A Two Stage Stochastic Equilibrium Model for Electricity Markets with Two Way Contracts

This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans, … Read more

An Algorithm and a Core Set Result for the Weighted Euclidean One-Center Problem

Given ${\cal A} := \{a^1,\ldots,a^m\} \subset \R^n$ with corresponding positive weights ${\cal W} := \{\omega_1,\ldots,\omega_m\}$, the weighted Euclidean one-center problem, which is a generalization of the minimum enclosing ball problem, involves the computation of a point $c_{\cal A} \in \R^n$ that minimizes the maximum weighted Euclidean distance from $c_{\cal A}$ to each point in ${\cal … Read more

Pricing with uncertain customer valuations

Uncertain demand in pricing problems is often modeled using the sum of a linear price-response function and a zero-mean random variable. In this paper, we argue that the presence of uncertainty motivates the introduction of nonlinearities in the demand as a function of price, both in the risk-neutral and risk-sensitive models. We motivate our analysis … Read more

Simultaneous Solution of Lagrangean Dual Problems Interleaved with Preprocessing for the Weight Constrained Shortest Path Problem

Conventional Lagrangean preprocessing for the network Weight Constrained Shortest Path Problem (WCSPP calculates lower bounds on the cost of using each node and edge in a feasible path using a single optimal Lagrange multiplier for the relaxation of the WCSPP. These lower bounds are used in conjunction with an upper bound to eliminate nodes and … Read more

Convergent Network Approximation for the Continuous Euclidean Length Constrained Minimum Cost Path Problem

In many path planning situations we would like to find a path of constrained Euclidean length in 2D that minimises a line integral. We call this the Continuous Length-Constrained Minimum Cost Path Problem (C-LCMCPP). Generally, this will be a non-convex optimization problem, for which continuous approaches only ensure locally optimal solutions. However, network discretisations yield … Read more

Computational study of a chance constrained portfolio selection problem

We study approximations of chance constrained problems. In particular, we consider the Sample Average Approximation (SAA) approach and discuss convergence properties of the resulting problem. A method for constructing bounds for the optimal value of the considered problem is discussed and we suggest how one should tune the underlying parameters to obtain a good approximation … Read more