Question

The supervisor at the Precision Machine Shop wants to determine the staffing policy that minimizes total operating costs. The average arrival rate at the tool​ crib, where tools are dispensed to the​ workers, is 5 machinists per hour. Each​ machinist's pay is ​$25 per hour. The supervisor can staff the crib either with a junior attendant who is paid ​$5 per hour and can process 10 arrivals per hour or with a senior attendant who is paid ​$18 per hour and can process 18 arrivals per hour. Which attendant should be​ selected?  

The _____ should be selected, with a total estimated hourly cost of $__

Answer 1

Case I

arrival rate lambda = 5 per hour

Service rate = 10 per hour

The waiting time for machinist = lambda / mu ( mu-lambda)

= 5 /10 x5 = 1/10 hour = 6 min.

Hourly waiting cost = [5 x 6 /60] x25 = 12.5 per hour

Total cost = attendant's pay + waiting cost = 5+12.5 =17.5

Case II

Waiting time = 5 / 18 x( 18-5) = 0.02136 hours = 1.2820 minutes

Total waiting time per hour = 1.2820 x5 = 6.41 min

Cost of waiting = 6.41 x25 /60 =2.67

Total cost = 18+2.67 = 20.67

As the cost is less in option I, the lower paid attendant is more economical.

Attendant I should be selected with a total estimated cost of 17.5