The Happy Toy Company’s R&D department is always looking for great ideas for new

Question

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:

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:

a. On average, how many ideas are in the mock-up stage? [Hint: Use Little’s Law.]

b. Among these stages, what is the highest implied utilization (as a %)?

c. Suppose at most half (50%) of the Happy Toy Company’s R&D department’s time is devoted to generating or processing new ideas for toys. [The remainder of R&D time is used for other activities such as improving existing toys.] Based on the data provided, what is the maximum number of toy ideas generated per week that the process can handle? Show your work.

Pr(Fail-40% Pr(Fail)-50% Pr(Fail)-65% Pr(Fail)-80% InitialMockup screening Safety testing Final decisiorn FOCus group

Explanation / Answer

a)

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

Output of 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

b)

Stage 1 - Initial Screening

Demand = 10 ideas per week = 10/(8*5) = 0.25 ideas per hour

Capacity = Number of members / Flow time = 2 / 2 hours = 1 per hour

Implied utilization = Demand / Capacity = 0.25/1 = 0.25

Output of stage 1 = 0.25*(1-0.4) = 0.15 per hour

Stage 2 - Mockup

Demand = Output of stage 1 = 0.15 ideas per hour

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

Capacity = Number of members / Flow time = unlimited

Implied utilization = Demand / Capacity = 0.25/infinity = 0

Output of stage 2 = 0.15 per hour

Stage 3 - Safety testing

Demand = Output of stage 2 = 0.15 ideas per hour

Flow time = 2 days = 2*8 = 16 hours

Capacity = Number of members / Flow time = 7/16 = 0.44 per hour

Implied utilization = Demand / Capacity = 0.15/0.44 = 0.3429

Output of stage 3 = 0.15*0.5 = 0.075 ideas per hour

Stage 4 - Focus group

Demand = Output of stage 3 = 0.075 ideas per hour

Flow time = 3 hours

Capacity = Number of members / Flow time = 1/3 = 0.33 per hour

Implied utilization = Demand / Capacity = 0.075/0.33 = 0.225

Output of stage 4 = 0.075*(1-0.65) = 0.02625 ideas per hour

Stage 5 - Final decision

Demand = Output of stage 4 = 0.02625 ideas per hour

Flow time = 4 hours

Capacity = Number of members / Flow time = 1/4 = 0.25 per hour

Implied utilization = Demand / Capacity = 0.02625/0.25 = 0.105

Output of stage 5 = 0.02625*(1-0.80) = 0.00525 ideas per hour

Highest implied utilization = 0.3429 or 34.3 % of Stage 3 (Safety testing)

c)

Bottleneck is Stage 5 (Final decision). Its capacity is 0.25 per hour.

Therefore, the process can handle a maximum of 0.25 ideas per hour or 10 ideas per week at final decision stage. Flow rate at Focus group stage = 0.25/(1-0.65) = 0.71 ideas per hour. But this is more than the capacity of stage 4. Hence maximum ideas that can be handled at stage 4 is 0.33 ideas per hour

Flow rate of Safety testing stage = 0.25/(1-0.5) = 0.5 ideas per hour. However, its capacity is only 0.44 ideas per hour. Hence maximum flow rate is 0.44

Flow rate at Initial screening stage = 0.44/(1-0.40) = 0.729 ideas per hour. This is less than capacity of this stage. Therefore, it is acceptable.

Maximum Number of ideas that the process can handle - 0.729 per hour = 0.729*8*5 = 29 ideas per week

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