Mick Karra is the manager of MCZ Drilling products which produces a variety of s
ID: 2419320 • Letter: M
Question
Mick Karra is the manager of MCZ Drilling products which produces a variety of specialty valves for oil field equipment. Recent activity in the oil fields has cause ddemand to increase drastically, and a decision has been made to open a new manufacturing facility. Three locations are being considered, and the size of the facility would not be the same in each location Thus, overtime might be necessary at times. The folowing table gives the total monthly cost (in 1000s) for each possible location under each demand posibility. The probabilities for the demand levels have been determined to be 20% for low demand, 30% for medium demand, and 50% for high demand
(a) Which location would be selected based on the optimistic criterion?
(b) which location would be selected based on the pessimistic criterion?
(c) which location would be selected based on the minimax regret criterion?
(d) which location should be selected to minimize the expected cost of operation?
(e) How much is a perfect forecast of the demand worth?
(f) which location would minimize the expected opportunity loss?
(g) what is the expecetd value of perfect information in this situation?
Demand is Low Demand is medium Demand is High Ardmore, OK 85 110 150 Sweetwater, TX 90 100 120 Lake Charles, LA 110 120 130Explanation / Answer
A) Location selected based on the optimistic criterion
Optimistic criterion is the choosing the best of best alternatives
optimistic criterion is the best of these three situations(i.e highest of 150,120,130), it is "150"(Ardmore, OK). Therefore the location seclected based on optimistic criterion is "Ardmore, OK"
B) Location selected based on the pessimistic criterion
Pessimistic criterion is choosing the best of worst alternatives.
Pessimistic criterion is best of these three situations (i.e, 85,90,110) i.e, "110" (Lake Charle, LA).
therefore the location selected on pessimistic criterion is "Lake Charle, LA"
C) Location selected based on minimax regret criterion.
Minimax regret criterion is also kwown as opportunity loss
Regret is calculated as best pay off - pay off recieved
from the above table regret table is calculated as follows: In case of the situation "Demand is low" maximum is of 3 alternatives is '110' ( 85,90,110). Each value is subtracted from the maximum value i.e 110-85 =25 , 110-90=20, 110-110=0, These vales 25,20,0 are regret values. In the same way for situations "Demand is medium", "Demand is high" is calculated the values for "Demand is medium" 120-110=10,120-100=20,120-120=0. the values are 10,20,0. "Demand is high" 150-150=0,150-120=30,150-130=20. The values are 0,30,20.
Regret table
Minimax regret criterion is the minimum of the maximum values (i.e 25,30,20) is "20" (Lake Charles, LA). Therefore the minimum regret criterion is "Lake Charles, LA"
G) expecetd value of perfect information (EVPI)
EVPI is the maximum payment for additional information. the formula for
EVPI =expecetd value with perfect information - expecetd value without perfect information
The maximum of these three alternatives is "125" (i.e, 125,108,123) is the expected value without perfect information.
The value for Expected value with perfect information is calculated by
The highest of the values 02*110+0.3*120+0.5*150=133. Therefore the Expected value with perfect information is "133".
Therefore Expecetd value of perfect information =Expected value with perfect information - expecetd value without perfect information = 133-125=8. The EVPI is "8"
F) Minimize the expected opportunity loss.
to calculate the expected oppotunity loss the regret table is needed as we calculated above
Regret table
Expected opportunity loss is calculated as
In case of Ardmore, OK = 0.2*25+0.3*10+0.5*0=8
In case of Sweetwater, TX= 0.2*20+0.3*20+0.5*30=25
In case of Lake Charles, LA=0.2*0+0.3*0+0.5*20=10
The Minimize expected opportunity loss is minimum of the three alternatives "8" (least of 8,25,10).
Demand is Low Demand is medium Demand is High best (these values are best out of the three situations) Ardmore, OK 85 110 150 150 Sweetwater, TX 90 100 120 120 Lake Charles, LA 110 120 130 130