Petroleum exploration is notoriously risky. Scarce resources are allocated to drilling opportunities with no guarantee that significant quantities of oil will be found. In the late 1980s and early 1990s the Phillips Petroleum Company was involved in oil and gas exploration along the eastern and southern coasts of the United States. In deciding how to allocate the annual exploration budget between drilling projects the company's managers faced two issues. First, they wanted a consistent measure of risk across projects. For example, they needed to compare projects offering a high chance of low returns, with those offering a low chance of high returns. Second, they needed to decide their level of participation in joint drilling projects with other companies. For example, the company could adopt a strategy of having a relatively small involvement in a wide range of projects. The use of decision trees and utility functions allowed managers to rank investment opportunities.
In this article we explore the process of building and solving management science models, using break-even analysis, also called profit analysis. Break-even is a good topic to expand our discussion of model building and solution because it is straightforward, relatively familiar to most people, and not overly complex. In addition, it provides a convenient means to demonstrate the different ways management science models can be solved mathematically (by hand), graphically, and with a computer (TaylorIII, 2006).
The purpose of break-even analysis is to determine the number of units of a product (i.e., the volume) to sell or produce that will equate total revenue with total cost. The point where total revenue equals total cost is called the break-even point, and at this point profit is zero. The break-even point gives a manager a point of reference in determining how many units will be needed to ensure a profit.
Thus, Monte Carlo simulation is often used in business for risk and decision analysis, to help make decisions given uncertainties in market trends, fluctuations, and other uncertain factors. In the science and engineering communities, MC simulation is often used for uncertainty analysis, optimization, and reliability-based design. In manufacturing, MC methods are used to help allocate tolerances in order to reduce cost. There are certainly other fields that employ MC methods, and there are also times when MC is not practical (for extremely large problems, computer speed is still an issue). However, MC continues to gain popularity, and is often used as a benchmark for evaluating other statistical methods comparing to fuzzy programming.