On Dec 2, 12:09 pm, Tushar Mehta <ng-underscore-poster-at-tushar-

hyphen-mehta.see-oh-em> wrote:

I haven't read your post in detail but a long time ago I shared

several tips on how to convert various non-linear criteria into linear

ones.

See my posts inhttp://groups.google.com/group/microsoft.public.excel.programming/bro...

If I can count correctly, the 3rd post by me shows how to "linearize"

a IF condition.

I have 4 cells that Solver is supposed to change to minimize thevalue

of one target cell, where the target cell sums a bunch of rows that

have changed values depending on the 4 aforementioned cells.

Whether I click min or max in solver, it says it solves the equation

fully but the results do not change for min or max compared to the pre-

solver values. To test if it was working, I (in short) click forthe

solver to find an exact target value I know for a fact exists locally

(and required only changing one cell value), but Solver says it cannot

find a feasible solution.

All of this tells me that the proper operations or operation sequence

is not happening during the execution of solver. I thought I'd fixed

the issue at first, when I rearranged the involved formulas so that

everything was on the same Excel sheet, but it didn't work.

Are there other Solver limitations I need to know about that could be

causing the issue? I was surprised that Microsoft Support and the

Solver Help file did not mention that I need to have all formula

references on the same tab, and so am concerned there's other

limitations I am not aware of.

I have tried changing all Solver Options too, but no help.

I will try to simplify the involved data below:

Solver changes these constants...

Cell A2 = 0.31

Cell A3 = 0.25.

Cell A4 = 0.67

Cell A5 = 0.52

to minimize the value of a target cell with the formula:

=SUM

(D41:E2000,I41:J2000,N41:O2000,S41:T2000,X41:Y2000,AC41:AD2000,AH41:AI2000,AM41:AN2000,AR41:AS2000,AW41:AX2000,BB41:BC2000)

The columns summed in the target cell formula above have their own

formulas. An example would be:

=IF(AND(C41<A$2,C41<((A$6*B41)+A$9)),1,0),

where C41 and B41 are constants I am not changing in solver, A$2is

one of the constants I am changing in solver, and A$6 and A$9 have

formulas that reference some of the constants I am changing but are

not directly inputted to the solver.

Thus, solver changing any of A$2 through A$5, will change A$9 and/or A

$6, which in turn changes the column values that are summed in the

target cell formula, thus changing the target cell value.

Thanks for any help,

K

Regards,

Tushar Mehta

Microsoft MVP Excel 2000-presentwww.tushar-mehta.com

Excel and PowerPoint tutorials and add-ins

Hi,

I found where you address the IF statement, but I'm having trouble

following. I think this is on the right path for me, so I'd appreciate

any patience and help to clarify. I've posted your previous post below

with questions at the end of each sentence:

"First, the IF statement. Suppose that a firm has a choice of 2

plants where it can produce a product. If it uses a particular plant

to

produce any amount of the product, it incurs a fixed cost of say

$50,000." -----Do I understand this as choose the plant that creates

more product for the fixed $50,000 price?

"This has the nature of an IF statement of the type [IF x>0 then K

else 0], where K is a constant." -----I don't get what x or K

represent. Does x = amount of product and K = $50,000?

"One can replace the IF with linear equations by introducing a binary

variable, b, and a large constant, say, M. Now, the IF statement

becomes

K*b

x <= M*b

b = 0/1 (b is binary)

x >= 0

How does it work? If x is anything other than 0, the x <= M*b will

be

satisfied only if b is 1. If b is 1, the K*b will evaluate to K!

Also,

since M is a very large number, once b is 1, x <= M*b will alwaysbe

true no matter how large x becomes". ----Does x represent essentially

the binary threshold (i.e. less than x then with this plant, more than

x go with the other plant). If so, can it be a non-zero number? ----

Also I don't get how the binary is applied in Excel.

Thanks!

K

Can anyone help clarify this please? I've seen a similar solution

elsewhere but I can't make out the explanations and thus how to fit to

my data. What is a binary variable in excel, how do I incorporate it

and wouldn't it also cause the function gaps or sudden jumps that

Solver has issues with? To simplify my example above I have the below

example, though the real Excel equaitions are more complicated:

I have a column with:

C1 =IF(A1<B1,1,0)

C2 =IF(A2<B1,1,0)

....

C1000 =IF(A1000<B1,1,0)

Then, D1 = sum(C1:C1000)

Solver is asked to reduce D1 (i.e. target cell) by changing B1.

I found a method using absolute values in the C column equation, e.g.

C1 =((A1-B1)+ABS(A1-B1))*(1/(2*(A1-B1))). This creates values of 0 or

1, but I think this will have the same issue since absolute values can

mess up functions too. I'm currently trying to work it in, which is

tough because the real C columns are IFAND arguments.

Thanks again,

K

I got using ABS to work in creating 0s and 1s and thus removed the IF

statement, but it seems to fail for the same reason as using IF in

SOLVER.

I was thinking I could remove ABS from the above equation C1 =((A1-

B1)+ABS(A1-B1))*(1/(2*(A1-B1))) and turn into:

C1 =(A1-B1). This creates negative and positive number, where

negatives would have = 0 in the ABS equation and 1 for the positives.

Then I'd sum the values in the target cell and ask Solver to maximize

the values. Thus it would try to push as many values above 1 as

possible.

The problem is twofold:

1. There will be a dependency on the magnitude of values, which is

incorrect in my case (all values should be equally important in my

case)

2. Because my real equation which I've simplified above is really not

an IF but instead IFAND statement, I need something that considers

only 1 of the criteria above 0 to be as good ("optimized") as ALL of

the criteria equaling 1)

It seems I need a way to get my neg and pos values to equal 0 and 1

respectively (or vice versa) PRE-solver, without using ABS or any

other Solver stopping functions

By the way, I just tried using SQRT of the squared values instead of

ABS and SOLVER doesn't work with it. I'm not surprised since I guess

Sqrt can cause gaps or jumps just like ABS. Now I'm getting worried.

In case anyone is paying attention, for which I am still holding out

desperate hope, I want to update my progress. Any new readers can

start at this post and hopefully understand the entire issue at hand.

To recap, I initially had IF statements that would equal 0 or 1

depending if a value was more or less some threshold value. Here, I

wanted Solver to change this threshold value to minimize the number of

1s (i.e. maximize the number of 0s). But Solver won't work with IF

statements.

Thus, I needed a workaround where I would essentially get 0s and 1s

without using a IF statements. I tried using ABS as a workaround but

Solver has issues with this too.

Currently, I've tried using sigmoidal functions:

-First, I normalize such that all former 1s are now negative numbers

and 0s are positive numbers (remember that I am using the convention

of wanting to minimize 1s and thus negative numbers in this

transformation). This gives me a range of data with no theoretical max

or min, but in practice gives between -0.39 and 1.07.

-Next, I want to cluster this continuous range of pos and neg values

as closely to 0 and 1, respectively so I use a sigmoidal function on

each data value in the general form of:

f(x)=1-1/(1+e^(-weight*x)),

where x = the given data value (the given pos or neg value being

compared to the threshold); e = 2.718; weight = a value I can change

to squeeze/stretch the sigmoid shape; and you can see I subtract all

from 1 in order to reverse 1s and 0s from = pos and neg, to 1=

negative values and 0 = positive values, respectively.

My results show that using weight = 1000 makes the sigmoid squeezed

horizontally enough to make almost all positive values = 0 (i.e. where

the values are close enough to 0 that Excel just outputs them as 0),

but before I reach a weight high enough to make all pos = 0 and neg =

1, I get #NUM! for many of my formerly negative values. It seems that

Excel has a lower resolution for small compared to large numbers, and

this limit of resolution is reached for many of my negative data point

values before I can increase the weight enough to make most of my

values essentially 0 and 1.

Do my explanations sound correct for what is going on? Any suggestions

on how to move forward?

Thanks,

k