[SCIP] How to understand the math formulation of the VRP example within the SCIP suite?

[Jakob Witzig]

Hi Tianci,

in graph theory, \delta(i) is a very common notation for the degree of 
some node i, you will find this in almost all books and even on 
wikipedia (https://en.wikipedia.org/wiki/Glossary_of_graph_theory#D). 
Thus, y(\delta(j)) is a short formulation for \sum_{e \in E : j \in e} 
y_{e}.

To understand the model, please compare constraints 1 and 2 and think 
about the correlation between this two if (a) y_{e} = 0, (b) y_{e} = 1, 
and (c) y_{e} = 2. The impact of y_{e} on the pricing problem and the 
pricing problem itself are described on the website you refer.

Cheers,
Jakob

Am 27.04.2016 um 04:55 schrieb zhangtiancy at 163.com:
> Hi,
>
> I'm learning the VRP example provided with the SCIP suite recently.
>
> The description of the math model seems rather abstract and some symbols
> are not explained, which made it difficult for me to understand.
>
> For example, what does the \delta(j) mean in the second constraint as
> presented in the webpage http://scip.zib.de/doc/examples/VRP/ ?
>
> I tried to look at some textbooks and online documents on the VRP
> problem, but they all looks different from the formulation presented in
> that webpage.
>
> Could anyone give me some instructions on how to make clear that model
> formulation?
>
> Thank you in advance!
>
> Sincerely,
>
> ------------------------------------------------------------------------
> Tianci
>
>
> _______________________________________________
> Scip mailing list
> Scip at zib.de
> http://listserv.zib.de/mailman/listinfo/scip
>


-- 
Jakob Witzig

Zuse Institute Berlin (ZIB)

Division Mathematical Optimization and Scientific Information
Research Group Mathematical Optimization Methods

Takustrasse 7
14195 Berlin

Tel. : +49 (0)30 84185-416
Fax  : +49 (0)30 84185-269
email: witzig at zib.de