33 lines
1.3 KiB
Mathematica
33 lines
1.3 KiB
Mathematica
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function [z,x_B,index_B] = simplex (type,A,h,c,sign)
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% Simplex method solver for a linear programming problem
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% Input arguments:
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% type = 'max' for maximization, 'min' for minimization
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% A = matrix holding the constraints coefficients
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% h = coefficients of the constraints inequalities (rhs vector)
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% c = coefficients of the objective function
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% sign = vector holding information about the constraints if the system
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% needs to be standardized (-1: less or equal, 0: equal, 1:vgreater or equal)
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m = size(A,1);
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n = size(A,2);
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% Compute the maximum number of basic solutions of the original
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% problem (i.e., the maximum number of iterations necessary to solve the problem)
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itMax = factorial(2*m+n)/(factorial(n+m)*factorial(m));
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% Writing the problem in standard form
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[A_aug,h,c_aug] = standardize(type,A,h,c,m,sign);
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% Determining a starting feasible initial basic solution
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[B,D,c_B,c_D,x_B,x_D,index_B,index_D] = auxiliary(A_aug,c_aug,h,m,n);
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% Solving the linear programming problem with the Simplex method
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[x_B,c_B,index_B] = simplexSolve(type,B,D,c_B,c_D,h,x_B,x_D,index_B,index_D,itMax);
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% Compute the value of the objective function
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z = sum(c_B' .* x_B) + sum(c_D' .* x_D);
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% Output of the solution
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[x_B,index_B] = printSol(z,x_B,index_B,m,n);
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end
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