Quantitative Assignment #4
1. Cycle time analysis
Company X has recently completed an analysis of its primary value-added process. As part of this analysis, the major flows have been mapped such that the process has been broken down into 10 sequential activities. To better understand the process, the times to complete each of these activities have been carefully monitored over the past month. The average (mean) and standard deviation of the activity times are recorded in parentheses next to the box representing the activity, as follows:
Standard
Activity Mean Deviation
1 8 2.4
2 4 1.2
3 15 2.1
4 3 3.0
5 1 0.4
6 10 6.0
7 5 2.8
8 3 3
9 20 4.5
10 4 0.3
1.a What is the average completion time for this value-added process?
1.b What is the standard deviation for the entire process?
1.c What is the probability that process will be completed in 75 hours?
1.d in 80 hours?
1.e in 70 hours?
1.f Develop a 95 percent confidence interval for the process.
1.g If you aren’t confident in your ability to make delivery promises, where should you target your improvement efforts? How would you proceed?
2. Little’s Law
2.a In a popular vacation destination in Asia, all of the hotel beds are generally booked in the summer season. On average, there are 2,800 tourists who stay for two weeks on average (i.e., 14 days). How many new tourists arrive, on average, per day in this vacation destination?
2.b At a local airport, 20 planes arrive on average per hour on the single runway, and these planes have to circle 3 minutes in the air, on average, before they can start their landing procedure. How many planes, on average, are circling in the air before they start landing?
2.c In a hospital emergency room, on average 30 patients arrive per hour. If the average number of patients present in the emergency room is 20, what is the average duration of stay of a patient in the emergency room?
3. Bottleneck Analysis I
A process requires six sequential steps with the following times. Assume only one machine at each step:
i. Step 1: 2 minutes
ii. Step 2: 3 minutes
iii. Step 3: 2 minutes
iv. Step 4: 4 minutes
v. Step 5: 1 minute
vi. Step 6: 5 minutes
3.a Which step is the process bottleneck?
3.b What is the capacity of the process in units per hour?
3.c What is the capacity of the process (in units per hour) if a second identical machine is added to Step 2?
4. Bottleneck Analysis II
Consider the standard process for cleaning teeth at a dentist’s office.
4.a Ignoring any waiting time, what is the cycle time (aka process flow time or throughput time)?
4.b How many resources are there?
4.c Calculate the capacity of each resources in patient per hour.
4.d Which resource is the bottleneck?
4.e What is the capacity of this dentist office?
4.f What is the capacity of this office if a second hygienist is hired?
Answer key
1.a 73
1.b 9.69
1.c 58.2%
1.d 76.5%
1.e 37.8%
1.f 54—92
2.a 200 per day
2.b 1 airplane
2.c 40 minutes
3.a Step 6
3.b 12 per hour
3.c 12 per hour
4.a 44 minutes
4.b 4
4.c Receptionist: 7.5 patients/hr; Hygienist: 2.5; X-ray machine: 10; Dentist: 4.6
4.d The hygienist
4.e 2.5 patients/hr
4.f 4.6 patients/hr
