Exploring Management Science: Art or Science of Decision Making

1. Chapter 1Introduction

2. What’s It All About? • Before we delve into management science-what it is, what it can be used for, and what it can not be used for-let us briefly look at the term - “Management”

3. Management “Is a process used to achieve certain goals through the utilization of resources”. • Resources-people, money, energy, materials, space, and time. • The resources are considered the inputs, and attainment of the goals the output of the process.

4. Productivity- a measure of success • The ratio of outputs to inputs that measures the degree of success of an organization and its individual parts • The degree of success of the manager’s job is often measured by the productivity.

5. Level of Productivity • The success of management or the level of productivity , depends primarily on the execution of certain managerial functions such as planning, organizing, directing and controlling. • To carry out these functions, managers engage in a continuous process of making decisions. • Therefore, management is considered by many as synonymous with decision making.

6. Decision Making-art or science • Art: Skill, dexterity, or the power of performing certain actions, acquired by experience, study, or observation; • Science: Science is a systematic activity that builds and organizes knowledge in the form of testable explanation and predictions about the world.

7. Decision Making-art or science • For years, managers have considered decision making to be a pure art-a talent acquired over a long period of time through experience (learning by trial and error). • It has been considered an art because a variety of individual styles can be used in approaching and successfully solving the same type of managerial problems in actual business practice. • These styles are often based on creativity, judgment, intuition, and experience rather than on systematic analytical approach.

8. Decision Making-art or science • However, the environment in which management must operate is changing. • Technological advancement is altering the manner in which organizations are structured and operate. • Such advances in technology cannot possibly be made or sustained without concurrent advances in the management of organizations. • Such unusual strides have been possible only because the art of management has increasingly been supplemented by science.

9. Factors Affecting Decision-Making • New technologies and better information distribution have resulted in more alternatives for management. • Complex operations have increased the costs of errors, causing a chain reaction throughout the organization. • Rapidly changing global economies and markets are producing greater uncertainty and requiring faster response in order to maintain competitive advantages. • Increasing governmental regulation coupled with political destabilization have caused great uncertainty.

10. Management Science • Management Science is the application of scientific methods, techniques and tools to problems involving the operations of systems so as to provide those in control of the operations with optimum solutions to the problems. • The application of the scientific method to the analysis and solution of managerial decision making problems.

11. Decision Making Process • For the moment assume that you are currently unemployed and that you would like a position that will lead to a satisfying career. Suppose that your job search has resulted the following offers :

13. Decision Making Process • In the example, we found that the first step of decision making process is the problem identification. Our problem is to identify a job. • After identification, we found a set of alternatives for job. So the second step is the determination of alternative solution. • The next step is determining the criteria that will be used to evaluate the four alternatives. For selecting the job, we can use single criteria or multiple criteria.

14. Decision Making Process • Single criterion decision problem-Salary • Multi-criteria decision problems- Starting salary, potential for advancement, job location. • The next step is to evaluate the alternative through rating. • After evaluating the alternative, now you can choose an alternative. This is the last step of decision making process.

15. Decision Making Process So the 5 step of decision making process are as follows: • Define the problem; • Identify the alternatives; • Determine the criteria; • Evaluate the alternatives; • Choose an alternative.

16. Problem Solving is the process of identifying a difference between the actual and desired state of affairs and then taking action to resolve the difference. • Decision Making is apart of problem solving. That’s why decision making process is the part of problem solving process.

17. Problem Solving Process • Define the problem; • Identify the alternatives; • Determine the criteria; • Evaluate the alternatives; • Choose an alternative; • Implement the decision; • Evaluate the result.

18. Take 2minutes with your partner to brainstorm on practical problem solving

19. An Alternative Classification of the Decision Making Process Analyzing the Problem Structuring the problem

20. Quantitative & Qualitative Analysis in Decision Making • The analyzing phase of the decision making process may take two basic forms: • Qualitative Analysis • Quantitative analysis

21. Qualitative Analysis • Qualitative analysis is based primarily on the manager’s judgment and experience; it includes the manager’s intuitive “feel” for the problem and is more an art than a science. • If the manager’s has had experience with similar problems, or if the problem is relatively simple, heavy emphasis may be placed upon a qualitative analysis.

22. 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. • When using quantitative approach, an analyst will concentrate on the quantitative facts or data associated with the problem and develop mathematical expressions that describe the objectives, constraints and other relationships that exist in the problem.

23. Quantitative Analysis • Quantitative Analysis Process • Model Development • Data Preparation • Model Solution • Report Generation

24. Model Development • 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.

25. Advantages of Models • Generally, experimenting with models (compared to experimenting with the real situation): • requires less time • is less expensive • involves less risk

26. 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.

27. Mathematical Models • Relate decision variables (controllable inputs) with fixed or variable parameters (uncontrollable inputs). • Frequently seek to maximize or minimize some objective function subject to constraints. • Are said to be stochastic if any of the uncontrollable inputs is subject to variation, otherwise are said to be deterministic. • Generally, stochastic models are more difficult to analyze. • The values of the decision variables that provide the mathematically-best output are referred to as the optimal solution for the model.

28. Transforming Model Inputs into Output Uncontrollable Inputs (Environmental Factors) Mathematical Model Output (Projected Results) Controllable Inputs (Decision Variables)

29. Examples of the components of Models

30. Example: Project Scheduling Consider a construction company building a 250-unit apartment complex. The project consists of hundreds of activities involving excavating, framing, wiring, plastering, painting, landscaping, and more. Some of the activities must be done sequentially and others can be done simultaneously. Also, some of the activities can be completed faster than normal by purchasing additional resources (workers, equipment, etc.). What is the best schedule for the activities and for which activities should additional resources be purchased?

31. Example: Project Scheduling • Question: How could management science be used to solve this problem? • Answer: Management science can provide a structured, quantitative approach for determining the minimum project completion time based on the activities' normal times and then based on the activities' expedited (reduced) times.

32. Example: Project Scheduling • Question: What would be the uncontrollable inputs? • Answer: • Normal and expedited activity completion times • Activity expediting costs • Funds available for expediting • Precedence relationships of the activities

33. Example: Project Scheduling • Question: What would be the decision variables of the mathematical model? The objective function? The constraints? • Answer: • Decision variables: which activities to expedite and by how much, and when to start each activity • Objective function: minimize project completion time • Constraints: do not violate any activity precedence relationships and do not expedite in excess of the funds available.

34. Example: Project Scheduling • Question: Is the model deterministic or stochastic? • Answer: Stochastic. Activity completion times, both normal and expedited, are uncertain and subject to variation. Activity expediting costs are uncertain. The number of activities and their precedence relationships might change before the project is completed due to a project design change.

35. Data Preparation • Data preparation is not a trivial step, due to the time required and the possibility of data collection errors. • A model with 50 decision variables and 25 constraints could have over 1300 data elements! • Often, a fairly large data base is needed. • Information systems specialists might be needed.

36. Model Solution • The analyst attempts to identify the alternative (the set of decision variable values) that provides the “best” output for the model. • The “best” output is the optimal solution. • If the alternative does not satisfy all of the model constraints, it is rejected as being infeasible, regardless of the objective function value. • If the alternative satisfies all of the model constraints, it is feasible and a candidate for the “best” solution.

37. Optimization is Everywhere It is embedded in language, and part of the way we think. – firms want to maximize value to shareholders – people want to make the best choices – We want the highest quality at the lowest price – When playing games, we want the best strategy – When we have too much to do, we want to optimize the use of our time – etc.

38. Take 3 minutes with your partner to brainstorm on where optimization might be used. (business, or sports, or personal uses, or politics, or …)

39. Model Solution • One solution approach is trial-and-error. • Might not provide the best solution • Inefficient (numerous calculations required) • Special solution procedures have been developed for specific mathematical models. • Some small models/problems can be solved by hand calculations • Most practical applications require using a computer

40. Model Testing and Validation • Often, goodness/accuracy of a model cannot be assessed until solutions are generated. • Small test problems having known, or at least expected, solutions can be used for model testing and validation. • If the model generates expected solutions, use the model on the full-scale problem. • If inaccuracies or potential shortcomings inherent in the model are identified, take corrective action such as: • Collection of more-accurate input data • Modification of the model

41. Report Generation • A managerial report, based on the results of the model, should be prepared. • The report should be easily understood by the decision maker. • The report should include: • the recommended decision • other pertinent information about the results (for example, how sensitive the model solution is to the assumptions and data used in the model)

42. Implementation and Follow-Up • Successful implementation of model results is of critical importance. • Secure as much user involvement as possible throughout the modeling process. • Continue to monitor the contribution of the model. • It might be necessary to refine or expand the model.

43. Example: Austin Auto Auction An auctioneer has developed a simple mathematical model for deciding the starting bid he will require when auctioning a used automobile. Essentially, he sets the starting bid at seventy percent of what he predicts the final winning bid will (or should) be. He predicts the winning bid by starting with the car's original selling price and making two deductions, one based on the car's age and the other based on the car's mileage. The age deduction is $800 per year and the mileage deduction is $.025 per mile.

44. Example: Austin Auto Auction • Question: Develop the mathematical model that will give the starting bid (B ) for a car in terms of the car's original price (P ), current age (A) and mileage (M ).

45. Example: Austin Auto Auction • Answer: The expected winning bid can be expressed as: P - 800(A) - .025(M ) The entire model is: B = .7(expected winning bid) B = .7(P - 800(A) - .025(M )) B = .7(P )- 560(A) - .0175(M )

46. Example: Austin Auto Auction • Question: Suppose a four-year old car with 60,000 miles on the odometer is up for auction. If its original price was $12,500, what starting bid should the auctioneer require? • Answer: B = .7(12,500) - 560(4) - .0175(60,000) = $5460

47. 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.

48. Example: Iron Works, Inc. • Mathematical Model • The total monthly profit = (profit per unit of product 1) x (monthly production of product 1) + (profit per unit of product 2) x (monthly production of product 2) = p1x1 + p2x2 We want to maximize total monthly profit: Max p1x1 + p2x2

49. Example: Iron Works, Inc. • Mathematical Model (continued) • The total amount of steel used during monthly production equals: (steel required per unit of product 1) x (monthly production of product 1) + (steel required per unit of product 2) x (monthly production of product 2) = a1x1 + a2x2 This quantity must be less than or equal to the allocated b pounds of steel: a1x1 + a2x2 <b

50. Example: Iron Works, Inc. • Mathematical Model (continued) • The monthly production level of product 1 must be greater than or equal to m : x1>m • The monthly production level of product 2 must be less than or equal to u : x2<u • However, the production level for product 2 cannot be negative: x2> 0