Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

market price; or inventory costs may be such as to make one
day inventory profitable - in such case, if the market price
is P 1 on the &4 th day, the firm will hold the goods until
the next day (when the expected market price is f) and then
sell the goods no matter what market price prevails; or
inventory costs may be such as to make two day inventory
holding profitable - in such a case, if the market price is
P 1 on the oc th day, the firm will hold the goods until the
oe. +1 st day. If the market price is P 2 or P 3 on the
oc. +1 St day, the goods will be sold then. If the price is
P 1, the goods will be held until the oC. +2 rid day (when the
expected market price is I) and then sold at whatever the
market price may be.
• For
Optimal outputs are found as follows:
For case one above, it is where .i.f t (Q).
For case two '
/ A
case three (assuming that the storage costs are
due when the goods leave the warehouse),
^
1.1 * Vx (Ka+14)( 1)i- P3 (X3 4)0E3) 14(t)
As the variance of the probability distribution of
prices and the • number of days of possible inventory holding
increases, the analysis becomes complicated at an increasing
rate.
Inventory holding in a multi-time period analysis has
been developed elsewilere. 12
•
12William Baumol et al, Studies on the Demand for Freight
Transportation, (Princeton, New Jersey, Mathematics,
August, 1967).
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