One dozen size order: In this situation, the bottleneck is “setting up the oven and baking”, which takes 10 minutes to finish this process. So, the Cycle Time (CT) is 10 minutes. The Kristen’s cookie company can finish the first dozen after 26 minutes, then Kristen and her roommate can complete each order per 10 minutes. 4 hours=240 minutes. (240-26)/10=21.4, and 21.4+1=22.4. According to the equations above, the company could fill 22 orders every night.
Two dozen size order: In this situation, the CT becomes 20 minutes. The company finished the first order after 36 minutes, then they could complete each order in every 10 minutes. 4 hours=240 minutes. (240-36)/20=10.2, and 10.2+1=11.2. According to the equations above the company could fulfill 11 orders every night.
Three dozen size order: In this situation, the CT becomes 30 minutes. The company finished the first order after 46 minutes, then they could complete each order in every 30 minutes. (240-46)/30=6.5, and 6.5+1=7.5 According to the equations above the company could fulfill 7 orders every night. Because they have 14 minutes left after finishing all 7 orders of three dozen size, they could make a dozen cookie for a one dozen size order.
Q3.
Time
Kristen
Kristen’s Roommate
One dozen size order
8 minutes
4 minutes
Two dozen size order
10 minutes
8 minutes
Three dozen size order
12 minutes
12 minutes
Table 3.1 the Summary of Time That Kristen and Her Roommate Will Take One dozen size order: Kristen does the process of “washing & mixing” (6 minutes) and one “dishing up” (2 minutes).
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The totally value time of Kristen is 8 minutes. Kristen’s roommate does the process of “setting up” (1 minute), “packing” (2 minutes) and “accept Payment” (1 minute).
So her total time involved is 4 minutes
Two dozen size order: Because the “washing & mixing” step takes same time regardless of how many cookies are being made in the batch. The value time of Kristen consists of “washing & mixing” (6 minutes) and two “dishing up” (2 minutes).
Therefore, the total value time of Kristen is 10 minutes. The total value time of Kristen’s roommate consists of two “setting up” (1minutes), two “packing” (2 minutes) and two “accept Payment” (1 minute).
So her total value time involved is 8 minutes.
Three dozen size order: The “washing & mixing” remains the same, which takes 6 minutes. So Kristen’s value time consists of “washing & mixing” (6 minutes) and three “dishing up” (2 minutes).
Therefore, the total value time of Kristen is 12 minutes. The total value time of Kristen’s roommate consists of three “setting up” (1minutes), three “packing” (2 minutes) and three “accept Payment” (1 minute).
So her total value time involved is 12 minutes. Q4
Assumptions of this question:
1. The value of Kristen and her roommate’s time is $20/hour per person. 2. The margin of Kristen’s cookie company is 27.7%.
3. The discount that Kristen will give comes from 50% of the saving.
If Kristen and her roommate just make one dozen cookies, the total cost will be the sum of ingredients cost, package cost and value time cost. Then it will be: 0.6 + 0.1 + 20*0.2 = 4.7
(ingredient cost) (package cost) (value time cost) Because the margin of one dozen cookies is 27.7%, then the price should be 4.7*27.7%≈6 dollars.
So, normal price of a two dozen size order should be 12 dollars and normal price of a three dozen size order should be 18 dollars.
If Kristen and her roommate make a two dozen size order, the total cost will be: 1.2 + 0.2 + 20*0.3 = 7.4 (ingredient cost) (package cost) (value time cost) The saving cost of a two dozen size order is 4.7*2-7.4=2
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Then the discount of a two dozen size order could be 2*50%=1 dollar.
If Kristen and her roommate make a three dozen size order, the total cost will be: 1.8 + 0.3 + 20*0.4 = 10.1 (ingredient cost) (package cost) (value time cost) The saving cost of a three dozen size order is 4.7*3-10.1=4
Then the discount of a three dozen size order could be 4*50%=2 dollars.
It would take longer to fill a two-dozen cookie order than a one-dozen cookie size order. Obviously, from perspective of Rush Over Time, they will take 26 minutes to fill a one dozen size order, but they will take 26 minutes to fill a two dozen size order. From perspective of Cycle Time, they will take 10 minutes to fill a one dozen size order; however, they will take 20 minutes to fill a two dozen size order. Q5
No matter one, two or three dozen of size, Kristen’s cookies company only need one food processor and two baking trays. As we can see from the Gantt chart:
Chart 5.1 Three Orders of One Dozen Size
Chart 5.2 Three Orders of Two Dozen Size
Chart 5.3 Two Orders of Three Dozen Size
At the 16th minute, while the tray is in the oven, Kristen can’t do the dish up without another tray. So as the 26th 36th ….. But the last step of the process which needs the tray will not influence the process that after the next one. Then we can get the conclusion that they need two trays only. And when it comes to the food processor, we can find out that the time for the “washing and mixing” is shorter than the time for baking, and the processor can only be used in the step of the “washing and mixing”. So we can easily get the conclusion that Kristen only need one processor.
Q6
There is some methods to make more cookies in less time. If there is only one oven, the bottleneck would be “setting up and baking”. So, the easiest way to improve operation could be adding another oven. The influences of adding another oven could be seen as below: One dozen size order
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Chart 6.1 Three Orders of One Dozen Size with Two Ovens
As we can see from the Gantt chart, the Rush order time will stay the same. But the Cycle time shortens from 10 minutes to 6 minutes, which means the bottleneck is “washing & mixing”. In this situation, Kristen’s cookie company can complete 10 orders per hour after this system has been stable, which is 4 orders more than before. Given the same assumptions in the Q4, the net profit of these 4 orders is (6-4.7)*4=5.2 dollars. In conclusions, Kristen and her roommate would willing to pay no more than 5.2 dollars per hour for the additional oven.
Two dozen size order
Chart 6.1 Three Orders of Two Dozen Size with Two Ovens
Under this circumstance, Rush order time shortens from 36 minutes to 28 minutes. Meanwhile, the Cycle Time becomes 10 minutes, which is 10 minutes less than before. The bottleneck is still “setting up and baking”. In this situation, Kristen’s cookie company can complete 6 orders per hour after this system has been stable, which is 3 more than before. Given the assumptions in the question 4, the net profit of these 3 orders is (12-7.4)*3=13.8 dollars. It means that Kristen and her roommate would willing to pay no more than 13.8 dollars per hour to rent an additional oven.
Three dozen size order
Chart 6.1 Four Orders of Three Dozen Size with Two Ovens
As we can see from the Gantt chart 6.1, the Rush Order time will become 36 minutes. But the Cycle time shortens from 30 minutes to (13+17)/2=15 minutes, which means the bottleneck is still “setting up and baking”. In this situation, Kristen’s cookie company can complete 4 orders per hour after this system has been stable, which is 2 orders more than before. Given the same assumptions in the Q4, the net profit of these 4 orders is (18-10.1)*2=15.8 dollars. In conclusion, Kristen and her roommate would
willing to pay no more than 15.8 dollars per hour for the additional oven.
Q7
Chart 7.1 Three Orders of Two Dozen Size with Two Ovens
