Optimizing the Expected Maximum of Two Linear Functions Defined on a Multivariate Gaussian Distribution

Published Online:https://doi.org/10.1287/ijoc.2022.1259

References

  • Balas E (1979) Disjunctive programming. Annals Discrete Math. 5:3–51.CrossrefGoogle Scholar
  • Balas E, Jeroslow R (1972) Canonical cuts on the unit hypercube. SIAM J. Appl. Math. 23(1):61–69.CrossrefGoogle Scholar
  • Balas E, Ceria S, Cornuéjols G (1993) A lift-and-project cutting plane algorithm for mixed 0–1 programs. Math. Programming 58(1):295–324.CrossrefGoogle Scholar
  • Bazovsky I (2004) Reliability Theory and Practice (Courier Corporation, North Chelmsford, MA).Google Scholar
  • Bergman D, Imbrogno J (2017) Surviving a national football league survivor pool. Oper. Res. 65(5):1343–1354.LinkGoogle Scholar
  • Bertsimas D, Natarajan K, Teo CP (2006) Tight bounds on expected order statistics. Probability Engrg. Inform. Sci. 20(4):667–686.CrossrefGoogle Scholar
  • Brown KC, Brown DJ (1986) Using order statistics to estimate real estate bid distributions. Management Sci. 32(3):289–297.LinkGoogle Scholar
  • Clair B, Letscher D (2007) Optimal strategies for sports betting pools. Oper. Res. 55(6):1163–1177.LinkGoogle Scholar
  • Clark CE (1961) The greatest of a finite set of random variables. Oper. Res. 9(2):145–162.LinkGoogle Scholar
  • Coffman E Jr, Flatto L, Garey M, Weber R (1987) Minimizing expected makespans on uniform processor systems. Adv. Appl. Probability 19(1):177–201.CrossrefGoogle Scholar
  • Cozad A, Sahinidis NV, Miller DC (2014) Learning surrogate models for simulation-based optimization. AIChE J. 60(6):2211–2227.CrossrefGoogle Scholar
  • David H, Nagaraja H (2004) Order Statistics. Wiley Series in Probability and Statistics (Wiley, New York).Google Scholar
  • Dimitrova DS, Ignatov ZG, Kaishev VK (2019) Ruin and deficit under claim arrivals with the order statistics property. Methodology Comput. Appl. Probability 21(2):511–530.CrossrefGoogle Scholar
  • Evans DL, Leemis LM, Drew JH (2006) The distribution of order statistics for discrete random variables with applications to bootstrapping. INFORMS J. Comput. 18(1):19–30.LinkGoogle Scholar
  • Gosavi A, et al. (2015) Simulation-Based Optimization (Springer, Berlin).CrossrefGoogle Scholar
  • Graham RL, Lawler EL, Lenstra JK, Kan AR (1979) Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals Discrete Math. 5:287–326.CrossrefGoogle Scholar
  • Haugh MB, Singal R (2021) How to play fantasy sports strategically (and win). Management Sci. 67(1):72–92.LinkGoogle Scholar
  • Hunter DS, Vielma JP, Zaman T (2016) Picking winners in daily fantasy sports using integer programming. Preprint, submitted April 6, https://arxiv.org/abs/1604.01455.Google Scholar
  • ILOG (2018) Cplex optimization studio. Accessed December 7, 2022, http://www.cplex.com.Google Scholar
  • Israeli E, Wood RK (2002) Shortest-path network interdiction. Networks 40(2):97–111.CrossrefGoogle Scholar
  • Kaplan EH, Garstka SJ (2001) March Madness and the office pool. Management Sci. 47(3):369–382.LinkGoogle Scholar
  • Kim S, Pasupathy R, Henderson SG (2015) A Guide to Sample Average Approximation (Springer, New York).CrossrefGoogle Scholar
  • Kleywegt AJ, Shapiro A, Homem-de Mello T (2002) The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12(2):479–502.CrossrefGoogle Scholar
  • Koutras VM, Koutras MV (2020) Exact distribution of random order statistics and applications in risk management. Methodology Comput. Appl. Probability 22(4):1539–1558.Google Scholar
  • McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: Part i: Convex underestimating problems. Math. Programming 10(1):147–175.CrossrefGoogle Scholar
  • McCormick ST, Rao MR, Rinaldi G (2003) Easy and difficult objective functions for max cut. Math. Programming 94(2–3):459–466.CrossrefGoogle Scholar
  • Nadarajah S, Kotz S (2008) Exact distribution of the max/min of two gaussian random variables. IEEE Trans. Very Large Scale Integration Systems 16(2):210–212.CrossrefGoogle Scholar
  • Nino-Mora J (2009) Stochastic scheduling. Encyclopedia Optim. 5:367–372.Google Scholar
  • Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, et al. (2011) Scikit-learn: Machine learning in Python. J. Machine Learn. Res. 12:2825–2830.Google Scholar
  • Pinedo ML (2005) Planning and Scheduling in Manufacturing and Services (Springer, Berlin).Google Scholar
  • Ranjbar M, Davari M, Leus R (2012) Two branch-and-bound algorithms for the robust parallel machine scheduling problem. Comput. Oper. Res. 39(7):1652–1660.CrossrefGoogle Scholar
  • Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika 52(3/4):591–611.CrossrefGoogle Scholar
  • Stec R, Novak A, Sucha P, Hanzalek Z (2019) Scheduling jobs with stochastic processing time on parallel identical machines. Proc. Internat. Joint Conf. on Artificial Intelligence (AAAI Press, Palo Alto, CA), 5628–5634.Google Scholar
  • Yang HC, Alouini MS (2011) Order Statistics in Wireless Communications: Diversity, Adaptation, and Scheduling in MIMO and OFDM Systems (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Youn H, Shemyakin A (2001) Pricing practices for joint last survivor insurance. Actuarial Res. Clearing House 1(2):3.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.