Trosper Tire Company has decided to hire a new mechanic to handle all tire chang

Question

Trosper Tire Company has decided to hire a new mechanic to handle all tire changes for customers ordering a new set of tires. Two mechanics have applied for the job. One has limited ex mechanic perience and can be hired for S28 per hour. It is expocted that this mechanic can ce an average of 6 customers per hour. The other mechanic has several years of experece Thi s mechanic can service an average of S customers per hour, but must be paid SS0 per hour Assume that customers arrive at the Trosper at the rate of 4 customers per hour. a) If the lower operating cost? How much lower? company assigns a customer waiting cost of $60 per hour, which mechanic prow bles b) At what value of the cost of waiting would the manager be indifferent in hiring either of the two mechanics?

Explanation / Answer

(a) Arrival rate, = 4 customers per hour

Mechanic-1:

Service rate of mechanic 1, = 6 customers per hour

Cost of mechanic 1, Cs = $ 28 per hour

Customer waiting cost, Cw = $ 60 per hour

Average number of customers in system L = /(-) = 4/(6-4) = 2

Operating cost per hour = Cs + Cw*L = 28 + 60*2 = $ 148 per hour

Mechanic-2:

Service rate of mechanic 2, = 8 customers per hour

Cost of mechanic 2, Cs = $ 50 per hour

Customer waiting cost, Cw = $ 60 per hour

Average number of customers in system L = /(-) = 4/(8-4) = 1

Operating cost per hour = Cs + Cw*L = 50 + 60*1 = $ 110 per hour

Mechanic 2 (experienced) provides lower operating cost.

Difference = 148 - 110 = $ 38 per hour

(b) At point of indifference, operating cost of mechanic 1 is equal to that of mechanic 2

28 + Cw*2 = 50 + Cw*1

Cw = (50-28)/(2-1) = 22

Waiting cost at point of indifference = $ 22 per hour

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