Transcript Assign7.4

a) How many to produce each 2 years
Is this an EOQ problem?
The question dictates that we do a run every two years. That
would mean, in a deterministic EOQ setting, that Q must equal
two years of mean demand, i.e., 32000. Hence, this question
does not give us the freedom to change when we do a run
(which is what EOQ is all about).
Problem 7.4
Q = 2 year demand
S =25000
C=5
R/yr = N(16000,4000)
Sales price P = 35
The question is whether 32000 is the best quantity we can print every tow years?
This asks about what the appropriate safety stock (or service level) should be.
This is answered via newsvendor logic. Answer these two questions:
What is my underage cost (cost of not having enough)? i.e., if I were to stock one
more unit, how much could I make?
Every catalog fetches sales of 35 and costs 5 to produce. The net marginal benefit of
each additional unit (MB), or the underage cost, is p – c = 35 - 5= 30.
What is my overage cost? i.e., if I had stocked one less unit, how much is saved?
The net marginal cost of stocking an additional unit (MC) = c – v = 5 – 0 = 5.
The optimal service level (or critical fractile): SL = 30/(30+5) = 0.857.
a) How many to produce each 2 years
Problem 7.4
Q = 2 year demand
S =25000
C=5
R/yr = N(16000,4000)
Sales price P = 35
The last step is to convert the SL into a printing quantity.
The total average demand for 2 years (R) = 32,000 with a standard deviation of 5657.
The optimal printing quantity, Q* is determined such that
Prob( R  ROP )  0.857
The optimal ROP is R + z s where z is read off from the standard Normal tables such
that area to the left of z is 0.857. That is, z = 1.07.
This gives ROP = Q* = 38,053 catalogs.
The optimal expected profit (when using Q* = 38053) is larger than $25,000, the fixed
cost of producing the catalog.