Decision Support Tools

This document discusses decision support tools such as payoff matrix and decision trees. It explains their advantages and when to use them. It also provides examples and calculations.

DECISION SUPPORT TOOLS
STUDENT ID:
[Pick the date]

Question 1
Part a)
A key advantage which the user derived in case of payoff is that it outlines the payoff with
various choices and states that are summarised in the form of a matrix. This tends to allow the
user not only optimum decision making but also the extent of superiority of a given choice
over others. In order to form a payoff matrix, the first step is to outline the possible states of
the variable out of control and also the available choices within the control. Then the
respective probability of the various states ought to be determined. Finally the payoff
associated with each choice and state is represented to complete the matrix (Medhi, 2016).
Part b)
Although decision trees and payoff matrix are overlapping tools which can be used to analyse
a given problem of decision making but there are certain situations where the use of decision
tree would be recommended. The decision tree tends to outline all the intermediate decisions
which is not the case with payoff matrix. Hence, decision tree would constitute a preferable
decision analysis tool where sequential decision making is involved owing to which the
intermediate decisions assume high importance (Hillier, 2016).
Part c) George has three key options that he can take, buy robot 1, buy robot 2 and third is
none means do not buy any of the two robots.
(1) Payoff matrix
(2) Optimist
Optimal action: To buy robot 1
Reason: Max value among maximum values
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(3) Pessimist
Optimal action: To not buy robots
Reason: Max value among minimum values
(4) Laplace
Optimal action: To buy robot 1 or robot 2
Reason: Max mean value
(5) Criterion of
regret
Optimal action: To buy robot 2
Reason: Minimum value among maximum row values
(6) Expected
monetary value
Optimal action: To buy robot 1
Reason: Max expected monetary value
(7) EVPI
Question 2
Part a) Computation of revise prior probability
Notation:
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Normal View Formula View
Part b) Computation of posterior probability for the case positive and favourable market =
0.628 (from the above)
Part c) Computation of EVSI and ENGSI
EVSI
ENGSI ENGSI = EVSI – Cost of survey = 9802 – 5000 = 4,802
Part d) EVPI (Expected value of perfect information)
EVPI
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Question 3
(1) Profit per flight per day and mean profit through Simulation Model
Prob Cum prob Demand Prob Cum prob No shows Avaiable seats 6
0.05 0 5 0.15 0 0 Reservation Costs 79
0.11 0.05 6 0.25 0.15 1 Compensation 50
0.2 0.16 7 0.26 0.4 2 FC per flight 350
0.18 0.36 8 0.23 0.66 3
0.16 0.54 9 0.11 0.89 4
0.12 0.7 10
0.1 0.82 11
0.08 0.92 12
MODEL RN Number Number Number Profit
Day RN Demand Demand No Shows no shows Seated Overbook Fare rev Comp. FC Per flight
1 0.359 7 0.834 3 4 0 316 0 350 -34
2 0.783 10 0.106 0 6 4 474 200 350 -76
3 0.744 10 0.735 3 6 1 474 50 350 74
4 0.160 7 0.453 2 5 0 395 0 350 45
5 0.095 6 0.898 4 2 0 158 0 350 -192
6 0.187 7 0.799 3 4 0 316 0 350 -34
7 0.303 7 0.927 4 3 0 237 0 350 -113
8 0.355 7 0.653 2 5 0 395 0 350 45
9 0.307 7 0.152 1 6 0 474 0 350 124
10 0.028 5 0.930 4 1 0 79 0 350 -271
11 0.679 9 0.064 0 6 3 474 150 350 -26
12 0.017 5 0.252 1 4 0 316 0 350 -34
13 0.073 6 0.640 2 4 0 316 0 350 -34
14 0.113 6 0.476 2 4 0 316 0 350 -34
15 0.045 5 0.247 1 4 0 316 0 350 -34
16 0.095 6 0.140 0 6 0 474 0 350 124
17 0.632 9 0.931 4 5 0 395 0 350 45
18 0.075 6 0.268 1 5 0 395 0 350 45
19 0.895 11 0.181 1 6 4 474 200 350 -76
20 0.913 11 0.267 1 6 4 474 200 350 -76
21 0.345 7 0.836 3 4 0 316 0 350 -34
22 0.388 8 0.183 1 6 1 474 50 350 74
23 0.805 10 0.591 2 6 2 474 100 350 24
24 0.154 6 0.399 1 5 0 395 0 350 45
25 0.902 11 0.993 4 6 1 474 50 350 74
26 0.340 7 0.442 2 5 0 395 0 350 45
27 0.678 9 0.061 0 6 3 474 150 350 -26
28 0.090 6 0.995 4 2 0 158 0 350 -192
29 0.238 7 0.704 3 4 0 316 0 350 -34
30 0.877 11 0.152 1 6 4 474 200 350 -76
Avg. Profit -21
Prob Cum prob Demand Prob Cum prob No shows Avaiable seats 6
0.05 0 5 0.15 0 0 Reservation Costs 79
0.11 =A2+B2 6 0.25 =E2+F2 1 Compensation 50
0.2 =A3+B3 7 0.26 =E3+F3 2 FC per flight 350
0.18 =A4+B4 8 0.23 =E4+F4 3
0.16 =A5+B5 9 0.11 =E5+F5 4
0.12 =A6+B6 10
0.1 =A7+B7 11
0.08 =A8+B8 12
MODEL RN Number Number Number Profit
Day RN Demand Demand No Shows no shows Seated Overbook Fare rev Comp. FC Per flight
1 =RAND() =VLOOKUP(B12,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D12,$F$2:$G$6,2,1) =IF(C12-E12>=6,"6",C12-E12) =IF(C12-E12-$J$1<=0,"0",C12-E12-F12) =F12*$J$2 =G12*$J$3 =$J$4 =H12-I12-J12
2 =RAND() =VLOOKUP(B13,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D13,$F$2:$G$6,2,1) =IF(C13-E13>=6,"6",C13-E13) =IF(C13-E13-$J$1<=0,"0",C13-E13-F13) =F13*$J$2 =G13*$J$3 =$J$4 =H13-I13-J13
3 =RAND() =VLOOKUP(B14,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D14,$F$2:$G$6,2,1) =IF(C14-E14>=6,"6",C14-E14) =IF(C14-E14-$J$1<=0,"0",C14-E14-F14) =F14*$J$2 =G14*$J$3 =$J$4 =H14-I14-J14
4 =RAND() =VLOOKUP(B15,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D15,$F$2:$G$6,2,1) =IF(C15-E15>=6,"6",C15-E15) =IF(C15-E15-$J$1<=0,"0",C15-E15-F15) =F15*$J$2 =G15*$J$3 =$J$4 =H15-I15-J15
5 =RAND() =VLOOKUP(B16,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D16,$F$2:$G$6,2,1) =IF(C16-E16>=6,"6",C16-E16) =IF(C16-E16-$J$1<=0,"0",C16-E16-F16) =F16*$J$2 =G16*$J$3 =$J$4 =H16-I16-J16
6 =RAND() =VLOOKUP(B17,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D17,$F$2:$G$6,2,1) =IF(C17-E17>=6,"6",C17-E17) =IF(C17-E17-$J$1<=0,"0",C17-E17-F17) =F17*$J$2 =G17*$J$3 =$J$4 =H17-I17-J17
7 =RAND() =VLOOKUP(B18,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D18,$F$2:$G$6,2,1) =IF(C18-E18>=6,"6",C18-E18) =IF(C18-E18-$J$1<=0,"0",C18-E18-F18) =F18*$J$2 =G18*$J$3 =$J$4 =H18-I18-J18
8 =RAND() =VLOOKUP(B19,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D19,$F$2:$G$6,2,1) =IF(C19-E19>=6,"6",C19-E19) =IF(C19-E19-$J$1<=0,"0",C19-E19-F19) =F19*$J$2 =G19*$J$3 =$J$4 =H19-I19-J19
9 =RAND() =VLOOKUP(B20,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D20,$F$2:$G$6,2,1) =IF(C20-E20>=6,"6",C20-E20) =IF(C20-E20-$J$1<=0,"0",C20-E20-F20) =F20*$J$2 =G20*$J$3 =$J$4 =H20-I20-J20
10 =RAND() =VLOOKUP(B21,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D21,$F$2:$G$6,2,1) =IF(C21-E21>=6,"6",C21-E21) =IF(C21-E21-$J$1<=0,"0",C21-E21-F21) =F21*$J$2 =G21*$J$3 =$J$4 =H21-I21-J21
11 =RAND() =VLOOKUP(B22,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D22,$F$2:$G$6,2,1) =IF(C22-E22>=6,"6",C22-E22) =IF(C22-E22-$J$1<=0,"0",C22-E22-F22) =F22*$J$2 =G22*$J$3 =$J$4 =H22-I22-J22
12 =RAND() =VLOOKUP(B23,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D23,$F$2:$G$6,2,1) =IF(C23-E23>=6,"6",C23-E23) =IF(C23-E23-$J$1<=0,"0",C23-E23-F23) =F23*$J$2 =G23*$J$3 =$J$4 =H23-I23-J23
13 =RAND() =VLOOKUP(B24,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D24,$F$2:$G$6,2,1) =IF(C24-E24>=6,"6",C24-E24) =IF(C24-E24-$J$1<=0,"0",C24-E24-F24) =F24*$J$2 =G24*$J$3 =$J$4 =H24-I24-J24
14 =RAND() =VLOOKUP(B25,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D25,$F$2:$G$6,2,1) =IF(C25-E25>=6,"6",C25-E25) =IF(C25-E25-$J$1<=0,"0",C25-E25-F25) =F25*$J$2 =G25*$J$3 =$J$4 =H25-I25-J25
15 =RAND() =VLOOKUP(B26,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D26,$F$2:$G$6,2,1) =IF(C26-E26>=6,"6",C26-E26) =IF(C26-E26-$J$1<=0,"0",C26-E26-F26) =F26*$J$2 =G26*$J$3 =$J$4 =H26-I26-J26
16 =RAND() =VLOOKUP(B27,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D27,$F$2:$G$6,2,1) =IF(C27-E27>=6,"6",C27-E27) =IF(C27-E27-$J$1<=0,"0",C27-E27-F27) =F27*$J$2 =G27*$J$3 =$J$4 =H27-I27-J27
17 =RAND() =VLOOKUP(B28,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D28,$F$2:$G$6,2,1) =IF(C28-E28>=6,"6",C28-E28) =IF(C28-E28-$J$1<=0,"0",C28-E28-F28) =F28*$J$2 =G28*$J$3 =$J$4 =H28-I28-J28
18 =RAND() =VLOOKUP(B29,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D29,$F$2:$G$6,2,1) =IF(C29-E29>=6,"6",C29-E29) =IF(C29-E29-$J$1<=0,"0",C29-E29-F29) =F29*$J$2 =G29*$J$3 =$J$4 =H29-I29-J29
19 =RAND() =VLOOKUP(B30,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D30,$F$2:$G$6,2,1) =IF(C30-E30>=6,"6",C30-E30) =IF(C30-E30-$J$1<=0,"0",C30-E30-F30) =F30*$J$2 =G30*$J$3 =$J$4 =H30-I30-J30
20 =RAND() =VLOOKUP(B31,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D31,$F$2:$G$6,2,1) =IF(C31-E31>=6,"6",C31-E31) =IF(C31-E31-$J$1<=0,"0",C31-E31-F31) =F31*$J$2 =G31*$J$3 =$J$4 =H31-I31-J31
21 =RAND() =VLOOKUP(B32,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D32,$F$2:$G$6,2,1) =IF(C32-E32>=6,"6",C32-E32) =IF(C32-E32-$J$1<=0,"0",C32-E32-F32) =F32*$J$2 =G32*$J$3 =$J$4 =H32-I32-J32
22 =RAND() =VLOOKUP(B33,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D33,$F$2:$G$6,2,1) =IF(C33-E33>=6,"6",C33-E33) =IF(C33-E33-$J$1<=0,"0",C33-E33-F33) =F33*$J$2 =G33*$J$3 =$J$4 =H33-I33-J33
23 =RAND() =VLOOKUP(B34,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D34,$F$2:$G$6,2,1) =IF(C34-E34>=6,"6",C34-E34) =IF(C34-E34-$J$1<=0,"0",C34-E34-F34) =F34*$J$2 =G34*$J$3 =$J$4 =H34-I34-J34
24 =RAND() =VLOOKUP(B35,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D35,$F$2:$G$6,2,1) =IF(C35-E35>=6,"6",C35-E35) =IF(C35-E35-$J$1<=0,"0",C35-E35-F35) =F35*$J$2 =G35*$J$3 =$J$4 =H35-I35-J35
25 =RAND() =VLOOKUP(B36,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D36,$F$2:$G$6,2,1) =IF(C36-E36>=6,"6",C36-E36) =IF(C36-E36-$J$1<=0,"0",C36-E36-F36) =F36*$J$2 =G36*$J$3 =$J$4 =H36-I36-J36
26 =RAND() =VLOOKUP(B37,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D37,$F$2:$G$6,2,1) =IF(C37-E37>=6,"6",C37-E37) =IF(C37-E37-$J$1<=0,"0",C37-E37-F37) =F37*$J$2 =G37*$J$3 =$J$4 =H37-I37-J37
27 =RAND() =VLOOKUP(B38,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D38,$F$2:$G$6,2,1) =IF(C38-E38>=6,"6",C38-E38) =IF(C38-E38-$J$1<=0,"0",C38-E38-F38) =F38*$J$2 =G38*$J$3 =$J$4 =H38-I38-J38
28 =RAND() =VLOOKUP(B39,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D39,$F$2:$G$6,2,1) =IF(C39-E39>=6,"6",C39-E39) =IF(C39-E39-$J$1<=0,"0",C39-E39-F39) =F39*$J$2 =G39*$J$3 =$J$4 =H39-I39-J39
29 =RAND() =VLOOKUP(B40,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D40,$F$2:$G$6,2,1) =IF(C40-E40>=6,"6",C40-E40) =IF(C40-E40-$J$1<=0,"0",C40-E40-F40) =F40*$J$2 =G40*$J$3 =$J$4 =H40-I40-J40
30 =RAND() =VLOOKUP(B41,$B$2:$C$9,2,1) =RAND() =VLOOKUP(D41,$F$2:$G$6,2,1) =IF(C41-E41>=6,"6",C41-E41) =IF(C41-E41-$J$1<=0,"0",C41-E41-F41) =F41*$J$2 =G41*$J$3 =$J$4 =H41-I41-J41
Avg. Profit =AVERAGE(K12:K41)
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Part 2)
The simulation in relation to the operations highlight thats while the flight remains profitable
but the same can be enhanced by enhancing the fares that are currently being charged.
However, one needs to be watchful in regards to the impact of higher price on demand as the
overbooking is being currently made as the revenues made from no shows tends to exceed the
compensation paid for overbooking. Another measure that the company could potentially
consider to enhance the profits is lower the compensation currently paid for overbooking.
However, in this option it would be interesting to consider the impact on overbooking and no
shows that this change would create (Lieberman, Nag, Hiller & Basu, 2015).
Part 3)
The Manager
May 14, 2019
Dear Sir
The simulation results along with the above recommendation clearly highlights that the for
higher profitability, it is worthwhile to consider higher fares. Making this change in the
simulation model leads to higher profit but the underlying assumption is that there is no
change in the demand distribution and also no shows. As a result, it makes sense for the
company to conduct relevant pilot studies in this context. Also, another viewpoint expressed
is that the compensation payment made on the overbooked ticket can be reduced to boost
profitability. The changes in the model do reflect higher profitability for the operations but it
is assumed that this would have any impact on the demand schedule for tickets and also the
probability of no booking. Thereby, before bringing in this change, pilot run must be
conducted to analyse the impact on the profitability of operations.
Yours Sincerely
STUDENT NAME
Question 4
Part a) Regression analysis
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(1) GMAT (X) and GPA(Y)
Y =mX +C
GPA Score = 2.094 + (0.002 * GMAT Score)
In order to opine on the underlying significance of the above linear regression, the slope
testing needs to be performed.
Relevant p value (GMAT slope) = 0.019
P value < Level of significance (0.05) implying that slope and linear relationship both are
statistically significant and not attributed to chance.
(2) AGE (X) and GPA(Y)
7

Y =m X 1+C
Y = 0.044X + 2.163
In order to opine on the underlying significance of the above linear regression, the slope
testing needs to be performed.
Relevant p value (Age slope) = 0.015
P value < Level of significance (0.05) implying that slope and linear relationship both are
statistically significant and not attributed to chance (Lind, Marchal &Wathen, 2015).
(3) GMAT (X1), AGE (X2) and GPA(Y)
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Y =mX 1+mX 2+C
GPA Score = 1.378 + (0.002 * GMAT Score) + (0.034 *AGE)
In order to opine on the underlying significance of the above linear regression, the ANOVA
related test is required which determines whether atleast one slope is significant.
Relevant p value (Significance F) = 0.005
P value < Level of significance (0.05) implying that the model is significant since it is not
possible that both slope are statistically insignificant (Shi & Tao, 2015).
Part 2) From the comparison of the three models outlined above, it is interesting to note that
GMAT & Age are both statistically significant variables for explaining the GPA score.
Hence, it is rational that both these variables ought to be included for the best model. This is
happening in Model 3. Further the model 3 as the best model is also supported from the fact
that coefficient of determination is the highest amongst the given models (Taylor & Cihon,
2014).
Part 3) GPS Scores Y=?
GMAT = X1 = 600
AGE = X2 = 29
Question 5
Part 1) Computation of break-even number of units and in dollars
9

Part 2) Computation of number of units for achieving a set PBT $600
Part 3) Computation of profit
10

Part 4) Number of units of product A and product B in dollars
Product A = 2X and Product B = X (As per given ratio)
Now,
Sum of gross profit = 12 x + 12x = 24 x
The equation ca be derived so as to find the x.4
Units of A and in dollars = 2x = 600 and 600*12 = $3600
Units of B and in dollars = x = 300 and 300*20 = $6000
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References
Hillier, F. (2016).Introduction to Operations Research.(6thed.). New York: McGraw Hill
Publications.
Lieberman, F. J., Nag, B., Hiller, F.S. & Basu, P. (2015).Introduction To Operations
Research (5thed.).New Delhi: Tata McGraw Hill Publishers.
Lind, A.D., Marchal, G.W. &Wathen, A.S. (2016).Statistical Techniques in Business and
Economics (15thed.). New York : McGraw-Hill/Irwin.
Medhi, J. (2016). Statistical Methods: An Introductory Text (4thed.). Sydney: New Age
International.
Shi, Z. N. & Tao, J. (2015).Statistical Hypothesis Testing: Theory and Methods (6thed.).
London: World Scientific.
Taylor, K. J. & Cihon, C. (2014).Statistical Techniques for Data Analysis (2nded.).
Melbourne: CRC Press.
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