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?