TomSym Publicity Campaign: Difference between revisions
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Problem type appears to be: mip | Problem type appears to be: mip | ||
Time for symbolic processing: 0. | Time for symbolic processing: 0.011273 seconds | ||
Starting numeric solver | Starting numeric solver | ||
===== * * * =================================================================== * * * | ===== * * * =================================================================== * * * |
Latest revision as of 09:34, 8 November 2011
This page is part of the TomSym Manual. See TomSym Manual. |
Problem description
The small company, Pronuevo, launches a new product into a regional market and wishes to have a publicity campaign using different media. It therefore contacts a regional publicity agency, PRCo, that specializes in this type of regional campaign and completely hands over this task for a total budget of $ 250,000. The agency knows the market well, that is, the impact of publicity in a local magazine or over the radio, or as a TV spot on the regional channel. It suggests addressing the market for two months through six different media. For each medium, it knows the cost and the number of people on which this medium has an impact. An index of the quality of perception of the campaign is also known for every medium.
The publicity agency establishes a maximum number of uses of every medium (for instance, not more than eight transmissions of a TV spot). The table below lists all this information. Pronuevo wants the impact of the publicity campaign to reach at least 100,000 people. Which media should be chosen and in which proportions to obtain a maximum index of perception quality?
Data for the publicity campaign
+------+------------------+----------+------+-------------+----------+ | | |People pot| Unit |Maximum |Perception| |Number|Media type | reached | cost | use | quality | +------+------------------+----------+------+-------------+----------+ | 1 |Free weekly newsp | 12,000 | 1,500| 4 weeks | 3 | | 2 |Monthly magazine | 1,500 | 8,000| 2 months | 7 | | 3 |Weekly magazine | 2,000 |12,000| 8 weeks | 8 | | 4 |Radio spot | 6,000 | 9,000|60 broadcasts| 2 | | 5 |Billboard 4x3 m | 3,000 |24,000| 4 boards | 6 | | 6 |TV spot | 9,000 |51,000| 8 broadcasts| 9 | +------+------------------+----------+------+-------------+----------+
Variables
budget Budget people Persons potentially reached per media costs Unit costs maxuse Maximum use quality Perception quality minpeople
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
budget = 250000;
people = [12000 1500 2000 6000 3000 9000]';
costs = [1500 8000 12000 9000 24000 51000]';
maxuse = [4 2 8 60 4 8]';
quality = [3 7 8 2 6 9]';
minpeople = 100000;
m = length(maxuse);
use = tom('use',m,1,'int');
% All variables are integer.
bnds = {0 <= use <= maxuse};
% Budget constraints
con1 = {costs'*use <= budget};
% Reach constraint
con2 = {people'*use >= minpeople};
% Objective
objective = -quality'*use;
constraints = {bnds, con1, con2};
options = struct;
options.solver = 'cplex';
options.name = 'Publicity Campaign';
sol = ezsolve(objective,constraints,[],options);
PriLev = 1;
if PriLev > 0
invest = sol.use;
for i = 1:length(invest),
if invest(i) ~= 0,
disp(['invest in ' num2str(invest(i)) ' uses of media number ' num2str(i)])
end
end
end
% MODIFICATION LOG
%
% 051201 med Created
% 060116 per Added documentation
% 060125 per Moved disp to end
% 090308 med Converted to tomSym
Problem type appears to be: mip Time for symbolic processing: 0.011273 seconds Starting numeric solver ===== * * * =================================================================== * * * TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31 ===================================================================================== Problem: --- 1: Publicity Campaign f_k -122.000000000000000000 f(x_0) 0.000000000000000000 Solver: CPLEX. EXIT=0. INFORM=101. CPLEX Branch-and-Cut MIP solver Optimal integer solution found FuncEv 1 Elapsed time: 0.003000 sec. invest in 4 uses of media number 1 invest in 2 uses of media number 2 invest in 8 uses of media number 3 invest in 4 uses of media number 4 invest in 4 uses of media number 5