Mick Kara is the manager of MCZ Drilling Products, which produces a variety of s
ID: 3202515 • Letter: M
Question
Mick Kara 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 caused demand 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 following table gives the total monthly cost (in $ 1,000s) for each possible location under each demand possibility. The probabilities for the demand levels have been determined to be 20% for low demand, 30% for medium demand, and 50% for high demand. Which location would be selected based on the optimistic criterion? Which location would be selected based on the pessimistic criterion? Which location would be selected based on the minimax regret criterion? Which location should be selected to minimize the expected cost of operation? i How much is a perfect forecast of the demand worth? Which location would minimize the expected opportunity loss? What is the expected value of perfect information in this situation?Explanation / Answer
Solution
Preparatory Work
Pay-off = Total Monthly Cost, being cost, optimistic criterion implies min-min and pessimistic criterion implies maxi-max
EMV (Expected Monetary Value) = sum of (pay-off x probability)
Now, to answer the questions,
Pay-off table alongwith row max, row min and EMV is given below:
Location
Demand (probability of demand)
Row
Row
EMV
Low (0.2)
Medium (0.3)
High (0.5)
min
max
Ardmore
85
110
150
85
150
125
Sweetwater
90
100
120
90
120
108
Lake Charles
110
120
130
110
130
123
a) Since min of row min is 85, preferred location is Ardmore under optimistic criterion
b) Since max of row max is 150, preferred location is Ardmore under pessimistic criterion
c) Since min of row max is 120, preferred location is Sweetwater under mini-max criterion
d) Since minimum EMV is 123, preferred location is Lake Charles under expected minimum cost .
Location
Demand (probability of demand)
Row
Row
EMV
Low (0.2)
Medium (0.3)
High (0.5)
min
max
Ardmore
85
110
150
85
150
125
Sweetwater
90
100
120
90
120
108
Lake Charles
110
120
130
110
130
123