Piecewise linear lower and upper bounds for the standard normal first order loss function

Applied Mathematics and Computation

Volumn 231, Issue , 2014, Pages 489-502

  Rossi, Roberto ^a   Tarim, S Armagan ^b   Prestwich, Steven ^c   Hnich, Brahim ^d  

^a UNIVERSITY OF EDINBURGH BUSINESS SCHOOL   (United Kingdom)

^b HACETTEPE UNIVERSITY   (Turkey)

^c UNIVERSITY COLLEGE CORK   (Ireland)

^d IZMIR UNIVERSITY OF ECONOMICS   (Turkey)

Author keywords

Complementary first order loss function; Edmundson Madansky; First order loss function; Jensen's; Minimax; Piecewise linear approximation

Indexed keywords

EDMUNDSON-MADANSKY; JENSEN'S; LOSS FUNCTIONS; MINIMAX; PIECEWISE LINEAR APPROXIMATIONS;

NORMAL DISTRIBUTION; PROBABILITY DENSITY FUNCTION; RANDOM VARIABLES;

PIECEWISE LINEAR TECHNIQUES;

EID: 84893325296     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2014.01.019     Document Type: Article

References (17)

1. Sven Axsater Inventory control 2006 Springer Verlag
2. John R. Birge, and François Louveaux Introduction to stochastic programming corrected ed. Springer Series in Operations Research and Financial Engineering 1997 Springer
3. Wlodzimierz Bryc A uniform approximation to the right normal tail integral Appl. Math. Comput. 127 2-3 2002 365 374
4. Steven K. De Schrijver, El-Houssaine Aghezzaf, and Hendrik Vanmaele Double precision rational approximation algorithm for the inverse standard normal first order loss function Appl. Math. Comput. 219 3 2012 1375 1382
5. Steven K. De Schrijver, El-Houssaine Aghezzaf, and Hendrik Vanmaele Double precision rational approximation algorithms for the standard normal first and second order loss functions Appl. Math. Comput. 219 4 2012 2320 2330
6. Karl Frauendorfer, and Michael Schürle Stochastic linear programs with recourse and arbitrary multivariate distributions Christodoulos A. Floudas, Panos M. Pardalos, Encyclopedia of Optimization 2001 Springer US 2488 2493
7. Momčilo M. Gavrilović Optimal approximation of convex curves by functions which are piecewise linear J. Math. Anal. Appl. 52 2 1975 260 282
8. Alyson Imamoto, and Ben Tang Optimal piecewise linear approximation of convex functions S.I. Ao, Craig Douglas, W.S. Grundfest, Lee Schruben, Jon Burgstone, Proceedings of the World Congress on Engineering and Computer Science 2008, WCECS 2008, October 22-24, 2008 2008 IAENG San Francisco, USA 1191 1194
9. Peter Kall, and Stein W. Wallace Stochastic programming Wiley Interscience Series in Systems and Optimization 1994 John Wiley & Sons
10. Jean M. Linhart Algorithm 885: computing the logarithm of the normal distribution ACM Trans. Math. Software 35 3 2008
11. Renata Mansini, Włodzimierz Ogryczak, and Maria Grazia Speranza Conditional value at risk and related linear programming models for portfolio optimization Ann. Oper. Res. 152 1 2007 227 256
12. Haim Shore Simple approximations for the inverse cumulative function, the density function and the loss integral of the normal distribution J. R. Stat. Soc. Ser. C (Appl. Stat.) 31 2 1982 108 114
13. Edward A. Silver, David F. Pyke, and Rein Peterson Inventory Management and Production Planning and Scheduling 1998 John Wiley & Sons New York
14. Lawrence V. Snyder, and Zuo-Jun M. Shen Fundamentals of Supply Chain Theory first ed. 2011 Wiley
15. S. Armagan Tarim, and Brian G. Kingsman Modelling and computing (Rn,Sn) policies for inventory systems with non-stationary stochastic demand Eur. J. Oper. Res. 174 1 October 2006 581 599
16. Gary R. Waissi, and Donald F. Rossin A sigmoid approximation of the standard normal integral Appl. Math. Comput. 1996 91 95
17. Marvin Zelen, and Norman C. Severo Probability functions Milton Abramowitz, Irene A. Stegun, Handbook of Mathematical Functions Applied Mathematics Series vol. 5 1964 GPO 925 995