Kinga Doll Company manufactures eight version of its popular girl doll, Shari. T

Question

Kinga Doll Company manufactures eight version of its popular girl doll, Shari. The
company operates on a 40-hour work week. The eight versions differ in doll skin, hair and eye color,
enabling most children to have a doll with a similar appearance to them. It currently sells an average
of 4,800 dolls (spread equally among its eight versions) per week to boutique toy retailers.
In simplified terms, doll making at Kinga involves three basic operations: molding the body and hair,
painting the face, and dressing the doll. 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 unit at each
step. Unlimited space for buffer inventory exists between the steps.

Process Step 1 Molding 2 Painting 3 Dressing
Setup (min) 12 24 0
Processing time (min /unit) 0.25 0.15 0.3
Assume that (i) setups need to be completed first (ii) a setup can only start once the batch has arrived at
the resource and (iii) all flow units of batch need to be processed at a resource before any of the units
of the batch can be moved to the next resource.

a. What is the process capacity in units per hour with a batch size of 1000 dolls?
b. What are the utilizations in molding, painting, and dressing operations given the batch size of 1000
dolls?
c. What is the time it takes for the first batch of 1000 dolls to go through an empty process?
d. Which batch size would minimize inventory without decreasing the process capacity?
e. What is the process capacity in units per hour with a batch size of 200 dolls?
f. What are the utilizations in molding, painting, and dressing operations given the batch size of 200
dolls?
g. Which batch size would minimize inventory without decreasing the current flow rate (sales rate)?

Explanation / Answer

a

The capacity depends on the resources, infrastructure and people the overall process has, and it is independent on the total amount produced. It is also given by the slowest of all of the steps in the process for this case where a process needs to be done to follow the next one. The step with the less capacity is the dressing, with 3,33 units/min, so that is the capacity of the overall process.

b

Demand rate = 4800 units/week * 1 week/5 days * 1 day/8 hours*1 hour/60 min= 2 units/min

Step 1: Molding

Utilization = demand rate/(rate of service) = (2 units/min)/(4 units/min) = 0.5 = 50%

Step 2: Painting

Utilization = demand rate/(rate of service) = (2 units/min)/(6.666 units/min) = 0.3 = 30%

Step 3:

Utilization = demand rate/(capacity) = (2 units/min)/(3.333units/min) = 0.60 = 60%

c

We calculate this time by using the capacity of the overall process (the capacity if the slowest step), it is, 3.333 units/min

time of process = 1000 units * 1 min/3.333 units = 300 min = 5 hours

d

To make the inventory rotate once a week, production has equal demand, and by kbowing that 4800 dolls are sold per week, then, production could equalize that number. So, a batch of 4800 dolls per week is good enough for acieving that goal. If demand changes take place, for instance, increases suddenly, then an optimal inventory could be left so as to meet these changes, but we do not have information to calculate that so far. The capacity is only decreased by idle times, which are not present in this exercise.

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