We compare different approaches of optimization under uncertainty in the context of pricing strategies for conspicuous consumption products in recession periods of uncertain duration and strength. We consider robust worst-case ideas and how the concepts of Value at Risk (VaR) and Conditional Value at Risk (CVaR) can be incorporated efficiently. The approaches are generic in … Read more
The Cauchy distribution has no moments (expected value, variance, etc.), because the defining integrals diverge. A way to “concentrate” the Cauchy distribution, in order to get finite moments, is suggested by an elementary problem in mechanics, giving the Cauchy distribution as a special case. The concentrated distribution has finite moments of all orders, while keeping … Read more
This paper formalizes and adapts the well known concept of Pareto efficiency in the context of the popular robust optimization (RO) methodology. We argue that the classical RO paradigm need not produce solutions that possess the associated property of Pareto optimality, and illustrate via examples how this could lead to inefficiencies and sub-optimal performance in … Read more
In the energy sector, there has been a transition from monopolistic to oligopolistic situations (pool markets); each time more companies’ optimization revenues depend on the strategies of their competitors. The market rules vary from country to country. In this work, we model the Iberian Day-Ahead Duopoly Market and find exactly which are the outcomes (Nash … Read more
We propose a dynamic traveling salesman problem (TSP) with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which a decision’s cost is known only probabilistically beforehand but is revealed dynamically before the decision is executed. We formulate the problem as a dynamic program (DP) and compare it to static counterparts to … Read more
The aim of this paper is to demonstrate a new approach to solve the linearized (n-1) security constrained optimal power flow (SCOPF) problem by a structure exploiting interior point solver. Firstly, we present a reformulation of the linearized SCOPF model, in which most matrices that need to be factorized are constant. Hence, most factorizations and … Read more
In the execution cost problem, an investor wants to minimize the total expected cost and risk in the execution of a portfolio of risky assets to achieve desired positions. A major source of the execution cost comes from price impacts of both the investor’s own trades and other concurrent institutional trades. Indeed price impact of … Read more
A generalized Weiszfeld method is proposed for the multi–facility location problem. The problem is relaxed using probabilistic assignments, and is decomposed into single facility location problems, that are coupled by these assignments, and can be solved in parallel. The probabilistic assignments are updated at each iteration, using the distances to the current centers. The method … Read more
In this paper, we address the optimal energy storage management and sizing problem in the presence of renewable energy and dynamic pricing. We formulate the problem as a stochastic dynamic programming problem that aims to minimize the long-term average cost of conventional generation used as well as investment in storage, if any, while satisfying all … Read more
This paper describes a multi-range robust optimization approach applied to the problem of capacity investment under uncertainty. In multi-range robust optimization, an uncertain parameter is allowed to take values from more than one uncertainty range. We consider a number of possible projects with anticipated costs and cash flows, and an investment decision to be made … Read more