Linear Programme - Solution ToMartin Service Station
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Transcript of Linear Programme - Solution ToMartin Service Station
3500 1000 -1500
7000 2000 -9000
0.4 0.3 0.3
heavy Moderate Light
Normal 0.7 0.8 0.9
Decision Alternatives
Heavy, s1
Moderate, s2 Light, s3
Blade Attachment, d1
New Snowplow, d2
Conditional Probability For A Given State of Nature
Test Results
Martin's Service Station is considering entering the snowplowing business for the coming winter season. Martin can purchase either a snowplow blade attachment for the station's pick-up truck or a new heavy-duty snowplow truck. Martin has analyzed the situation and believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits have been determined. Martin is willing to pay $50 for additional information on the weather.
Unreasonable 0.3 0.2 0.1
Answerpart a - bayes probability- 5 marks
we use bayes theorem see text for steps
S1=normal
State of nature (1) prior prob(2)
H 0.4 0.7M 0.3 0.8L 0.3 0.9
S2 =unreasonable
State of nature (1) prior prob(2)
H 0.4 0.3M 0.3 0.2L 0.3 0.1
part a
981.65
1,455 0.79
1,455 forecast 0.21 3235.714285714
The probabilities for the states of nature are P(s1) = 0.4, P(s2) = 0.3, and P(s3) = 0.3. Suppose that Martin decides to wait until September before making a final decision. Estimates of the probabilities associate with a normal (
condit prob(S1/h,), S1/m,S1/l (3)
condit prob(S2/H,), S2/M,S2/L (3)
No test
no FORECAST
12501250
New plow
700
part bGet the forecast, If normal get the blade, if unreasonable get the plow. The expected value is 1455
part cEVSI EWSI+ COST OF SURVEY - EWOSI
1,455 50 1250 255part dEVPI EWPI -EWOPI REVENUE
2950
EWOPI 1,250
EVPI 1,700part eEfficiency evsi/evpi 0.15
EWPI ( assume the best of all situation)
=0.4*7000+0.3*2000+0.3*-1500
blade
Martin's Service Station is considering entering the snowplowing business for the coming winter season. Martin can purchase either a snowplow blade attachment for the station's pick-up truck or a new heavy-duty snowplow truck. Martin has analyzed the situation and believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits have been determined. Martin is willing to pay $50 for additional information on the weather.
0.28 0.350.24 0.300.27 0.34
0.79 1.00
S2 =unreasonable
0.12 0.570.06 0.290.03 0.140.21 1.00
Payoffsadjust for SOP
982 H/N 0.35 3,450
M/N 0.30 950
L/N 0.34 -1,550
0new plow
-37H/N 0.35443 6,950M/N 0.303797 1950L/N 0.341772 -9,050
2,021
H/U 0.57 3,450
M/U 0.29 950
0 L/U 0.14 -1,550
) = 0.3. Suppose that Martin decides to wait until September before making a final decision. Estimates of the probabilities associate with a normal (
Joint prob(4)
posterior prob=col(4)/.79
Joint prob(4)
posterior prob=(4)/.21
New plow
3,236
H/U 0.57 6,950M/U 0.29 1950L/U 0.14 -9,050
HM 0.4 3,500 1400L 0.3 1000 300
0.3 -1,500 -4501250 expected value
0 expected valueH 0.4 7,000 2800M 0.3 2000 600L 0.3 -9,000 -2700
Get the forecast, If normal get the blade, if unreasonable get the plow. The expected value is 1455 700 expected value
) = 0.3. Suppose that Martin decides to wait until September before making a final decision. Estimates of the probabilities associate with a normal (N) or unreasonably cold (U) September are as follows
) September are as follows
payoffs states of nature maximax maximin
alternatives stable moderate high max payoff choice min payoff
Houses 70000 30000 10000 70000 10000
Shopping center80000 20000 5000 80000 best 5000
Leasing 40000 30000 20000 40000 20000
payoffs states of nature equally likely hurwicz
alternatives stable moderate high max payoff choice realism
Houses 70000 30000 10000 36666.666667 best 40000
Shopping center 80000 20000 5000 35000 42500
Leasing 40000 30000 20000 30000 30000
alpha
regrets states of nature equally likely
alternatives good fair poor max payoff choice
Houses 10000 0 10000 10000 best
Shopping center 0 10000 15000 15000
Leasing 40000 0 0 40000
f)probablities 0.30 0.40 0.30
Decsion good fair poor
Houses 21,000 12,000 3,000 36,000 best
Shopping center 24,000 8,000 1,500 33,500
Leasing 12,000 12,000 6,000 30,000
0 moveEWOPI
g most to be paid for additional informationuse regret table
0.30 0.40 0.30
Decsion market down
Houses 3,000 0 3,000 6,000 best
Shopping center 0 4,000 4,500 8,500
Leasing 12,000 0 0 12,000
Expected value
Expected value
market up
market stable
Expected regret
Min expeted regret
or EVPI =ewpi -ewopi
ewopi=382part f 36,000
ewpi =0.3*80000+0.4*30000+0.3*20000 42,000
EVPI =ewpi -ewopi (42000-36000)= 6,000
The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
Material Costschoice Decision Stable
Houses $70,000 105,000
best Leasing 40,000
Determine the best decision, using the following decision criteria.choice
best
0.5
Alternative stable moderate high Equal likelihood
Houses 70000 30000 10000
80000 20000 5000
Leasing 40000 30000 20000
Shopping center
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz (a = .2)
Shopping center
The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
Material CostsIncrease$30,000 20,000
40,000
Determine the best decision, using the following decision criteria.
Minimax regret
Hurwicz (a = .2)
The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table:
3 semester MA
Month Fund Priceforecast error
1 63 1/42 60 1/83 61 3/44 64 1/4 61.71 2.54 2.54 6.46 3.96%
5 59 3/8 62.04 (2.67) 2.67 7.11 4.49%
6 57 7/8 61.79 (3.92) 3.92 15.34 6.77%
7 62 1/4 60.50 1.75 1.75 3.06 2.81%
8 65 1/8 59.83 5.29 5.29 28.00 8.13%
9 68 1/4 61.75 6.50 6.50 42.25 9.52%
10 65 1/2 65.21 0.29 0.29 0.09 0.45%
11 68 1/8 66.29 1.83 1.83 3.36 2.69%
12 63 1/4 67.29 (4.04) 4.04 16.34 6.39%
13 64 3/8 65.63 (1.25) 1.25 1.56 1.94%
14 68 5/8 65.25 3.38 3.38 11.39 4.92%
15 70 1/8 65.42 4.71 4.71 22.17 6.71%
16 72 3/4 67.71 5.04 5.04 25.42 6.93%
17 74 1/8 70.50 3.63 3.63 13.14 4.89%
18 71 3/4 72.33 (0.58) 0.58 0.34 0.81%
19 75 1/2 72.88 2.63 2.63 6.89 3.48%
20 76 3/4 73.79 2.96 2.96 8.75 3.85%
21 74.67 AVERAGE 3.12 12.45 4.63%
MAD mse MAPE
weighted three-quarter
Month Fund Priceforecast error
1 63 1/4 0.1
2 60 1/8 0.3
3 61 3/4 0.6
4 64 1/4 61.4125 2.84 2.84 8.05 4.42%
5 59 3/8 63.0875 (3.71) 3.71 13.78 6.25%
6 57 7/8 61.075 (3.20) 3.20 10.24 5.53%
7 62 1/4 58.9625 3.29 3.29 10.81 5.28%
8 65 1/8 60.65 4.47 4.47 20.03 6.87%
9 68 1/4 63.5375 4.71 4.71 22.21 6.90%
10 65 1/2 66.7125 (1.21) 1.21 1.47 1.85%
11 68 1/8 66.2875 1.84 1.84 3.38 2.70%
12 63 1/4 67.35 (4.10) 4.10 16.81 6.48%
absolute error
Squared error
Absolute % error
absolute error
Squared error
Absolute % error
13 64 3/8 64.9375 (0.56) 0.56 0.32 0.87%
14 68 5/8 64.4125 4.21 4.21 17.75 6.14%
15 70 1/8 66.8125 3.31 3.31 10.97 4.72%
16 72 3/4 69.1 3.65 3.65 13.32 5.02%
17 74 1/8 71.55 2.58 2.58 6.63 3.47%
18 71 3/4 73.3125 (1.56) 1.56 2.44 2.18%
19 75 1/2 72.5625 2.94 2.94 8.63 3.89%
20 76 3/4 74.2375 2.51 2.51 6.31 3.27%
21 75.875AVERAGE 2.98 10.18 4.46%
next period MAD mse MAPE
exponential
Month Fund Priceforecast error
1 63 1/4 63.25
2 60 1/8 63.25 (3.13) 3.13 9.77 5.20%
3 61 3/4 62.00 (0.25) 0.25 0.06 0.40%
4 64 1/4 61.90 2.35 2.35 5.52 3.66%
5 59 3/8 62.84 (3.46) 3.46 12.01 5.84%
6 57 7/8 61.45 (3.58) 3.58 12.81 6.18%
7 62 1/4 60.02 2.23 2.23 4.96 3.58%
8 65 1/8 60.91 4.21 4.21 17.74 6.47%
9 68 1/4 62.60 5.65 5.65 31.94 8.28%
10 65 1/2 64.86 0.64 0.64 0.41 0.98%
11 68 1/8 65.12 3.01 3.01 9.06 4.42%
12 63 1/4 66.32 (3.07) 3.07 9.42 4.85%
13 64 3/8 65.09 (0.72) 0.72 0.51 1.11%
14 68 5/8 64.80 3.82 3.82 14.59 5.57%
15 70 1/8 66.33 3.79 3.79 14.38 5.41%
16 72 3/4 67.85 4.90 4.90 24.01 6.74%
17 74 1/8 69.81 4.32 4.32 18.62 5.82%
18 71 3/4 71.54 0.21 0.21 0.05 0.30%
19 75 1/2 71.62 3.88 3.88 15.04 5.14%
20 76 3/4 73.17 3.58 3.58 12.80 4.66%
21 74.60 average 2.99 11.25 4.45%
alpha 0.4 MAD mse MAPE
MAD mse MAPE3 MA 3.117647 12.45118 4.63%weighted average 2.982353 10.18482 4.46%
absolute error
Squared error
Absolute % error
exponential 2.989146 11.24746 4.45%
Using MAD the weighted average is most accurateUsing MSE the weighted average is most accurateusing MAPE the exponential is most accurate
(a) F4 = 400.000, F5 = 406.67, F6 = 423.33, F7 = 498.33, F8 = 521.67, F9 = 571.67; (b) F2 = 400.00, F3 = 410.00, F4 = 398.00, F5 = 402.40, F6 = 421.92, F7 = 452.53, F8 = 460.00, F9 = 498.02; (c) 3-sem. MAD = 80.33, exp. smooth. MAD = 87.16
= 521.67, F9 = 571.67; (b) F2 = 400.00, F3 = 410.00, F4 = 398.00, F5 = 402.40, F6 = 421.92, F7 = 452.53, F8 = 460.00, F9 = 498.02; (c) 3-sem. MAD = 80.33, exp. smooth. MAD = 87.16
= 460.00, F9 = 498.02; (c) 3-sem. MAD = 80.33, exp. smooth. MAD = 87.16