Coren Chemical, Inc., develops industrial chemicals that are used by other manuf
ID: 1940854 • Letter: C
Question
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, 1000 gallons, 1500 gallons and 2000 gallons. Using historical data, David Coren was able to determine that the probability of selling 500 gallons of K-1000 is .2. The probabilities of selling 1000, 1500 and 2000 gallons are .3, .4 and .1 respectively. The question facing David is how 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 d3veloper. 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.
Explanation / Answer
For the decision tree, start with a box and 4 branches. Branch 1 - 500 gallons produced. Branch 2 - 1000 gallons produced. Branch 3 - 1500 gallons produced. Branch 4 - 2000 gallons produced. Now, from each of those 4 branches you want to know what were to happen if there was demand for 500 gallons, 1000, gallons, 1500 gallons, and 2000 gallons. From branch 1 add 4 more branches. 1 - 500 gallons demanded. 2 - 1000 gallons demanded. 3 - 1500 gallons demanded. 4 - 2000 gallons demanded. Do this for the other 3 branches that you started with.