A manager is trying to decide whether to build a small, medium, or large facilit
ID: 465291 • Letter: A
Question
A manager is trying to decide whether to build a small, medium, or large facility. The demand can be low, average, or high, with the estimated probabilities being 0.40, 0.35, and 0.25 respectively.
A small facility is expected to earn an after- tax net present value of just $17000 if demand is low. If demand is average, the small facility is expected to earn $25000; it can be increased to medium size to earn a net present value of $50000. If demand is high, the small facility is expected to earn $50000 and can be expanded to medium size to earn $60000 or to large size to earn $100000.
A medium size facility is expected to lose an estimated $25000 if demand is low and earn $90000 if demand is average. If demand is high, the medium- sized facility is expected to earn a net present value of $125000. It can be expanded to a large size for a net payoff of $145000.
If a large facility is built and demand is high, earnings are expected to be $150000. If demand is average for the large facility, the present value is expected to be $80000; if demand is low, the facility is expected to lose $50000.
1, Choose the correct decision tree below. Note that each payoff is given in thousands
a,
b,
c,
d,
b, What should management do to achieve the highest expected payoff? Choose the best options
The management should build a (large/medium or small facility) in order to achieve the highest expected payoff of $... (enter the number as a whole number)
c, Which alternative is best according to each of the following decision criterion? (Fill in the box)
Criterion Decision Value of Return Maximin Large/ Medium or Small Facility? $... thousands Maximax Large/ Medium or Small Facility? $... thousands Minimax Regret Large/ Medium or Small Facility? $... thousands Expand to Irg $145 Do nothing $125 -550 $150 Med S90 - $25 $100 High 0 25 High 0.25 580 Small $50 Avgo. 4 pand to med. $50 $17 S25Explanation / Answer
Correct decision tree is (b)
In the figure a, the decision node (2) is wrong. Correct position of this decision node (2) is for Medium facility decision under high demand state.
In figure c, the payoff of large facility decision when demand is low is taken wrong, it should be -$50. Similarly the payoff of medium facility decision when demand is low is taken wrong, it should be -$25.
In Figure (d), the representations of nodes are wrong. The Nodes 2, 3, and 4 are event nodes but are shown as decision nodes.
Thus, correct decision tree is figure b.
b.
First determine payoff at decision nodes 2, 3, and 4.
Payoff at node 2 = maximum ($145, $125) = $145
Thus, decision at node 2 is to expand to large facility and payoff is $145.
Payoff at node 3 = maximum($100, $80, $50)
Thus, decision at node 3 is to expand to large facility and payoff is $100.
Payoff at node 4 = maximum($50, $25)
Thus, decision at node 3 is to expand to large facility and payoff is $100.
Expected Monetary Value for Large facility alternative
EMVL=0.25 x $150 + 0.35 x $80 + 0.40 x (-$50)
EMVL= $45.5
EMVM = 0.25 x $145 + 0.35 x $90 + 0.40 x (-$25)
EMVM= $57.75
EMVS = 0.25 x $100 + 0.35 x $50 + 0.40 x $17
EMVS = $49.3
Highest EMV is $57.75 for the decision of build Medium facility.
According to EMV rule, management should build a medium facility in order to achieve the highest expected payoff of $57,750.
State of Nature
Decision Alternative
High Demand
Average Demand
Low Demand
EMV
Minimum
Maximum
Small Facility
100
50
17
49.3
17
100
Medium Facility
145
90
-25
57.75
-25
145
Large Facility
150
80
-50
45.5
-50
150
Probabilities
0.25
0.35
0.4
Maximum
150
90
17
Opportunity/Regret Payoff table
State of Nature
Maximum
Decision Alternative
High Demand
Average Demand
Low Demand
Small Facility
50
40
0
50
Medium Facility
5
0
42
42
Large Facility
0
10
67
67
Maximax decision rule:
This approach selects the alternative which maximizes the maximum payoff among all events
Maximum payoffs of small, medium and large facilities are ($100, $145, $150) respectively.
Maximum payoff among the alternative’s maximum payoff is $150 for the Large facility alternative.
Thus, alternative of large facility maximizes the maximum payoff among all events.
Maximin Decision Rule:
This approach selects the alternative which maximizes the minimum payoff among all events.
Minimum payoffs of small, medium and large facilities are ($17, -$25, -$50) respectively.
Maximum payoff among the alternative’s minimum payoff is $17 for the small facility alternative.
Thus, alternative of small facility maximizes the minimum payoff among all events.
Regret Table:
First develop regret table by subtracting maximum payoff among the each event and subtracting each payoff of event from this value.
MINIMAX REGRET decision rule
According to this rule select alternative which minimizes the maximum opportunity loss value of each alternative.
Maximum regret value of small, medium and large facilities are $50, $42, $67.
Minimum payoff among the dealers maximum opportunity loss value is $42 for the medium Facility.
Thus, alternative of building medium facility minimizes the maximum opportunities loss among all events.
Criterion
Decision
Value of Return
Maximin
Medium Facility
$17,000
Maximax
Large Facility
$150,000
Minimax Regret
Medium
$42,000
State of Nature
Decision Alternative
High Demand
Average Demand
Low Demand
EMV
Minimum
Maximum
Small Facility
100
50
17
49.3
17
100
Medium Facility
145
90
-25
57.75
-25
145
Large Facility
150
80
-50
45.5
-50
150
Probabilities
0.25
0.35
0.4
Maximum
150
90
17
Opportunity/Regret Payoff table
State of Nature
Maximum
Decision Alternative
High Demand
Average Demand
Low Demand
Small Facility
50
40
0
50
Medium Facility
5
0
42
42
Large Facility
0
10
67
67
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