Saturday, December 5, 2015

How Can a Simple Rule in Set Theory help us to derive strategies in Strategic Management?

One of the most important and also hardest step of a strategic analysis or designing strategic plan is to derive and to develop strategies by using of SWOT matrix. Because we have to compare and to match SO (strengths – opportunities) Strategies, WO (weakness – opportunities) Strategies, ST (strengths – threats) Strategies and WT (weaknesses – threats) Strategies to make new ones by thinking and using of our own ideas. Consequently, we need to take high level of focus and concentration on our job. Unfortunately, by using only SWOT matrix as a tool, we are not able to focus at ease on all strengths, opportunities, weaknesses and threats simultaneously. The purpose of this article is to increase students and strategic analysts’ convenience to have better concentration on content of SWOT matrix to make reasonable strategies. In this case, a new simple rule in set theory has been utilized to solve a case in excel and then by using of the result of excel case and also Monte Carlo method, a template on excel spreadsheet to derive strategies has been made and presented.

A new simple rule in set theory

In the reference with item 5 and rule 5 included in article of “Are These Rules new Conjectures in Set Theory?” posted on link:, we have below formula:

N' = n - r +1

One of the properties this rule is, to invert members of a set for instance:

 A = {1, 2, 3, 4}

 B = {(4-1+1), (4-2+1), (4-3+1), (4-4+1)}

 I used this property to solve a case in excel.

Case: How can we turn a matrix to 180 degree in excel?

We can easily turn a matrix to 90 degree by using of TRANSPOSE’ formula in excel. I am not a specialist in excel maybe there is another formula to turn a matrix to 180 degree. Here, I am willing to show you my solution to solve this case step by step by an example as follows:

- Assume we have a matrix of 16*8 including members of a, b, c…

- Copy matrix between cells N1:U1 and N16:U16

- On cell M1 to M16 fill numbers 1 to 16

- On cell A1 fill formula = 16 – M1 + 1 which is the same n - r +1 and copy to A16
- On cell B1 copy below formula and copy to K1 and A16 to K16
I have enclosed new matrix below cited:

A template on spreadsheet to derive strategies in Strategic Management

Assume, we have made SWOT matrix and we will derive SO strategies. I used an example extracted from book of “Strategic Management Concepts and Cases” Thirteenth Edition by Fred R. David, Chapter 6 and Figure 6-3 as follows:


S1. Inventory turnover up 5.8 to 6.7

S2. Average customer purchase up $97 to $128

S3. Employee morale is excellent

S4. In – store promotions = 20% increase in sales

S5. Newspaper advertising expenditures down 10%

S6. Revenues from repair/service in-store up 16%

S7. In-store technical support persons have MIS degrees

S8. Store’s debt-to-total assets ratio down 34%

O1. Population of city growing 10%
O2. Rival computer store opening 1mile away
O3. Vehicle traffic passing store up 12%
O4. Vendors average six new products/yr
O5. Senior citizen use of computers up 8%
O6. Small business growth in area up 10%
O7. Desire for Web sites up 18% by Realtors
O8. Desire for Web sites up 12% by small firms
I utilized from Monte Carlo method in which I had already explained this method in many articles such as below ones:
-A Monte Carlo Analysis on Case of Nike, Inc.: Cost of Capital (link:
-Application of Pascal’s Triangular plus Monte Carlo Analysis to Find the Least Squares Fitting for a Limited Area (link:
- Application of Pascal’s Triangular plus Monte Carlo Analysis to Design a Strategic Plan (link:
How should we make Cut Off tables?
First of all, we should divide the probability distribution in accordance with the number of Strengths (S) and Opportunities (O).
The most crucial thing to bear in mind is, to make two Cut Off tables for Strengths (S) in which the probability distribution is constant but Strengths (S) are inverse and also this is for Opportunities (O). In this case, we will cover all Strengths (S) and Opportunities (O) on template.
In this step, we have to use to turn a matrix to 180 degree in excel.
I have attached the example for Cut Off tables as follows:

Now, we have four cell which we can change Strengths (S) and Opportunities (O) by each click on ENTER or F9 and also it cover all Strengths (S) and Opportunities (O) just like below cited:

Of course, for having a complete template, we should continue all above steps for WO (weakness – opportunities), ST (strengths – threats) and WT (weaknesses – threats).