Question

The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 2 hours and a standard deviation of 1.5 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $35 per hour cost for customers waiting during the repair process. What are the arrival rate and service rate in jobs per hour

Answer 1

The correct answer is:

• 
  `\lambda=0.375 \ jobs \ per \ hour`
• 
  `\mu=0.5 \ jobs \ per \ hour`

Explanation:

The given values are:

Service time varies,

Repair time = 2 hours

Standard deviation = 1.5 hours

Robotics uses per hour cost,

= $35

Company's cost per hour,

= $28

(a)

⇒ Arrival rate = Jobs per hours

then,

=
`(8 \ hours)/(3 \ jobs)`

=
`2.666 \ hours \ per \ job`

The jobs per hour will be:

⇒
`\lambda=(1)/(2.666)`

`=0.375`

(b)

⇒ Service rate = jobs per hour

then,

μ =
`(1 \ repair \ job)/(2 \ hours)`

=
`0.5 \ jobs`