10 May Logistics And Operations Management
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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