Problem Set 1 (Group homework)

Due on May 23 (Wednesday) before class

Q1. A toy company produces talking teddy bears. For the final assembly the head goes through the following three stations: add eyes (10 secs), add nose (10 secs), and add both ears (together 10 secs). In parallel to the head finishing, the torso goes through the three stations: add legs (together 5 secs), add voice module (15 secs), and add arms (together 5 secs). Then the finished head will be attached to the finished body (5 secs). Before the final packing station (10 secs), the teddy receives a bow tie (5 secs). Assume this is a fully automated process.

a) Draw a simple process flow diagram.

b) What is the theoretical flow time to finish one teddy bear (ignoring time spent waiting in buffers between machines)? Please explain!

c) Which station is the bottleneck? Please explain!

d) Assuming the production has been started up in the morning and is running smoothly now. What is the time between two finished teddy bears? Show your calculation!

e) Draw a Gantt chart for the production of the first three teddy bears in the morning. Use different colors/patterns or numbers (1, 2, 3) to distinguish the bars for the three different teddy bears.

Q2. Consider a bagel store selling three types of bagels that are produced according to the process flow diagram outlined below. We assume the demand is 180 bagels a day, of which there are 30 grilled cheddar & veggie, 110 veggie only, and 40 cream cheese. Assume that the workday is 10 hours long and each activity is staffed with one worker.

Moreover, we assume the following activity times:

Activity times are independent of which bagel type is processed at a resource (for example, cutting a bagel takes the same time for a cream cheese bagel as for a veggie bagel).

a) Where in the process is the bottleneck for each kind of bagel? Where is the bottleneck for the product mix? Is it possible to satisfy the demand for the whole day?

b) Given the product mix, how many units can the process produce within one hour?

Q3. The market at the UBC farm every Saturday morning offers fresh organic produce that mostly comes from the farm itself. The counter opens at 9am. However, customers start lining up at 8:30am. Customers show up at a rate of 30/hr until 9:30am and then at a rate of 15/hr until 10:30. The counter can serve at a rate of 20/hr, and the counter works till all customers served.

a) Draw a graph of the number of customers waiting in the line. Start the graph at 8:30am and show the number of waiting customers until the line is empty again. (Use the continuous time setting.)

b) Using the inventory build-up diagram, calculate the average number of customers in line.

c) How long an average person spends in the line? (Hint: Littles Law.)

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Q4. Read “Case: Shouldice Hospital – a Cut Above” and answer the following questions (You can find the case on WebCT under the “Assignments” folder. Ignore the questions after the case)[1]:

1. Consider the following linear flow-chart:

Pre-surgery
     examinations,
     orientation, etc.

Surgery

Recovery

Patient

Healthy individual

What is the flow unit? What are the resources needed for each of the above tasks?

2. Analyze the current operations in the hospital by answering the following four questions:

a) What is the capacity rate (per week) of the hospital?

b) What is the weekly throughput rate of the hospital?

c) What is the average bed utilization?

d) How many patients will be in the hospital during each day of the week? Draw a discrete inventory build-up diagram with days of the week plotted on the x-axis and number of patients plotted on the y-axis.

3. The vice president of the hospital wants to increase the throughput rate of the hospital. She has a target of increasing the weekly throughput rate by 20% (as compared to the existing throughput rate). One option to increase throughput is to add Saturday operations (i.e., admit 30 patients on Friday for Saturday operation, while still maintaining 30 operations from Monday to Friday).

a) What is the average bed utilization?

b) How many patients will be in the hospital during each day of the week? Draw a discrete inventory build-up diagram with days of the week plotted on the x-axis and number of patients plotted on the y-axis.

4. The surgeons and other hospital unions reject the idea of having Saturday operations. The vice president is determined to increase the throughput rate by 20% without changing Shouldice practice (i.e. each surgeon still operates on four patients per day; each operation still takes one hour; operating rooms can be used from 7:30am till 3:30pm; committed to 3-day process).

a) Does any capacity needed to be added to the hospital? If so, what resources need to added?

b) Suggest a plan to increase the throughput rate of the hospital by 20% while maintaining five-day operations and adding as few additional resources as possible.

[1] To learn more about the Shouldice Hospital case, visit http://www.youtube.com/watch?v=Yr1Jg9gC3QA.