Introduction to Quantitative Analysis PDF

Introduction to Quantitative Analysis What is Quantitative Analysis? (1 of 4) Quantitative analysis is a scientific approach to managerial decision making in which raw data are processed and manipulated to produce meaningful information Quantitative analysis analyzes numbers to generate useful lea...

Introduction to Quantitative Analysis What is Quantitative Analysis? (1 of 4) Quantitative analysis is a scientific approach to managerial decision making in which raw data are processed and manipulated to produce meaningful information Quantitative analysis analyzes numbers to generate useful learning from information. It applies statistical / mathematical methods and computational processes to study and make sense of data so you can spot patterns, connections, and how things change over time – giving insight to guide decision Introduction Mathematical tools have been used for thousands of years Quantitative analysis can be applied to a wide variety of problems – Not enough to just know the mathematics of a technique – Must understand the specific applicability of the technique, its limitations, and assumptions – Successful use of quantitative techniques usually results in a solution that is timely, accurate, flexible, economical, reliable, and easy to understand and use Examples of Quantitative Analyses Taco Bell saved over $150 million using forecasting and employee scheduling quantitative analysis models Netflix uses quantitative analysis to inform its movies and seasons production, including cast, genre, etc. Pakistan’s polio eradication strategy puts business analytics at its core. The BA platform is integrated with the population database at NADRA, and reports on children distribution across geographical regions. Continental Airlines saved over $40 million every year using quantitative analysis models to quickly recover from weather delays and other disruptions Quantitative Analysis Quantitative factors are data that can be accurately calculated – Different investment alternatives – Interest rates – Financial ratios – Cash flows and rates of return – Flow of materials through a supply chain Quantitative Analysis Qualitative factors are more difficult to quantify but affect the decision process – The weather – State and federal legislation – Technological breakthroughs – The outcome of an election Quantitative Analysis Quantitative and qualitative factors may have different roles Decisions based on quantitative data can be automated Generally quantitative analysis will aid the decision-making process Important in many areas of management – Production/Operations Management – Supply Chain Management – Business Analytics Business Analytics (1 of 3) A data-driven approach to decision making – Allows better decisions – Large amounts of data – Information technology is the key – and hence the rise of the Business Analytics in recent times – Statistical and quantitative analysis are used to analyze the data and provide useful information Business Analytics (2 of 3) Descriptive analytics – the study and consolidation of historical data Predictive analytics – forecasting future outcomes based on patterns in the past data Prescriptive analytics – the use of optimization methods The Quantitative Analysis Approach Defining the Problem Develop a clear and concise statement of the problem to provide direction and meaning – This may be the most important and difficult step – Go beyond symptoms and identify true causes – Concentrate on only a few of the problems – selecting the right problems is very important – Specific and measurable objectives may have to be developed Developing a Model (1 of 2) Models are realistic, solvable, and understandable mathematical representations of a situation Different types of models Developing a Model (2 of 2) Mathematical model – a set of mathematical relationships Models generally contain variables and parameters – Controllable variables, decision variables, are generally unknown  How many items should be ordered for inventory? – Parameters are known quantities that are a part of the model  What is the cost of placing an order? Required input data must be available Acquiring Input Data Input data must be accurate – GIGO rule Data may come from a variety of sources – company reports, documents, employee interviews, direct measurement, or statistical sampling Developing a Solution Manipulating the model to arrive at the best (optimal) solution 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 Testing the Solution Both input data and the model should be tested for accuracy and completeness before analysis and implementation – New data can be collected to test the model – Results should be logical, consistent, and represent the real situation Analyzing the Results Determine the implications of the solution – Implementing results often requires change in an organization – The impact of actions or changes needs to be studied and understood before implementation Sensitivity analysis, postoptimality analysis, determines how much the results will change if the model or input data changes – Sensitive models should be very thoroughly tested Implementing the Results Implementation incorporates the solution into the company – Implementation can be very difficult – People may be resistant to 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 in the process is an important component of success How to Develop a Quantitative Analysis Model (1 of 3) A mathematical model of profit: Profit = Revenue − Expenses Revenue and expenses can be expressed in different ways How to Develop a Quantitative Analysis Model (2 of 3) 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 v = variable cost per unit f = fixed cost X = number of units sold How to Develop a Quantitative Analysis Model (3 of 3) Profit = Revenue − (Fixed cost + Variable cost) The parameters of this model Profit = (Selling price per areunit)(Number f, v, and s asofthese units are sold) the− [Fixed cost + (Variable costs per inputs inherent in unit)(Number the model. of units sold)] The decision variable of interest Profit = sX − [f + vX] is X. Profit = sX − f − vX where s = selling price per unit v = variable cost per unit f = fixed cost X = number of units sold Example - Time Pieces (1 of 3) A company buys, sells, and repairs old clocks – Rebuilt springs sell for $8 per unit – Fixed cost of equipment to build springs is $1,000 – Variable cost for spring material is $3 per unit s=8 f = 1,000 v=3 Number of spring sets sold = X Profits = $8X − $1,000 − $3X If sales = 0, profits = − f = − $1,000 If sales = 1,000, profits = [($8)(1,000) − $1,000 − ($3) (1,000)] = $4,000 Example - Time Pieces (2 of 3) Companies are often interested in the break-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) Fixed cost BEP = (Selling price per unit)  (Variable cost per unit) Example - Time Pieces (3 of 3) BEP for the Time Pieces company BEP = $1,000÷($8 − $3) = 200 units Sales of less than 200 units of rebuilt springs will result in a loss Sales of over 200 units of rebuilt springs will result in a profit Advantages of Mathematical Modeling 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. Models Categorized by Risk Mathematical models that do not involve risk or chance are called deterministic models – All of the values used in the model are known with complete certainty Mathematical models that involve risk or chance are called probabilistic models – Values used in the model are estimates based on probabilities Possible Problems in the Quantitative Analysis Approach (1 of 2) Defining the problem – Problems may not be easily identified – Conflicting viewpoints – Impact on other departments – Beginning assumptions – Solution outdated Developing a model – Fitting the textbook models – Understanding the model Possible Problems in the Quantitative Analysis Approach (2 of 2) Acquiring accurate input data – Using accounting data – Validity of the data Developing a solution – Hard-to-understand mathematics – Only one answer is limiting Testing the solution  Solutions not always intuitively obvious Analyzing the results  How will it affect the total organization Implementation – Not Just the Final Step (1 of 2) Lack of commitment and resistance to change – Fear formal analysis processes will reduce management’s decision-making power – Fear previous intuitive decisions exposed as inadequate – Uncomfortable with new thinking patterns – Action-oriented managers may want “quick and dirty” techniques – Management support and user involvement are important Implementation – Not Just the Final Step (2 of 2) Lack of commitment by quantitative analysts – Analysts should be involved with the problem and care about the solution – Analysts should work with users and take their feelings into account