2. The company SchoolDesk produces desks of different sizes for kindergartens, p

Question

2. The company SchoolDesk produces desks of different sizes for kindergartens, primary and secondary schools, and colleges. The legs of the desks all have the same diameter, with different lengths: 40 cm for the smallest ones, for medium height, and 70ch for the largest ones. These legs are cut from steel bars of 1.5 meters. The company has received an order for 108 small, 125 medium and 100 large desks. How should this order be produced if the company wishes to minimize the trim loss? a. Find all possible cutting patterns. b. Write an integer programming model in order to find the optimal solution.

Explanation / Answer

VARIABLES

patterns - different cutting patterns

demand - different length demand

loss - each pattern loss

lengths - length  

patterns = [ 0 0 2 0 2 3 0 0 1 3 0 5;...

0 1 0 2 1 0 1 2 0 0 3 0;...

2 1 1 0 0 0 2 1 2 1 0 0];

demand = [108;125;100]*4;

loss = [10 20 0 30 10 30 0 10 20 10 20 0];

lengths = [150;200];

p = size(patterns,2);

use = tom('use',p,1,'int');

% Bounds

bnds = {use >= 0};

% Minimum demand must be met

con = {pattern*use >= demand};

% Objective

objective = sum(lengths(1)*use(1:end/2) + lengths(2)*use(end/2+1:end));

% Constant to be deducted from objective

objective = objective - 75200;

constraints = {bnds,con};

options = struct;

options.solver = 'cplex';

options.name = 'cutting steel bars';

sol = ezsolve(objective,constraints,[],options);

loss = sum(sol.use.*loss);

Prilev = 1;

if Prilev > 0

x = sol.use;

idx = find(x);

order = [x(idx) idx];

disp(['a minimum loss of' num2str(loss) ' is found with this combination

for i = 1:length(idx),

disp(['cut' num2str([order(i,1)]) ' bar(s) in pattern ' num2str([order(i,1)]

end

end

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