Consider a workstation with five machines. The arrival rate of jobs is 13.5 jobs
ID: 349601 • Letter: C
Question
Consider a workstation with five machines. The arrival rate of jobs is 13.5 jobs per hour (with c 2 a = 1). Each machine takes 0.3 hour per job with a natural CV of 1 2 (that is, c 2 0 = 0.25). The mean time to failure for any machine is 36 hours, and repair times are exponential with a mean time to repair of 4 hours.
(a) Show that the SCV of effective process times is 2.65.
(b) What is the utilization of a single machine when it is allocated one-fifth of the demand (that is, 2.7 jobs per hour) assuming ca is still equal to 1?
(c) What is the utilization of the station with an arrival rate of 13.5 jobs per hour?
Explanation / Answer
Process time, p = 0.3 hour
Mean time to failure, Mf = 36 hours
Mean time to repair, Mr = 4 hours
Machine availability, A = Mf/(Mf+Mr) = 36/(36+4) = 0.9
Mean effective process time, te = p/A = 0.3/0.9 = 0.333 hour
(a) SCV of effective process time, ce2 = CVp2 + (1+Cr2)*A*(1-A)*Mr/p = 0.25+(1+1)*0.9*(1-0.9)*4/0.3 = 2.65
(b) Interarrival time, a = 1/2.7 = 0.37 hours
Utilization of a single machine, te/a = 0.33/0.37 = 0.90
(c) Interarrival time, a = 1/13.5 = 0.0741 hours
Utilization of the station = te/(ma) = 0.33/(5*0.0741) = 0.90