1 / 57

Lecture

Lecture. 1. MGMT 650 Management Science and Decision Analysis. Agenda. Operations Management Chapter 1 Management Science & relation to OM Quantitative Analysis and Decision Making Cost, Revenue, and Profit Models Management Science Techniques Introduction to Linear Programming.

terence
Télécharger la présentation

Lecture

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 1 MGMT 650 Management Science and Decision Analysis

  2. Agenda • Operations Management • Chapter 1 • Management Science & relation to OM • Quantitative Analysis and Decision Making • Cost, Revenue, and Profit Models • Management Science Techniques • Introduction to Linear Programming

  3. Organization Finance Marketing Operations Operations Management The management of systems or processes that create goods and/or provide services

  4. Production of Goods vs. Delivery of Services • Production of goods – tangible output • Delivery of services – an act • Service job categories • Government • Wholesale/retail • Financial services • Healthcare • Personal services • Business services • Education

  5. Scope of Operations Management • Operations Management includes: • Forecasting • Capacity planning • Scheduling • Managing inventories • Assuring quality • Deciding where to locate facilities • And more . . . • The operations function • Consists of all activities directly related to producing goods or providing services

  6. Management Science • The body of knowledge involving quantitative approaches to decision making is referred to as • Management Science • Operations research • Decision science • It had its early roots in World War II and is flourishing in business and industry with the aid of computers

  7. Problem Solving and Decision Making • Steps of Problem Solving (First 5 steps are the process of decision making) • Define the problem. • Identify the set of alternative solutions. • Determine the criteria for evaluating alternatives. • Evaluate the alternatives. • Choose an alternative (make a decision). --------------------------------------------------------------------- • Implement the chosen alternative. • Evaluate the results.

  8. Quantitative Analysis and Decision Making • Potential Reasons for a Quantitative Analysis Approach to Decision Making • The problem is complex • The problem is very important • The problem is new • The problem is repetitive

  9. Physical – – Schematic – Mathematical Models A model is an abstraction of reality. Tradeoffs What are the pros and cons of models?

  10. A Simulation Model

  11. Models Are Beneficial • Easy to use, less expensive • Require users to organize • Systematic approach to problem solving • Increase understanding of the problem • Enable “what if” questions: simulation models • Specific objectives • Power of mathematics • Standardized format

  12. Quantitative Approaches • Linear programming: optimal allocation of resources • Queuing Techniques: analyze waiting lines • Inventory models: management of inventory • Project models: planning, coordinating and controlling large scale projects • Statistical models: forecasting

  13. Analysis of Trade-offs • How many more jeans would Levi need to sell to justify the cost of additional robotic tailors? • Cost of additional robotic tailors vs Inventory Holding Cost

  14. Product Mix Example

  15. A Linear Programming Model • Objective – profit maximization Maximize 60X1 + 50X2 • Subject to Assembly 4X1 + 10X2 <= 100 hours Inspection 2X1 + 1X2 <= 22 hours Storage 3X1 + 3X2 <= 39 cubic feet X1, X2 >= 0

  16. Cost, Revenue and Profit Models

  17. Cost Classification of Owning and Operating a Passenger Car

  18. Cost-Volume Relationship

  19. Cost-Volume Relationship

  20. Amount ($) Total cost = VC + FC Total variable cost (VC) Fixed cost (FC) 0 Q (volume in units) Cost-Volume Relationships Total revenue Amount ($) 0 Q (volume in units)

  21. Cost-Volume Relationships Profit Total revenue Amount ($) Total cost 0 BEP units Q (volume in units)

  22. Example: Ponderosa Development Corp. • Ponderosa Development Corporation (PDC) is a small real estate developer that builds only one style house. • The selling price of the house is $115,000. • Land for each house costs $55,000 and lumber, supplies, and other materials run another $28,000 per house. Total labor costs are approximately $20,000 per house. • Ponderosa leases office space for $2,000 per month. The cost of supplies, utilities, and leased equipment runs another $3,000 per month. • The one salesperson of PDC is paid a commission of $2,000 on the sale of each house. PDC has seven permanent office employees whose monthly salaries are given on the next slide.

  23. Example: Ponderosa Development Corp. EmployeeMonthly Salary President $10,000 VP, Development 6,000 VP, Marketing 4,500 Project Manager 5,500 Controller 4,000 Office Manager 3,000 Receptionist 2,000

  24. Example: Ponderosa Development Corp. • Identify all costs and denote the marginal cost and marginal revenue for each house. • Write the monthly cost function c (x), revenue function r (x), and profit function p (x). • What is the breakeven point for monthly sales of the houses? • What is the monthly profit if 12 houses per month are built and sold? • Determine the BEP for monthly sale of houses graphically.

  25. Graph of costs and Break-even point

  26. Example: Step Fixed Costs • A manager has the option of purchasing 1, 2 or 3 machines • Fixed costs and potential volumes are as follows: • Variable cost = $10/unit and revenue = $40/unit • If the projected annual demand is between 580 and 630 units, how many machines should the manager purchase?

  27. Break-Even Problem with Step Fixed Costs Total Cost FC + VC = TC Total Revenue BEVs FC + VC = TC 3 machines FC + VC = TC 2 machines 1 machine Quantity Step fixed costs and variable costs.

  28. Assumptions of Cost-Volume Analysis • One product is involved • Everything produced can be sold • Variable cost per unit is the same regardless of volume • Fixed costs do not change with volume • Revenue per unit constant with volume • Revenue per unit exceeds variable cost per unit

  29. Fixed Variable Total City Cost Cost Cost Akron $30,000 $75 $180,000 Bowling Green $60,000 $45 $150,000 Chicago $110,000 $25 $160,000 Cost-Volume & Locational Break-Even Analysis Three locations: Total Cost = Fixed Cost + Variable Cost x Volume

  30. – $180,000 – – $160,000 – $150,000 – – $130,000 – – $110,000 – – – $80,000 – – $60,000 – – – $30,000 – – $10,000 – – Chicago cost curve Annual cost Bowling Green cost curve Akron cost curve Akron lowest cost Chicago lowest cost Bowling Green lowest cost | | | | | | | 0 500 1,000 1,500 2,000 2,500 3,000 Volume Locational Break-Even Analysis Graph of Break-Even Points

  31. Linear Programming – Chapter 2 George Dantzig – 1914 -2005

  32. Linear Programming • Concerned with optimal allocation of limited resources such as • Materials • Budgets • Labor • Machine time • among competitive activities • under a set of constraints

  33. Variables Objective function Constraints Non-negativity Constraints Linear Programming Example Maximize 60X1 + 50X2 Subject to 4X1 + 10X2 <= 100 2X1 + 1X2 <= 22 3X1 + 3X2 <= 39 X1, X2 >= 0 • What is a Linear Program? • A LP is an optimization model that has • continuous variables • a single linear objective function, and • (almost always) several constraints (linear equalities or inequalities)

  34. Linear Programming Model • Decision variables • unknowns, which is what model seeks to determine • for example, amounts of either inputs or outputs • Objective Function • goal, determines value of best (optimum) solution among all feasible (satisfy constraints) values of the variables • either maximization or minimization • Constraints • restrictions, which limit variables of the model • limitations that restrict the available alternatives • Parameters: numerical values (for example, RHS of constraints) • Feasible solution: is one particular set of values of the decision variables that satisfies the constraints • Feasible solution space: the set of all feasible solutions • Optimal solution: is a feasible solution that maximizes or minimizes the objective function • There could be multiple optimal solutions

  35. Another Example of LP: Diet Problem • Energy requirement : 2000 kcal • Protein requirement : 55 g • Calcium requirement : 800 mg

  36. Example of LP : Diet Problem • oatmeal: at most 4 servings/day • chicken: at most 3 servings/day • eggs: at most 2 servings/day • milk: at most 8 servings/day • pie: at most 2 servings/day • pork: at most 2 servings/day Design an optimal diet plan which minimizes the cost per day

  37. Step 1: define decision variables • x1 = # of oatmeal servings • x2 = # of chicken servings • x3 = # of eggs servings • x4 = # of milk servings • x5 = # of pie servings • x6 = # of pork servings Step 2: formulate objective function • In this case, minimize total cost • minimize z = 3x1 + 24x2 + 13x3 + 9x4 + 24x5 + 13x6

  38. Step 3: Constraints • Meet energy requirement 110x1 + 205x2 + 160x3 + 160x4 + 420x5 + 260x6 2000 • Meet protein requirement 4x1 + 32x2 + 13x3 + 8x4 + 4x5 + 14x6  55 • Meet calcium requirement 2x1 + 12x2 + 54x3 + 285x4 + 22x5 + 80x6  800 • Restriction on number of servings 0x14, 0x23, 0x32, 0x48, 0x52, 0x62

  39. So, how does a LP look like? minimize 3x1 + 24x2 + 13x3 + 9x4 + 24x5 + 13x6 subject to 110x1 + 205x2 + 160x3 + 160x4 + 420x5 + 260x6 2000 4x1 + 32x2 + 13x3 + 8x4 + 4x5 + 14x6  55 2x1 + 12x2 + 54x3 + 285x4 + 22x5 + 80x6  800 0x14 0x23 0x32 0x48 0x52 0x62

  40. Optimal Solution – Diet ProblemUsing LINDO 6.1 • Cost of diet = $96.50 per day

  41. Optimal Solution – Diet ProblemUsing Management Scientist • Cost of diet = $96.50 per day

  42. Guidelines for Model Formulation • Understand the problem thoroughly. • Describe the objective. • Describe each constraint. • Define the decision variables. • Write the objective in terms of the decision variables. • Write the constraints in terms of the decision variables • Do not forget non-negativity constraints

  43. Graphical Solution of LPs • Consider a Maximization Problem Max 5x1 + 7x2 s.t. x1< 6 2x1 + 3x2< 19 x1 + x2< 8 x1, x2> 0

  44. Graphical Solution Example • Constraint #1 Graphed x2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 x1< 6 (6, 0) x1

  45. Graphical Solution Example • Constraint #2 Graphed x2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 (0, 6 1/3) 2x1 + 3x2< 19 (9 1/2, 0) x1

  46. Graphical Solution Example • Constraint #3 Graphed x2 (0, 8) 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 x1 + x2< 8 (8, 0) x1

  47. Graphical Solution Example • Combined-Constraint Graph x2 x1 + x2< 8 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 x1< 6 2x1 + 3x2< 19 x1

  48. Graphical Solution Example • Feasible Solution Region x2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 Feasible Region x1

  49. Graphical Solution Example • Objective Function Line x2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 (0, 5) Objective Function 5x1 + 7x2 = 35 (7, 0) x1

  50. Graphical Solution Example • Optimal Solution x2 Objective Function 5x1 + 7x2 = 46 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 Optimal Solution (x1 = 5, x2 = 3) x1

More Related