Question

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.

Answer 1

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

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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

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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.