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Re: [Help-glpk] Building set of sets from plain set

From: Andrew Makhorin
Subject: Re: [Help-glpk] Building set of sets from plain set
Date: Wed, 10 Dec 2008 08:55:28 +0300

> AMPL has specific arc/node based variables and constraints that are
> similar to your example (see example below).  Seems like this also
> allows efficient sparse network generation.

> set V;
> set E within (V cross V);

> param cost {E} >= 0;      # shipment costs per ton

> minimize Total_Cost;

> node Supply {k in V}: net_out = 0;
> node Demand {k in V}: net_in = 0;

> arc Ship {(i,j) in E} >= 0, <= link_cap[i,j],
>    from Demand[i], to Supply[j], obj Total_Cost cost[i,j]; 

> arc Through {k in V} >= 0, <= city_cap[k],
>    from Supply[k], to Demand[k];

Thank you for information.

Yes, this Ampl feature looks like an attempt to specify some
constraints by columns rather than by rows that is more efficient in
case of network models. Or may be due to network solvers.

However, this Ampl feature seems to me quite artificial. I would not
like to be limited only by network models. The feature which I plan to
include in Mathprog is much more general and able to cover network
models as a particular case of lp problems.

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