2. Department of Business Administration SPRING 200 7 -0 8 Management Science by Asst. Prof. Sami Fethi © 2007 Pearson Education

3. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 2 Outline: What You Will Learn... The Management Science Approach to Problem Solving Model Building : Break-Even Analysis Computer Solution Management Science Modeling Techniques Business Usage of Management Science Techniques Management Science Models in Decision Support Systems

4. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 3 The Management Science Approach Management science uses a scientific approach to solving management problems. It is used in a variety of organizations to solve many different types of problems. It encompasses a logical mathematical approach to problem solving. Management Science, also known as Operations Research, Decision Sciences, etc., involves a philosophy of problem solving in a logical manner.

5. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 4 The Management Science Process Figure 1.1 The Management Science Process

6. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 5 Steps in the Management Science Process Observation - Identification of a problem that exists (or may occur soon) in a system or organization. Definition of the Problem - problem must be clearly and consistently defined, showing its boundaries and interactions with the objectives of the organization. Model Construction - Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem. Model Solution - Models solved using management science techniques. Model Implementation - Actual use of the model or its solution.

7. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 6 Example of Model Construction (1 of 3) Information and Data: Business firm makes and sells a steel product Product costs $5 to produce Product sells for $20 Product requires 4 pounds of steel to make Firm has 100 pounds of steel Business Problem: Determine the number of units to produce to make the most profit, given the limited amount of steel available.

8. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 7 Example of Model Construction (2 of 3) Variables: X = number of units to produce (decision variable) Z = total profit (in $) Model: Z = $20X - $5X (objective function) 4X = 100 lb of steel (resource constraint) Parameters: $20, $5, 4 lbs, 100 lbs (known values) Formal Specification of Model: maximize Z = $20X - $5X subject to 4X = 100

9. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 8 Example of Model Construction (3 of 3) Model Solution Consider the constraint equation: 4x = 100 or x = 25 units Substitute this value into the profit function: Z = $20x - $5x = (20)(25) – (5)(25) = $375 (Produce 25 units, to yield a profit of $375)

10. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 9 Model Building: Break-Even Analysis (1 of 8) Used to determine the number of units of a product to sell or produce (i.e. volume) that will equate total revenue with total cost. The volume at which total revenue equals total cost is called the break-even point. Profit at break-even point is zero.

11. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 10 Model Building: Break-Even Analysis (2 of 8) Model Components Fixed Costs (cf) - costs that remain constant regardless of number of units produced. Variable Cost (cv) - unit production cost of product. Total variable cost (vcv) - function of volume (v) and unit variable cost. Total Cost (TC) - total fixed cost plus total variable cost. Profit (Z) - difference between total revenue vp (p = unit price) and total cost, i.e. Z = vp - cf - vcv

12. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 11 Model Building: Break-Even Analysis (3 of 8) Computing the Break-Even Point The break-even point is that volume at which total revenue equals total cost and profit is zero: vp - c f – vc v = 0 or v = c f /(p - c v ) (Break-Even Point)

13. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 12 Model Building: Break-Even Analysis (4 of 8) Example: Western Clothing Company Fixed Costs: c f = $10000 Fixed Costs: c f = $10000 Variable Costs: c v = $8 per pair Variable Costs: c v = $8 per pair Price : p = $23 per pair Price : p = $23 per pair The Break-Even Point is: v = (10,000)/(23 -8) e.i., v = cf/(p - cv) = 666.7 pairs = 666.7 pairs This gives the company a point of reference from which to determine how many pairs of jeans it needs to produce and sell in order to gain a profit.

14. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 13 Model Building: Break-Even Analysis (5 of 8) Figure 1.2 Break-Even Model

15. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 14 Sensitivity Analysis If we develop a general relationship for determining the break even volume, this enables us to see how the level of profit or loss is directly affected by changes in volume. When we develop such a model, we assume that our parameters fixed and variable costs and price are constant. In reality such parameter are frequently uncertain and can rarely be assumed to be constant and changes in any of the parameters can affect the model solution. Such changes on a management model is called sensitivity analysis- observing how sensitive the model is to changes.

16. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 15 Model Building: Break-Even Analysis (6 of 8) Figure 1.3 Sensitivity Analysis - Break-even Model with a Change in Price

17. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 16 Model Building: Break-Even Analysis (7 of 8) Figure 1.4 Sensitivity Analysis - Break-Even Model with a Change in Variable Cost

18. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 17 Model Building: Break-Even Analysis (8 of 8) Figure 1.5 Sensitivity Analysis - Break-Even Model with a Change in Fixed Cost

19. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 18 Break-Even Analysis: Excel Solution (1 of 5) Exhibit 1.1

20. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 19 Break-Even Analysis: Excel QM Solution (2 of 5) Exhibit 1.2

21. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 20 Break-Even Analysis: Excel QM Solution (3 of 5) Exhibit 1.3

22. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 21 Break-Even Analysis: QM Solution (4 of 5) Exhibit 1.4

23. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 22 Break-Even Analysis: QM Solution (5 of 5) Exhibit 1.5

24. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 23 Classification of Management Science Techniques Figure 1.6 Modeling Techniques

25. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 24 Characteristics of Modeling Techniques Linear Mathematical Programming - clear objective; restrictions on resources and requirements; parameters known with certainty. Probabilistic Techniques - results contain uncertainty. Network Techniques - model often formulated as diagram; deterministic or probabilistic. Forecasting and Inventory Analysis Techniques - probabilistic and deterministic methods in demand forecasting and inventory control. Other Techniques - variety of deterministic and probabilistic methods for specific types of problems.

26. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 25 Business Use of Management Science Some application areas: - Project Planning - Capital Budgeting - Inventory Analysis - Production Planning - Scheduling Interfaces - Applications journal published by Institute for Operations Research and Management Sciences (INFORMS)

27. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 26 Management Science Models Decision Support Systems (1 of 2) A decision support system (DSS) is a computer-based system that helps decision makers address complex problems that cut across different parts of an organization and operations. A DSS is normally interactive, combining various databases and different management science models and solution techniques with a user interface that enables the decision maker to ask questions and receive answers. Online analytical processing system (OLAP), the analytical hierarchy process (AHP), and enterprise resource planning (ERP) are types of decision support systems. Decision support systems are most useful in answering “what- if?” questions and performing sensitivity analysis.

28. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 27 Management Science Models Decision Support Systems (1 of 2) Figure 1.7 A Decision Support System

29. Operations Research © 2007/08, Sami Fethi, EMU, All Right Reserved. Ch 1: Management Science 28 The End Thanks