A shoe assembly plant buys leather tops and soles from its suppliers. The leather tops have no color on them when bought. The assembly plant first dies the leather with colors like black, beige, brown and cream. Then it sews the colored leather tops to the soles. Finally leather tops are polished with an agent that depends on the color of the shoe. Basically there are three operations in the shoe plant: Coloring, Sewing and Polishing. The activity times and set up times for these operations are given in minutes as follows: Operation       Coloring Sewing Polishing Activity time        0.25     0.20      0.15 Set up time           30       20        45 Soles and the leather top-sole assemblies are processed in batches in all operations. The batch sizes are kept the same at all operations. Before a batch goes through an operation, the shoe plant must set up the machines for that operation. a) How many leather tops can be colored in an hour with a batch size of 40? b) Explain why sewing cannot be the bottleneck operation under any batch size. c) For which batch sizes is coloring the bottleneck operation? Here your answer can be an interval of batch sizes rather than a single number because there are many batch sizes which make coloring the bottleneck

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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A shoe assembly plant buys leather tops and soles from its suppliers. The leather
tops have no color on them when bought. The assembly plant first dies the leather with colors like
black, beige, brown and cream. Then it sews the colored leather tops to the soles. Finally leather tops
are polished with an agent that depends on the color of the shoe. Basically there are three operations
in the shoe plant: Coloring, Sewing and Polishing. The activity times and set up times for these
operations are given in minutes as follows:
Operation       Coloring Sewing Polishing
Activity time        0.25     0.20      0.15
Set up time           30       20        45

Soles and the leather top-sole assemblies are processed in batches in all operations. The batch sizes
are kept the same at all operations. Before a batch goes through an operation, the shoe plant must
set up the machines for that operation.
a) How many leather tops can be colored in an hour with a batch size of 40?
b) Explain why sewing cannot be the bottleneck operation under any batch size.
c) For which batch sizes is coloring the bottleneck operation? Here your answer can be an interval of
batch sizes rather than a single number because there are many batch sizes which make coloring the
bottleneck

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