1. (10) Suppose jobs arrive at a single-machine workstation at a rate of 29 per

Question

1. (10) Suppose jobs arrive at a single-machine workstation at a rate of 29 per hour and the average process time is 1.75 minutes a. What is the utilization of the machine? b. Suppose that inter-arrival and process times are exponential i) What is the average time a job spends at the station (i.e. waiting plus process time)? i) What is the average number ofjobs at the station? iii) What is the long run probability of finding more than three jobs at the station? c. Process times are not exponential, but instead have a mean of 2 minutes and a standard deviation of five minutes, i What is the average time a job spends at the station? ii) What is the average number ofjobs at the station? ii) What is the average number of jobs in the queue? 2. (10) Consider a simple two-station line as below. The first machine takes 30mins per job. The second machine takes 24mins per job. Both have SCV-1. Both machines have exponential process times (Ce(1)-ce(2) 1). Between the two machines there is enough room for 4 jobs. So B- 4 jobs; b B+2 6 jobs Station 1 Finite buffer Station2 Unlimited raw materials What is the throughput? What is the partial WIP (i.c. WIP waiting at the first machine or at the second machine, but not in process at the first machine)? What is the total cycle time for the line, not including time in raw material? (Hint: Use Little's law with partial WIP and the throughput and then add the process time at the first machine) first machine) a. b. c. d. What is the total WIP in the ine? (Hint: Use Little's law with the total cycle time and throughput.)

Explanation / Answer

Kendall's notation M/M/1 Comment Arrival rate A 29 per hour Service rate S 34.29 60/1.75 U Utilization ratio U=A/S 0.84583

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