Robust mean absolute deviation problems on networks with linear vertex weights

This article deals with incorporating the mean absolute deviation objective function in several robust single facility location models on networks with dynamic evolution of node weights, which are modeled by means of linear functions of a parameter. Specifically, we have considered two robustness criteria applied to the mean absolute deviation problem: the MinMax criterion, and the MinMax regret criterion. For solving the corresponding optimization problems, exact algorithms have been proposed and their complexities have been also analyzed.Ministerio de Ciencia e Innovación MTM2007-67433-C02-(01,02)Ministerio de Ciencia e Innovación MTM2009-14243Ministerio de Ciencia e Innovación MTM2010-19576-C02-(01,02)Ministerio de Ciencia e Innovación DE2009-0057Junta de Andalucía P09-TEP-5022Junta de Andalucía FQM-584

New results on minimax regret single facility ordered median location problems on networks

We consider the single facility ordered median location problem with uncertainty in the parameters (weights) defining the objective function. We study two cases. In the first case the uncertain weights belong to a region with a finite number of extreme points, and in the second case they must also satisfy some order constraints and belong to some box, (convex case). To deal with the uncertainty we apply the minimax regret approach, providing strongly polynomial time algorithms to solve these problems

Robustness and macroeconomic policy

This paper considers the design of macroeconomic policies in the face of uncertainty. In recent years, several economists have advocated that when policymakers are uncertain about the environment they face and find it difficult to assign precise probabilities to the alternative scenarios that may characterize this environment, they should design policies to be robust in the sense that they minimize the worstcase loss these policies could ever impose. I review and evaluate the objections cited by critics of this approach. I further argue that, contrary to what some have inferred, concern about worst-case scenarios does not always lead to policies that respond more aggressively to incoming news than the optimal policy would respond absent any uncertainty.Macroeconomics - Econometric models

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Candia-Vejar, A (reprint author), Univ Talca, Modeling & Ind Management Dept, Curico, Chile.Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR. approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model

Managing ecological systems with unknown threshold locations

The optimal management of ecological systems is challenging because the locations of thresholds between desirable and undesirable regimes are generally unknown to the decision-maker. However, it is possible to learn about the resilience of an ecological system by intelligently perturbing the system using adaptive management (Arrow et al. 1995). Previous research has modelled optimal decisions in systems with hysteretic thresholds (Mäler et al. 2003), derived necessary conditions for optimal control when the locations of thresholds are unknown (Nævdal 2006; Nævdal and Oppenheimer 2007), and used stochastic dynamic programming to examine the effect of this form of uncertainty on risk averse behaviour (Brozovic and Schlenker 2011). This thesis extends previous research to model the effect on optimal decisions of learning about the locations of thresholds via a process of adaptive management. A dynamic programming framework is developed and applied to various ecological contexts, including numerical simulations of a shallow lake ecosystem, and used to demonstrate the role of learning. This thesis demonstrates that learning can be modelled by updating the prior probability distribution for a threshold’s location and by adjusting the boundary between the regions of a system’s state-space that could and could not contain the threshold. The model captures the trade-off faced by the decision-maker between the costs of crossing a threshold and shifting to an undesirable alternative regime, and the benefits of learning about the threshold location. Explicit consideration of the value of information means the decision-maker will generally make decisions that incur a greater risk of crossing the threshold in order to learn about its location. This finding is independent of the initial prior probability distribution used to model threshold location and the type of ecosystem dynamics considered. By explicitly modelling the value of information, this thesis better demonstrates the nature of optimal decision-making in the adaptive management of ecological systems

Managing ecological systems with unknown threshold locations

The optimal management of ecological systems is challenging because the locations of thresholds between desirable and undesirable regimes are generally unknown to the decision-maker. However, it is possible to learn about the resilience of an ecological system by intelligently perturbing the system using adaptive management (Arrow et al. 1995). Previous research has modelled optimal decisions in systems with hysteretic thresholds (Mäler et al. 2003), derived necessary conditions for optimal control when the locations of thresholds are unknown (Nævdal 2006; Nævdal and Oppenheimer 2007), and used stochastic dynamic programming to examine the effect of this form of uncertainty on risk averse behaviour (Brozovic and Schlenker 2011). This thesis extends previous research to model the effect on optimal decisions of learning about the locations of thresholds via a process of adaptive management. A dynamic programming framework is developed and applied to various ecological contexts, including numerical simulations of a shallow lake ecosystem, and used to demonstrate the role of learning. This thesis demonstrates that learning can be modelled by updating the prior probability distribution for a threshold’s location and by adjusting the boundary between the regions of a system’s state-space that could and could not contain the threshold. The model captures the trade-off faced by the decision-maker between the costs of crossing a threshold and shifting to an undesirable alternative regime, and the benefits of learning about the threshold location. Explicit consideration of the value of information means the decision-maker will generally make decisions that incur a greater risk of crossing the threshold in order to learn about its location. This finding is independent of the initial prior probability distribution used to model threshold location and the type of ecosystem dynamics considered. By explicitly modelling the value of information, this thesis better demonstrates the nature of optimal decision-making in the adaptive management of ecological systems