In the simplex method, how is a pivot column selected? A pivot row? A pivot ele

timer Asked: Jul 21st, 2014
account_balance_wallet $5

Question Description

In the simplex method, how is a pivot column selected?  A pivot row? A pivot element?  Give examples of each.

Tutor Answer

Benson K
School: Boston College

Thank you for the opportunity to help you with your question!

1) Pivot column corresponds to a negative value (normally the smallest, or one of them if there are several smallest values) in the index row if the problem is to maximize the object function, or to a positive value (normally the greatest) in the index row if the problem is to minimize (if all the values in the index row are non-negative/non-positive the maximum/minimum is already attained). In the example given these values are 0, 0, 2, -4, 0, 1, so when maximizing the pivot (leading) column should be #4 (corresponding to value -4); when minimizing it is #3 (value 2 - the greatest positive) as shown.

2) The pivot column being determined, consider all POSITIVE components in it (if there is no positive element in the pivot column, the object function is unbounded - infinite optimum). Compare the ratios of each free term and the corresponding positive element in the pivot column - the least of them determines the pivot (leading) row. If there is more than one least ratio, make an arbitrary choice between the corresponding rows. In the example the pivot column is #3, both elements 2 and 4 are positive, so we must compare 10/2 and 13/4 - the second one is the smallest, so the pivot row is #2. If the pivot column was #4, the only ratio is 13/3 in the 2nd row - it is again pivot row.

3) The common element of the pivot row and the pivot column is the pivot element (it is always positive in the standard simplex-method according the above). After the iteration the pivot column should become a unit vector with 1 instead of the pivot element.

Please let me know if you need any clarification. I'm always happy to answer your questions.

flag Report DMCA

Good stuff. Would use again.

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors