2DA3 MT Notes PDF

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DATA ANALYTICS Decision Making Managers’ responsibility: -

To make strategic, tactical, or operational decisions.

Strategic decisions: ◦ Involve higher-level issues concerned with the overall direction of the organization. ◦ Define the organization’s overall goals and aspirations for the future.

Tactical decisions: ◦ Concern how the organization should achieve the goals and objectives set by its strategy. ◦ Are usually the responsibility of midlevel management.

Operational decisions: ◦ Affect how the firm is run from day to day. ◦ Are the domain of operations managers, who are the closest to the customer.

Decision making can be defined as the following process: 1. Identify and define the problem. 2. Determine the criteria that will be used to evaluate alternative solutions. 3. Determine the set of alternative solutions. 4. Choose an alternative.

Common approaches to making decisions include: o Tradition. o Intuition. o Rules of thumb. o Using the relevant data available. Business analytics: Scientific process of transforming data into insight for making better decisions. Used for data-driven or fact-based decision making, which is often seen as more objective than other alternatives for decision making.

Tools of business analytics can aid decision making by: o Creating insights from data. o Improving our ability to more accurately forecast for planning. o Helping us quantify risk. o Yielding better alternatives through analysis and optimization. Descriptive analytics: Encompasses the set of techniques that describes what has happened in the past; examples include: ◦ Data queries. ◦ Reports. ◦ Descriptive statistics. ◦ Data visualization (including data dashboards). ◦ Data-mining techniques. ◦ Basic what-if spreadsheet models.

Data mining: The use of analytical techniques for better understanding patterns and relationships that exist in large data sets. Examples of data-mining techniques include: ◦ Cluster analysis. ◦ Sentiment analysis.

Predictive analytics: Consists of techniques that use models constructed from past data to predict the future or forascertain the impact of one variable on another. Survey data and past purchase behavior may be used to help predict the market share of a new product.

Techniques used in Predictive Analytics include: o Linear regression. o Time series analysis. o Data mining is used to find patterns or relationships among elements of the data in a large database; often used in predictive analytics. o Simulation involves the use of probability and statistics to construct a computer model to study the impact of uncertainty on a decision.

Prescriptive Analytics: Indicates a best course of action to take: o A forecast or prediction, when combined with a rule, becomes a prescriptive model. o Prescriptive models that rely on a rule or set of rules are often referred to as rule-based models.

Simulation optimization: Combines the use of probability and statistics to model uncertainty with optimization techniques to find good decisions in highly complex and highly uncertain settings.

Decision analysis: ◦ Used to develop an optimal strategy when a decision maker is faced with several decision alternatives and an uncertain set of future events. ◦ Employs utility theory, which assigns values to outcomes based on the decision maker’s attitude toward risk, loss, and other factors.

Big data: Any set of data that is too large or too complex to be handled by standard data-processing techniques and typical desktop software. IBM describes the phenomenon of big data through the four Vs (as shown in Figure 1.1): -

Volume. Velocity. Variety. Veracity

Financial Analytics: Use of predictive models to: o Forecast financial performance. o Assess the risk of investment portfolios and projects. o Construct financial instruments such as derivatives. o Construct optimal portfolios of investments. o Allocate assets. Simulation is also often used to assess risk in the financial sector.

Human Resource (HR) Analytics: New area of application for analytics. The HR function is charged with ensuring that the organization: ◦ Has the mix of skill sets necessary to meet its needs. ◦ Is hiring the highest-quality talent and providing an environment that retains it. ◦ Achieves its organizational diversity goals. Marketing Analytics: A better understanding of consumer behavior through the use of scanner data and data generated from social media has led to an increased interest in marketing analytics. o A better understanding of consumer behavior through marketing analytics leads to: ◦ Better use of advertising budgets. ◦ More effective pricing strategies. ◦ Improved forecasting of demand. ◦ Improved product-line management. ◦ Increased customer satisfaction and loyalty.

Health Care Analytics: o Descriptive, predictive, and prescriptive analytics are used to improve: ◦ Patient, staff, and facility scheduling. ◦ Patient flow. ◦ Purchasing. ◦ Inventory control. o Use of prescriptive analytics for diagnosis and treatment may prove to be the most important application of analytics in health care

Supply-Chain Analytics: -

The core service of companies such as UPS and FedEx is the efficient delivery of

goods, and analytics has long been used to achieve efficiency. -

The optimal sorting of goods, vehicle and staff scheduling, and vehicle routing are

all key to profitability for logistics companies such as UPS and FedEx. -

Companies can benefit from better inventory and processing control and more

efficient supply chains. Web Analytics: o The analysis of online activity, which includes, but is not limited to, visits to web sites and social media sites such as Facebook and LinkedIn. o Leading companies apply descriptive and advanced analytics to data collected in online experiments to determine the best way to: ◦ Configure web sites. ◦ Position ads. ◦ Utilize social networks for the promotion of products and services

Strategic decision: A decision that involves higher-level issues and that is concerned with the overall direction of the organization, defining the overall goals and aspirations for the organization’s future.

Tactical decision: A decision concerned with how the organization should achieve the goals and objectives set by its strategy.

Operational decisions: A decision concerned with how the organization is run from day to day.

Business analytics: The scientific process of transforming data into insight for making better decisions.

Descriptive analytics: Analytical tools that describe what has happened.

Predictive analytics: Techniques that use models constructed from past data to predict the future or to ascertain the impact of one variable on another.

Prescriptive analytics: Techniques that analyze input data and yield a best course of action

Data mining: The use of analytical techniques for better understanding patterns and relationships that exist in large data sets

Simulation: The use of probability and statistics to construct a computer model to study the impact of uncertainty on the decision at hand.

Rule-based model: A prescriptive model that is based on a rule or set of rules.

Big data: Any set of data that is too large or too complex to be handled by standard data-processing techniques and typical desktop software.

Optimization models: A mathematical model that gives the best decision, subject to the situation’s constraints. Simulation optimization: The use of probability and statistics to model uncertainty, combined with optimization techniques, to find good decisions in highly complex and highly uncertain settings.

Decision analysis: A technique used to develop an optimal strategy when a decision maker is faced with several decision alternatives and an uncertain set of future events.

Utility theory: The study of the total worth or relative desirability of a particular outcome that reflects the decision maker’s attitude toward a collection of factors such as profit, loss, and risk.

Referencing: The method by which you refer to a cell or series of cells in a formula.

Filtering: to display only the rows that meet certain conditions.

Sorting: Arranging data according to our requirements.

Mean (arithmetic mean): A measure of central location computed by summing the data values and dividing by the number of observations.

Median: A measure of central location provided by the value in the middle when the data are arranged in ascending order.

Mode: A measure of central location defined as the value that occurs with greatest frequency.

Variance: A measure of variability based on the squared deviations of the data values about the mean.

Range: A measure of variability defined to be the largest value minus the smallest value.

Scatter chart: A graphical presentation of the relationship between two quantitative variables. One variable is shown on the horizontal axis and the other on the vertical axis.

Time series: Data that are collected over a period of time (minutes, hours, days, months, years, etc.).

Histogram: A graphical presentation of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data constructed by placing the bin intervals on the horizontal axis and the frequencies, relative frequencies, or percent frequencies on the vertical axis. Categorical data: Data for which categories of like items are identified by labels or names. Arithmetic operations cannot be performed on categorical data.

Pivot table: is a table of grouped values that aggregates the individual items of a more extensive table within one or more discrete categories.

Break-Even Point Ex.

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Production Cost: $3.50 Fixed Cost: $234,000 Variable Cost: $2/each

3.50x = 234,000 + 2x 3.50x – 2x = 234,000 1.50x = 234,000 x = 156,000

Total Cost = Fixed Cost + (Variable Cost x Number of Units) Profit = Revenue - Cost Sum Product Function: Sum of (Units Sold x Price) ^n

(total revenue/sales)

Prescriptive Analysis - Linear Programming (LP) Optimization Problems: -

Can be used to support and improve managerial decision making. Optimization is the process of finding the optimal (min/max) objective function by changing decision variables with respect to restrictions known as constraints. Can be linear or nonlinear “In nutshell, Businesses have limited resources; Optimization problems are to identify optimal resource allocation to achieve most favorable results.”

Why Linear Programming? Typical Applications: -

Production scheduling and inventory planning that satisfies demand in future periods, while minimizing the total production, transportation and inventory costs. Investment portfolio identification from a variety of stock and bond investment alternatives that maximizes the return on investment. In marketing, fixed advertising budget allocation among alternative advertising media such as web, radio, television, newspaper, and magazine to maximize advertising effectiveness. Identifying production capacity for production that involves complex compositions.

Problem formulation or modeling: Process of translating the verbal statement of a problem into a mathematical statement. Describe the objective, constraint, and decision variables Mathematical model: A set of mathematical relationship

Linear programming model (or linear program): when the objective function and all constraint functions are linear functions of the decision variables. Linear function: Mathematical function in which each variable appears in a separate term and is raised to the first power.

To find the optimal solution to the problem modeled as a linear program: ◦ The optimal solution must have the highest objective function value. ◦ The optimal solution must be a feasible solution—a setting of the decision variables that satisfies all of the constraints of the problem. ◦ Search over the feasible region—the region which consists of all points that simultaneously satisfy all constraints in the problem, representing a set of all possible solutions. ◦ Find the solution that gives the best objective function value.

Objective function: The expression that defines the quantity to be maximized or minimized in a linear programming model. Constraints: Restrictions that limit the settings of the decision variables. Decision variable: A controllable input for a linear programming model. -

When there are only two decision variables and the functions of these variables are linear, they form lines in two-dimensional space.

Nonnegativity constraints: A set of constraints that requires all variables to be nonnegative. If constraints are inequalities, the constraint cuts the space in two: ◦ The line and the area on one side of the line is the space the satisfies that constraint. ◦ These subregions are called half spaces. ◦ The intersection of the half spaces make up the feasible region Identify the direction where we obtain a better objective value. Move the contour line (in that direction) to find the last corner point (of the feasible region) that contour lines pass. The point is called the Optimal Solution -

Find the value of the objective function for the optimal solution found

• To solve a linear optimization problem we only have to search the extreme points of the feasible region to find the optimal solution. • Extreme points are found where constraints intersect on the boundary of the feasible region. Graphically speaking, extreme points are the feasible solution points occurring at the vertices, or “corners,” of the feasible region. With two-variable problems, extreme points are determined by the intersection of the constraint lines

Linear Programming / LP Assumptions 1) Certainty ◦ All parameters are known. Input data values, which are coefficients used in the objective function and constraints, are known as “certainty” 2) Proportionality ◦ If the level of any activity is multiplied by a constant factor, then the contribution of that activity in the objective function or constraints will be multiplied by the same factor. 3) Additivity ◦ Total of all activities equals the sum of individual activities. 4) Divisibility ◦ Non-integer variables are acceptable 5) Linearity

Analyzing the Answer Report -

A binding constraint is one that holds as an equality at the optimal solution. The slack value for each less-than-or-equal-to constraint indicates the difference between the left-hand and right-hand values for a constraint. This is interpreted as the “amount of unused resources”

Special Cases of Linear Program Outcomes An alternative optimal solution is one in which the optimal objective function contour line coincides with one of the binding constraint lines on the boundary of the feasible region. In these situations, more than one solution provides the optimal value for the objective function.

Infeasibility means no solution to the linear programming problem satisfies all the constraints, including nonnegativity conditions. Graphically, a feasible region does not exist. -

Infeasibility occurs because: o Management’s expectations are too high. o Too many restrictions have been placed on the problem

An infeasible problem when solved in Excel Solver: ◦ Will return a message indicating that no feasible solutions exists —indicating no solution to the linear programming problem will satisfy all constraints. ◦ Careful inspection of your formulation is necessary to identify why the problem is infeasible. ◦ One of the approaches is to drop one or more constraints and re-solve the problem. ◦ If we find an optimal solution for this revised problem, then the constraint(s) that were omitted, in conjunction with the others, are causing the problem to be infeasible. Provide details to management on: ◦ Minimum amounts of resources that must be available. ◦ The amounts currently available. ◦ Additional amounts that would be required to accomplish this level of production Unbounded: The situation in which the value of the solution may be made infinitely large —for a maximization linear programming, may be made infinitely small—for a minimization linear programming (without violating any of the constraints)

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Solving an unbounded problem using Excel Solver returns a message “Objective Cell values do not converge.” In linear programming models of real problems, the occurrence of an unbounded solution means that the problem has been improperly formulated. If a profit maximization problem results in an unbounded solution, the mathematical model does not represent the real-world problem sufficiently. In many cases, this error is the result of inadvertently omitting a constraint during problem formulation. (Missing Constraints)

Sensitivity analysis: The study of how the changes in the input parameters of an optimization model affect the optimal solution. -

It helps in answering the questions: o How will a change in a coefficient of the objective function affect the optimal solution? o How will a change in the right-hand-side value for a constraint affect the optimal solution?

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Because sensitivity analysis (often referred to as post optimality analysis) is concerned with how these changes affect the optimal solution, the analysis does not begin until the optimal solution to the original linear programming problem has been obtained

Why Sensitivity Analysis? -

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Certainty assumption for LP is not true for most real-world problems Conditions are dynamic and changing What if one or more coefficients change? o For example, profit changes from $9 to $11  What’s the effect on solution? o Simply use computer to make necessary changes to model, then quickly re-solve it! If change is definite… o ◦ For example, we know with certainty: profit is decreased from $10 to $9  Re-solve the model and obtain new optimal solution Hypothetical changes in input data values e.g. profit may be any value from $5 to $20 It’s impractical to re-solve the model with respect to all possibilities! Shows how sensitive the solution is to change in each input data Determines a range for each input data in which the solution is optimal. Obtain this information from the current solution itself without re-solving

Which parameters change? We examine: ◦ Changes in objective function coefficients (OFC) ◦ Changes in RHS ◦ Changes in only one input data value at a time ◦ Either in one OFC or one RHS value

◦ Not included: simultaneous changes in several input data values

Allowable Increase/Decrease in Solver Sensitivity Report help us find the range of optimality, which are possible values for the profit of a table within which the current optimal corner solution remains optimal -

Note: we consider a change to only a single objective function coefficient If they change simultaneously, the result may not apply.

1) Objective function coefficient allowable increase (decrease): The allowable increase/decrease of an objective function coefficient is the amount the coefficient may increase(decrease) without causing any change in the values of the decision variables in the optimal solution. The allowable increase/decrease for the objective function coefficients can be used to calculate the range of optimality 2) Right-hand side allowable increase (decrease): The allowable increase (decrease) of the right-hand side of a constraint is the amount the right-hand side may increase (decrease) without causing any change in the shadow p...