Question

A large trucking company has an internal mechanics team to conduct frequent express oil changes mid-day for the truck drivers. Two men have applied for the open mechanic position. Frank Goodard is fresh out of trade school and expects a $16 per hour salary. His average service time for an oil change is 12 minutes. Carl Johnson is a veteran mechanic who expects $32 per hour. His average service time is 9 minutes for an oil change. A trucker drivers' time is figured at $12 per hour. Truckers arrive for their oil changes at an average rate of 4 per hour.

a.	What is the average waiting time a truck driver would spend in the system under each applicant?
b.	Which applicant should be hired?

Answer 1

Arrival time (A) = 4 per hour

Truck drivers cost per hour = 12$

For Frank:

Service time (S) = 12 min or 60/12 per hour = 5 per hour

Average number of people in line waiting (Lq) = A^2/(S*(S-A)) = 4^2/(5*(5-4)) = 3.2

Average number in system (Ws) = Lq + A/S = 3.2 + 4/5 = 4.0

Average waiting time in system (Wt) = 1/(S-A) hours = 1/(5-4) hour = 1 hour or 60 min.

Total cost per hour = Per hour salary of Frank + Average number in system*Truck drivers cost per hour

= 16 + 4*12 = 64$

For Carl:

Service time (S’) = 9 min or 60/9 per hour = 6.67 per hour

Average number of people in line waiting (Lq’) = A^2/(S’(S’-A)) = 4^2/(6.67(6.67-4)) = 0.90

Average number in system (Ws’) = Lq’ + A/S’ = 0.90 + 4/6.67 = 1.50

Average waiting time in system (Wt’) = 1/(S’-A) hours = 1/(6.67-4) hour = 0.37 hours or 0.37*60 min = 22.47 min

Total cost per hour = Per hour salary of Carl + Average number in system*Truck drivers cost per hour

= 32 + 1.5*12 = 50$

a) Average waiting times are:

Frank (Wt) = 60 min

Carl (Wt’) = 22.47 min

b) Carl should be hired as the cost per hour is lower than that of Frank