[SOLVED] RSM 270H1F Introduction to Operations Management

RSM 270H1F Introduction to Operations Management
This is the sample questions for lecture 2 for your preparation.
Problem 1 Consider the emergency department at Toronto General Hospital. Define in this process the flow unit, input rate, output rate, flow time and inventory. Patients, Patient arrival rate, Rate at which treated patients leave the ED, Time required to diagnose and treat a patient, The number of patients waiting in the various waiting rooms
Problem 2 Consider a process consisting of three steps. Step 1 takes each worker 10 minutes to complete, step 2 takes each worker 5 minutes to complete, and step 3 takes each worker 16 minutes to complete. You have 6 workers. How would you assign workers to maximize your capacity (you cannot merge any two steps together). Which step is the bottleneck? What is the process capacity? Assuming the input rate is 12 units per hour, what is the utilization of each worker? What is the average utilization? what is cycle time?

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We allocate 2 workers to step 1, 1 worker to step 2, and 3 workers to step 3. capacity of each worker at step 1= 1 unit per minute and the capacity of step 1 (both workers combined)
is 2/10 units per minute = 12 units per hour.
Step 2: one worker. The capacity of the worker:
1/5 units per minute = 12 units per hour. Step 3, 3 workers, each worker capacity 1/16 units per minute.
The capacity of 3 workers combined 3/16 units per minute = 11.25 units per hour.
The capacity of the whole process is 11.25 units per hour.
The utilization of each worker on step 1 is 11.25/12, the utilization of the worker on step 2 is 11.25/12 and the utilization of each worker on step 3 is 1. The average utilization is (2 11.25/12 + 11.25/12 + 3 1)/6 = 23.25/24. The cycle time is 1/11.25hours per cycle =5 minutes 20 seconds per cycle.
Problem 3 Consider a sandwich place where 3 workers in series. The place always has people standing in the line. customers are leaving the store at the rate of 36 per hour. Also we observe that worker 1 is busy only 50% of the time, worker 2 is always working(100% of the time), and worker 3 is busy 75% of the time. Who is the bottleneck? what are the capacities of the worker 1,2 and 3?
Since we always have people in the line, the output rate is equal to the capacity of the process, therefore the capacity is 36 customers per hour. The bottleneck is worker 2 with utilization equal to 1, and his capacity is equal to the capacity of the process, 36 customers per hour. The capacity of worker 1 is 36/.5 = 72 customers per hour, and the capacity of worker 3 is 36/.75 = 48 customers per hour.

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