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diff --git a/code/linprog/MoulderProblem_RHSchange.sce b/code/linprog/MoulderProblem_RHSchange.sce new file mode 100644 index 0000000..95721c5 --- /dev/null +++ b/code/linprog/MoulderProblem_RHSchange.sce @@ -0,0 +1,78 @@ +// Example problem of sensitivity analysis - changes in RHS + +//Reference : Bradley, Hax, and Magnanti,"Applied Mathematical Programming", Addison-Wesley, 1977, chapter 3 + +//A custom molder has one injection-molding machine and two different dies to fit the machine. Due to differences in number of cavities and cycle times, withthe first die he can produce 100 cases of six-ounce juice glasses in six hours,while with the second die he can produce 100 cases of ten-ounce fancy cocktail glasses in five hours. The molder is approached by a new customer to produce a champagne glass. The production time for the champagne glass is 8 hours per hundred cases. He prefers to operate only on a schedule of 60 hours of production per week. He stores the week’s production in his own stockroom where he has an effective capacity of 15,000 cubic feet. A case of six-ounce juice glasses requires 10 cubic feet of storage space, while a case of ten-ounce cocktail glasses requires 20 cubic feet due to special packaging.The storage space required for the champagne glasses is 10 cubic feet per one case. The contribution of the six-ounce juice glasses is $5.00 per case; however, the only customer available will not accept more than 800 cases per week. The contribution of the ten-ounce cocktail glasses is $4.50 per case and there is no limit on the amount that can be sold where as the contribution of champagne glasses is $6.00 per case with no limit on the bound. How many cases of each type of glass should be produced each week in order to maximize the total contribution? +//============================================================================= +// 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; + +nProducts = 3; +TotalProcessingTime = 60; +RequiredTime = [6 5 8]; +StokeRoomCapacity = 15000; +RequiredSpace = [10 20 10]*100; +Demand = 8; +Revenue = [5 4.5 6]; +nVar = nProducts // Each variable indicates number of hundreds of units of each product + +// Linear constraints +// Processing time constraint +A1 = RequiredTime; +b1 = TotalProcessingTime; +// Space constraint +A2 = RequiredSpace; +b2 = StokeRoomCapacity; +// Demand constraint +nDemand = length(Demand); +A3 = eye(nDemand,nVar); +b3 = Demand'; + +A = [A1;A2;A3]; b = [b1;b2;b3]; + +//Addition of slack variables +nInEqConstraints = length(b); +Aeq = eye(nInEqConstraints,nInEqConstraints); +Aeq = [A Aeq]; +beq = b; + +Cost = -[Revenue zeros(1,nInEqConstraints)]'; +lb = zeros(1,size(Aeq,2)); + +[xopt,fopt,exitflag,output,lambda]=linprog(Cost, [],[], Aeq, beq, lb,[]); +clc; +select exitflag +case 0 + mprintf('The optimum solution has been found \n') + disp(xopt(1:nVar)', "The optimum number of six-ounce juice glasses,ten-ounce fancy cocktail glasses and champagne glass") + SlackVariables = xopt(nVar+1:length(xopt)); + disp(SlackVariables',"The surplus resource available") + Index = find(SlackVariables>0); + newbeq = beq(Index) - SlackVariables(Index); + changedbeq = beq; + changedbeq(Index) = newbeq; + mprintf(' The value beyond %f of the RHS value of constraint number %d will not change the optima. \n ',newbeq,Index) + mprintf('\n The optimal cost is %f',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 |