screening testing group decision In initial screening a staff member spends 2 hours considering the idea. In mock-up, the idea is sent to one of many suppliers to produce a physical mock-up of the toy. There is essentially unlimited capacity at this stage, but it takes 4 days to get the mockup built even though multiple mockups can be built simultaneously. In safety testing each idea requires 2 days from a staff member to have the idea checked for safety. In focus groups each idea requires 3 hours from a staffmember to have the idea test marketed. Finally, the management team meets for 4 hours per idea to decide if the toy should be added to its line of products sold to customers. At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The following table summarizes the process: Time per idea put Pr(Success) Pr(Fail) Staffing into this stage 40% 2 hours Screening Mock-up Safety 60% 2 4 days 2 days 3 hours 4 hours 50% 50% 7 Focus group 35% 65% 1 Final decision 20% 80% 1 For example, there are 7 staff members that work in the safety stage. In each stage each idea is processed by only one staff member: for example, once one of the 7 staff members starts working on an idea in the safety stage, the idea completes that stage in 2 days (and either exits or moves to the focus group stage). Everyone works 8 hours per day, 5 days a week. i. On average, how many ideas are in the mock-up stage? ii. Which stage has the highest implied utilization (as a %)?

Practical Management Science
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Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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4. Happy Toy Company's R&D
The Happy Toy Company's R&D department is always looking for great ideas for new toys. On
average, the R&D department generates about 10 new toy ideas a week. To go from idea to approved
product, the idea must go through 5 stages:
Pr(Fail) = 40%
Pr(Fail) = 50% Pr(Fail) = 65%
Pr(Fail) = 80%
Initial
Safety
testing
Focus
Final
decision
Mockup
screening
group
In initial screening a staff member spends 2 hours considering the idea. In mock-up, the idea is sent to
one of many suppliers to produce a physical mock-up of the toy. There is essentially unlimited capacity
at this stage, but it takes 4 days to get the mockup built even though multiple mockups can be built
simultaneously. In safety testing each idea requires 2 days from a staff member to have the idea checked
for safety. In focus groups each idea requires 3 hours from a staff member to have the idea test marketed.
Finally, the management team meets for 4 hours per idea to decide if the toy should be added to its line
of products sold to customers.
At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The
following table summarizes the process:
Time per idea put
Pr(Success) Pr(Fail) Staffing
into this stage
40%
2 hours
Screening
Mock-up
Safety
60%
2
4 days
2 days
50%
50%
7
Focus group
35%
65%
1
3 hours
Final decision
20%
80%
1
4 hours
For example, there are 7 staff members that work in the safety stage. In each stage each idea is processed
by only one staff member: for example, once one of the 7 staff members starts working on an idea in
the safety stage, the idea completes that stage in 2 days (and either exits or moves to the focus group
stage). Everyone works 8 hours per day, 5 days a week.
i.
On average, how many ideas are in the mock-up stage?
ii.
Which stage has the highest implied utilization (as a %)?
Transcribed Image Text:4. Happy Toy Company's R&D The Happy Toy Company's R&D department is always looking for great ideas for new toys. On average, the R&D department generates about 10 new toy ideas a week. To go from idea to approved product, the idea must go through 5 stages: Pr(Fail) = 40% Pr(Fail) = 50% Pr(Fail) = 65% Pr(Fail) = 80% Initial Safety testing Focus Final decision Mockup screening group In initial screening a staff member spends 2 hours considering the idea. In mock-up, the idea is sent to one of many suppliers to produce a physical mock-up of the toy. There is essentially unlimited capacity at this stage, but it takes 4 days to get the mockup built even though multiple mockups can be built simultaneously. In safety testing each idea requires 2 days from a staff member to have the idea checked for safety. In focus groups each idea requires 3 hours from a staff member to have the idea test marketed. Finally, the management team meets for 4 hours per idea to decide if the toy should be added to its line of products sold to customers. At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The following table summarizes the process: Time per idea put Pr(Success) Pr(Fail) Staffing into this stage 40% 2 hours Screening Mock-up Safety 60% 2 4 days 2 days 50% 50% 7 Focus group 35% 65% 1 3 hours Final decision 20% 80% 1 4 hours For example, there are 7 staff members that work in the safety stage. In each stage each idea is processed by only one staff member: for example, once one of the 7 staff members starts working on an idea in the safety stage, the idea completes that stage in 2 days (and either exits or moves to the focus group stage). Everyone works 8 hours per day, 5 days a week. i. On average, how many ideas are in the mock-up stage? ii. Which stage has the highest implied utilization (as a %)?
Expert Solution
Step 1

a)

Input of the stage 1 = 10 ideas per week = 10/(8*5) = 0.25 ideas per hour

Output of the stage 1 = 0.25*0.6 = 0.15 ideas per hour. This is the input to Mockup stage

Mockup stage

Flow rate, R - 0.15 ideas per hour

Flow time, T = 4 days = 4*8 = 32 hours

Using Little's law, Number of ideas in Mockup stage, I = RT = 0.15*32 = 4.8 ideas

 

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