TomSym Choice of Loans: Difference between revisions
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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== |
Revision as of 17:24, 2 November 2011
This page is part of the TomSym Manual. See 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
% 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.
Problem setup
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
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