Practice Process and Capacity Problems SOLUTIONS Modules 1 and 2
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Practice Problems: Processes
1.
Butternut is a ski resort in Massachusetts. One of their triple chair lifts unloads 1296 skiers per hour at the top of
the slope. (A triple chair lift can carry three passengers per chair.) The ride from the bottom to the top takes 5
minutes. How many skiers
are riding on the lift at any one time?
Use Little’s Law. 1296skier/hour*1hour/60min*5 min=108 skiers
2.
Consider the baggage check in of a small airline. Data indicates that from 9 am to 10 am, 255 passengers checked in. It was also observed that the average number of passengers in line for check in was 35. How long did the average passenger wait in line? We can use Little’s law to compute the flow time, since we know both the flow rate as well as the inventory level:
Flow Time = Inventory / Flow Rate = 35 passengers / 255 passengers per hour = 0.14 hours 35 passengers / 255 passengers per hour * 60 min/1 hour= 8.24 minutes
3.
The following table shows financial data for Dirt Cheap Wholesale and Kwiki-Mart, two US retailers.
DIRT CHEAP WHOLESALE
KWIKI-MART STORES
Inventories ($MM)
4754
40894
Sales (net $MM)
59217
397206
COGS ($MM)
52762
326606
Assume that both companies have an average annual holding cost rate of 20% (i.e. it costs both retailers $2 to hold an item that they procured for $10 for one entire year).
How many days, on average, does a product stay in Dirt Cheap’s inventory before it is sold? Assume that stores operate 365 days a year.
Dirt Cheap has a COGS=$52762M = flow rate R. Inventory I = $4754M. Therefore, flow time T = I/R = 4754/52762 = .09 years, or 32.89 days.
How much lower (expressed in $’s) is, on average, the inventory cost for Dirt Cheap compared to Kwiki-Mart of a house hold cleaner valued at $5 COGS? Assume that the unit cost of the house hold cleaner is the same for both companies and that the price and the inventory turns of an item are independent.
Inventory turns for Dirt Cheap =52762/4754 = 11.10. Inventory turns for Kwiki-Mart =
326606/40894
= 7.99. Holding costs per year = 20%. This means inventory costs per unit for Dirt Cheap = .20/11.1* 5 = $0.09. For Kwiki-Mart, the inventory costs per unit = .20/7.99*5 = $0.13. So Dirt Cheap’s costs are 4 cents lower.
Practice Problems: Capacity
1.
Assume a bakery produces and sells only one type of bread – white bread. The bakery operates two parallel baking lines, each equipped with a mixer, proofer, and an oven. In addition, the bakery operates a single packaging line, which is shared by the two bread- making lines. The cycle times through each step in the baking process are as follows: Mixer: 3⁄4 hour/ 100 loaves Proofer: 3⁄4 hour/100 loaves Oven: 1 hour/ 100 loaves The cycle time through the packaging line is 3⁄4 hour/ 100
loaves. Each “recipe” that is started in a mixer is pulled from raw materials sitting in inventory, and after the bread has been packaged, it may sit in inventory before being shipped out to stores.
Draw a process flow diagram for the process described above. Capacity: 133*2 133*2 100*2 133
Capacity of each bread-making line: min (100 loaves/3⁄4 hour, 100 loaves/3⁄4 hour, 100 loaves/ hour) Note that there are 2 of each of mixing, proofing and baking so we can pool those so that capacity doubles. Capacity of packaging: 100 loaves/ 3⁄4 hour = 133.33 loaves/hr Capacity set by packaging process at 133.33 loaves/hr.
If the whole process runs at the capacity indicated in (b), what is the utilization of the packaging process? 100% as dictated by Packaging
The bakery is considering replacing some of its existing equipment with more advanced and faster equipment. The choice is between purchasing 2 new ovens that are each capable of baking a batch of 100 loaves in 3⁄4 hour OR purchasing a new packaging line that is capable of packaging a batch of 100 loaves in 1⁄2 hour. What option would allow the greatest increase in the bakery’s overall capacity? They must purchase the new packaging line to get any improvement in capacity. New capacity of packaging: 100 loaves/ 1⁄2 hour = 200 loaves/hr
The new process capacity would become 200 loaves/hr. 2.
Consider the following four step process:
A
B
C
D
Capacity
8 9 10 8
New Capacity
16
The following data are available for the four steps:
A
B
C
D
Activity time per unit (min)
0.25
0.33
0.2
0.5
Capacity per worker (units/min)
4
3
5
2
Number of workers
2
3
2
4
Suppose the steps in activity D are made easier, so the activity time per unit in step D is reduced by 50% (to 0.25 min per unit). If the assignment of workers to steps remains the same, by how much does the capacity of the entire process increase
in units per min?
Answer = Before the change the process capacity is min (4 x 2, 3 x 3, 5 x 2, 2 x 4) = 8 units per min. If the activity time is cut in half for stage D, then process capacity for step D is (1/0.25) x 4 = 16 units per min
(or 4*4 =.16) Step A can only produce 8 units per minute, so the total capacity of the process doesn’t increase.
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