Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk

In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds.</p

An economic exploration of prevention versus response in animal related bioterrorism decision making

Animal disease outbreaks either through deliberate terroristic act or accidental introductions present a serious economic problem. This work concentrates on the economics of choosing strategies to mitigate possible agricultural terrorism and accidental introduction events largely in the animal disease management setting. General economic issues and the economic literature related to agricultural terrorism broadly and animal disease concerns specifically are reviewed. Basic economic aspects, such as the economic consequences of outbreaks, costs and benefits of various mitigation strategies, and stochastic characteristics of the problem are discussed. A conceptual economic model is formulated to depict the animal disease outbreak related decision making process. The key element of this framework is the choice between ex ante versus ex post mitigation strategies. The decision of investing in preventative and/or responsive strategies prior to the occurrence of an event versus relying on response and recovery actions after an outbreak event needs careful consideration. Comparative statics investigations reveal that factors that affect this decision are event probability, and severity, as well as costs, benefits, and effectiveness of various mitigation strategies. A relatively simplified empirical case study is done analyzing the economic tradeoffs between and optimum levels of ex ante detection, as a form of prevention, and ex post slaughter, as a form of response. The setting chosen involves Foot and Mouth Disease management. Empirical investigation is done on the conditions under which it is economically more advantageous to invest in ex ante detection as opposed to relying just on ex post response. Results show that investment in ex ante activities becomes more advantageous as the probability and severity of an agricultural terrorism event increases, response effectiveness decreases, and costs of surveillance decrease. Also spread rate is found to play a key role in determining optimal combination of ex ante and ex post strategies with more done ex ante the faster the disease spread. Finally, an economic framework is posed for future work given availability of a more detailed epidemiologic model. Access to such a model will allow for incorporation of wider spectrum of strategies including numerous possibilities for prevention, detection, response and market recovery facilitation. The framework allows more localized options, multiple possible events and incorporation of risk aversion among other features