Techniques For Decision Making Under Certainty, Risk, And Uncertainty

Decision Making under Certainty

The decision making under certainty is identifying the best option or alternative and to optimize the outcome. In decision making under certainty the various outcomes are known and their values are certain. Hence the task is merely to optimize the required criterion such as to minimize the cost or to maximize the profits. Since perfect information is rarely available on all the various parameters impacting decision, hence this technique (decision making under certainty) is less often used. Moreover in normal circumstances there is cost of information hence this cost aspect also needs to be analyzed and expected value of perfect information (EVPI) needs to be calculated. E.g. If you want to make a decision of buying a soap ‘Dove’ or ‘Pears’ and the benefits of both the soaps are same, then cost of soaps are considered. Pears soap is cheaper than Dove, so the decision will be to buy Pears.

In decision making under risk, the outcomes are known as also the probabilities of occurrence are known and in such scenario, instead of optimizing the outcome we instead optimize the expected monetary value (EMV) of outcome. The highest EMV will be selected. E.g. if there is 1% probability of earning $1000 in option A while there is 90% probability of earning $ 50 in option B , the option B shall be preferred as the EMV of option B is $ 45 (90% of $ 45) rather than EMV of $ 10 in option A (1% of $ 1000).

Under uncertainty, only the outcomes are known but not their probability. Here the selection is based on maximax, maximin or equally likely methods for the positive or cautious or neutral perspective/s respectively.

	Good Economy	Poor Economy Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper
Probability	0.3	0.7
Share Market	80000	-20000
Bonds	30000	20000
Real Estate	25000	15000

Table 1

S. No		Good Economy	Poor Economy	Best Result (Max)
1	Share Market	80000	-20000	80000 (Max 80000,-20000)
2	Bonds	30000	20000	30000 (Max 30000,20000)
3	Real Estate	25000	15000	25000 (Max 25000,15000)
				80000 (Max(80000,30000,25000))

Table 2

As per Table 2, the optimist would choose share market investment because the share market returns (under best conditions) are the maximum of the maximum returns in any investment group i.e. return of $80,000 [maximax] (csuFOBJBS, Decision Analysis part 1, 2014)

S. No		Good Economy	Poor Economy	Best Result (Min)
1	Share Market	80000	-20000	-20000 (Min 80000,-20000)
2	Bonds	30000	20000	20000 (Min 30000,20000)
3	Real Estate	25000	15000	15000 (Min 25000,15000)
				20000 (Max(-20000,20000,15000))

Table 3

As per Table 3, mentioned figures the pessimist will choose where he gets maximum returns out of minimum returns (pessimist option) of any investment class. The investment in Bonds will ensure him returns of $20,000/- under any circumstances [maximin].

S. No		Regret in Good Economy	Regret in Poor Economy	Max Regret (Max)
1	Share Market	Max (80000,30000,25000) – 80000 = 0	Max (-20000,20000,15000) – (-20000) = 40000	Max (0,40000) = 40000
2	Bonds	Max (80000,30000,25000) – 30000 = 50000	Max (-20000,20000,15000) – 20000 = 0	Max (50000,0) = 50000
3	Real Estate	Max (80000,30000,25000)- 25000 55000	Max (-20000,20000,15000)- 15000 5000	Max (55000,5000) = 55000
				Min Regret = Min (40000,50000,55000) = 40000

Table 4

As per Table 4, the criterion of regret shows regret is share market has minimum of regrets. (csuFOBJBS, Decision Analysis part 2, 2014)

S. No		Good Economy	Poor Economy	Expected Value
	Probability	0.3	0.7
1	Share Market	80000	-20000	0.3 * 80000 + 0.7 * -20000 = 10000
2	Bonds	30000	20000	0.3 * 30000 + 0.7 * 20000 = 23000
3	Real Estate	25000	15000	0.3 * 25000 + 0.7 * 15000 = 18000
				Max(10000,23000,18000) = 23000

Table 5

As per Table 5, based on probability of a good economy = 0.3, the expected monetary values suggest optimum action of investing in Bonds with expected return of $23,000

S. No		Good Economy – Payoff	Poor Economy – Payoff
	Probability	0.3	0.7
1	Share Market	80000	-20000
2	Bonds	30000	20000
3	Real Estate	25000	15000
	Max Payoff	Max (80000,30000,25000) = 80000	Max (-20000, 20000,15000) = 20000
	Expected value with perfect information	Max Payoff * Probability = 80000 * 0.3 = 24000	Max Payoff * Probability = 20000 * 0.7 = 14000

Table 6

Expected value without perfect information (EMV) = Maximum expected monetary value i.e. (Max EMV) = $23,000

As per Table 6:

Expected value with perfect information = $24000 + 14000 = $38,000

Expected value of perfect information (EVPI) = Expected value with perfect information – Expected value without perfect information = $38,000 – $23,000 = $15,000

S. No		Good Economy	Poor Economy	Expected Monetary Value
	Probability	0.5	0.5
1	Large Shop (a1)	80000	-40000	(0.5 * 80000) + (0.5 * (-40000)) = 20000
2	Small Shop (a2)	30000	-10000	(0.5 * 30000) + (0.5 * (-10000)) = 10000
				Max (20000,10000) = 20000

Table 7

Based on expected market value, Jerry should choose, large shop (a1) as the expected return is higher at $ 20,000 as compared to return of $ 10,000 in small shop (a2).

Decision Making under Risk

The prior probability of Good Market Signal =

Probability (says good) = Probability (says good | actual good market) * Probability (actual good market) + Probability (says good but actual bad market) * Probability (actual bad market)

= 0.8 * 0.5 + 0.4 * 0.5 = 0.6

The prior probability of Poor Market Signal = 1 – 0.6 = 0.4

Probability (says good | actual good market) * Probability (good market) = Probability (good market & says good) * Probability (says good)

0.8 * 0.5 = Probability (good market & says good) * 0.6
Hence, Probability (good market & says good) = 0.8 * 0.5 / 0.6 = 2/3
And Probability (bad market & says good) = 1 – 2/3 = 1/3

Probability(says good & bad market) Probability(bad market) = Probability( good market & says bad) Probability(says bad)
0.2 * 0.5 = Probability(good market & says bad) * 0.4
Hence , Probability(good market & says bad) = 0.2*0.5/0.4 = 0.25
And , Probability(bad market & says bad) = 1-0.25 = 0.75

Expected profit (good market & large shop):

EMV (large) = 80000 * (2/3) – 40000 * (1/3) = 40000

Expected profit (good market & small shop):

EMV (small) = 30000 * (2/3) – 10000 * (1/3) = 16666.67

Hence if the prediction is for good market then large shop should be opened.

Expected profit (bad market & large shop):

EMV (large) = 80000 * 0.25 – 40000 * 0.75 = -10000

Expected profit (bad market & small shop):

EMV (small) = 30000 * 0.25 – 10000 * 0.75 = 0

Hence if the prediction is for bad market then small shop should be opened.

The posterior probability of a good market given that his friend has provided an

unfavorable market prediction.

Probability(says good & bad market) Probability(bad market) = Probability(good market & says bad ) Probability(says bad)
0.2 * 0.5=Probability ( good market & says bad ) * 0.4
Hence, Probability(good market & says bad ) = 0.2 * 0.5 / 0.4 = 0.25
Hence, Probability( bad market & says bad ) = 1 – 0.25 = 0.75

Therefore 0.25 is the required probability

After engaging his friend the expected monetary value, i.e. EMV (info) improves to $ 24000 from $ 20000 previously. Hence he stands to gain $ 4000. However, there is cost of information i.e. $ 3000 so his net gain would be $ 1000 if he engages his friend’s services. (csuFOBJBS, Value of information v2, 2015)

Data

Selling Price: $ 60 to $ 80 (uniform distribution)

Fixed Cost $ 1500 / month

Profit Margin: 20% to 30% of selling price

Prob	Cum Probability	Demand
0.05	0.05	100
0.10	0.15	120
0.20	0.35	140
0.30	0.65	160
0.25	0.9	180
0.10	1	200

Table 8

Monthly Demand: LOOKUP(RAND(), Cumm Probability, Demand)

Profit Margin: 20% (Minimum profit) + 30%-20% (Max margin – Min Margin) * Rand()

Selling price = =RANDBETWEEN (Min Selling price, Maximum Selling price)

Monthly Profit = Monthly Demand * Profit Margin * Selling price – Fixed Cost

Month	Monthly Demand	Profit Margin	Selling Price	Monthly Profit
1	100	0.266360392	70	364.52
2	140	0.247115827	65	2248.45
3	100	0.215591232	65	1401.34
4	140	0.230139687	78	2513.13
5	140	0.233413401	63	2058.71
6	160	0.255822859	62	2537.76
7	140	0.296303417	65	2696.36
8	120	0.28794513	64	2211.42
9	120	0.244070117	71	2079.48
10	120	0.243390276	70	2044.48
11	120	0.260346493	73	2280.64
12	160	0.240350633	61	2345.82

Table 9

Month	OH Cost	MH	Batches
1	$80,000	2,200	300
2	40,000	2,400	120
3	63,000	2,100	250
4	45,000	2,700	160
5	44,000	2,300	200
6	48,000	3,800	170
7	65,000	3,600	260
8	46,000	1,800	160
9	33,000	3,200	150
10	66,000	2,800	210
Total	530,000	26,900	1,980

Table 10

Highest MH = 3800 therefore highest OH Cost = 48000

Lowest MH = 1800 therefore lowest OH Cost = 46000

Variable Cost (per unit) = (Highest OH Cost – Lowest OH cost)/ (Highest MH – Lowest MH)

Decision Making under Complete Uncertainty

= (48000 – 46000) / (3800 – 1800)

= 2000 / 2000 = $ 1 per unit

Total Fixed Cost = Highest OH Cost – (Highest MH * Variable Cost)

= 48000 – (3800 * 1)

= 48000 – 3800 = $44200

Cost Volume = Fixed Cost + (Variable Cost * Machine Hours)

= 44200 + (1 * 3000) = 44200 + 3000 = $47200

Regression Analysis

Overhead Cost against Machine Hours

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.104236344
R Square	0.010865215
Adjusted R Square	-0.112776633
Standard Error	15447.61363
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	20969865.79	20969865.79	0.087876521	0.774444342
Residual	8	1909030134	238628766.8
Total	9	1930000000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	59198.7845	21473.78291	2.75679347	0.024797288	9680.152308	108717.4167	9680.152308	108717.4167
MH	-2.304380856	7.773521992	-0.296439742	0.774444342	-20.23015471	15.621393	-20.23015471	15.621393

Y = Intercept + Slope * units

OH= 59198.7845 – 2.304380856 * MH

Since the P value (in table above) is high and R (or R square) is low, hence correlation is low and result is not statistically significant and not a good fit.

Overhead Cost against Batches

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.911766618
R Square	0.831318365
Adjusted R Square	0.810233161
Standard Error	6379.219736
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1604444444	1604444444	39.42662116	0.000238105
Residual	8	325555555.6	40694444.44
Total	9	1930000000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6555.555556	7666.867952	0.855050015	0.417393566	-11124.27365	24235.38476	-11124.27365	24235.38476
Batches	234.5679012	37.35715567	6.279062124	0.000238105	148.4221458	320.7136567	148.4221458	320.7136567

Y = Intercept + Slope * units

OH= 6555.555556 + 234.5679012 * Batches

Since the P value (in table above) is low and R (or R square) is high, hence correlation is high and result is statistically significant and good fit.

Overhead Cost against Machine Hours and Batches

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.912733424
R Square	0.833082304
Adjusted R Square	0.785391534
Standard Error	6783.92168
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1607848846	803924423.2	17.46841786	0.001900021
Residual	7	322151153.5	46021593.36
Total	9	1930000000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9205.657918	12704.91845	0.724574341	0.492215314	-20836.70036	39248.0162	-20836.70036	39248.0162
MH	-0.930666774	3.421799934	-0.271981645	0.793483511	-9.021937883	7.160604336	-9.021937883	7.160604336
Batches	233.827453	39.8202902	5.872068031	0.000616648	139.6674291	327.987477	139.6674291	327.987477

OH= 9205.657918 – 0.930666774 * MH + 233.827453 * Batches

Since the P value (in table above) is low and R (or R square) is high, hence correlation is high and result is statistically significant and good fit.

Using both Machine Hours and Batches, the R square is highest and P value is lowest. Hence this model should be preferred in future.

The best model is OH against both MH & Batches. The second best is OH against Batches. This is because the Rsquare is highest and p value lowest. Hence the correlation is high.