Chapter 1 Introduction to Managerial Decision Modeling Management Science - BMGT 555 Professor Ahmadi

Learning Objectives Define decision model and describe its importance. Understand two types of decision models: deterministic and probabilistic models. Understand steps involved in developing decision models in practice. Understand use of spreadsheets in developing decision models. Discuss possible problems in developing decision models.

Introduction Quantitative approaches to decision making are based on the scientific method. Names for this body of knowledge include: Management Science, Operations Research, and Decision Science. It had its early roots in World War II and is flourishing in business and industry with the aid of computers in general and the microcomputer in particular. Some of the primary applications areas of this body of knowledge are management, marketing, production scheduling, capital budgeting, and transportation.

Types of Problem Information Quantitative data - numeric values that indicate how much or how many. Production quantity Rate of return Financial ratios Cash flows Qualitative data - labels or names used to identify an attribute - Pending state or federal legislation New technological breakthrough

Role of Spreadsheets in Decision Modeling Computers are an integral part of decision making. Spreadsheet packages are capable of handling management decision modeling techniques. Have built-in functions and procedures, such as: Goal Seek Data Table Solver Chart Wizard, and others.

Models Models are representations of real objects or situations. Three forms of models are iconic, analog, and mathematical. Iconic models are physical replicas (scalar representations) of real objects. Analog models are physical in form, but do not physically resemble the object being modeled. Mathematical models represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses.

Mathematical Models Cost/benefit considerations must be made in selecting an appropriate mathematical model. Frequently a less complicated (and perhaps less precise) model is more appropriate than a more complex and accurate one due to cost and ease of solution considerations. Mathematical models relate decision variables with fixed or variable parameters. Frequently mathematical models seek to maximize or minimize some objective function subject to constraints. The values of the decision variables that provide the mathematically-best output are referred to as the optimal solution for the model.

Types of Decision Models Deterministic Models Stochastic Models

Transforming Model Inputs into Output Uncontrollable Inputs Controllable Inputs (Decision Variables) Output (Projected Results) Mathematical Model

Steps Involved in Decision Modeling 1. Formulation. 2. Solution. 3. Interpretation.

Step 1: Formulation Defining the problem. Develop clear and concise problem statement. Developing a model. Select and develop a decision model. Select appropriate problem variables. Develop relevant mathematical relation for consideration and evaluation.

Step 1: Formulation (Continued ) Acquiring input data. Collect accurate data for use in the model. Possible data sources are: Official company reports. Accounting, operating, and financial information. Views, and opinions from knowledgeable individuals.

Step 2: Solution Developing a solution involves: Manipulating model to arrive at the best (optimal) solution. Solution of a set of mathematical expressions. Alternative trial and error iterations. Complete enumeration of all possibilities or utilization of an algorithm. Series of steps repeated until best solution is attained.

Step 2: Solution (Continued ) Testing a solution involves: Prior to implementation of model solution, testing the solution. Testing of solution is accomplished by examining and evaluating: Data utilized in the model and On the model itself.

Step 3: Interpretation Interpretation and What-if Analysis. Analyzing the results and sensitivity analysis. Vary data input values and examine differences in various optimal solutions. Make changes in the model parameters and examine differences in various optimal solutions.

Example: Iron Works, Inc. Iron Works, Inc. (IWI) manufactures two products made from steel and just received this month's allocation of b pounds of steel. It takes a1 pounds of steel to make a unit of product 1 and it takes a2 pounds of steel to make a unit of product 2. Let x1 and x2 denote this month's production level of product 1 and product 2, respectively. Denote by p1 and p2 the unit profits for products 1 and 2, respectively. The manufacturer has a contract calling for at least m units of product 1 this month. The firm's facilities are such that at most u units of product 2 may be produced monthly. Develop a mathematical model for the above.

The Model Mathematical Model Summary Max p1x1 + p2x2 s.t. a1x1 + a2x2 < b x1 > m x2 < u x1 & x2 > 0 Suppose b = 2000, a1 = 2, a2 = 3, m = 60, u = 720, p1 = 100, p2 = 200. Rewrite the model with these specific values.

Transforming Model Inputs into Output Uncontrollable Inputs: 100, 200, 2, 3, 2000, 60, 720 Output: Profit Z Controllable Inputs: x1 , x2 The Model: Max Z = 100x1 + 200x2 2 x1 + 3 x2 < 2000 x1 > 60 x2 < 720

Possible Problems in Developing Decision Models Defining the Problem. Conflicting Viewpoints. Impact on Other Departments. Beginning Assumptions. Solution Outdated. Developing a Model. Fitting the Textbook Models. Understanding the Model.

Possible Problems in Developing Decision Models -continued Acquiring Input Data. Validity of Data. Developing a Solution. Hard-to-Understand Mathematics. Only One Answer is Limiting. Testing the Solution. Analyzing the Results.

Implementation – Not Just The Final Step Decision models assist decision maker by providing scientific method, model, and process which is defensible and reliable. Overcome sole reliance upon intuition, hunches, and experience. Mathematical models are the primary forms of models used in Management Science.

Summary Decision Models and Modeling - The three types of models are Iconic, Analog, and Mathematical models. Mathematical Decision models are classified into two categories: Deterministic models. Stochastic (Probabilistic) models. Approach includes three primary steps: Formulation. Solution. Implementation.

The End of Chapter 1