Question Details Coren Chemical, Inc., develops industrial chemicals that are us

Question

Question Details
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

a. David is deciding how much K-1000 to produce. The results are based on two factors: first, how much David produces, and second, how much David needs to sell. The amount of profit made is affected in three ways: David makes $4 on each gallon he produces and sells. Danid loses $3 on each gallon he has to salvage. David loses $5 on each gallon he has to buy elsewhere. Now we test each batch size: 500 gal: 20% selling 500 and making $2000 (4*500sold) 30% selling 1000 and making -$500 (4*500sold-5*500shortage) 40% selling 1500 and making -$3000 (4*500sold-5*1000shortage) 10% selling 2000 and making -$5500 (4*500sold-5*1500shortage) 1000 gal: 20% selling 500 and making $500 (4*500sold-3*500salvage) 30% selling 1000 and making $4000 (4*1000sold) 40% selling 1500 and making $1500 (4*1000sold-5*500shortage) 10% selling 2000 and making -$1000 (4*1000sold-5*1000shortage) 1500 gal: 20% selling 500 and making -$1000 (4*500sold-3*1000salvage) 30% selling 1000 and making $2500 (4*1000sold-3*500salvage) 40% selling 1500 and making $6000 (4*1500sold) 10% selling 2000 and making $3500 (4*1500sold-5*500shortage) 2000 gal: 20% selling 500 and making -$2500 (4*500sold-3*1500salvage) 30% selling 1000 and making $1000 (4*1000sold-3*1000salvage) 40% selling 1500 and making $4500 (4*1500sold-3*500salvage) 10% selling 2000 and making $8000 (4*2000sold) the decision tree will be crafted as follows: a square representing a decision with four branches labeled 500, 1000, 1500, 2000 that lead to circles, representing chance. Each of these circles has four branches labeled 500 (20%), 1000 (30%),1500 (40%), 2000 (10%) leading to triangles that repesent results. each of these triangles is labeled with the result of that matches its production and sales value. b. expected value for 500 production .2*2000 +.3*-500+ .4*-3000+ .1*-5500=-$1500 expected value for 1000 production .2*500 +.3*4000+ .4*1500+ .1*-1000=$1800 expected value for 1500 production .2*-1000 +.3*2500+ .4*6000+ .1*3500=$3300 expected value for 2000 production .2*-2500 +.3*1000+ .4*4500+ .1*8000=$2400 1500 production has the highest expected value at $3300 so 1500 is the best batch size. c. if the David had perfect information (ie he knew how much was going to be sold) his expected value is this: .2*2000+.3*4000+.4*6000+.1*8000=4800 tis is because he will not have any gallons left over or shortaged.

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