Question

manufacturer is studying a proposal to install an automatic device at one of its production operations. The device would perform the operation in exactly 0.5 minutes. At present, there is a (single server) manual operation with an average service rate of 60 per hour and exponential service times. The arrival rate is 50 products per hour and Poisson distributed. Each minute saved per product at the operation is worth $2. Assume that the total production for the year is 1,500.

1.

What is the average time in the system in the manual operations?

		4.6 minutes
		4.8 minutes
		8.4 minutes
		6 minutes

2. What is the average time in the system in the automatic operations?

		0.67 minutes
		2.1 minutes
		1.76 minutes
		0.48 minutes

3.

If your answer to questions (1) and (2) of the Problem are 5 and 2.5 minutes, respectively, how much is the savings per product due to the automatic device for one year?

		$9400
		$6000
		$8700
		$7500

4.

If the device costs $4000, should the device be installed, i.e., would it offset its cost in one year (Yes/No) (based on your answer to the previous part)?

		Yes
		No

Answer 1

1. Answer : 6 minutes

2. Answer : 0.67 minutes

3. Answer : $7500

4. Answer : YES, the device should be installed.