A company is about to begin production of a new product. The manager of the depa
ID: 407664 • Letter: A
Question
A company is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants to know how often his machine will be available for other work. The machine will produce the item at a rate of 200 units a day. 80 units will be used daily in assembling the final product.
The company operates five days a week, 50 weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $300. Inventory holding costs will be $10 per unit per year.
a) What production run quantity should be used to minimize total annual setup and holding costs?
b) What is the length of a production run in days?
c) During production, at what rate will inventory build up?
d) If the manager wants to run another job between runs of this item, and needs a minimum of 10days per cycle of this job for the other work, will there be enough time?
Explanation / Answer
Assume Demand
D
40000
per year
Daily demand
d
160
per day
Holding cost
h
10
per year
production rate
p
200
units per day
Consumption rate
c
80
units per day
working days
250
no.of days
Set up cost
s
300
$ per setup
a) Economic production quantity = Sqrt((2 X s X D)/h) X Sqrt(p/(p-c))
= Sqrt((2 X 300 X 40000)/10) X Sqrt(200/(200-80))
= 2000
b) Production run time = EPQ/p = 2000/200 = 10 days
c) During production time, 200 units are produced per day and only 80 are being consumed. Hence, (200-82) = 160 units per day are added to inventory.
d) Total Cycle time = EPQ/c = 2000/80 = 25 days
I.e. it takes 10 days to produce all units but 25 days to finish complete assembly. Hence there is a gap of 15 days between where no production takes place but assembly continues.Since the additional item takes only 10 days, it can be incorporated in the middle of the runs.
Please note that this could change if demand assumed changes. The more the demand, the less likely that a new product could be run in the middle.
Assume Demand
D
40000
per year
Daily demand
d
160
per day
Holding cost
h
10
per year
production rate
p
200
units per day
Consumption rate
c
80
units per day
working days
250
no.of days
Set up cost
s
300
$ per setup
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