There are several popular quantitative techniques in business used by owners today to analyze data and make decisions.

## Regression Analysis in Decision Making

Suppose you're a sales manager who's trying to predict next month's numbers. Instinctively, you believe that sales are affected by the weather, competitor's promotions, level of consumer confidence and on and on. But, which of these factors has the most influence on sales? Regression analysis is a technique that helps to provide the answers.

Regression analysis is a way to sort out which variables have the most impact and which should be ignored. The dependent variable is the main factor that you're trying to predict; the independent variables are the factors you suspect will impact the dependent variable.

## Using Regression Analysis

The first step in conducting a regression analysis is to gather the historical data of the dependent and independent variables and plot them on a chart. For example, in our illustration, you could plot the average inches of rainfall per month against sales for the same month. Then, draw a line that roughly runs through the middle of the data points. This is called the regression line.

The dispersion of data points around the regression line will give some indication of the correlation between the amount of rain and sales. With this information, a prediction of future sales can be made based on weather forecasts.

## Linear Programming to Find Solutions

Many situations in business involve optimizing the use of several resources. Linear programming is a simple technique that finds the optimal solution for a complex set of constraints by making a few assumptions. An example will help to illustrate its application.

Consider a farmer who has 110 acres of land and is trying to decide whether to plant wheat or barley. He has a budget of \$10,000 and 1,200 man-days of labor available. These are the constraints.

Wheat costs \$100/acre in seed and fertilizer, uses 10 man-days/acre and produces a profit of \$50/acre.

Barley costs \$200/acre, consumes 30 man-days/acre and nets a profit of \$120/acre.

How much of each crop should the farmer plant to maximize his profits?

## Applying Linear Programming

The application of linear programming to this problem reveals that if the farmer plants 60 acres of wheat and 20 acres of barley, he would reap a maximum profit of \$5,400.

Notice that in this case, the farmer only plants crops on 80 acres and does not use the full 110 acres that he has available. That is because of the budget constraints and the limitation of labor man-days.

These are the types of problems that can be put into mathematical formulas and solved with linear programming techniques.

## Game Theory in Decision Making

Game theory is a study of the interactions between several people in which each person's payoff is affected by the decisions made by others. All of us use game theory in the decisions made on a daily basis.

## Game Theory and the Prisoner's Dilemma

Game theory is best described using the example of the Prisoner's Dilemma.

The police have brought in two suspects for a crime and are interrogating them in separate rooms. The suspects, who cannot communicate with each other, are offered the following options:

• Confess and agree to testify against your partner and you will be set free if your partner does not confess.
• If your partner confesses and you do not, you will be convicted and receive a maximum three years sentence.
• If both of you confess, you will each receive two years in prison.
• If neither of you confesses, each of you will be sentenced to prison for one year.

Which choice should each suspect make? Confess or not confess?

In summary, the suspect who confesses either gets two years in jail or goes free. Not confessing means that the suspect would receive a prison sentence of either one or three years. In this dilemma, the best strategy for each suspect is to confess, regardless of the decision made by the other suspect.

## The Prisoner's Dilemma in Business

In the business world, this type of problem is often seen in the battle between two companies; take Pepsi and Coca-Cola, for example.

Should Pepsi lower its prices? Will Coke respond by dropping its price? What happens to the profits of each company in this case? How will profits respond if each company maintains its high prices?

Using game theory to construct a payoff for each alternative will reveal the best course of action for each company in this pricing dilemma.

## Using Decision Trees to Choose the Best Option

Decision trees are another quantitative technique that managers can use to find the best solution when faced with uncertainty. It is a flowchart diagram that identifies all the decision choices and the payoffs from each alternative. The branches of the tree represent each decision alternative, and the leaves are the payoffs.

Let's take an example. Suppose you like the food business and are considering whether to (1) buy a food truck and start selling fruit smoothies on college campuses or (2) take out a lease and open a sandwich deli in the lobby of an office building. Pro-forma profit projections show the smoothie truck would make an annual profit of \$125,000 while the deli would show a profit of \$85,000. Big difference.

Just on profits, you would go with the truck. But, it's not that simple. The smoothie truck has a 60 percent chance of success, but the sandwich deli has a 90 percent probability of success.

## Using Decision Trees to Weigh Possible Scenarios

What happens if another juice truck shows up on your campus? The college administration refuses to guarantee that they won't sell rights to one of your competitors. How would that affect your probability of success?

Meanwhile, the terms of your lease with the building for the sandwich deli precludes the possibility of a competitor also getting space in the office lobby. You've practically got a captive market with all those employees going past your deli every day.

Constructing a decision tree with all the alternatives with related probabilities and expected payoffs will find the choice with the highest projected return.

## The Challenge of Inventory Management

Inventory is a substantial investment of money and labor expense for all businesses. Managing inventory and controlling costs is a complex challenge.

Raw materials must get ordered and delivered on time. Production processes must move smoothly with the least waste and defects. Finished products need warehouse space for storage and final shipments to customers.

Software programs coordinate all of these activities with formulas that calculate costs, estimate time frames, determine quantities needed, place orders with vendors, set production schedules and create delivery schedules. The number of activities required to manage inventory is almost endless.

## Limitations of Quantitative Techniques

Quantitative techniques cannot be used to explain social issues, which makes them less effective to examine sociology. Mathematical data can show what is happening, but it cannot explain why. Qualitative research based on observation is needed for this insight.

Human emotions, beliefs or perceptions cannot be put into numbers and, therefore, cannot be defined with mathematical equations.

Business managers have a wide range of quantitative analysis techniques to help them analyze vast amounts of data and make more informed decisions. Regression analysis finds the effects of independent variables on a dependent variable to make better forecasts; decision trees find the pathway in a forest of options to the highest payoff. Quantitative techniques are tools that every small business owner should be familiar with and use them every day.