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Management Science Modeling Lecture One

Management Science Modeling Lecture One. Introduction to Modeling (Chapter One). Chapter Topics. The Management Science Approach. The Management Science Process. Figure 1.1. Steps in the Management Science Process. Example of Model Construction (1 of 3). Information and Data:

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Management Science Modeling Lecture One

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  1. Management Science Modeling Lecture One Introduction to Modeling (Chapter One) MS Modeling S 2010

  2. Chapter Topics MS Modeling S 2010

  3. The Management Science Approach MS Modeling S 2010

  4. The Management Science Process Figure 1.1 MS Modeling S 2010

  5. Steps in the Management Science Process MS Modeling S 2010

  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. MS Modeling S 2010

  7. Example of Model Construction (2 of 3) Variables: X = # 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 MS Modeling S 2010

  8. Example of Model Construction (3 of 3) Model Solution: Solve the constraint equation: 4x ≤ 100 (4x)/4 ≤ (100)/4 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) MS Modeling S 2010

  9. Model Building: Break-Even Analysis (1 of 9) • Used to determine the number of units of a product to sell or produce 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. MS Modeling S 2010

  10. Model Building:Break-Even Analysis (2 of 9) Model Components • Fixed Cost (cf) - costs that remain constant regardless of number of units produced. • Variable Cost (cv) - unit production cost of product. • Volume (v) – the number of units produced or sold • Total variable cost (vcv) - function of volume (v) and unit variable cost. MS Modeling S 2010

  11. Model Building:Break-Even Analysis (3 of 9) Model Components • 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. MS Modeling S 2010

  12. Model Building:Break-Even Analysis (4 of 9) Computing the Break-Even Point The break-even point is that volume at which total revenue equals total cost and profit is zero: The break-even point MS Modeling S 2010

  13. Model Building: Break-Even Analysis (5 of 9) Example:Western Clothing Company Fixed Costs: cf = $10000 Variable Costs: cv = $8 per pair Price : p = $23 per pair The Break-Even Point is: v = (10,000)/(23 -8) = 666.7 pairs MS Modeling S 2010

  14. Model Building: Break-Even Analysis (6 of 9) Figure 1.2 MS Modeling S 2010

  15. Model Building: Break-Even Analysis (7 of 9) Figure 1.3 MS Modeling S 2010

  16. Model Building: Break-Even Analysis (8 of 9) Figure 1.4 MS Modeling S 2010

  17. Model Building: Break-Even Analysis (9 of 9) Figure 1.5 MS Modeling S 2010

  18. Break-Even Analysis: Excel Solution (1 of 5) Exhibit 1.1 MS Modeling S 2010

  19. Break-Even Analysis: Excel QM Solution (2 of 5) Exhibit 1.2 MS Modeling S 2010

  20. Break-Even Analysis: Excel QM Solution (3 of 5) Exhibit 1.3 MS Modeling S 2010

  21. Break-Even Analysis: QM Solution (4 of 5) Exhibit 1.4 MS Modeling S 2010

  22. Break-Even Analysis: QM Solution (5 of 5) Exhibit 1.5 MS Modeling S 2010

  23. Classification of Management Science Techniques Figure 1.6 Modeling Techniques MS Modeling S 2010

  24. Characteristics of Modeling Techniques • Linear Mathematical Programming -clear objective; restrictions on resources and requirements; parameters known with certainty. (Chap 2-6, 9) • Probabilistic Techniques -results contain uncertainty. (Chap 11-13) • Network Techniques - model often formulated as diagram; deterministic or probabilistic. (Chap 7-8) • Other Techniques - variety of deterministic and probabilistic methods for specific types of problems including forecasting, inventory, simulation, multicriteria, etc. (Chap 10, 14-16) MS Modeling S 2010

  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) MS Modeling S 2010

  26. Decision Support Systems (DSS) A decision support system is a computer-based system that helps decision makers address complex problems that cut across different parts of an organization and operations. Features of Decision Support Systems • Interactive • Use databases & management science models • Address “what if” questions • Perform sensitivity analysis Examples include: ERP – Enterprise Resource Planning OLAP – Online Analytical Processing MS Modeling S 2010

  27. Management Science Models Decision Support Systems (2 of 2) Figure 1.7 A Decision Support System MS Modeling S 2010

  28. Do you have any questions about this chapter? MS Modeling S 2010

  29. Assignment for Chapter One Problems #4, 10, 12, 22, and 24 MS Modeling S 2010

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