I. OPERATIONS RESEARCH:
1) Wal-Mart Stores
Wal-Mart, a discount store chain, has completed its new store in Rock Springs, Maryland. The 150,000 square foot store operates seven days per week and requires the following number of full-time employees working each day of the week.
Number of Employees
Sunday 45
Monday 20
Tuesday 28
Wednesday 35
Thursday 32
Friday 44
Saturday 55
Each employee must work five consecutive days each week and then has two days off. For example, any employee who works Sunday through Thursday has Friday and Saturday off. The store currently has a total of 60 employees available to work. Wal-Mart has developed the following prioritized goals for employee scheduling:
• The store wants to avoid hiring any additional employees.
• The most important days for the store to be fully staffed are Saturday and Sunday.
• The next most important day to be fully staffed is Friday
• The store wants to be fully staffed from Monday through Thursday.
• The store wants to avoid layoffs for any current employees unless overstaffing cannot be avoided.
a. Formulate a linear goal programming model to determine the number of employees who should begin their five-day workweek each day of the week in order to achieve the store’s objectives.
b. Determine the solution that will best achieve the company’s goals in employee scheduling using the Management Scientist software. Interpret the solution results including the levels of goal achievement. Provide a recommendation if applicable.
II. BUSINESS STATISTICS:
Use Excel for your solutions – SEE EXCEL Spreadsheets attached!
2) Buyer's Guide:
The Buyer's Guide section of the Web site for Car and Driver magazine provides reviews and road tests for cars, trucks, SUVs, and vans. The average ratings of overall quality, vehicle styling, braking, handling, fuel economy, interior comfort, acceleration, dependability, fit and finish, transmission, and ride are summarized for each vehicle using a scale ranging from 1 (worst) to 10 (best). A portion of the data for 14 Sports/GT cars is shown here (https://www.caranddriver.com, January 7, 2004).
Sports/GT Overall Handling Dependability Fit and Finish
Acura 3.2CL 7.80 7.83 8.17 7.67
Acura RSX 9.02 9.46 9.35 8.97
Audi TT 9.00 9.58 8.74 9.38
BMW 3-Series/M3 8.39 9.52 8.39 8.55
Chevrolet Corvette 8.82 9.64 8.54 7.87
Ford Mustang 8.34 8.85 8.70 7.34
Honda Civic Si 8.92 9.31 9.50 7.93
Infinity G35 8.70 9.34 8.96 8.07
Mazda RX-8 8.58 9.79 8.96 8.12
Mini Cooper 8.76 10.00 8.69 8.33
Mitsubishi Eclipse 8.17 8.95 8.25 7.36
Nissan 35OZ 8.07 9.35 7.56 8.21
Porsche 911 9.55 9.91 8.86 9.55
Toyota Celica 8.77 9.29 9.04 7.97
a. Develop an estimated regression equation using handling, dependability, and fit and finish to predict overall quality.
b. Another Sports/GT car rated by Car and Driver is the Honda Accord. The ratings for handling, dependability, and fit and finish for the Honda Accord were 8.28, 9.06, and 8.07, respectively. Estimate the overall rating for this car.
c. Provide a 95% confidence interval for overall quality for all sports and GT cars with the characteristics listed in part (b).
d. Provide a 95% prediction interval for overall quality for the Honda Accord described in part (b).
e. The overall rating reported by Car and Driver for the Honda Accord was 8.65. How does this rating compare to the estimates you developed in parts (b) and (d)?