Projects per year
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.
|Number of pages||22|
|Journal||Applied Mathematics and Computation|
|Publication status||Published - 15 Mar 2014|
- First order loss function
- Complementary first order loss function
- Piecewise linear approximation
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- 2 Finished
Confidence-based optimization for inventory management at a local grocery store
Rossi, R. & Yao, X.
1/09/13 → 31/08/14
Project: University Awarded Project Funding
Veg-i-trade: 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
- 1 Participation in conference
20th Conference of the International Federation of Operational Research Societies
Roberto Rossi (Speaker)2014
Activity: Participating in or organising an event types › Participation in conference