MT 235 MT235 Math for Management Science Professor Jeffrey L. Ringuest

MT 235 Decision Analysis Decision Science, Management Science, Operations Research, Operational Research Applying the methods of science to management decision making Methods of Science - logic, mathematics, computers and the use of models

MT 235 A Modeling Approach to Decision Making Mental model - picturing in your “minds eye” Visual model - blueprints, schematics, maps Physical models - scale models and prototypes

MT 235 A Modeling Approach to Decision Making Mathematical models - mathematical symbols are used to represent decision variables which are then related by the appropriate math functions to describe a real system or decision problem

MT 235 Benefits of Models Less costly to analyze than real system or problem Can be analyzed more rapidly Facilitate “what if” and “what’s best” analysis Provide insight about real problem or system

MT 235 Benefits of Models “By modeling various alternatives for future system design, Federal Express has, in effect, made its mistakes on paper. Computer modeling works; it allows us to examine many different alternatives and it forces the examination of the entire problem.” Frederick W. Smith, Chairman and CEO Federal Express Corporation

MT 235 Benefits of Models “Think of every enterprise, whether it is Intel or a hotel, involved in adjusted capacity-demand pricing. … If this can be done computers-to- computers in real time, you’ll see another power of 10 increase in the efficiency of the work in the economic system. Now how do we get there? … Bits and pieces of it exist in decision theory and operations research.” Andy Grove, CEO Intel Corp.

MT 235 Benefits of Models “Level 3, at its heart, is a technology-based company and frankly, the central technology is operations research and optimization, which I tend to think is going to revolutionize all of business over the next 20 years.” James Q. Crowe, CEO Level 3 Communications

MT 235 Benefits of Models “Based on Eastman Kodak Company’s records for 1990 to 1999, we estimate that decision analysis contributed around a billion dollars to the organization over time. The data also reflect the many roles decision analysis can play. Aside from the monetary benefits, it promotes careful thinking

MT 235 Benefits of Models about strategies and alternatives, improved understanding and appreciation of risk, and use of systematic decision-making principles.” - from Robert T. Clemen and Robert C. Kwit, “The value of decision analysis at Eastman Kodak Company, ”, Interfaces, Vol. 31, No. 5, September - October 2001.

MT 235 The Modeling Process The process of building a model begins with an understanding of the real world system. Management must be able to answer questions such as:

MT 235 The Modeling Process What drives the system under consideration? What are the key factors which predict the behavior of the system? What problems are relevant to management? What are the appropriate measures of success?

MT 235 The Modeling Process The next step in the modeling process involves simplifying and abstracting from the real world system. This model formulation step is exceptionally important.

MT 235 The Modeling Process Should the model be too complex it may be difficult if not impossible to solve. If the model is too simple management may not be willing to trust results obtained with the model fearing that the model is unrealistic.

MT 235 The Modeling Process Once a model is formulated an appropriate solution methodology must be identified. Data must also be collected to estimate the parameters of the model.

MT 235 The Modeling Process That solutions are available at this point does not mean that the managerial questions have been answered. These solutions must be interpreted. Interpretation may be thought of as a reversal of the formulation step.

MT 235 The Modeling Process Formulation required that the broad description of the real world system be narrowed and abstracted. Interpretation requires that the narrow meaning of the solution be broadened and applied to the actual situation.

MT 235 The Modeling Process This set of steps; understanding, formulation, solution and interpretation should provide new insights on the real world system. This insight may well provide new understanding of the problem and restart the modeling process. Thus, the modeling process should be an iterative one.