Quantitative Methods

Course Lecturer Name(s):  Dr. Curlan Gilchrist

Course Director Name: Dr. Curlan Gilchrist

Course Lecturer(s) Contact Information:  cgilchrist@sgu.edu

Course Director Contact Information: cgilchrist@sgu.edu 

Course Lecturer(s) Office Hours:  Mon & Fri: 3:00pm – 4:00pm (appointment) 

Course Director Office Hours: Mon & Fri: 3:00pm – 4:00pm (appointment)

Course Lecturer(s) Office Location:  Ground Floor, Caribbean House

Course Director Office Location: Ground floor, Caribbean House

Course Support:   Mahalia Charles ( mcharl11@sgu.edu )

Course Management tool: To learn to use Sakai, the Course management tool, access the link https://apps.sgu.edu/members.nsf/mycoursesintro.pdf

Course Description: 

This course will provide an intensive study of descriptive, inferential statistical, and some selected selective quantitative techniques required for business decision making.  Data analysis and interpretation would be emphasized. Topics in descriptive statistics would include construction, interpretation, and use of index numbers, and an in-depth analysis of Bayes’ Theorem.  Inferential statistics and quantitative techniques would include a detail study of decision making under certainty, hypothesis testing, and multiple regressions and forecasting. Inventory Control Models, and Transportation and Assignment Models. At the end of this course, students should be able to apply the statistical and quantitative tools, methods, and techniques learned to understand, analyze, and solve business problems

Course Objectives: 

1. To provide an understanding of the value and use of quantitative methods in  problem solving and decision-making.
2. To be able to apply a variety of statistical and quantitative techniques to a wide range of business situations. 
3. To recognize which statistical techniques and methods are applicable in problem solving for management decision making.

Student Learning Outcomes:

When you have completed this course you should be able to:

1. appreciate that statistical analysis of data improves business decisions and improves business competitiveness. 
2. Select the correct statistical method for a given data analysis requirement.
3. Develop expertise in describing data, hypothesis testing and model interpretation.
4. Achieve a practical level of competence in applying quantitative methods to business applications.
5. Recognize the application of different techniques in time series analysis and forecasting.
6. Development competence in the use of Excel as a tool for data processing. 

Program Outcomes Met By This Course:

ISLO-2: Students will be able to utilize the relevant ICT tools to analyze problems and propose solutions that aid in management decision making.

SAS Grading Scale: Grades will be assigned as follows:

A  = 89.5% or better

B+ = 84.5 - 89.4%

B  = 79.5 - 84.4%

C+ = 74.5 - 79.4%

C = 69.5 - 74.4%

D = 64.5 - 69.4%

F = 64.4% or less 

Course Materials:

Text: McClave Bension Sincich, “Statistics for Business and Economics”, Tenth or any later edition                             

Barry Render, Ralph M Stair Jr, Michael E Hanna; “Quantitative Analysis For Management” Eleventh Edition

Course Grading Requirement:

Evaluations:

1. Quizzes-10%                                              
2. Assignment-10%
3. Midterm Examination-25%
4. Final examination- 50%
5. Attendance and participation-5%

Course Requirements:

To obtain the most from this course, students should attend every class meeting. If you miss class, it is your responsibility to obtain the information covered in your absence. Students should have total access to the required text. It is expected you would have read the assigned material before class and be prepared to seek clarification where necessary. You should go away from the lectures and think carefully about what you have heard and assimilate further material from the textbook while paying attention to business events and opportunities appearing in the news.

Course Schedule: 

Methods of describing and presenting data sets

• Index numbers and application 
• Simple index
• Aggregate index
• Laspeyres  index
• Paasche index
• Probability Concepts and Applications 
• Introduction 
• Fundamental Concepts 
• Types of Probability 
•  Mutually Exclusive and Collectively Exhaustive Events  Adding Mutually Exclusive Events 
• Law of Addition for Events That Are Not Mutually Exclusive 
• Statistically Independent Events 
• Statistically Dependent Events 
• Revising Probabilities with Bayes’ Theorem  General Form of Bayes’ Theorem 
• Further Probability Revisions 
• Random Variables 
• Probability Distributions 
• Probability Distribution of a Discrete Random Variable 
• Expected Value of a Discrete Probability Distribution 
• Variance of a Discrete Probability Distribution 
• Probability Distribution of a Continuous Random Variable 
• The Binomial Distribution 
• The Normal Distribution 
• The F Distribution 
• The Exponential Distribution 
• The Poisson Distribution 

Decision Analysis 

• Introduction 
• The Six Steps in Decision Making 
• Types of Decision-Making Environments 
• Decision Making Under Uncertainty  Optimistic 
• Pessimistic 
• Criterion of Realism (Hurwicz Criterion) 
• Equally Likely (Laplace) 
• Minimax Regret 
• Decision Making Under Risk  Expected Monetary Value 
• Expected Value of Perfect Information
• Expected Opportunity Loss 
• Sensitivity Analysis 
• Using Excel QM to Solve Decision Theory Problems 

Programme Evaluation and Review Technique(PERT) and the Critical Path Method(CPM)

• The framework of PERT and CPM
• Determining the Critical Path
• Drawing the Network
• Critical activities and the Critical Path

Regression Models 

• Introduction 
• Scatter Diagrams
• Simple Linear Regression 
• Measuring the Fit of the Regression Model 
• Coefficient of Determination 
• Correlation Coefficient 
• Using Computer Software for Regression
• Assumptions of the Regression Model 
• Estimating the Variance 
• Testing the Model for Significance  Triple A Construction Example 
• The Analysis of Variance (ANOVA) Table 
• Triple A Construction ANOVA Example 
• Multiple Regression Analysis 
• Evaluating the Multiple Regression Model 

 Forecasting 

• Introduction 
• Types of Forecasts 
• Time-Series Models 
• Causal Models 
• Qualitative Models 
• Scatter Diagrams and Time Series 
• Measures of Forecast Accuracy 
• Time-Series Forecasting Models 
• Components of a Time Series 
• Moving Averages 
• Exponential Smoothing 
• Using Excel QM for Trend-Adjusted Exponential Smoothing 
• Trend Projections 
• Seasonal Variations 
• Seasonal Variations with Trend 
• The Decomposition Method of Forecasting with Trend and Seasonal Components 
• Using Regression with Trend and Seasonal Components 

Inventory Control Models 

• Introduction 
• Importance of Inventory Control 
• Decoupling Function 
• Storing Resources 
• Irregular Supply and Demand 
• Quantity Discounts 
• Avoiding Stockouts and Shortages
• Inventory Decisions 
• Economic Order Quantity: Determining How Much to Order 
• Inventory Costs in the EOQ Situation 
• Finding the EOQ 
• Purchase Cost of Inventory Items 
• Sensitivity Analysis with the EOQ Model  Reorder Point: Determining When to Order 
• EOQ Without the Instantaneous Receipt Assumption
• Annual Carrying Cost for Production Run Model 
• Annual Setup Cost or Annual Ordering Cost 
• Determining the Optimal Production Quantity 
• Brown Manufacturing Example
• Quantity Discount Models 
• Brass Department Store Example 
• Use of Safety Stock 
• Single-Period Inventory Models 
• Marginal Analysis with Discrete Distributions 
• Café du Donut Example 
• Marginal Analysis with the Normal Distribution 
• Newspaper Example  ABC Analysis 
• Dependent Demand: The Case for Material Requirements Planning 
• Material Structure Tree 
• Gross and Net Material Requirements Plan 
• Two or More End Products  Just-in-Time Inventory Control 
• Enterprise Resource Planning 

Transportation and Assignment Models  Introduction

• The Transportation Problem 
• A General LP Model for Transportation Problems 
• The Assignment Problem 
• Linear Program for Assignment Example 
• The Transshipment Problem 
• Linear Program for Transshipment Example 
• The Transportation Algorithm 
• Developing an Initial Solution: Northwest Corner Rule 
• Stepping-Stone Method: Finding a Least-Cost Solution 
• Special Situations with the Transportation Algorithm 
• Unbalanced Transportation Problems 
• Degeneracy in Transportation Problems 
• More Than One Optimal Solution 
• Maximization Transportation Problems 
• Unacceptable or Prohibited Routes 
• Other Transportation Methods 
• Facility Location Analysis 
• Factory for Hardgrave Machine Company
• The Assignment Algorithm
• The Hungarian Method (Flood’s Technique) 
• Making the Final Assignment 
• Special Situations with the Assignment Algorithm 
• Unbalanced Assignment Problems 
• Maximization Assignment Problems