# Re: Question

From: FAROUK AMINU <f.aminu_at_lancaster.ac.uk>
Date: Mon 23 Oct 2000 06:04:00 PM GMT
Message-ID: <Pine.GSO.4.21.0010231749040.21164-100000@unixa.lancs.ac.uk>
```Dear Warwick,

I will start by forwarding my gratitute to you for having sometime to
go through my problem.

To answer your questions, actually what I would like to implement is a
case where I have n-nodes of a graph with costs Ci, i = 1,..,n
associated with the edges of the graph. Cij are costs of going from node i
to node j. The ordering I need to implement is just like a sequence of the
edges such that the costs for traversing edge i (Ci) is the accumulated
cost of all the edges traversed so far plus the cost of going from the
second node of the previous edge to the first node of the current edge
plus the cost of traversing the current edge itself.
I presented the problem this way because I need to know exactly which edge
is traversed after which and what is the resulting cost? I also intend to
have the Cis to be the accumulators so as to be able to impose some
restrictions on each of the Cis.

It took me some long time thinking on how to make the Cis take their
values based on the positions of the edges in the sequence. The only thing
that could come to my mind was using if-then-else, but this could mean
writing the constraints n! times because any permutation of the edges
needs a new constraint, in the situation where n is big then this is not
possible.

I presented a three node version of the problem but in essence I need to
implement a bigger version of the problem with a large number of nodes.

I shall try your formulation and thank you once more for your kind
assistance.

with regards,

Farouk
===============================================================================
UMARU FAROUK AMINU
DEPARTMENT OF MANAGEMENT SCIENCE
LANCASTER UNIVERSITY
LANCASTER
LA1 4YX
U.K.

+44 (0)1524 593865 (School)
+44 (0)1524 383619 (Home)
+44 (0)1524 844885 (Fax)
```
Received on Mon Oct 23 19:04:11 2000

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