Question

In: Operations Management

An aircraft repair service reimburses its customers for the time that an aircraft spends at their...

An aircraft repair service reimburses its customers for the time that an aircraft spends at their facility. Total costs are the sum of these reimbursements (waiting costs) and the salaries of their technicians. A customer is reimbursed $203 per hour for the time that the aircraft is out of service, and the cost of a service technician (including equipment and materials) is $1,196 per hour. Use Table 1 and Table 2. a. How many service technicians should be on call, if there are (on average) 4 aircraft arriving per hour, and each technician can complete 5 services per hour (Poisson distributions)? HINT: Calculate the total cost, which is the sum of waiting cost and service cost. Number of technician(s) b. The service rate could be made faster ( (5.71 repairs per hour) if the company invests in new software, which would cost $100 per service technician. Is it cost-effective for the company to invest in this software? HINT: the service cost is higher, but the time that it takes to get through the system, hence the waiting cost, is lower. (Round your cost amount to 2 decimal places and all other calculations to 3 decimal places. Omit the "$" sign in your response.) , because the daily total cost with the new software is $ which is lower than without the new software.

Expert Solution

Arrival rate, = 4 per hour

Service rate, = 5 per hour

/ = 4/5 = 0.8

Waiting cost, Cw = $ 203 per hour

Service cost, Cs = $ 1196 per hour

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

a)

Refer the following table and look up

/ = 0.8

For M = 1, Value of Lq = 3.2, where M is the number of service technicians

L = Lq+/ = 3.2+0.8 = 4

Service cost = M*Cs = 1*1196 = $ 1196 per hour

Waiting cost (Cost of aircraft out of service) = L*Cw = 4*203 = $ 812

Total operating cost per hour = 1196 + 812

= $ 2,008

We see that Service cost is more than waiting cost, which means that if we add another technician, then the total service cost itself will be 2*1196 = 2,392, which is greater than the total cost with 1 technician.

Therefore, optimal number of technicians = 1

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

b)

New service cost, Cs = 1196+100 = $ 1296 per hour

/ = 4/5.71 = 0.7

Refer the following table and look up / = 0.7

For M = 1, Value of Lq = 1.633, where M is the number of service technicians

L = Lq+/ = 1.633+0.7 = 2.333

Service cost = M*Cs = 1*1296 = $ 1296 per hour

Waiting cost (Cost of aircraft out of service) = L*Cw = 2.333*203 = $ 473.67

Total operating cost per hour = 1296 + 473.67

= $ 1,769.67

We see that this cost is lower than part (a). Therefore, it is cost effective for this company to invest in this software

because the daily total cost with the new software is $ 1,769.67 which is lower than without the new software.

keosha answered 3 months ago

An automotive repair shop has determined that the average service time on an automobile is 2...

An automotive repair shop has determined that the average service time on an automobile is 2 hours with a standard deviation of 30 minutes. A random sample of 36 services is selected. (a) What is the probability that the sample of 36 will have a mean service time greater than 115 minutes? (b) Assume the population consists of 400 services. Determine the standard error of the mean.

A customer service department asks its customers to rate their over-the-phone service on a scale of...

A customer service department asks its customers to rate their over-the-phone service on a scale of 1-20 immediately after their service has been completed. The department then matches each customer's rating with the number of minutes the person waited on hold. The accompanying table shows the ratings and number of minutes on hold for 10 randomly selected customers. The regression line for the data is (^ is above the Y) Y=16.85-0.15x. Use this information to complete parts a through d....

Describe the relationship between a star’s mass and the time a planet spends in its CHZ....

Describe the relationship between a star’s mass and the time a planet spends in its CHZ. What kind of star is the better candidate in terms of one of its planets being able to spend the maximum amount of time in the CHZ – a low-mass star, or a high-mass star? Explain.

Customers arrive at a service center according to a Poisson process with a mean interarrival time...

Customers arrive at a service center according to a Poisson process with a mean interarrival time of 15 minutes. If two customers were observed to have arrived in the first hour, what is the probability that at least one arrived in the last 10 minutes of that hour?

1) In a service system with impatient customers, is 1/a (1/interarrival time) the same as the...

1) In a service system with impatient customers, is 1/a (1/interarrival time) the same as the flow rate? please explain.

2. The same sample of 48 aircraft revealed that the average time that the aircraft was...

2. The same sample of 48 aircraft revealed that the average time that the aircraft was down for “C” check was 27 days with a standard deviation of 5 days. The VP of operations wants to know how long the next aircraft due inspection will be out of service. Can you give him an estimate based on a 90% degree of confidence?

A company's customer service department asks its customers to rate their over-the-phone service on a scale...

A company's customer service department asks its customers to rate their over-the-phone service on a scale of 1–20 immediately after their service has been completed. The company then matches each customer's rating with the number of minutes the person waited on hold. The accompanying table shows the ratings and numbers of minutes on hold for 10 randomly selected customers. Complete parts a through c below. Minutes Rating 1 14 7 12 3 20 8 15 5 13 2 17 5...

The time a customer spends using a service is distributed with pdf f(x) = λ^k x^(k−1)...

The time a customer spends using a service is distributed with pdf f(x) = λ^k x^(k−1) e^(−λx) / (k − 1)! , x ≥ 0. In the pdf there are two parameters: k and λ. You can assume (if you need to) that k is an integer larger than or equal to 1 (k = 1, 2, . . .), and λ is a real, non-negative number (λ ≥ 0). You have been observing a process that is supposed to...

Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time,...

Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 2.7 hours per call. Requests for copier repairs come in at a mean rate of 1.8 per eight-hour day (assume Poisson) a. Determine the average number of customers awaiting repairs. (Round your answer to 2 decimal places.) Number of customers b. Determine system utilization. (Round your answer to 2 decimal places. Omit the "%" sign in your...

SkiBlu, Ltd., divides its customers into Gold customers and Silver customers. The company has one full-time...

SkiBlu, Ltd., divides its customers into Gold customers and Silver customers. The company has one full-time customer representative per 1,000 Gold customers and one full-time customer representative per 10,000 Silver customers. Customer representatives receive salaries plus bonuses of 10 percent of customer gross margin. SkiBlu spends 90 percent of its promotion costs on Gold customers to encourage their loyalty. Customer Costs Total Gold Silver Number of customers 85,000 35,000 50,000 Average customer representative salary $ 75,000 $ 75,000 Promotion costs...