# Practical Precautionary Resource Management Using Robust Optimization

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## Abstract

Uncertainties inherent in fisheries motivate a precautionary approach to management, meaning an approach specifically intended to avoid bad outcomes. Stochastic dynamic optimization models, which have been in the fisheries literature for decades, provide a framework for decision making when uncertain outcomes have known probabilities. However, most such models incorporate population dynamics models for which the parameters are assumed known. In this paper, we apply a robust optimization approach to capture a form of uncertainty nearly universal in fisheries, uncertainty regarding the values of model parameters. Our approach, developed by Nilim and El Ghaoui (Oper Res 53(5):780–798, 2005), establishes bounds on parameter values based on the available data and the degree of precaution that the decision maker chooses. To demonstrate the applicability of the method to fisheries management problems, we use a simple example, the Skeena River sockeye salmon fishery. We show that robust optimization offers a structured and computationally tractable approach to formulating precautionary harvest policies. Moreover, as better information about the resource becomes available, less conservative management is possible without reducing the level of precaution.

## Keywords

Precautionary management Robust optimization Dynamic optimization Fisheries management Numerical methods## Notes

### Acknowledgments

This research was conducted with support from Maryland Sea Grant under award R/FISH/EC-103 from the National Oceanic and Atmospheric Administration, US Department of Commerce, and Texas AgriLife Research with support from the Cooperative State Research, Education & Extension Service, Hatch Project TEX8604. We acknowledge the help of Ray Hilborn who provided some of the data used in the empirical application, Michele Zinn for editorial assistance, and reviewers for many helpful comments.

## Supplementary material

## References

- Anderies JM, Rodriguez AA, Janssen MA, Cifdaloz O (2007) Panaceas, uncertainty, and the robust control framework in sustainability science. Proc Natl Acad of Sci 104(39):15194–15199CrossRefGoogle Scholar
- Andersen P, Sutinen JG (1984) Stochastic bioeconomics: a review of basic methods and results. Mar Res Econ 1(2):117–136Google Scholar
- Ascough JC II, Maier HR, Ravalico JK, Strudley MW (2008) Future research challenges for incorporation of uncertainty in environmental and ecological decision-making. Ecol Model 219:383–399CrossRefGoogle Scholar
- Bewley TF (2011) Knightian decision theory and econometric inferences. J Econ Theory 146(3):1134–1147CrossRefGoogle Scholar
- Cai Y, Huang GH, Nie XH, Li YP, Tan Q (2007) Municipal solid waste management under uncertainty: a mixed interval parameter fuzzy-stochastic robust programming approach. Environ Eng Sci 24(3):338–352CrossRefGoogle Scholar
- Chen C, Huang GH, Li YP, Zhou Y (2013) A robust risk analysis method for water resources allocation under uncertainty. Stoch Environ Res Risk Assess 27(3):713–723CrossRefGoogle Scholar
- Ciriacy-Wantrup SV (1952) Resource conservation: economics and policies. University of California Press, BerkeleyGoogle Scholar
- Doole G, Kingwell R (2010) Robust mathematical programming for natural resource modeling under parametric uncertainty. Nat Res Model 23(3):285–302CrossRefGoogle Scholar
- Doyen L, Béné C (2003) Sustainability of fisheries through marine reserves: a robust modeling analysis. J Environ Manag 69(1):1–13CrossRefGoogle Scholar
- Ellsberg D (1961) Risk, ambiguity and savage axioms. Q J Econ 75(4):643–679CrossRefGoogle Scholar
- FAO (1996) Precautionary approach to fisheries management, part 1: guidelines on the precautionary approach to capture fisheries and species introductions. Lysekil, Sweden, June 6–13. FAO Fisheries Technical Paper, No. 350, Part 1. RomeGoogle Scholar
- Gaivoronski AA, Sechi GM, Zuddas P (2012) Balancing cost-risk in management optimization of water resource systems under uncertainty. Phys Chem Earth 42:98–107CrossRefGoogle Scholar
- Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J Math Econ 18(2):141–153CrossRefGoogle Scholar
- Gilboa I, Postlewaite AW, Schmeidler D (2008) Probability and uncertainty in economic modeling. J Econ Perspect 22(3):173–188CrossRefGoogle Scholar
- Gollier C, Jullien B, Treich N (2000) Scientific progress and irreversibility: an economic interpretation of the ‘precautionary principle’. J Public Econ 75(2):229–253CrossRefGoogle Scholar
- Hansen LP, Sargent TJ (2001) Robust control and model uncertainty. Am Econ Rev 91(2):60–66CrossRefGoogle Scholar
- Hansen LP, Sargent TJ (2007) Robustness. Princeton University Press, Princeton, NJGoogle Scholar
- Hansen LP, Sargent TJ, Turmuhambetova G, Williams N (2006) Robust control and model misspecification. J Econ Theory 128(1):45–90CrossRefGoogle Scholar
- Hanson FB, Ryan D (1998) Optimal harvesting with both population and price dynamics. Math Biosci 148(2):129–146CrossRefGoogle Scholar
- Hilborn R, Walters CJ (1992) Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Chapman and Hall, LondonCrossRefGoogle Scholar
- Jin D, Herrera GE (2010) A stochastic bioeconomic model with research. Mar Res Econ 20(3):249–261Google Scholar
- Johnson FA (2011) Learning and adaptation in the management of waterfowl harvests. J Environ Manag 92(5):1385–1394CrossRefGoogle Scholar
- Lempert RJ, Collins MT (2007) Managing the risk of uncertain threshold responses: comparison of robust, optimum, and precautionary approaches. Risk Anal 27(4):1009–1026CrossRefGoogle Scholar
- Manski CF (2011) Policy analysis with incredible certitude. Econ J 121(554):F261–F289CrossRefGoogle Scholar
- McAllister M, Kirchner C (2002) Accounting for structural uncertainty to facilitate precautionary fishery management: illustration with Namibian orange roughly. Bull Mar Sci 70(2):499–540Google Scholar
- McCarthy MA, Possingham HP (2007) Active adaptive management for conservation. Conserv Biol 21(4):956–963CrossRefGoogle Scholar
- Nilim A, El Ghaoui L (2005) Robust control of Markov decision processes with uncertain transition matrices. Oper Res 53(5):780–798CrossRefGoogle Scholar
- Punt AE (2006) The FAO precautionary approach after almost 10 years: have we progressed towards implementing simulation-tested feedback-control management systems for fisheries management? Nat Res Model 19(4):441–464CrossRefGoogle Scholar
- Randall A (2011) Risk and precaution. Cambridge University Press, New YorkCrossRefGoogle Scholar
- Regan HM, Ben-Haim Y, Langford B, Wilson WG, Lundberg P, Andelman SJ, Burgman MA (2005) Robust decision-making under severe uncertainty for conservation management. Ecol Appl 15(4):1471–1477CrossRefGoogle Scholar
- Ricker WE (1954) Stock and recruitment. J Fish Res Board Can 11:559–623CrossRefGoogle Scholar
- Rodriguez AA, Cifdaloz O, Anderies JM, Janssen MA, Dickeson J (2011) Confronting management challenges in highly uncertain natural resource systems: a robustness–vulnerability trade-off approach. Environ Model Assess 16(1):15–36CrossRefGoogle Scholar
- Roseta-Palma C, Xepapadeas A (2004) Robust control in water management. J Risk Uncertain 29(1):21–34CrossRefGoogle Scholar
- Savage LJ (1954) The foundations of statistics. Wiley, New YorkGoogle Scholar
- Sethi G et al (2005) Fishery management under multiple uncertainty. J Environ Econ Manag 50(2):300–318CrossRefGoogle Scholar
- Shaw WD, Woodward RT (2008) Why environmental and resource economists should care about non-expected utility models. Res Energy Econ 30(1):66–89CrossRefGoogle Scholar
- Tyre AJ, Michaels S (2011) Confronting socially generated uncertainty in adaptive management. J Environ Manag 92(5):1365–1370CrossRefGoogle Scholar
- Vardas G, Xepapadeas A (2010) Model uncertainty, ambiguity and the precautionary principle: implications for biodiversity management. J Environ Res Econ 45(3):379–404CrossRefGoogle Scholar
- Wald A (1950) Statistical decision functions. Wiley, New YorkGoogle Scholar
- Walters C (1975) Optimal harvest strategies for salmon in relation to environmental variability and uncertain production parameters. J Fish Res Board Can 32(10):1777–1785CrossRefGoogle Scholar
- Williams BK (1996) Adaptive optimization and the harvest of biological populations. Math Biosci 136(1):1–20CrossRefGoogle Scholar
- Williams BK (2011) Adaptive management of natural resources—framework and issues. J Environ Manag 92(5):1346–1353CrossRefGoogle Scholar
- Woodward RT, Shaw WD (2008) Allocating resources in an uncertain world: water management and endangered species. Am J Agric Econ 90(3):593–605CrossRefGoogle Scholar
- Xepapadeas A, Roseta-Palma C (2003) Instabilities and robust control in fisheries. Discussion paper, Department of Economics, University of Crete, GreeceGoogle Scholar