Question

5.8. An orange grower in Florida faces a dilemma. The hw zemperature weather forecast is for cold weather, and there is a 50% chance that the tonight will be coid enough to freeze and destroy his entire is worth some $50,000. He can take two possibie actions to try to alle- t the temperature drops. Fist, he could set burners in the viate his loss FIGURE 5.26 Cost-to-loss ratio problem. Take No Action a -p) FIGURE 5.27 More general version of the cost- Take Procective to-loss probiem. Aczicn (1-4) Take No Action orchard; this would cost $5,000, but he could still expect to incur dam- age of approximately $15,000 to $20,000. Second, he couid set up sprinklers to spray the trees. If the temperature drops, the water would freeze on the fruit and provide some insulation. This method is cheaper ($2,000), bur less effective. With the sprinklers he could expect to incur as much as $25,000 to $30,000 of the loss with no protective action.

Assume that the grower's loss ncurred with the burners would be $17,500 and that the loass incurred with the sprinklers would be $27,500. Find the EVPI using the payoff table approach.

Answer 1

Payoff table is following:

	Cold	No Cold
Probability	0.5	0.5
Take no action	-50000	0
Set up burners	-22500	-5000
Set up sprinklers	-29500	-2000

Note that for burners and sprinklers options, cost of setting up is added to the loss, in the above payoff table.

Expected Value (EV) of Take no action = -50000*0.5+0*0.5 = $ -25000

Expected Value (EV) of Set up burners = -22500*0.5-5000*0.5 = $ -13750

Expected Value (EV) of Set up sprinklers = -29500*0.5-2000*0.5 = $ -15750

Maximum EV is -13750 associated with Set up burners

Therefore, Expected Value without Perfect Information, EVw/oPI = $ -13750

Expected Value with Perfect Information, EVwPI = 0.5*MAX(-50000, -22500, -29500) + 0.5*MAX(0, -5000, -2000)

= $ -11250

EVPI = EVwPI - EVw/oPI

= -11250 - (-13750)

= $ 2500