Projects per year
Abstract
The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the standard normal cumulative distribution and probability density function. However, the standard normal cumulative distribution does not admit a closed form solution and cannot be easily linearised. Several works in the literature discuss approximations for either the standard normal cumulative distribution or the first order loss function and their inverse. However, a comprehensive study on piecewise linear upper and lower bounds for the first order loss function is still missing. In this work, we initially summarise a number of distribution independent results for the first order loss function and its complementary function. We then extend this discussion by focusing first on random variable featuring a symmetric distribution, and then on normally distributed random variables. For the latter, we develop effective piecewise linear upper and lower bounds that can be immediately embedded in MILP models. These linearisations rely on constant parameters that are independent of the mean and standard deviation of the normal distribution of interest. We finally discuss how to compute optimal linearisation parameters that minimise the maximum approximation error.
Original language  English 

Pages (fromto)  489502 
Number of pages  22 
Journal  Applied Mathematics and Computation 
Volume  231 
DOIs  
Publication status  Published  15 Mar 2014 
Keywords
 First order loss function
 Complementary first order loss function
 Piecewise linear approximation
 Minimax
 Edmundson–Madansky
 Jensen’s
Fingerprint
Dive into the research topics of 'Piecewise linear approximations of the standard normal first order loss function'. Together they form a unique fingerprint.Projects
 2 Finished

Confidencebased optimization for inventory management at a local grocery store
Rossi, R. & Yao, X.
1/09/13 → 31/08/14
Project: University Awarded Project Funding

Vegitrade: Logistic chain modelling and packaging modelling as input for microbiological risk assessment
Rossi, R., van der Vorst, J. G. A. J. & Rijpkema, W. A.
1/03/09 → 28/02/13
Project: Project from a former institution
Activities
 1 Participation in conference

20th Conference of the International Federation of Operational Research Societies
Roberto Rossi (Speaker)
2014Activity: Participating in or organising an event types › Participation in conference