Coren Chemical, Inc., develops industrial chemicals
that are used by other manufacturers to produce photographic
chemicals, preservatives, and lubricants.
One of their products, K-1000, is used by several
photographic companies to make a chemical that is
used in the film-developing process. To produce
K-1000 efficiently, Coren Chemical uses the batch
approach, in which a certain number of gallons is
produced at one time. This reduces setup costs and
allows Coren Chemical to produce K-1000 at a competitive
price. Unfortunately, K-1000 has a very
short shelf life of about one month.
Coren Chemical produces K-1000 in batches
of 500 gallons, 1,000 gallons, 1,500 gallons, and
2,000 gallons. Using historical data, David Coren
was able to determine that the probability of selling
500 gallons of K-1000 is 0.2. The probabilities of
selling 1,000, 1,500, and 2,000 gallons are 0.3, 0.4,
and 0.1, respectively. The question facing David ishow many gallons to produce of K-1000 in the next
batch run. K-1000 sells for $20 per gallon. Manufacturing
cost is $12 per gallon, and handling costs and
warehousing costs are estimated to be $1 per gallon.
In the past, David has allocated advertising costs to
K-1000 at $3 per gallon. If K-1000 is not sold after
the batch run, the chemical loses much of its important
properties as a developer. It can, however, be
sold at a salvage value of $13 per gallon. Furthermore,
David has guaranteed to his suppliers that
there will always be an adequate supply of K-1000.
If David does run out, he has agreed to purchase a
comparable chemical from a competitor at $25 per
gallon. David sells all of the chemical at $20 per gallon,
so his shortage means that David loses the $5 to
buy the more expensive chemical.
(a) Develop a decision tree of this problem.
(b) What is the best solution?
(c) Determine the expected value of perfect information.
