not know their names. In this paper we give a mixed strategy which has an expected meeting time of