# t9 - iii Can the upper bound(z = 41 in the example on the...

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iii) Can the upper bound (z = 41, in the example) on the optimal value z# of the integer program be improved while the problem is being solved? The answer to the first question is an unqualified yes. When moving from a region to one of its subdivisions, we add one constraint that is not satisfied by the optimal linear-programming solution over the parent region. Moreover, this was one motivation for the dual simplex algorithm, and it is natural to adopt that algorithm here. Referring to the sample problem will illustrate the method. The first two subdivisions L1 and L2 in that example were generated by adding the following constraints to the original problem: For subdivision 1 : x2 # 4 or x2 - s3 = 4 (s3 # 0); For subdivision 2 : x2 # 3 or x2 + s4 = 3 (s4 # 0). In either case we add the new constraint to the optimal linear-programming tableau. For subdivision 1, this gives: (-z) - 5 4 s1 - 3 4 s2 = -411 4 x1 + 9 4 s1 - 1 4 s2 = 9 4 j x2 - 5 4 s1 + 1 4 s2 = 15 4 9> => ; Constraints from the

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## This note was uploaded on 10/15/2011 for the course MBAHRM 565 taught by Professor Profbhattacharya during the Spring '11 term at IIT Kanpur.

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t9 - iii Can the upper bound(z = 41 in the example on the...

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