Today your team will formulate a strategy to execute next class meeting (“round 2 game day”). The following questions guide you through the most important considerations in formulating a strategy; your deliverable is the answers to these questions.
1. Describe the arrival process during peak demand (days 120 to 180). Specifically, quantify:
• the average arrival rate (in samples per day)
• a, the average inter-arrival time (in hours)
• CVa, the coefficient of variation of inter-arrival times2
2. Recall that step-1 processing times do not fluctuate. Describe the service process in station 1, specifically,
• p, the step-1 processing time (in hours)
• the capacity of a single machine in station 1 (in samples per day)
• CVp, the coefficient of variation of step-1 processing times
3. Given the answers for questions 1 and 2, compute the average time in station 1’s queue (Tq) and the total time in station 1 (T = Tq + p) when there are 2, 3, 4, 5, and 6 machines in station 1.3 You are free to organize your work however you want.
4. Given the results in question 3, how many total machines does your team recommend having at station 1 during peak demand (days 120-180)?
5. Suppose that your team invests in enough capacity in stations 1 and 2 so that each is demand-constrained (i.e., capacity is more than 24 jobs per day in each station). What minimum number of machines in station 1 and station 2 makes this happen?
6. On the basis of question 6, how many total machines does your team recommend having at station 3 during peak demand (days 120-180)?
7. The time in queue formula (Tq) cannot reliably approximate station 2’s queueing delays.5 A good rule of thumb would be to buy enough station-2 machines so that their average utilization is at most 80% during the peak demand (days 120- 180). How many total machines is this?
8. You now have a choice of two contracts:
• Contract 1, $400/sample with $4.17 rebate for every hour of delay after 72 hours.
• Contract 2, $480/sample with $40 rebate for every hour of delay after 12 hours.
9. Which contract does your team wish to use? Will your team do a lower capacity investment and use contract 1, a higher capacity investment and use contract 2, or some mixture of both? Describe your team’s strategy on managing the tradeoff of customer responsiveness and cost of capacity.