Technical Note—Time Inconsistency of Optimal Policies of Distributionally Robust Inventory Models

References

• Ahmed S, Cakmak U, Shapiro A (2007) Coherent risk measures in inventory problems. Eur. J. Oper. Res. 182(1):226–238.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376.Crossref, Google Scholar
• Bertsimas D, Iancu D, Parrilo P (2010) Optimality of affine policies in multistage robust optimization. Math. Oper. Res. 35(2):363–394.Link, Google Scholar
• de Ruiter FJCT, Brekelmans RCM, den Hertog D (2016) The impact of the existence of multiple adjustable robust solutions. Math. Programming 160(1–2):531–545.Crossref, Google Scholar
• Delage E, Iancu D (2015) Robust multistage decision making. Aleman DM, Thiele AC, eds. The Operations Research Revolution, TutORials in Operations Research (INFORMS, Catonsville, MD), 20–46.Link, Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• Esfahani PM, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1–2):115–166.Crossref, Google Scholar
• Iancu DA, Petrik M, Subramanian D (2015) Tight approximations of dynamic risk measures. Math. Oper. Res. 40(3):655–682.Link, Google Scholar
• Iancu DA, Trichakis N (2014) Pareto efficiency in robust optimization. Management Sci. 60(1):130–147.Link, Google Scholar
• Iyengar GN (2005) Robust dynamic programming. Math. Oper. Res. 30(2):257–280.Link, Google Scholar
• Jiang R, Guan Y (2016) Data-driven chance constrained stochastic program. Math. Programming 158(1–2):291–327.Crossref, Google Scholar
• Nilim A, El Ghaoui L (2005) Robust control of Markov decision processes with uncertain transition matrices. Oper. Res. 53(5):780–798.Link, Google Scholar
• Ruszczyński A, Shapiro A (2006) Conditional risk mappings. Math. Oper. Res. 31(3):544–561.Link, Google Scholar
• Ruszczyński A (2010) Risk-averse dynamic programming for Markov decision processes. Math. Programming 125(2):235–261.Crossref, Google Scholar
• Scarf H (1958) A min-max solution of an inventory problem. Arrow KJ, Karlin S, Scarf H, eds. Studies in the Mathematical Theory of Inventory and Production (Stanford University Press, Stanford, CA).Google Scholar
• Schmüdgen K (2017) The Moment Problem (Springer International Publishing, Cham, Switzerland).Crossref, Google Scholar
• Shapiro A (2001) On duality theory of conic linear problems. Goberna MA, Lopez MA, eds. Semi-Infinite Programming: Recent Advances (Kluwer Academic Publishers, Dordrecht, Netherlands), 135–165.Crossref, Google Scholar
• Shapiro A (2016) Rectangular sets of probability measures. Oper. Res. 64(2):528–541.Link, Google Scholar
• Shapiro A (2017) Interchangeability principle and dynamic equations in risk averse stochastic programming. Oper. Res. Lett. 45(4):377–381.Crossref, Google Scholar
• Shapiro A (2018) Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming. Working paper, Georgia Institute of Technology, Atlanta.Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming: Modeling and Theory, 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• Wiesemann W, Kuhn D, Rustem B (2013) Robust Markov decision processes. Math. Oper. Res. 38(1):153–183.Link, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Xin L, Goldberg DA (2013) Time (in)consistency of multistage distributionally robust inventory models with moment constraints. Preprint, submitted April 10, https://arxiv.org/abs/1304.3074.Google Scholar
• Zipkin PH (2000) Foundations of Inventory Management (McGraw-Hill, Boston).Google Scholar