Formally show the sensitivity of the EOQ formula with respect to the holding and setup costs…

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a) Formally show the sensitivity of the EOQ formula with respect to the holding and

setup costs. That is, formulate the EOQ as a function of holding and setup costs,

and calculate the partial derivatives. Keeping everything else constant, how

does the optimal order quantity change if holding costs double? And if setup

costs double? (6 points)

b) The SIT@SP building is open year-round and faces a constant demand of 10

packages of printer paper per week. Holding a package of printer paper in stock

costs 5% per year of its price of 10$. The fixed costs of ordering a batch from

the store are 10$. What is the optimal number of packages to buy with each

order? An order takes 3 days to be delivered. When should the order be placed?

(5 points)

c) The facility services representative mistakenly read the wrong line from the

printer paper demand table, and took the value from TUM Campus Straubing

(also starts with S). Therefore, she estimated a demand of 30 packages of

printer paper per week instead of 10. How much larger are total costs per week

because of this mistake, as a percentage of the total costs per week under the

optimal order quantity? (7 points)

d) TUM Campuses Munich Downtown, Garching, and Straubing open year-round

and are currently stocking their printer paper separately, per campus. They order from the store in Munich for 6€ per package, holding costs are estimated at

5% per year of that price, and the fixed cost per order is 7€. Downtown uses

100 packages per week, Garching uses 50 packages per week, and Straubing

uses 30 packages per week. A student that followed Introduction to SCM at

TUM Asia notices that it is better to order centrally, and informs the President.

He, in turn, decides that all paper is from now on stocked and ordered centrally.

However, ordering centrally leads to an extra cost of on average 0.20€ per demanded package, for extra distribution. Compare the costs per year in the new

situation with those in the old situation. Did the President make the right decision?


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