Introduction to Quantitative Analysis

Transcription

1 Chapter 1 Introduction to Quantitative Analysis Quantitative Analysis for Management, Tenth Edition, by Render, Stair, and Hanna 2008 Prentice-Hall, Inc. Introduction Traditionally business decisions have been based on subjective factors Though mathematical tools have been used for thousands of years, the formal study of it to make management decisions began in twentieth century Quantitative analysis is based on numeric data analysis, modeling and mathematical calculations Quantitative analysis can be used to solve a wide variety of problems in business, government, health care, education, 1 2 Introduction What is Operations Management? It s not enough to just know how the mathematics of a technique (model) works One must understand the specific applicability of the technique (model), its limitations, and its assumptions The terms management science, operations management or research, and quantitative analysis are often interchangeable A set of activities that creates value in the form of goods and services by carefully managing the business operations to produce and distribute products and services efficiently and effectively Increase profit Reduce cost One of three major functions (marketing, finance, and operations) of any organization and is integrally related to all the other business functions

2 What is Operations Management? Operations Management (OM) is such a costly part of an organization A large percentage of the revenue of most firms is spent in the OM function OM provides a major opportunity for an organization to improve its profitability and enhance its service to society What is Operations Management? Operations management involves using quantitative analysis methods to help people analyze complicated business processes and make good decisions These techniques are especially useful for helping understand and deal with business complexity and uncertainty Examples of Quantitative Analyses Taco Bell saved over $150 million using demand forecasting and employee scheduling quantitative analysis models NBC television increased revenues by over $200 million by using quantitative analysis to develop better sales plans for advertisers Continental Airlines saved over $40 million using quantitative analysis models to quickly recover from weather delays and other disruptions What is Quantitative Analysis? Quantitative analysis (QA) is a scientific approach to managerial decision making no whim, emotions and guesswork. The heart of QA is the processing and manipulating of raw data into meaningful information Raw Data Quantitative Analysis Meaningful Information Qualitative analysis Qualitative analysis involves the investigation of factors in a decision-making problem that cannot be quantified

3 What is Quantitative Analysis? In solving real problems, both quantitative and qualitative factors must be considered Quantitative factors might be different investment alternatives, interest rates, inventory levels, demand, or labor cost Qualitative factors such as the weather condition, state and federal legislation, the outcome of an election, technology breakthroughs, etc. may be difficult to quantify but can affect the decision-making process What is Quantitative Analysis? In most cases quantitative analysis will be an aid to the decision-making process. The results of quantitative analysis will be combined with other (qualitative) information in making the final decisions The Quantitative Analysis Approach 1. Defining the Problem Figure 1.1 Defining the Problem Developing a Model Acquiring Input Data Developing a Solution Testing the Solution Analyzing the Results Implementing the Results The first step is to develop a clear and concise statement of the problem that gives direction and meaning to the subsequent steps This may be the most important and difficult step It is essential to go beyond the symptoms of the problem and identify true causes Several problems may exist. It is necessary to concentrate on only a few of the problems selecting the right problems is very important If the problem is difficult to quantify, specific and measurable objectives may have to be developed (e.g. inadequate hospital health care delivery raise # of beds, doctors, reduce waiting time )

4 2. Developing a Model Quantitative analysis models are realistic, solvable, and understandable mathematical representations of a situation $ Sale es $ Advertising There are other types of models Scale models Schematic models Mathematic models 2. Developing a Model QA Models generally contain variables (controllable and uncontrollable) and parameters Variables are measurable quantities that are subject to change and are generally unknown (e.g. $ sales, $ advertising) Controllable variables are generally the decision variables (e.g. $ advertising) Parameters are known quantities that are a part of the problem (e.g. cost per second rate for the ads) Acquiring Input Data Input data must be obtained for the model to make it useful and they must be accurate GIGO rule Garbage In Process Garbage Out Data may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement, or statistical sampling Developing a Solution The best (optimal) solution to a problem is found by manipulating the model until a solution is found that is practical and can be implemented Common techniques are Solving equations Trial and error trying various approaches and picking the best result Complete enumeration trying all possible values Using an algorithm a series of repeating steps to reach a solution The input data and model determine the accuracy of the solution 1 16

5 5. Testing the Solution Both input data and the model should be tested for accuracy before the solution can be analyzed and implemented Collect additional data from a different source to validate the accuracy of both the model and model input data Results should be logical, consistent, and represent the real situation 6. Analyzing the Results Determine the implications of the solution Implementing results often requires actions and changes in an organization The impact of actions or changes needs to be studied and understood before implementation Sensitivity analysis determines how much the results of the analysis will change if the model or input data changes A model is only an approximation of reality Sensitive models should be very thoroughly tested to ensure their accuracy and validity Implementing the Results Implementation incorporates the solution into the company Implementation can be very difficult People can resist changes Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented Changes occur over time, so even successful implementations must be monitored to determine if modifications are necessary Modeling in the Real World Quantitative analysis models are used extensively by real organizations to solve real problems In the real world, quantitative analysis models can be complex, expensive, and difficult to sell Following the steps of quantitative analysis is an important component of success, but not a guarantee

6 How To Develop a Quantitative Analysis Model Developing a model is an important part of the quantitative analysis approach Let s look at a simple mathematical model of profit Profit = Revenue Expenses How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit costs times the number of units Profit = Revenue (Fixed cost + Variable cost) Profit = (Selling price per unit)(number of units sold) [Fixed cost + (Variable costs per unit)(number of units sold)] Profit = sx [f + vx] Profit = sx f vx where s = selling price per unit f = fixed cost v = variable cost per unit X = number of units sold How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable The parameters costs are the of this product model of unit costs times the number are f, v, of and units s as these are the inputs inherent in the model Profit = Revenue (Fixed Profit and cost X + are Variable variables cost) Profit = (Selling price per unit)(number of units The decision variable of sold) [Fixed cost + (Variable costs per interest is X unit)(number of units sold)] Profit = sx [f + vx] Profit = sx f vx where s = selling price per unit f = fixed cost v = variable cost per unit X = number of units sold Pritchett s Precious Time Pieces The company buys, sells, and repairs old clocks and clock parts. Rebuilt springs sell for $10 per unit. Fixed cost of equipment to build springs is $1,000. Variable cost for spring material is $5 per unit. s = 10 f = 1,000 v = 5 Number of spring sets sold = X Profits = sx f vx = 10X X If sales = 0, profits = $1,000 If sales = 1,000, profits = [(10)(1,000) 1,000 (5)(1,000)] = $4,

7 Pritchett s Precious Time Pieces Companies are often interested in their break-even even point (BEP). The BEP is the number of units sold that will result in $0 profit. 0 = sx f vx, or 0 = (s v)x f Solving for X, we have f = (s v)x X = f s v Pritchett s Precious Time Pieces Companies are often interested in their break-even even point (BEP). The BEP is the number of units sold BEP for Pritchett s Precious Time Pieces that will result in $0 profit. 0 = BEP sx = f $1,000/($10 vx, or 0 $5) = (s = 200 v)x units f Solving Sales for of less X, we than have200 units of rebuilt springs will result in a loss f = (s v)x Sales of over 200 units f of rebuilt springs will result in a profit X = s v BEP = Fixed cost (Selling price per unit) (Variable cost per unit) BEP = Fixed cost (Selling price per unit) (Variable cost per unit) Bagels R Us Assume you are the new owner of Bagels R Us and you want to develop a mathematical model for your daily profits and breakeven point. Your fixed overhead is $100 per day and your variable costs are 0.50 per bagel (these are GREAT bagels). You charge $1 per bagel. (Price per Unit) (Number Sold) Profits = Revenue Expenses Fixed Cost (Variable Cost/Unit) (Number Sold) Profits = $1*Number Sold $100 $.50*Number Sold Bagels R Us f = $100, s = $1, v = $.50 BEP = f / (s v) BEP = $100 / ($1 $.50) BEP = 200 units When the number of units sold is equal to 200, the profit is

8 Advantages of Mathematical Modeling Models Categorized by Risk 1. Models can accurately represent reality 2. Models can help a decision maker formulate problems 3. Models can give us insight and information 4. Models can save time and money in decision making and problem solving 5. A model may be the only way to solve large or complex problems in a timely fashion 6. A model can be used to communicate problems and solutions to others 1 29 Mathematical models that do not involve risk are called deterministic models We know all the values used in the model with complete certainty (the outcome is also certain) E.g. profit and break-even models Mathematical models that involve risk, chance, or uncertainty are called probabilistic models Values used in the model are estimates based on probabilities (the outcome is not certain) E.g. market for a new product: good (60%), not good (40%) 1 30 Computers and Spreadsheet Models Computers and Spreadsheet Models Developing a solution, testing the solution, and analyzing the results are important steps in quantitative analysis approach Since mathematical models are used, these steps require mathematical calculations. Two computer programs can be used to make these steps easier: 1) QM for Windows 2) Excel QM QM for Windows An easy to use decision support system for use in POM and QM courses This is the main menu of quantitative models 1 31 Program

9 Computers and Spreadsheet Models Excel QM s Main Menu (2003) Works automatically within Excel spreadsheets Computers and Spreadsheet Models Excel QM s Main Menu (2007) Program 1.2A 1 33 Program 1.2B 1 34 Computers and Spreadsheet Models Computers and Spreadsheet Models Excel QM for the Break- Even Problem Excel QM Solution to the Break- Even Problem Program 1.3A 1 35 Program 1.3B 1 36

10 Computers and Spreadsheet Models Using Goal Seek in the Break- Even Problem Program Possible Problems in the Quantitative Analysis Approach (Inventory analysis example will be used) Defining the problem problems are not easily identified Conflicting viewpoints financial and sales people have different view about the inventory Impact on other departments inventory is tied with cash flows and production Beginning assumptions problem implies solution, e.g. inventory is too low? Solution outdated (the problem changed) 1 38 Possible Problems in the Quantitative Analysis Approach Developing a model Fitting the textbook models they may not fit a manager s perception of a problem (e.g. reducing holding & ordering cost vs. cash flow & customer satisfaction) Understanding the model trade-off between the complexity and ease of understanding (e.g. assume the demand is known and constant, o.w. probability need to be used) Possible Problems in the Quantitative Analysis Approach Acquiring input data not a simple task Using accounting data it may not include holding & ordering costs Validity of data lack of good & clean data Developing a solution Hard-to-understand mathematics managers tend to remain silent instead of being critical Only one answer is limiting no options

11 Possible Problems in the Quantitative Analysis Approach Testing the solution Complex models tend to give solutions not so obvious to managers and tend to be rejected A review process is necessary to convince the managers and correct any errors in the models Analyzing the results Even small changes in organization are difficult to bring about Implementation Not Just the Final Step Lack of commitment and resistance to change from management Management may fear the use of formal analysis processes will reduce their decision-making power or just feel uncomfortable about using them Action-oriented managers may want quick and dirty techniques Management support and user involvement are critical to the success (manager: 98%, user: 70%, QA: 40%) Implementation Not Just the Final Step Lack of commitment by quantitative analysts Analysts should be involved with the problem and care about the solution be an integral part of the department facing the problem Analysts should work with users and take their feelings into account (e.g. not insisting on the users to follow computer-calculated order quantities) Summary Quantitative analysis is a scientific approach to decision making The approach includes Defining the problem Developing a model Acquiring input data Developing a solution Testing the solution Analyzing the results Implementing the results

12 Summary Potential problems include Conflicting viewpoints The impact on other departments Beginning assumptions Outdated solutions Fitting textbook models Understanding the model Acquiring good input data Hard-to-understand mathematics Obtaining only one answer Testing the solution Analyzing the results Summary Implementation is not the final step Problems can occur because of Lack of commitment to the approach Resistance to change (Homework #1: see the course website)