Reference no: EM13334168
1. A company offers ID theft protection using leads obtained from client banks.
Three employees each work 40 hours a week on the leads. These employees are each paid $25 per hour.
Each employee identifies an average of 3,000 potential leads a week. There are no duplications in these three lists. An average of 4 percent of the potential leads actually sign up for the service, paying a one-time fee of $70. Material costs are $1,000 per week, and overhead costs are $9,000 per week. Consider the output as the fees generated.
Calculate all productivity factors to three decimal places (x.xxx)
a) What are the labor hours productivity and the multifactor productivity for this operation?
b) From the results in a) suppose the company wants to improve the multifactor productivity by 10% by reducing the labor hours used. What must the reduction in labor hours per employee per week be to achieve this goal?
c) Use the original information in the problem to answer this part. Suppose the company realizes that its overhead costs were miscalculated. The company needs the multifactor productivity to be at least 1.200. While keeping all of the other values from the original information the same, what is the maximum value that the overhead costs per week can be to ensure the multifactor productivity is at least 1.200?
2. Among other services and products that Karl's Copiers provides, it sells and repairs photocopy machines. It is now the end of December, 2014 and the manager needs to plan his service staffing for January, 2015. The manager first needs to forecast the number of service calls for January, 2015. Following are the record of service calls for the past 12 months.
|
Month
|
Number of Service Calls
|
Month
|
Number of Service Calls
|
|
January
|
30
|
July
|
31
|
|
February
|
24
|
August
|
38
|
|
March
|
27
|
September
|
37
|
|
April
|
31
|
October
|
36
|
|
May
|
37
|
November
|
32
|
|
June
|
34
|
December
|
29
|
You have been asked by the manager to help with the forecast for January, 2015. He has asked you to provide forecasts for January using the following three methods:
- Moving Average
- Weighted Moving Average
- Exponential Smoothing
He has also asked you to determine which of these three forecasts he should select. To make this assessment, he has asked that you compare the actual number of service calls to what the forecasts would have been for September through December, 2014 using each of the three methods.
i) For the moving average, use a three month moving average.
ii) For the weighted moving average, use a two-period weighted average with a weight of 0.70 for the most recent month and the remaining weight(s) consistent with this forecasting method as we applied it.
iii) For exponential smoothing, use an α = 0.25, and using a starting forecast for July, 2014 of 33.
a) Prepare a forecast for January, 2015 using each of the three methods.
b) Recommend which of these three methods the manager should use for January, 2015 based on the results of evaluation of the forecasts for September through December. Your selection criteria must be based on one of the numerical evaluation methods we have learned and used this semester. Only saying "it is the easier method" is not acceptable.
3. Prydain Pharmaceuticals is reviewing it employee health-care program. Currently, the company pays a fixed fee of $300 per month for each employee, regardless of the number or dollar amount of medical claims filed. Another health-care provider, ABC Health, has offered to charge the company $100 per month per employee and $30 per claim filed. If your calculations result in non-integer (non whole numbers) results, leave them that way and do not round the results to integer values.
a) Based on this information, over what range of claims filed per month per employee should Pyrdain stay with its current program and for what range should it select ABC Health's offer?
b) Suppose that the average number of claims filed per month per employee is currently five (5). ABC Health has indicated that the $30 per claim filed is negotiable. With everything else being the same, what is the maximum Prydain would be willing to pay to be indifferent between the two plans?
c) Suppose a third insurer, MedCare, charges $200 per month per employee and $10 per claim filed. Considering only ABC Health and MedCare, over what range of claims filed per month would Pyrdain prefer each of the two alternatives?
4. a) How is a typical forecasting process similar to the PDCA (equivalently the PDSA) cycle? Discuss and illustrate the similarities.
b) Using a smaller call center (about 100 service representatives), briefly describe and/or illustrate how any two of the four core processes in a firm are related.
5. Smith Manufacturing is currently considering using one of three suppliers. For a specific part, Smith's upper specification limit (USL) is 13.8 centimeters (cm) and its lower specification limit (LSL) is 10.8 centimeters (cm).
a) The first supplier, ABC, can adjust its mean but cannot reduce its standard deviation. Its standard deviation is 0.3 cm. What is the range (lower and upper limits) for the mean of the process if ABC wants its process capability index (Cpk) to satisfy at least Smith's minimum acceptable value of 1.4?
b) The second supplier, DEF, cannot adjust the mean of its process which is currently 11.8 cm. However it can improve its standard deviation if necessary. What is the maximum standard deviation (σ) allowed if DEF wants its process capability index (Cpk) to be at least the minimum acceptable value of 1.4?
c) The third supplier, GEF has a process whose standard deviation is 0.6 cm and the mean of its process is 12.0. Smith is willing to adjust its specification limits if necessary to achieve a Cpk of 1.4? What are the values of the specification limits that would be required to achieve the minimum acceptable Cpk?
6. Dotz's Bakery bakes fresh apple pies each morning for sale that day. A pie costs $2.00 to make and sells for $4.00. Any pies left at the end of the day are sold at that time to another organization at a discounted price of $1.50. Based on her past experience, the bakery's manager expects to sell between 10 and 12 pies per day. Based on historical sales records, the bakery manager estimates the probabilities of the different apple pie demand levels as the following:
|
# of Pies
|
10
|
11
|
12
|
|
Probability
|
0.30
|
0.35
|
0.35
|
a) Construct the decision tree that can be used to determine how many pies the bakery should bake daily.
b) Determine the number of pies to bake to maximize the expected daily profits.
c) Suppose the bakery is uncertain about the probabilities provided in the problem. It is all right with the probability for the demand for 10 pies being 0.30 and does not believe this should be changed. It is not certain about the probabilities for the demand for 11 and 12 pies each being 0.35. What are the probabilities for selling 11 pies and for selling 12 pies that make the expected profit for the 11 pie decision equal to the expected profit for the 12 pie decision?
7. The Dynaco Manufacturing Company is going to build a new plant to manufacture ring bearings (used in automobiles and trucks). The site selection team is evaluating three sites, and they have scored the critical success factors for each as shown below. The weights reflect the same relative importance as we have used and discussed. They want to use these ratings to compare the locations.
|
Critical Success Factors
|
Weight
|
Site 1
|
Site 2
|
Site 3
|
|
Labor Cost
|
????
|
$6 million
|
$5 million
|
$6.5 million
|
|
Labor pool and climate
|
0.30
|
80
|
65
|
90
|
|
Proximity to suppliers
|
0.20
|
100
|
91
|
75
|
|
Community environment
|
0.15
|
75
|
80
|
80
|
|
Proximity to customers
|
0.10
|
65
|
90
|
95
|
|
Shipping modes
|
0.10
|
65
|
50
|
90
|
The non-economic scores are on a 0 to 100 basis with 100 being best.
a) Using the factor rating (scoring) method that we learned during the class, which site should Dynaco use based on the above information? Please fill in any missing information.
b) Currently the Site 1 Proximity to Customers score is 65. Dynaco is interested in learning what the value of the Proximity to Customers score for Site 1 must be so that the resulting total factor score for Site 1 is equal to that for Site 3. What must this score be so that the resulting total scores for the two sites are equal?
8. Holding goods in inventory is costly because inventoried goods are susceptible to breakage and other forms of physical damage. Typically, the amount of damage (in dollars) increases with the level of inventory (expressed in dollars), but some of the damage is unrelated to the amount of inventory. The following data show a company's inventory damage experience.
|
Period
|
Inventory Level (Millions of Dollars)
|
Damage (Thousands of Dollars)
|
Average Age of Inventory (Days)
|
|
1
|
$11
|
$80
|
31
|
|
2
|
$15
|
$90
|
45
|
|
3
|
$13
|
$70
|
98
|
|
4
|
$10
|
$60
|
15
|
|
5
|
$7
|
$50
|
25
|
|
6
|
$9
|
$70
|
31
|
|
7
|
$13
|
$80
|
82
|
You are interested in developing a forecast for the Damage for period 9.
a) You believe that there is a cause-and-effect relationship between damage and the inventory level. You believe that the damage is a function of the inventory level.
Develop and provide the linear regression equation for the damage given the inventory level using the appropriate independent and dependent variables.
b) How good is the relationship you found in a)? Based on the considerations used during class related to the strength of the relationship, would you recommend using this relationship? Explain your reasoning.
c) If the forecasted inventory level for period 9 is $15,000,000, what is the forecasted damage for Period 9?
d) Your boss believes that there might be a cause-and-effect relationship between damage and the average age of the inventory. He wonders if the damage level might be influenced by the average age of the inventory. Based on the information provided, what would you tell him? Explain your answer. If you do agree with your boss, what would you forecast the damage level for inventory with an average age of 60 days?
9. As a hospital administrator of a large hospital, you are concerned with the absenteeism among nurses' aides. The issue has been raised by registered nurses, who feel they often have to perform work normally done by their aides. To get the facts, absenteeism data were gathered for the last 15 days. This is considered a representative period for future conditions. After taking random samples of 96 personnel files each day, the following data were produced:
|
Day
|
Aides Absent
|
Day
|
Aides Absent
|
|
1
|
6
|
9
|
11
|
|
2
|
5
|
10
|
3
|
|
3
|
3
|
11
|
5
|
|
4
|
2
|
12
|
3
|
|
5
|
3
|
13
|
2
|
|
6
|
8
|
14
|
5
|
|
7
|
5
|
15
|
11
|
|
8
|
6
|
|
|
Assume that there is sufficient data for preparing control charts. Because your assessment of absenteeism is likely to come under careful scrutiny, you would like to use 2σ control limits. You are not interested in the reasons for the absence but just if there is an absence or not. You want to be sure to identify any instances of unusual absences. If some are present, you will have to explore them on behalf of the registered nurses.
a) Calculate the 2σ (sigma) control limits. The centerline should be based on the data from these 15 days. All calculations should be to three decimal places (x.xxx).
b) After finding the control limits, prepare and provide the appropriate control chart.
c) Using this sample information and the control chart, do the data indicate that absenteeism is a problem or not for the hospital's nurses' aides? Why or why not?
d) Suppose that the administrator has obtained data from an industry association that indicates the acceptable industry standards for absenteeism has upper and lower limits of 0.135 and 0.035 respectively. Considering the performance based on the daily samples from the control chart, what would you conclude about the hospital's experiences compared to the industry's standards? Explain your answer.
10. The Bijou Theater in Bellevue shows vintage movies. For this problem, the system can be considered the purchasing of the ticket. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers' parking lot receipts and punching their frequent watcher cards as well as selling tickets. Because of these added services, many customers don't get in until after the feature has started. Assume that the arrivals follow a Poisson arrival distribution and the service times are exponentially distributed. There is an infinite population and an infinite queue.
a) What is the average time it takes for the customer to enter the theater measured from the time the customer arrives at the theater line to purchase a ticket?
b) What is the average number of customers waiting in line to purchase a ticket?
c) What is the probability that there are at least two others waiting in line to buy a ticket?
d) What would be the effect on the total time it takes for the customer to enter the theater by having a second ticket taker doing nothing but validations and card punching, thereby cutting the average service time to 20 seconds per customer? This ticket taker does not directly wait on any customers but only supports the ticket seller.
e) Suppose the cost of the first ticket taker is $20 per hour while the cost of the second ticket taker is only $10 per hour. Also, suppose the cost of both waiting and buying the tickets (cost of good will and lost customers) is valued at $6 per hour per customer. What is the cost of each option (the single ticket taker and the two ticket taker options) that the theater is considering?