### Daniel Hamilton (University of Edinburgh)

#### Diet problems

*Wednesday 27 January 2010 at 15.30, JCMB 6206*

##### Abstract

Diet problems are optimisation problems where typically several raw materials
are combined at minimum cost to make a product, subject to nutrient
requirements.

The simplest type of diet problem is the Blending Problem, which was one of
the first LPs solved. With the introduction of intermediate mixing bins the
Pooling Problem is formed. We look at solving this NLP using SLP. When several
factories are combined together we get a large NLP, that we call the
Multifactory Problem. We solve this using decomposition by factory. We also
look at using decomposition to find the global minimum to this highly
nonconvex problem. A further type of diet problem that has integer constraints
we call the Silo Problem. This is an MINLP, which we solve by decomposition
into NLP and ILP.

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