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author | RemyaDebasis | 2018-07-23 20:08:46 +0530 |
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committer | RemyaDebasis | 2018-07-23 20:08:46 +0530 |
commit | 392bc1326ebccd63e40cb55a82116208a54f2478 (patch) | |
tree | a98a596b8c4b64baa45966e3cc1ab75651def780 /code/linprog/AirforceBombDuality.sce | |
parent | 69460c03b8b53068d60fd08d3180efc91e627603 (diff) | |
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-rw-r--r-- | code/linprog/AirforceBombDuality.sce | 73 |
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diff --git a/code/linprog/AirforceBombDuality.sce b/code/linprog/AirforceBombDuality.sce new file mode 100644 index 0000000..3bc2ef3 --- /dev/null +++ b/code/linprog/AirforceBombDuality.sce @@ -0,0 +1,73 @@ +//Reference: J.K. Sharma,"OPerations Research Theory and Applications", Macmillan Publishers India Ltd., 5th edition, 2013, Chapter 4. + +//An Air Force is experimenting with three types of bombs P,Q and R in which three kinds of explosives, viz., A, B and C will be used. Taking the various factors into account, it has been decided to use the maximum 600 kg of explosive A, at least 480 kg of B and exactly 540 kg of explosive C. Bomb P requires 3,2,2 kg, bomb Q requires 1,4,3 kg and bomb R requires 4,2,3 kg of explosives A,B and C respectively. Bomb P is estimated to give the equivalent of a 2 ton explosion, bomb Q, a 3 ton of explosion and bomb R, a 4 ton of explosion respectively. Under what production schedule can the Air Force make the biggest bang? +//============================================================================= +// Copyright (C) 2018 - IIT Bombay - FOSSEE +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt +// Author: Remya Kommadath +// Organization: FOSSEE, IIT Bombay +// Email: toolbox@scilab.in +//============================================================================ + +clc; +// =============================Primal Model=================================== +nVar = 3; + +// Linear inequalities +A = [3 1 4; -2 -4 -2]; +b = [600 -480]'; +nIneqCon = length(b); + +// Linear equality +Aeq = [2 3 3]; +beq = 540; +nEqCon = length(beq); + +lb = zeros(1,nVar); +ub = []; + +Cost = -[2 3 4 ]'; + +// =============================Dual Model=================================== + +// Inequality constraints +dual_A = -[A;Aeq]'; +dual_beq = Cost; +n_dualIneq = length(dual_beq); +Coeff_Slack = [eye(n_dualIneq,n_dualIneq);]; +dual_Aeq = [dual_A Coeff_Slack]; +dual_Cost = [b;beq; zeros(n_dualIneq,1)]; + +dual_nVar = length(dual_Cost); +lb = [zeros(1,nIneqCon) -%inf*ones(nEqCon) zeros(1,(dual_nVar-nIneqCon-nEqCon))]; +ub = []; + +[xopt,fopt,exitflag,output,lambda]=linprog(dual_Cost, [],[], dual_Aeq, dual_beq, lb,ub); +clc + +select exitflag +case 0 + disp(xopt(1:nIneqCon+nEqCon)',"Dual values of the primal constraints") + disp(xopt(nIneqCon+nEqCon+1:dual_nVar)',"Dual values of the primal variables") + TopRow = ["Variable " "Rate of change in optima"]; + Table = string([(1:length(xopt))' -xopt]); + disp("The change in optima due to one unit increase in each variables are given as below") + disp([TopRow;Table]) + disp(["The optimal cost is ", string(fopt)]) +case 1 + disp("Primal Infeasible") +case 2 + disp("Dual Infeasible") +case 3 + disp("Maximum Number of Iterations Exceeded. Output may not be optimal") +case 4 + disp("Solution Abandoned") +case 5 + disp("Primal objective limit reached") +case 6 + disp("Dual objective limit reached") +end |