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Lab 5

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Hassan Ibrahim
Hassan Ibrahim

The document provides instructions to solve a linear programming problem using GAMS. It defines the objective function and constraints of the problem. It then performs some modifications to the constraint coefficients based on if-else statements. It conducts a sensitivity analysis by changing the right hand side of one constraint and resolves the problem. It writes the results to a text file before and after the sensitivity analysis.

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Cairo University, Software Packages, Faculty of Computers and Information, Lab # 1 Decision Support Department, Solve the below problems using GAMS IDE: Max z = 5x1 + 4x2 Subject to c1 6x1 + 4x2 24 , c2 x1 + 2x2 6 , c3 -x1 1 , c4 x2 2 , x1 , x2 0 Display the optimal solution . If- elseif Check if coefficient of x2 in c3 less than 1, then make it 1 else if coefficient of x2 in c2 more than 1 and coefficient of x1 in c1 more than 2 ; then put coefficient of x1 in c3 equal -1 else let coefficient of x1 in c4 equal 0 Sensitivity analysis Change the value of r.h.s of c2 from 6 to 10. See the impact on the solution. Writing to file Write the results on a text file before and after sensitivity analysis.
$eolcom -> Sets i / i1,i2 / j / j1 * j4 / ; parameters objcoeff(i) / i1 5, i2 4/ rhs(j)/j1 24, j2 6, j3 1, j4 2 /; Table d(j,i) i1 i2 j1 6 4 j2 1 2 j3 -1 0 j4 0 1 ; if (d("j3","i2")<1, d("j3","i2")=1 ; elseif (d("j2","i2")>1) and (d("j1","i1")>2),d("j3","i1")=-1; else d("j4","i1")=0;); Variables x(i) z ; Positive Variable x ; Equations profit constraint(j) ; profit .. z =e= sum(i, objcoeff(i)*x(i)) ; constraint(j) .. sum(i,d(j,i)* x(i)) =l= rhs(j) ; Model examp /all/ ; Solve examp using lp max z; display x.l,z.l; file results /exampresults.txt/ -> write to afile put results; put 'First example results'// ;
loop (i,put i.tl, x.l(i)/); put 'objective value' z.l//; rhs("j2") = 10; -> senstivity analysis Solve examp using lp max z; display x.l,z.l; put results; -> write to afile put 'Senstivity Example results'// ; -> write text to a file loop (i,put i.tl, x.l(i)/); -> t1 means value of i put 'objective value' z.l//; -> / is endl

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Lab 5

  • 1. Cairo University, Software Packages, Faculty of Computers and Information, Lab # 1 Decision Support Department, Solve the below problems using GAMS IDE: Max z = 5x1 + 4x2 Subject to c1 6x1 + 4x2 24 , c2 x1 + 2x2 6 , c3 -x1 1 , c4 x2 2 , x1 , x2 0 Display the optimal solution . If- elseif Check if coefficient of x2 in c3 less than 1, then make it 1 else if coefficient of x2 in c2 more than 1 and coefficient of x1 in c1 more than 2 ; then put coefficient of x1 in c3 equal -1 else let coefficient of x1 in c4 equal 0 Sensitivity analysis Change the value of r.h.s of c2 from 6 to 10. See the impact on the solution. Writing to file Write the results on a text file before and after sensitivity analysis.
  • 2. $eolcom -> Sets i / i1,i2 / j / j1 * j4 / ; parameters objcoeff(i) / i1 5, i2 4/ rhs(j)/j1 24, j2 6, j3 1, j4 2 /; Table d(j,i) i1 i2 j1 6 4 j2 1 2 j3 -1 0 j4 0 1 ; if (d("j3","i2")<1, d("j3","i2")=1 ; elseif (d("j2","i2")>1) and (d("j1","i1")>2),d("j3","i1")=-1; else d("j4","i1")=0;); Variables x(i) z ; Positive Variable x ; Equations profit constraint(j) ; profit .. z =e= sum(i, objcoeff(i)*x(i)) ; constraint(j) .. sum(i,d(j,i)* x(i)) =l= rhs(j) ; Model examp /all/ ; Solve examp using lp max z; display x.l,z.l; file results /exampresults.txt/ -> write to afile put results; put 'First example results'// ;
  • 3. loop (i,put i.tl, x.l(i)/); put 'objective value' z.l//; rhs("j2") = 10; -> senstivity analysis Solve examp using lp max z; display x.l,z.l; put results; -> write to afile put 'Senstivity Example results'// ; -> write text to a file loop (i,put i.tl, x.l(i)/); -> t1 means value of i put 'objective value' z.l//; -> / is endl