Mathematical modeling uses quantitative analysis to help decision-makers make better decisions. Quantitative analysis is based on commonly accepted principles and methods. It is a scientific approach to decision making. We can teach the fundamentals. It is up to you to recognize when and where they are applicable. On the other hand, qualitative analysis is based on judgment and experience. It is more of an art than a science and it cannot be formally taught.

Life would be easy if all problems could be solved to completion using some quantitative method. Unfortunately, such nice and neat problems are often rare in real life. In the presence of qualitative factors, quantitative analysis should be used in conjunction with qualitative analysis. Our ability to conduct such quantitative analysis has grown tremendously in recent years due to computing capability.

Throughout the semester, we will be using quantitative methods to model approximations of real life problems. A mathematical model represents a problem by a system of symbols and mathematical relationships or equations. The model must be simple enough to understand and solve, but complex enough to represent reality. Tradeoff: realism in the model for ease of model development and solution.

The purpose, or value, of any model is that it enables us to make inferences about the real situation by studying and analyzing the model. In general, experimenting with models requires less time and is less expensive than experimenting with the real situation.
 

*Seven Step Modeling Process

Define the Problem

Define the right problem clearly, concisely, and coherently. We want to solve the problem, not just some problem. Be sure that you are attacking the problem and not just a symptom.

Data Collection

A seemingly small problem may require thousands of inputs. Data are not often readily available. Even of they are, they may not be complete or in the appropriate form.

Model Formulation

Develop a mathematical representation of the problem.

Model Verification

Pretest model. Confirm that assumptions are satisfied and valid. Evaluate whether or not level of complexity is appropriate.

Selection of Alternative

Use the model to recommend decisions or strategies. Some solution procedures find the optimal solution to the problem. This is not always possible or practical, so others use heuristics to find "good" solutions.

Often the solution procedure is determined based on the way you choose to model the problem.

Some models are descriptive rather than prescriptive.

Presentation of Results

Effectively and credibly communicate model and results. Document logic. Sell your solution - don't just report a bunch of numbers.

Implementation of Model

Monitor and update over time. Provide necessary training.
 

* Based on Winston, Wayne L. and S. Christian Albright, Practical Management Science: Spreadsheet Modeling and Applications, 1997, Duxbury.
 
 

All seven steps are not required for every model developed. These should be regarded as guidelines.

We will be using a variety of forecasting models this semester due to the type of client project that we have. The course can be easily modified to include queueing models, inventory models, linear programming models, simulation models, ...