Question

In: Operations Management

In the service department of the NAPA (National Auto Parts Association), mechanics requiring parts for auto...

In the service department of the NAPA (National Auto Parts Association), mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 60 per hour, and a clerk can fill requests at the rate of 20 per hour (exponential). If the cost for a parts clerk is $20 per hour and the cost for a mechanic is $50 per hour, answer the following three questions (Because of the high arrival rate, an infinite source may be assumed.)

  • Please analyze the total cost per hour (clerks’ hourly cost and mechanics’ time spent in system) when there are 4 clerks to staff the counter?
  • Please analyze the total cost per hour (clerks’ hourly cost and mechanics’ time spent in system) when there are 5 clerks to staff the counter?
  • Is there a need to have 6 clerk to staff the counter? Please explain why with analysis.

Solutions

Expert Solution

Arrival rate, = 60 per hour

Service rate, = 20 per hour

Cost for parts clerk, Cs = $ 20 per hour

Cost for mechanic, Cw = $ 50 per hour

/ = 60/20 = 3

----------------------------------------------------------------------------------------------

1)

Number of clerks, M = 4

Look for /= 3 and M=4 n the following table:

For /= 3 and M=4, Lq = 1.528

Average number of mechanics in system, L = Lq+/ = 1.528+3 = 4.528

Total cost per hour = M*Cs + L*Cw = 4*20+4.528*50 = $ 306.4

----------------------------------------------------------------------------------------------

2)

Using 5 clerks

Look for /= 3 and M=5 n table 18.4

Lq = 0.354

Average number of mechanics in system, L = Lq+/ = 0.354+3 = 3.354

Total cost per hour = M*Cs + L*Cw = 5*20+3.354*50 = $ 267.7

----------------------------------------------------------------------------------------------

3)

Using 6 clerks

Look for /= 3 and M=6 n table 18.4

Lq = 0.099

Average number of mechanics in system, L = Lq+/ = 0.099+3 = 3.099

Total cost per hour = M*Cs + L*Cw = 6*20+3.099*50 = $ 275

Total cost per hour for 6 clerks is higher than 5 clerks.

Therefore, there is NO need to have 6 clerks.

keosha answered 1 year ago
Next > < Previous

Related Solutions

A NAPA auto parts supplier wants information about how long car owners plan to keep their...
A NAPA auto parts supplier wants information about how long car owners plan to keep their cars. a simple random sample of 31 car owners results in a mean of 7.01 years and a standard deviation of 3.74 years, respectively. Assume the sample is drawn from a normally distributed population. a) Find a 95%confidence interval estimate of the mean. b) Find a 95% confidence interval estimate of the population standard deviation. c) If several years pass and you want to...
Parts Emporium, Inc., is a wholesale distributor of automobile parts formed by two disenchanted auto mechanics,...
Parts Emporium, Inc., is a wholesale distributor of automobile parts formed by two disenchanted auto mechanics, Dan Block and Ed Spriggs. Originally located in Block’s garage, the firm showed slow but steady growth for 7 years before it relocated to an old, abandoned meat-packing warehouse on Chicago’s South Side. With increased space for inventory storage, the company was able to begin offering an expanded line of auto parts. This increased selection, combined with the trend toward longer car ownership, led...
Question No.1    An auto parts supplier sells Hardy-brand batteries to car dealers and auto mechanics....
Question No.1    An auto parts supplier sells Hardy-brand batteries to car dealers and auto mechanics. The annual demand is approximately 1500 batteries. The supplier pays 25 R.O for each battery and estimates that the annual holding cost is 30% of the battery's value. It costs approximately 30 R.O to place an order. The supplier currently orders 125 batteries per month. a. Determine the EOQ. b. How many orders will be placed per year using the EOQ? c. Determine the...
Question No.1    An auto parts supplier sells Hardy-brand batteries to car dealers and auto mechanics....
Question No.1    An auto parts supplier sells Hardy-brand batteries to car dealers and auto mechanics. The annual demand is approximately 1500 batteries. The supplier pays 25 R.O for each battery and estimates that the annual holding cost is 30% of the battery's value. It costs approximately 30 R.O to place an order. The supplier currently orders 125 batteries per month. a. Determine the EOQ. b. How many orders will be placed per year using the EOQ? c. Determine the...
9. The Speedy Auto Service Center can buy auto parts from Southeast Auto Supply at a...
9. The Speedy Auto Service Center can buy auto parts from Southeast Auto Supply at a series discount of 30/20/5 and from Northwest Auto Supply for 25/20/15. a. Which auto parts supplier offers a better deal to Speedy? b. If Speedy orders $23,000 in parts at list price per month, how much will they save in a month by choosing the lower-priced supplier (versus the alternative)?
Domestic Auto Parts Domestic Auto Parts (DAP), a $1 billionsubsidiary of a U.S. auto parts...
Domestic Auto Parts Domestic Auto Parts (DAP), a $1 billion subsidiary of a U.S. auto parts manufacturing company, manufactured and marketed original and after-market parts for automobile producers in the U.S. It distributed products directly to original equipment automakers as well as to large retail chains. DAP was currently number four in market share in the U.S. out of nine direct competitors. Its 9% return on capital was respectable but less than that of its leading competitors. DAP’s current product...
Emirates Top Auto Parts (ETAP) is an independent auto parts dealer that sells auto parts and...
Emirates Top Auto Parts (ETAP) is an independent auto parts dealer that sells auto parts and delivers parts and tools to mechanic shops around the city. Identify possible actors and use cases involved in ETAP’s business functions. Create a use case diagram for ETAP’s operations. For the use case where the customer buys parts, complete a use case description table For the use case where the customer buys parts, create a class diagram. For the use case where the customer...
UML Diagrams Osceola Auto Parts Osceola Auto Parts is an independent auto parts dealer that sells...
UML Diagrams Osceola Auto Parts Osceola Auto Parts is an independent auto parts dealer that sells auto parts, runs tests on customers’ cars,and delivers parts and tools to mechanic shops around town. Tasks 1. Identify possible actors and use cases involved in Osceola’s business functions. 2. Using dia, create a use case diagram for Osceola’s operations. 3. Select one of the use cases and create a class diagram. 4. Using dia, create a sequence diagram for the use case you...
What are the mission statements for the National Criminal Justice Association (NCJA), Department Enforcement Agency (DEA),...
What are the mission statements for the National Criminal Justice Association (NCJA), Department Enforcement Agency (DEA), Georgia Department of Corrections, and Baptist World Charities and how it fit into the organizational structure? How are these statements different?
Tuscaloosa National Bank has two service departments, the Human Resources (HR) Department and the Computing Department....
Tuscaloosa National Bank has two service departments, the Human Resources (HR) Department and the Computing Department. The bank has two other departments that directly service customers, the Deposit Department and the Loan Department. The usage of the two service departments’ output for the year is as follows:     User of Service Provider of Service HR Computing HR 0 25 % Computing 20 % 0 Deposit 70 % 65 % Loan 10 % 10 %    The budgeted costs in the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT