Problem maxt unbounded 42x xigs2 if at any iteration

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: are non-positive, and the objective coefkient is (-) for maximization [or (+) for minimization] for that variable then, the problem is unbounded in the direction of that variable l l ernate Optimal Problem Special Cases Unbounded uftxr-20~~+$04 Iteration 0 Sk -.4yt.I*50 0 2~+4~s 100 @ Basic Xl ?I 5 x4 Soln I -2 -1 0 0 0 x3 1 -1 1 0 10 4 1 0 0 1 40 nr . . Special Cases Alternate Optimal Aiternate Optimal Iteration 0 If in an optimal tableau The coeffkient of any non-basic variable is zero in the z-row then, the probkm has alternate optimal solutions with equioptimal objective values Basic l z l x1 I I x2 x4 0 -4 -2 saln x3 010 I xJ 1 2 10 5 4 1 1 0 4 . . EM-602 / QM-710 (NJ) Lecture 5 Page 5-7 1 Alternate Optimal (iterationa 1 L 2) IL-h 0 2 0 1 1 -1 0 -1 2 see problem 2-l 7 1 1 Infeasible Problem X 24 3 3 I[q ~~~ I 01101 Special Cases Infeasible Iteration8 0 & 1 Infeasible Basic if, in an optimal tableau, An artifictai variable is basic and has value > zero, and The objective function value contains M if minimizing [or (A) if maximizing] then the probtem is infeasible Note: if the artiftciai variable is basic but with zero value, the problem is feasible, but had one or more redundant constraints L l x1 ~2 q ~q R, SoIn u 0 0 0 01 0 112 2 0 M 2+4M 0 4-SY 1 0 0 -1 1 -4 0 1 2 4 -3-3M_2-4M ;I:: 4-l 1 -1215 l L l+Skl g2 2 Ri -5 .. Homework Assignment Due in 1 we&k l Note: Textbook problem # 341 l l The remainder of the slides are presented for your reference only They were not discussed in class and are thus not included in the scope of the course EM-602 / QM-710 (NJ) Lecture 5 Page 5-8 Dual Problem Degenerate For every LP problem (called the Primal) we can derive a related symmetrkal LP (called the Dual) l The solution of the Primal LP automatically gives the optlmal solution to the Dual l The solution of the Dual LP automatkally gives the optimal solution to the Primal l The decision variables and objective for the primal are XJ and r; and for the dual they are y and w If In successive iterations of the tableau l The objective function value stays the same l the non-basic variable’s z-row entry is nonzero l the bask variable’s z-row entries are zero then the solution at this point is degenerate Note: Degeneracy may be temporary (degenerate point is suboptimal) or permanent (degenerate at optlmallty) Dual Problem Dual Problem l l l For every prlmal constraint there is a dual variable For every primal variable there is a dual constraint The co...
View Full Document

This document was uploaded on 03/31/2014 for the course MS 602 at NJIT.

Ask a homework question - tutors are online