TomSym Choice of Loans - Revision history

Mbot at 13:33, 8 November 2011

2011-11-08T13:33:05Z

← Older revision		Revision as of 09:33, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: lp		Problem type appears to be: lp
	Time for symbolic processing: 0.~~015755~~ seconds		Time for symbolic processing: 0.013581 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *

Mbot at 21:24, 2 November 2011

2011-11-02T21:24:13Z

← Older revision		Revision as of 17:24, 2 November 2011
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	Rates offered by the banks for the different projects		Rates offered by the banks for the different projects

			<pre>
	+------+------+------+----+		+------+------+------+----+
	\| \|London\|Munich\|Rome\|		\| \|London\|Munich\|Rome\|
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	\|Bank 3\| 5.5% \| 5.8% \|6.5%\|		\|Bank 3\| 5.5% \| 5.8% \|6.5%\|
	+------+------+------+----+		+------+------+------+----+
			</pre>

	Depending on the location of the shops and the evaluation of the related risks, each bank decides to finance at most $ 3 million over 8 years with different interest rates for the shops. Determine the amount to borrow from each bank for financing each shop in order to minimize the total expenses of Mr Chic.		Depending on the location of the shops and the evaluation of the related risks, each bank decides to finance at most $ 3 million over 8 years with different interest rates for the shops. Determine the amount to borrow from each bank for financing each shop in order to minimize the total expenses of Mr Chic.
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	==Variables==		==Variables==

			<pre>
	rates The rates		rates The rates
	costs Cost per site		costs Cost per site
	maxloan Max loan per bank		maxloan Max loan per bank
	loanlength Length of the loan in years		loanlength Length of the loan in years
			</pre>

	==Reference==		==Reference==

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== Mr Chic, director of a chain of shops selling clothes, wishes to open three new..."

2011-11-02T21:01:19Z

Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== Mr Chic, director of a chain of shops selling clothes, wishes to open three new..."

New page

{{Part Of Manual|title=the TomSym Manual|link=[[TomSym|TomSym Manual]]}}

==Problem description==

Mr Chic, director of a chain of shops selling clothes, wishes to open three new shops: one in London, one in Munich, and one in Rome. To open a new shop costs respectively $ 2.5 million, $ 1 million and $ 1.7 million. To finance his project, he calls at three different banks.

Rates offered by the banks for the different projects

+------+------+------+----+
| |London|Munich|Rome|
+------+------+------+----+
|Bank 1| 5.0% | 6.5% |6.1%|
|Bank 2| 5.2% | 6.2% |6.2%|
|Bank 3| 5.5% | 5.8% |6.5%|
+------+------+------+----+

Depending on the location of the shops and the evaluation of the related risks, each bank decides to finance at most $ 3 million over 8 years with different interest rates for the shops. Determine the amount to borrow from each bank for financing each shop in order to minimize the total expenses of Mr Chic.

==Variables==

rates The rates
costs Cost per site
maxloan Max loan per bank
loanlength Length of the loan in years

==Reference==

Applications of optimization... Gueret, Prins, Seveaux

<source lang="matlab">
% Marcus Edvall, Tomlab Optimization Inc, E-mail: tomlab@tomopt.com
% Copyright (c) 2005-2009 by Tomlab Optimization Inc., $Release: 7.2.0$
% Written Oct 7, 2005. Last modified Apr 8, 2009.
</source>

==Problem setup==

<source lang="matlab">
rates = [ 5.0 6.5 6.1 ;...
5.2 6.2 6.2 ;...
5.5 5.8 6.5 ];

costs = [2.5 1.0 1.7]'*1e6;
maxloan = 3e6;
loanlength = 8;

b = size(rates,1);
s = size(rates,2);

borrow = tom('borrow',b,s);

% No variables are binary.
bnds = {0 <= borrow};

% Shop constraints
con1 = {sum(borrow,1)' == costs};

% Bank constraints
con2 = {sum(borrow,2) <= maxloan};

% Objective
rates = rates/100;
objective = sum(sum(borrow.*(rates./(1-(1+rates).^(-loanlength)))));

constraints = {bnds, con1, con2};
options = struct;
options.solver = 'cplex';
options.name = 'Depot Location';
sol = ezsolve(objective,constraints,[],options);

PriLev = 1;
if PriLev > 0
temp = sol.borrow;
for i = 1:s,
site = temp(:,i);
idx = find(site);
disp(['To finance shop at site ' num2str(i)])
for j = 1:length(idx),
disp([' take a loan of ' num2str(site(idx(j))) ...
' in bank ' num2str(idx(j))])
end
end
end

% MODIFICATION LOG
%
% 051130 med Created.
% 060116 per Added documentation.
% 090308 med Converted to tomSym
</source>

<pre>
Problem type appears to be: lp
Time for symbolic processing: 0.015755 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Depot Location f_k 822180.656176676160000000
f(x_0) 0.000000000000000000

Solver: CPLEX. EXIT=0. INFORM=1.
CPLEX Dual Simplex LP solver
Optimal solution found

FuncEv 4 Iter 4
Elapsed time: 0.002000 sec.
To finance shop at site 1
take a loan of 2500000 in bank 1
To finance shop at site 2
take a loan of 1000000 in bank 3
To finance shop at site 3
take a loan of 500000 in bank 1
take a loan of 1200000 in bank 2

</pre>