The Operations manager for a large law office must choose between two copiers to
ID: 452603 • Letter: T
Question
The Operations manager for a large law office must choose between two copiers to lease. A Hijet copier, costs 8 dollars per hour to lease, can complete a copying job in 6 minutes, on average. Bluejet copier which leases for 16 dollars per hour can complete a copying job in 3 minutes. In a work day of 8 hours 56 copying jobs can be expected. The time of the employees tasked with copying is valued at 10 per hour.
1) For a Hijet copier, how many employees can be expected to be at the copier, both waiting on line and using the machine?
2) On a hourly Basis, What is the total cost of the regular copier ?
3) For Bluejet copier, how many employees can be expected to be at the copier, both waiting on line and using the machine?
4) what had to be assumed about how long the copying jobs take ?
5) what had to be assumed about how many employees need to use the copier at any given time ?
Explanation / Answer
Arrival rate lambda = 7/ hour (i.e 56/8)
Service rate mu µ = 10 /hour (service time)
Number of stations m = 1
Utilization rho = /mµ = 7/(1*10) = 0.7
Assume arrivals Poisson distribution and service time are exponentially distributed.
Average number in waiting line Lq can be obtained from the formula below,
Lq = 2/ (1-) = 1.633
Average waiting time from Little’s Law, Wq = 0.233
Average time-in-system (waiting time +service time) = 0.333
Average number-in-system (waiting+getting served) = 2.333
Costs of the Waiting Line System: The total cost of this waiting line system is the sum of the cost of waiting and cost of service.
Total Cost = Cost of Waiting + Cost of Service
= ( cw Ls ) + (cs k ) where k =number of hours, cw = cost of waiting = $10.00 per hour
cs = cost of service = $8.00 per hour
Total Cost = ($10 *2.33) + ($8 * 8) = $ 87.333
Arrival rate lambda = 7/ hour (i.e 56/8)
Service rate mu µ = 20 /hour (service time)
Number of stations m = 1
Utilization rho = /mµ = 7/(1*10) = 0.7
Assume arrivals Poisson distribution and service time are exponentially distributed.
Average number in waiting line Lq can be obtained from the formula below,
Lq = 2/ (1-) = 0.188461538
Average waiting time from Little’s Law, Wq = 0.026923077
Average time-in-system (waiting time +service time) = 0.076923077
Average number-in-system (waiting+getting served) = 0.538461538
Costs of the Waiting Line System: The total cost of this waiting line system is the sum of the cost of waiting and cost of service.
Total Cost = Cost of Waiting + Cost of Service
= ( cw Ls ) + (cs k ) where k =number of hours, cw = cost of waiting = $10.00 per hour
cs = cost of service = $16.00 per hour
Total Cost = ($10 * 0.538461538) + ($16* 8) = $ 133.3846154
Answer : 2.33, rounding off 3 employees.
Answer : Total cost = $ 87.33
Answer : 0.538, rounding off 1 employee.
The arrival rate is assumed to be 7 documents per hour.
If the arrival rate is 10 documents per hour, the ideal time of the machine can be also utilised.
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