Abstract
We consider a production planning problem under uncertainty in which companies have to make product allocation decisions such that the risk of failing regulatory inspections of sites - and consequently losing revenue - is minimized. In the proposed decision model the regulatory authority is an adversary. The outcome of an inspection is a Bernoulli-distributed random variable whose parameter is a function of production decisions. Our goal is to optimize the conditional value-at-risk (CVaR) of the uncertain revenue. The dependence of the probability of inspection outcome scenarios on production decisions makes the CVaR optimization problem non-convex. We give a mixed-integer nonlinear formulation and devise a branch-and-bound (BnB) algorithm to solve it exactly. We then compare against a Stochastic Constraint Programming (SCP) approach which applies randomized local search. While the BnB guarantees optimality, it can only solve smaller instances in a reasonable time and the SCP approach outperforms it for larger instances.
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References
Facts about current good manufacturing practices (cGMPs), U.S. Food and Drug Administration, http://www.fda.gov/Drugs/DevelopmentApprovalProcess/Manufacturing/ucm169105.htm
Abrams, C., von Kanel, J., Muller, S., Pfitzmann, B., Ruschka-Taylor, S.: Optimized Enterprise Risk Management. IBM Systems Journal 46(2), 219–234 (2007)
Beroggi, G.E.G., Wallace, W.A.: Operational Risk Management: A New Paradigm for Decision Making. IEEE Transactions on Systems, Man, and Cypernetics 24(10), 1450–1457 (1994)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton (2005)
Liebenbergm, A.P., Hoyt, R.E.: The Determinants of Enterprise Risk Management: Evidence From the Appointment of Chief Risk Officers. Risk Management and Insurance Review 6, 37–52 (2003)
Frigo, M.L., Anderson, R.J.: A Strategic Framework for Governance, Risk, and Compliance. Strategic Finance 44, 20–61 (2009)
Rasmussen, M.: Corporate Integrity: Strategic Direction for GRC, 2008 GRC Drivers, Trends, and Market Directions (2008)
Bamberger, K.A.: Technologies of Compliance: Risk and Regulation in a Digital Age. Texas Law Review 88, 670–739 (2010)
Elisseeff, A., Pellet, J.-P., Pratsini, E.: Causal Networks for Risk and Compliance: Methodology and Applications. IBM Journal of Research and Development 54(3), 6:1–6:12 (2010)
Pratsini, E., Dea, D.: Regulatory Compliance of Pharmaceutical Supply Chains. In: ERCIM News, no. 60
Muller, S., Supatgiat, C.: A Quantitative Optimization Model for Dynamic risk-based Compliance Management. IBM Journal of Research and Development 51, 295–307 (2007)
Silver, E.A., Pyke, D.F., Peterson, R.: Inventory Management and Production Planning and Scheduling, 3rd edn. John Wiley and Sons, Chichester (1998)
Graves, S.C.: Manufacturing Planning and Control. In: Resende, M., Paradalos, P. (eds.) Handbook of Applied Optimization, pp. 728–746. Oxford University Press, NY (2002)
Mula, J., Poler, R., Garcia-Sabater, J.P., Lario, F.C.: Models for Production Planning Under Uncertainty: A Review. International Journal of Production Economics 103, 271–285 (2006)
Laumanns, M., Pratsini, E., Prestwich, S., Tiseanu, C.-S.: Production Planning for Pharmaceutical Companies Under Non-Compliance Risk (submitted) (2010)
Acerbi, C.: Coherent Measures of Risk in Everday Market Practice. Quantitative Finance 7(4), 359–364 (2007)
Acerbi, C., Tasche, D.: Expected shortfall: A Natural Coherent Alternative to Value at Risk. Economic Notes 31(2), 379–388 (2002)
Alexander, G.J., Baptista, A.M.: A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model. Management Science 50(9), 1261–1273 (2004)
Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent Measures of Risk. Mathematical Finance 3, 203–228 (1999)
Rockafellar, R.T., Uryasev, S.P.: Optimization of Conditional Value-at-Risk. The Journal of Risk 2, 21–41 (2000)
Rockafellar, R.T., Uryasev, S.P.: Conditional Value-at-Rsk for a General Loss Distribtion. Journal of Banking and finance 26, 1443–1471 (2002)
Walsh, T.: Stochastic Constraint Programming. In: 15th European Conference on Artificial Intelligence (2002)
Belotti, P., Lee, J., Liberti, L., Margot, F., Wachter, A.: Branching and Bounds Tightening Techniques, for Non-Convex MINLP. Optimization Methods and Software 24(4-5), 597–634 (2009)
Clausen, J.: Branch and Bound Algorithms - Principles and Examples. Parallel Computing in Optimization (1997)
Gendron, B., Crainic, T.G.: Parallel Branch-And-Bound Algorithms: Survey and Synthesis. Operations Research 42(6), 1042–1066 (1994)
Prestwich, S.D., Tarim, S.A., Rossi, R., Hnich, B.: Evolving Parameterised Policies for Stochastic Constraint Programming. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 684–691. Springer, Heidelberg (2009)
Prestwich, S.D., Tarim, S.A., Rossi, R., Hnich, B.: Stochastic Constraint Programming by Neuroevolution With Filtering. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 282–286. Springer, Heidelberg (2010)
Craenen, B., Eiben, A.E., Marchiori, E.: How to Handle Constraints with Evolutionary Algorithms. In: Chambers, L. (ed.) Practical Handbook of Genetic Algorithms, pp. 341–361 (2001)
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Kawas, B., Laumanns, M., Pratsini, E., Prestwich, S. (2011). Risk-Averse Production Planning. In: Brafman, R.I., Roberts, F.S., Tsoukiàs, A. (eds) Algorithmic Decision Theory. ADT 2011. Lecture Notes in Computer Science(), vol 6992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24873-3_9
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DOI: https://doi.org/10.1007/978-3-642-24873-3_9
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