1. Consider a two-station production line with single machines. Jobs arrive to the first station at an average rate of 5 per hour with a squared coefficient of variation equal to 1.96. Effective processing times average 0.125 hours with a squared coefficient of variation equal to 0.81.

a) What is the first station’s utilization?

b) What is the squared coefficient of variation of the arrivals to the second station?

c) If an identical second machine is added to the first station, do you expect the SCV of arrivals to the second station to increase or decrease? Why? (Start by thinking about how utilization will change.)

2. Suppose jobs arrive at a single-machine workstation at a rate of 20 per hour and the average process time is 2.5 minutes.

a) What is the utilization of the machine?

b) Suppose that the inter-arrival and process times are such that and .

i) What is the average time a job spends at the station (i.e. waiting plus process time)?

ii) What is the average number of jobs at the station?

c) Now suppose instead that the SCV of process times is 4, with a mean process time of 2.5 minutes (unchanged).

i) What is the average time a job spends at the station?

ii) What is the average number of jobs at the station?

3. Consider a workstation with 11 machines, each requiring one hour of process time per job with an SCV of 5. Each machine costs $10,000. Jobs arrive at a rate of 10 per hour with SCV equal to 1 and they must be filled. Management has specified a maximum allowable average response time (i.e. time a job spends at the station) of 2 hours. Currently it is just over 3 hours (check this). Analyze the following options and determine which is best for reducing average response time.

a) Perform more preventive maintenance at a cost of $8000 (over lifetime of the machines). The effect of this on *tr* and *tf* is that ultimately *ce2* is reduced to 1.

b) Add another identical machine to the workstation at a cost of $10,000.

c) Modify the existing machines to make them faster without changing the SCV, at a cost of $8500. The modified machines would have *te* = 0.96 hours and *ce2* = 5.

You may use the VUT spreadsheet used for the example in the video to help you in comparing the options.