Payoff Table and Tree Part2

ACCA F5 - Performance Management 

Expected Event: The likelihood of occurrence of a event out of all possible event is expected event. In above situation, say for a typical day it is highly probable that the day will be sunny. Say in probability term the chance that it will be a sunny day is 80% and the probability for cloudy day is (100% - 80%) 20%.

EVENT	Cloudy	Sunny
For a typical day it is expected that the probability of event is	20%	80%

(EVs) Expected values = Expected value is the payoff for each combination of even and action multiplied by the probability of occurrence of events, summed over all events.

Expected value table for payoff:

ACTION        \     EVENT	Cloudy	Sunny	Expected value for each action
	20%	80%
Small batch	225 * 20% = 45	250 * 80% = 200	= 45 + 200 = 245
Medium batch	337.5 * 20% = 67.5	600 * 80% = 480	= 67.5 + 480 =547.5
Large batch	80 * 20% = 16	1180 * 80% = 944	= 944 + 16 = 960

Expected value table for opportunity loss:

ACTION        \     EVENT	Cloudy	Sunny	Expected value for each action
	20%	80%
Small batch	112.5 * 20% = 22.5	930 * 80% = 744	= 22.5 + 744
Medium batch	0 * 20% = 0	580 * 80% = 448	= 0 + 464
Large batch	257.5  * 20% = 51.5	0 * 80% = 0	= 51.5 + 0

Choice for Perfect information: Represent best outcome for past collected data.

ACTION        \              EVENT	Cloudy	Sunny
Small batch	225	250
Medium batch	337.5	600
Large batch	80	1180
Payoff maximization for perfect information	337.5	1180

Expected value for perfect condition: (Expected value under certainty) Payoff generated by choosing alternatives with maximum payoff for each possible event multiplied by the probability of occurrence of event.

ACTION     \     EVENT	Cloudy 20%	Sunny 80%	Expected value for (perfect condition) certainty
Choice for perfect information	337.5 * 20% = 67.5	1180 * 80% = 944	67.5 + 944 = 1011.5

EV's for perfect information: Extra payoff generated under certainty to that of best alternative.

EV's for perfect information

Expected value under certainty - Expected value for best alternative = 1011.5 - 960 = 51.5

The Tree

Expected Event: The likelihood of occurrence of a event out of all possible event is expected event. In above situation, say for a typical day it is highly probable that the day will be sunny. Say in probability term the chance that it will be a sunny day is 80% and the probability for cloudy day is (100% - 80%) 20%.

EVENT	For a typical day it is expected that the probability of event is
Cloudy	20%
Sunny	80%

(EVs) Expected values = Expected value is the payoff for each combination of even and action multiplied by the probability of occurrence of events, summed over all events.

Expected value payoff tree:

Decision Point	Alternatives	Event  Point	Events	Probability	Happening Point	Outcome	Quantifying Outcome	Expected Values
	Small batch		Cloudy	20%		Sales	237.5 * 20% = 47.5	=47.5-2.5 =45
						Return	(12.5) * 20% = (2.5)
			Sunny	80%		Sales	250 * 80% = 200	=200
						Return	0 * 80% = 0
	Medium batch		Cloudy	20%		Sales	450 * 20% = 90	=90-22.5 =67.5
						Return	(112.5) * 20% = (22.5)
			Sunny	80%		Sales	600 * 80% = 480	=480
						Return	0 * 80% = 0
	Large batch		Cloudy	20%		Sales	560 * 20% = 112	=112-96 = 16
						Return	(480) * 20% = (96)
			Sunny	80%		Sales	1260 * 80% = 1008	=1008-64 =944
						Return	(80) * 80% = (64)

Expected value tree for opportunity loss:

Alternatives	Events	Regret	Expected Value
Small batch	Cloudy	112.5 * 20% = 22.5	= 22.5 + 744 = 766.5
	Sunny	930 * 80% = 744
Medium Batch	Cloudy	0 * 20% = 0	= 0 + 464 = 464
	Sunny	580 * 80% = 464
Large Batch	Cloudy	257.5 * 20% = 51.5	= 51.5 + 0 = 515
	Sunny	0 * 80% =0

Choice for Perfect information: Represent best outcome for past collected data.

Alternatives	Events	Probability	Outcome	Quantifying Outcome	Expected Values for cloudy	Expected Values for sunny
Small batch	Cloudy	20%	Sales	237.5 * 20% = 47.5	=47.5-2.5 =45
			Return	(12.5) * 20% = (2.5)
	Sunny	80%	Sales	250 * 80% = 200		=200
			Return	0 * 80% = 0
Medium batch	Cloudy	20%	Sales	450 * 20% = 90	=90-22.5 =67.5
			Return	(112.5) * 20% = (22.5)
	Sunny	80%	Sales	600 * 80% = 480		=480
			Return	0 * 80% = 0
Large batch	Cloudy	20%	Sales	560 * 20% = 112	=112-96 = 16
			Return	(480) * 20% = (96)
	Sunny	80%	Sales	1260 * 80% = 908		=1008-64 =944
			Return	(80) * 80% = (64)
Payoff maximization for perfect information					67.5	944
Expected value for (perfect condition) certainty = 67.5 + 944 = 1011.5

EV's for perfect information: Extra payoff generated under certainty to that of best alternative.

EV's for perfect information

Expected value under certainty - Expected value for best alternative = 1011.5 - 960 = 51.5