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I NTRODUCTION TO MANAGERIAL DECISION MODELING

I NTRODUCTION TO MANAGERIAL DECISION MODELING. OBJECTIVES. Define management science Define and classify decision models List and explain steps involved in developing decision models Remind breakeven analysis with computer applications

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I NTRODUCTION TO MANAGERIAL DECISION MODELING

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  1. INTRODUCTION TO MANAGERIAL DECISION MODELING

  2. OBJECTIVES • Define management science • Define and classify decision models • List and explain steps involved in developing decision models • Remind breakeven analysis with computer applications • Make a classification of management science modeling techniques • Give examples of management science applications • Discuss possible problems in developing decision models

  3. Management Scienceis the scientific approach to executive decision making, which consists of:1.The artof mathematical modeling of complex situations, 2. The scienceof the development of solution techniques used to solve these models, 3. The ability to effectively communicate the results to the decision maker WHAT IS MANAGEMENT SCIENCE?

  4. 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 • It is also referred to as: Decision Modeling QuantitativeAnalysis Operations Research

  5. USES OF DECISION MODELS (1 of 2) • They can solve complex problems. • They provide analytical framework for evaluating modern business problems • They are subject to limitations • They provide techniques applicable in many areas such as: • Accounting, Economics, and Finance • Logistics, Management, and Marketing • Production, Operations, and Transportation

  6. USES OF DECISION MODELS (2 of 2) They can be applied when: • designing and implementing new operations or procedures • evaluating an ongoing set of operations or procedures • determining and recommending corrective action for operations and procedures that are producing unsatisfactory results

  7. TYPES OF PROBLEM INFORMATION • Quantitative data - numeric values that indicate how much or how many. • Rate of return. • Financial ratios. • Cash flows. • Qualitative data - labels or names used to identify an attribute - • Outcome of an upcoming election. • New technological breakthrough.

  8. 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

  9. TYPES OF DECISION MODELS-I (by purpose of the model) Decision Models Optimization Models Predictive Models

  10. Optimization Modelsseek to maximize a quantity (eg. profit) or minimize a quantity (eg. cost, time, etc.) that may be restricted by a set of constraints (limitations on the availability of capital, workers, supplies, machines etc.) OPTIMIZATION MODELS

  11. PREDICTIVE MODELS At times however, the function of a model is not to maximize or minimize any particular quantity, but to describe or predict events given certain conditions These models are known as Predictive Models. These techniques do not generate an answer or a recommended decision. Instead they provide descriptive results: results that describe the system being modeled. They usually provide important input to optimization models

  12. TYPES OF DECISION MODELS-II (by the degree of certainty of the data) Decision Models Deterministic Models Probabilistic Models

  13. DETERMINISTIC MODELS • Deterministic models assume: • Complete certainty. • All information needed is available with fixed and known values. • Most commonly used deterministic modeling technique is Linear Programming.

  14. PROBABILISTIC MODELS • Probabilistic models are also called stochastic models. • Probabilistic models • assume some of data is not known with certainty. • take into account that information will be available after the decision is made.

  15. STEPS INVOLVED IN DECISION MODELING(Management Science Approach) 1.Formulation. 2. Solution. 3. Interpretation.

  16. OVERVIEW OF THE STEPS IN THE MANAGEMENT SCIENCE PROCESS (1 of 3) • Observation - Identification of a problem that exists in the system or organization. • Definition of the Problem - problem must be clearly and consistently defined showing its boundaries and interaction with the objectives of the organization. • Developing a clear and concise problem statement

  17. OVERVIEW OF THE STEPS IN THE MANAGEMENT SCIENCE PROCESS (2 of 3) • Developing a model –Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem. • Amanagement science model is an abstract representation of an existing problem situation. It can be in the form of a graph or chart, but most frequently a Management Science model consists of a set of mathematical relationships that are made up of numbers and symbols.

  18. OVERVIEW OF THE STEPS IN THE MANAGEMENT SCIENCE PROCESS (3 of 3) • Model Solution-Models are solved using management science techniques. • Model Implementation -Actual use of the model or its solution.

  19. STEP 1: MODEL FORMULATION (1 of 2) Developing a model requires to: • identify the decision variables • develop the decision model by quantifying the objective (function to be optimized-profit, cost, etc) and constraints (restrictions on resource availability etc.), ie. develop relevant mathematical relations for consideration and evaluation. • collect accurate data to use as an input in model

  20. STEP 1: MODEL FORMULATION (2 of 2) Possible data sources are: • Official company reports. • Accounting, operating, and financial information. • Views, and opinions from knowledgeable individuals

  21. STEP 2: MODEL SOLUTION (1 of 3) • Developing a solution may involve: • Solution of a set of mathematical expressions to arrive at best (optimal) solution, or • Alternative trial and error iterations, or • Complete enumeration of all possibilities or • Utilization of an algorithm.

  22. STEP 2: MODEL SOLUTION (2 of 3) An appropriate solution technique may be an optimization algorithm (series of steps repeated until the best solution is attained) or a heuristic algorithmMost algorithmsare intended to provide an optimal solution for a model. Sometimes, however, problems can prove to be too complex or time consuming to employ optimization algoritms. In such cases a heuristicprocedure may be preferred

  23. STEP 2: MODEL SOLUTION (3 of 3) • Prior to implementation of model solution, the solution is tested • Testing of solution is accomplished by examining and evaluating: • Datautilized in the model and • Themodelitself.

  24. STEP 3:IMPLEMENTATION & INTERPRETATION (1 of 2) • Optimal solution must be implemented carefully. • Solution implementation usually requires making changes within the organization. • Recommendations often require changes in data, data handling, resource mixes, systems, procedures, policies, and personnel • Managers and others may resist recommended solutions.

  25. STEP 3:IMPLEMENTATION & INTERPRETATION (2 of 2) Interpretation and What-if Analysis. Analyzing the results and sensitivity analysis. (Examine changes in optimal solution as a result of changes in input values and model parameters)

  26. EXAMPLES

  27. EXAMPLE (1 of 2) • 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 profitgiven the limited amount of steel available.

  28. EXAMPLE (2 of 2) Variables: X = number of units (decision variable) Z = total profit 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

  29. BREAK-EVEN ANALYSIS (1 of 4) • Used todetermine 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 (zero profit) is called the break-even point. • Profit at break-even point is zero.

  30. BREAK-EVEN ANALYSIS (2 of 4) Model Components: • Fixed Costs (FC) - costs that remain constant regardless of number of units produced. $’s necessary to invest in facilities • Variable Cost (VC) - unit cost of product. • Total variable cost (Q.VC) - function of volume (Q) and variable per-unit cost. • Total Cost (TC) - total fixed cost plus total variable cost. • Profit (Z) - differencebetween total revenue vp (p = price) and total cost.

  31. BREAK-EVEN ANALYSIS (3of 4) Profit = Total Revenue - Total Cost Profit = Revenue - Fixed Cost - Variable Cost Where: Revenue = [Sales price ($/unit) x Number (units)] Variable Cost = [Variable cost ($/unit) x Number (units)] Fixed Cost = $ necessary to invest in facilities (buildings, equipment, processes, etc.) = constant dollar value.

  32. BREAK-EVEN ANALYSIS (4of 4) Z = P.Q - FC – VC.Q Set profit equal to 0: P.Q=FC+VC.Q Compute the Break-Even Point: Break-even quantity = FC/(P - VC)

  33. EXAMPLE I: BREAK-EVEN ANALYSIS (1 of 10) Example: Western Clothing Company FC = $10000 VC= $8 per pair P = $23 per pair Q= 666.7 pairs, break-even point

  34. EXAMPLE I: BREAK-EVEN ANALYSIS (2 of 10) Graphical Solution

  35. EXAMPLE I: BREAK-EVEN ANALYSIS (3 of 10) Sensitivity Analysis : Break-Even Model with a Change (Increase) in Price

  36. EXAMPLE I: BREAK-EVEN ANALYSIS (4 of 10) Sensitivity Analysis : Break-Even Model with a Change (Increase) in VariableCost

  37. EXAMPLE I: BREAK-EVEN ANALYSIS (5 of 10) Sensitivity Analysis : Break-Even Model with Changes in Fixed and Variable Costs

  38. EXAMPLE I: BREAKEVEN ANALYSIS Excel Computer Solution (6 of 10)

  39. EXAMPLE I:BREAKEVEN ANALYSISExcel QM Computer Solution (7 of 10)

  40. EXAMPLE I:BREAKEVEN ANALYSISExcel QM Computer Solution (8 of 10)

  41. EXAMPLE I:BREAKEVEN ANALYSISExcel QM Computer Solution (9 of 10)

  42. EXAMPLE I:BREAKEVEN ANALYSISExcel QM Computer Solution (10 of 10)

  43. EXAMPLE II: BREAK-EVEN ANALYSIS (1 of 5) Problem: Bill's company, Pritchett's Precious Time Pieces, buys, sells, and repairs old clocks and clock parts. Bill sells rebuilt springs for unit price $10. Fixed cost of equipment to build springs is $1,000. Variable cost per unit is $5 for spring material.

  44. EXAMPLE II: BREAK-EVEN ANALYSIS (2 of 5) Profit = $10Q - $1,000 - $5Q Break-even quantity = FC/(P - VC) BE = $1,000 / [$10 - $5 ] = 200 springs.

  45. EXAMPLE II: BREAK-EVEN ANALYSIS (3 of 5) • Breakeven point (BEP) in dollars can be computed: BEP$ = Fixed cost + Variable cost per unit x BEP • For Bill Pritchett's example, compute BEP$: $1,000 + $5 x 200 = $2,000

  46. EXAMPLE II: BREAK-EVEN ANALYSIS (4 of 5)

  47. EXAMPLE III: USING GOAL SEEK TO FIND THE BREAK-EVEN POINT (5 of 5)

  48. MANAGEMENT SCIENCE MODELING TECHNIQUES (1 of 4)

  49. MANAGEMENT SCIENCE MODELING TECHNIQUES (2 of 4) • Linear Mathematical Programming Techniques a. Linear Programming Models b. Transportation Models c. Assignment Models d. Integer Programming Models e. Goal Programming

  50. MANAGEMENT SCIENCE MODELING TECHNIQUES (3 of 4) • Probabilistic Techniques a. Decision Analysis b. Waiting Line (Queuing) Models c. Simulation Models d. Forecasting Models • Network Techniques a. Network Flow b. Project Management Techniques (PERT/CPM)

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