Multiple Optimal Solution using Excel Solver

H

Haitao

Is anybody who knows how to use Excel Solver to get
multiple optimal solution for linear programming problem?
Thanks a lot!!
 
M

Mike Middleton

Haitao -
Is anybody who knows how to use Excel Solver to get multiple optimal
solution for linear programming problem? <

I usually make a very small change to an objective function coefficient or a
right-hand-side constraint and then rerun Solver.

For example, if the objective function (target cell) is 75*X1 + 50*X2, I
rerun Solver using 75.00001*X1 + 50*X2.

You often can get good "hints" of what to change by examining Solver's
Sensitivity Report.

- Mike Middleton, www.usfca.edu/~middleton
 
M

Mark Wiley

Haitio,

The only way I know of to investigate alternative optima is to iteratively
solve the model.

Here is what I would do. Run your original model and, as Mike suggested,
have it output a sensitivity report. The report indicates a reduced gradient
for each adjustable cell. Loosely speaking, the reduced gradient indicates
the penalty incurred if an adjustable cell were forced into the solution.
Adjustable cells with a final value of greater than zero should have a
reduced gradient of zero (i.e., there is no penalty to force them into the
solution - they are already in the solution). An adjustable cell with a zero
final value and a reduced gradient of -5 means forcing the adjustable cell
to 1 resolving would lower the target cell to be maximized by 5. In a
situation in which you have adjustable cells with final values of zero and
reduced gradients of zero implies they could be forced into the solution
with no penalty (i.e., there are alternative optima).

So, look for an adjustable cell with final value of zero and a reduced
gradient of zero. Add a constraint that the original target cell is equal to
the optimal value. Then specify the adjustable cell with the final value of
zero and a reduced gradient of zero as the new target cell to be maximized.
You should end up with a new solution with the same original optimized
target cell value.

If there are multiple adjustable cells with zero final values and reduced
gradient values in the original sensitivity report, then you can go through
and maximize those one by one.

Hope this helps.

Regards,

Mark Wiley

=================================================================

LINDO Systems, Inc. Tel: (312)988.7422

1415 North Dayton Fax: (312)988.9065

Chicago, IL 60622 URL: http://www.lindo.com

=================================================================

P.S., Shameless plug: LINDO Systems makes an Industrial strength
optimization add-in for Excel named What'sBest as well as other optimization
tools (linear, nonlinear, global, integer, quadratic). If you ever need
something to solve larger models than Excel's solver handles please check us
out.
 

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