Kinga Doll Co. manufactures 8 versions of its popular girl doll, Shari. The comp
ID: 328050 • Letter: K
Question
Kinga Doll Co. manufactures 8 versions of its popular girl doll, Shari. The company operates on a 40-hour work week. The eight versions differ in doll skin color, hair, and eye color, enabling most children to have a doll with similar appearance to them. It currently sells an average of 4,000 dolls weekly to boutique toy retailers (demand is spread equally among the 8 versions). In simplified terms, doll making involves 3 basic process steps: molding the body and hair, painting the face, and dressing the doll. It is a batch process. Changing over between versions requires setup time at the molding and painting stations due to the different colors of plastic pellets, hair and eye color paint required. The table below lists the setup times for a batch and the processing times for each of each step. Unlimited space for buffer inventory exists between these steps.
Assume that (i) setups need to be completed first; (ii) a setup can only start once the batch has arrived at the process step, and (iii) all flow units of a batch need to be processed at a process step before any of the units of the batch can be moved to the next process step.
Process Step
Molding
Painting
Dressing
Setup Time
15 min
30 min
No setup
Processing Time
0.25 min/unit
0.15 min/unit
0.30 min/unit
Which batch size would minimize inventory without decreasing the current flow rate?
a. Batch size between 10 and 20 units
b. Between 20 and 30 units
c. Between 30 and 40 units
d. Between 50 and 60 units
e. Between 60 and 70 units
Process Step
Molding
Painting
Dressing
Setup Time
15 min
30 min
No setup
Processing Time
0.25 min/unit
0.15 min/unit
0.30 min/unit
Explanation / Answer
Current requirement is 4000 dolls per 40 hour week
Flow rate = 4000/40 = 100 dolls per hour or 0.6 minute per doll
The inventory will be minimum when flow rate of 0.6 is matched with that of process having highest processing time
Let at x units Molding is equal to flow rate of 0.6
15 + 0.25*x = 0.6*x
x = 43 units
Let at x units Molding is equal to flow rate of 0.6
30 + 0.15*x = 0.6*x
x = 67 units
Dressing is not a concern as rate is less than flow rate
Ans: E (67 units)
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