Question

Larry Jones, the mechanic at the muffler shop, can install new mufflers at an average rate of 3 per hour. Customers who need new mufflers arrive on average 2.5 per hour. A) Assuming that this system can be modeled as M/M/1 queue, find the key operating characteristics of this system. (Average wait time, Average queue length, Average time in the system). B) The shop owners are interested in cost factors as well as service performance. They estimate that the cost of customer waiting time in terms of customer dissatisfaction and lost goodwill, is $40/hour for time spent waiting in line. Larry makes $40/hour (with fringe). What is the cost to shop of the current system for Larry and the customer dissatisfaction? If an additional mechanic could be hired for the same price (effectively doubling the rate of installation), would it worth it? C) Instead of hiring a new mechanic, suppose new machinery could help Larry work faster. An investment of $150,000 investment would cut the time to 18.5 minutes/muffler. Would you recommend either of these investments? Why or why not?

Answer 1

A)

B) Assuming 8 hour day

Cost of customer dissatisfaction in a day = Cost of customer dissatisfaction per hour* Average waiting time*no. of customers serviced in a day

=40*1.67*3*8 = $1,600

Cost of Larry for 8 hour shift = 40*8 = $320

Total Cost = $1,920

Cost of customer dissatisfaction = 40*0.07*3*2*8 = $134.4

Cost of Larry and other for 8 hour shift = 40*8*2 = $640

Total Cost = $774.4

Yes. Hiring another technician would save $1,145.6/day

C)

Cost of customer dissatisfaction = 1.03*40*3.24*8 = $1,067.9

Cost of Larry for 8 hour shift = 40*8 = $320

Total Cost = $1,387.9

The incremental saving per day = $ 1,920 - $1,388 = $532

Days to recover $150,000 = 150000/532 = 282 or ~ 9 months

So the investment can be recovered in 9 months and can be made.