Question

A manager needs to hire short-term employees to meet production demands. The manager would like to hire one of three possible short-term workers. Ten hours are demanded with 50% probability, 20 hours are demanded with 30% probability, and 30 hours are demanded with 20% probability. The table below represents the alternatives and possible states of nature.

	States of Nature
	(Worker hours demanded)
Alternatives	10 hr total pay	20 hr total pay	30 hr total pay
Worker 1	$1,000	$1,800	$2,400
Worker 2	$900	$1,800	$2,500
Worker 3	$950	$1,750	$2,550

What is the expected value of perfect information? [a]

Do not use $.

Answer 1

EXPECTED VALUE 10HOURS 20HOURS 30HOURS Expected value WORKER -1 1000*0.5 1800*0.30 2400*.20 500 540 480 1520 WORKER -2 900*0.5 1800*0.30 2500*0.20 450 540 480 1470 WORKER -3 950*0.5 1750*.30 2550*.20 475 525 510 1510 NOTE EXPECTED VALUE = TOTAL PAY * PROBABLITY FOR EACH ALTERNATIVE SINCE THE EXPECTED VALUE FOR WORKER -2 IS LESS. THE MANAGER WOULD HIRE WORKER -2 i.e 1470 EXPECTED VALUE FOR PERFECT INFORMATION maximum payment for additional information EVPI= EVWPI -EVWOPI ( EVWPI- Expected value with perfect information) ( EVWOPI- Expected value withouth perfect information) EXPECTED VALUE FOR PERFECT INFORMATION 10HOURS 20HOURS 30HOURS WORKER -1 1000 1800 2400 WORKER -2 900 1800 2500 WORKER -3 950 1750 2550 450 525 480 1455 ( total) (900*0.5) (1750*0.3) (2440*0.2) EXPECTED VALUE FOR PERFECT INFORMATION EVPI= EVWPI -EVWOPI ( EVWPI- Expected value with perfect information) ( EVWOPI- Expected value withouth perfect information) 1455 -1470 -15 { FOR COST EVWPI < EVWOPI} EXPECTED VALUE FOR PERFECT INFORMATION 15