Duality

Duality - EMSE 154-254 . Linear programming Sensitivity...

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EMSE 154-254 . Instructor: Hernan Abeledo 1 Linear programming – Sensitivity Analysis and Duality Theory See XPRESS model ABCD and output. model "ABCD" uses "mmxprs" declarations x1, x2, x3: mpvar end-declarations A:= 8*x1 + 6*x2 + x3 <= 48 B:= 4*x1 + 2*x2 + 1.5*x3 <= 20 C:= 2*x1 + 1.5*x2 + 0.5*x3 <= 8 D:= x2 <= 5 Z:= 60*x1 + 30*x2 + 20*x3 maximize(Z) writeln("Total return: " , getobjval) writeln("x1= " , getsol(x1), ", reduced cost= ", getrcost(x1)) writeln("x2= " , getsol(x2), ", reduced cost= ", getrcost(x2)) writeln("x3= " , getsol(x3), ", reduced cost= ", getrcost(x3)) end-model
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EMSE 154-254 . Instructor: Hernan Abeledo 2 Output: Optimal value: z= 280 x1= 2, reduced cost= 0 x2= 0, reduced cost= -5 x3= 8, reduced cost= 0 Additional Mosel output: suppose we include the following print statements: writeln("A activity = " , getact(A), ", A slack = " , getslack(A),", A Dual value = ", getdual(A)) writeln("B activity = " , getact(B), ", B slack = " , getslack(B),", B Dual value = ", getdual(B)) writeln("C activity = " , getact(C), ", C slack = " , getslack(C),", C Dual value = ", getdual(C)) writeln("D activity = " , getact(D), ", D slack = " , getslack(D),", D Dual value = ", getdual(D)) New output is : A activity = 24, A slack = 24, A Dual value = 0 B activity = 20, B slack = 0, B Dual value = 10 C activity = 8, C slack = 0, C Dual value = 0 D activity = 0, D slack = 5, D Dual value = 10 Activity: Evaluation of left hand side of constraint at optimal solution.
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This note was uploaded on 01/02/2010 for the course EMSE 254 taught by Professor Hernanabeledo during the Fall '08 term at GWU.

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Duality - EMSE 154-254 . Linear programming Sensitivity...

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