Reference no: EM13334312

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?