Week 5     Global Competition - a Competitive Index


Through the various projects during weeks 1-4, you should have seen numerous applications of linear algebra to problems in science, engineering, business and society. While certainly not all encompassing, they may have provided reasonable exposure to what mathematical models can be used for.

This project, however, is much less about linear algebra and much more about your role in business or industry. It seeks to have you consider your potential place in the global workplace as well as the very nature of global competition.

Finally, a mathematical model is proposed, which, if implemented, would provide a mechanism for quantifying competition.

Part One Who Would You Like to Work for?

In this part, you, as a team, must pick a company you would like to work for. This may be any company at all. The only restriction is that it is not a governmental agency or department; it is part of the "private sector". It is probably a good idea if the company in question relates to the majors of some, if not all, of the members of your team.

Once you have decided upon a company, please include a description of the company in your project. Your description should include: product, brief history, size (employees and sales) at the least.

Additionally, you should include a list of who you feel the competition of your company is.

Finally, what jobs have you taken with this company (one per team member)?

Part Two How do you measure your company?

In this part, the goal is to come up with a list of characteristics or attributes which one would use to judge a company by in terms of its ability to compete in the global marketplace. These are also called indicators in some circles. Whatever term you wish to use, as a team, you need to make a list of any criteria you would use in comparing one company with another, where both are competing.

As a starting point, you might consider things such as : value of stock (if public), market share, revenue per employee, money spent on employee improvement, investment in new equipment or technology, quality of product (needs refinement) and so on.

Your list should include at least 7 such attributes, with a brief discussion of why you chose each and what the unit of measurement in each case would be. No actual data needed here.

Now that you have a list of attributes, you have to decide, in relative terms, how important each one is. To this end, for each attribute, assign a number, called a weight, between 0 and 1, which indicates its relative importance. Additionally, the total of all your weights should add up to one. In your writeup, have two columns, one with the attribute and one with the associated weight. At the bottom of the second column, total them up.

So you can relate this to real life at bit more, include a brief description of the DowJones stock index and the Consumer Price Index

The sum total at any given instant in time of all of the attributes you have chose, with possible weighting factors added, is a measure of the competitive level of your company and may be called a competitive index. Since that number may look kind of arbitrary, the usual method (such as in stock market indices) is to divide the current index value by the value for the first month considered (the so called base month). So if the value is greater than 1, things have improved; less than 1 means things have declined.

Part Three   What Independent Variables are There?

From elementary calculus, especially functions, we know that independent variables are those which may be set to any value within a permissible domain. Dependent variables, or output variables, are the results of setting those independent variables.

If you are a manager within a company, then in its simplest form, your job is to make decisions about the setting of independent variables. For that reason, they are often called decision variables. Examples might be: how much to spend on advertising, who to hire and with what background, who to buy raw materials from, what information to get from customers and so on.

In making these decisions, you hope to positively affect the indicators of your company (the dependent variables). If you spend more on advertising, you hope the market share goes up. If you pick the best supplier of raw materials, you hope the quality of your product goes up. If you spend more on salaries, you hope to hire better people, and so on. Since there is no nice functional relationship like in elementary calculus, you are not sure of what impact your choices will make - you often have to sit back and hope the desired result happens. Sometimes one goal may be met while another is not. The Florida Marlins last year had one of the highest payrolls in Major League Baseball. For that spending they won the World Series! But on the other hand, they were $30 million in the red and had to be sold.

In this section, for your particular company, list what you feel are the most important decision variables. You should have at least 5 and preferably more. In listing them, include your reasons on why you feel intelligent choice of them should have a positive impact on the attributes described in Part Two.

Part Four     A Mathematical Model

Where does all this lead? We have a number of attributes we would like to increase so that our index increases. We have a list of decision variables we can control. But it is not clear what quantitative relationship exists between the two groups. If there were, then it would be easier to pick values for the decision variables!

Here is where regression analysis (see Project #1 of Week 1 ) If one performs linear regression analysis on data from the recent history of the company, then relationships between the variables may be quantified. The upshot is that a model of the form:

can be set up where:

            Y = an mx1 column of dependent variables (attributes which make up the index from Part Two)

            X = an nx1 column of independent or decision variables (from Part Three )

and      A = an m x n matrix whose entries are defined as

            aij = effect of a one unit change in xj on yi

or, in elementary calculus terms, aij is the derivative of yi with respect to x j.

The problem then becomes one of seeking to optimize the index discussed in part two by best choice of the decision variables, X. This is a project for another course!


This particular project should have caused you to have thought about your own future as it makes a contribution to a company in todays economy and world. Further, it should have pointed out that the very nature of competition can be quantified and that techniques such as those introduced in Ma 2071 might be used to analyze it. If one can productively use mathematics to better perform one's job or manage one's company, then the mathematics is useful and worthy of the time you have put in while learning it. That has been a goal of this course.

This Project:

You should turn in a written paper with an introduction, results for parts 1-3, and a conclusion which summarizes what you feel you gained from this project. Working as a team, this should not take more than a few hours. It is not intended to. Please hand this in no later than 10:00 am on Monday, Feb 16.