CASE STUDY 2 Linear Programming Chemicals, Inc. is a petroleum manufacturing pla

Question

CASE STUDY 2 Linear Programming Chemicals, Inc. is a petroleum manufacturing plant located in the Middle East. It has been in existence over the past 15 years. They are currently working on their strategic plans for the year 2016 to 2021. The growth of export petroleum sales over the past couple of years has been good, but the sales could grow even more, if the planned high-tech oil refinery is built near the city where Chemicals, Inc. is located. Chemicals, Inc, is considering three strategies. First is to increase its current production operations, the second is to move closer to the proposed new oil refinery and the third is to do nothing. Strong growth as a result of the presence of the new oil refinery has a 55 percent probability and moving closer to it, would give annual returns of $390,000 per year. Weak growth however, would mean annual returns of $230,000. If nothing was done in the first year of 2015, and strong growth occurred, the strategy to increase its current production would be reconsidered. Strong growth with an increased production would give annual returns of $380,000 per year. Weak growth however would mean annual returns of $200,000. With no changes, there would be returns of $340,000 per year if there is strong growth and $210,000 per year if growth is weak. Increasing production will cost $ 174,000 and moving to a location closer to the refinery will cost $ 420,000. If growth is strong and the production is increased during the second year, the cost would also be $174,000. The cost to operate are the same for all strategies. After reviewing their options based on the decision trees and recommendations that you earlier proposed, Chemicals, Inc. realized that doing nothing will generate more profits and benefits than the other two alternatives. However, they wanted to develop an improved aviation fuel to be used by commercial jets at minimal cost. The fuel is a mixture of two fuels (Avgas A and Avgas B). There are 4,000 gallons of Avgas A and 8,000 gallons of Avgas B available. It needs no fewer than 6,000 gallons to fuel a jet to its farthest destination which has a maximum fuel storage capacity of 8,000 gallons. The mixed fuel must have an octane rating of no less than 80. The octane rating is the weighted average of the individual octanes, weighted in proportion to the respective volumes. During mixture, the amount of Avgas obtained equals to the sum of the amounts put in. Avgas A has an octane of 95 and costs $2.40 per gallon. Avgas B has an octane of 75 and costs $1.80 per gallon. In presenting your findings to Chemicals, Inc., they would like to see: a. The equations expressing this information. b. Your solutions using the graphical method. c. The optimal equation that would meet their objective.

Explanation / Answer

Decisions are with respect to the options/alternate actions on the part of the company.

1. Do not act, Continue with the existing system

2. Increase production at existing place

3. Move closer to proposed refinery

Also in case of no action presently if there is strong growth reconsider the strategy of increased production.

There are two possibilities or say two states in the terminology of decision tree. Either there will be strong growth or week growth that determines the net pay-off .

Decisions have bearings for the period 2016 to 2021, say for six years. Returns are mentioned as per year and costs are related to one time actions of increasing production and moving closer to proposed refinery location.

The given information is represented in the decision table as follows:

The expected pay-off, EMV (returns -cost) are calculated for each end points of the branches of the decision tree as follows:

Based on the above analysis, the best decision is to do nothing. There is small error about the return figure of A2 under strong growth so the table is revisedas follows but decision remains the same.

Now let us reconsider the decision when there is strong growth about increasing production in 2016.

With increased production in case of strong growth, the annual return increases by 40,000(380,000-340000) whereas cost for increased production is 174,000 so net gain of 26,000 during remaining five years (200000-174000)

Therefore the final decision is Do nothing in the current year and if there is strong growth then go for increased production.

Returns per year 2015 S TA T E S Actions Strong growth Week growth A1 Increase Production $380,00 $200,00 A2 Move closer to Refinery $390,00 $230,00 A3 Do nothing $340,00 $210,00 Probability 0.55 0.45

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