Question

A vendor for the local ballpark food stand is questioning whether to stock his concession with a large or small inventory. He believes that it will depend upon the size of the crowd. He has developed a payoff matrix for the various alternatives (stocking decision) and states the nature (size of crowd). What is the answer using the criterion of minimax regret?

		PROFIT
	LARGE	AVERAGE	SMALL
ALTERNATIVES	CROWD	CROWD	CROWD
LARGE INVENTORY	$220,000	$50,000	-$2,000
SMALL INVENTORY	$90,000	$70,000	-$5,000
PROBABILITY	.20	.50	.30

Answer 1

minimax regret

LARGE INVENTORY - LARGE CROWD - REGRET = 220000-220000=0

SMALL INVENTORY - LARGE CROWD - REGRET = 220000-90000=130000

LARGE INVENTORY - AVG CROWD - REGRET = 70000-50000= 20000

SMALL INVENTORY - AVG CROWD - REGRET = 70000-70000 = 0

LARGE INVENTORY - SMALL CROWD - REGRET = -2000+2000 = 0

SMALL INVENTORY - SMALL CROWD - REGRET = -2000+5000 = 3000

From the above :

0	20000	0
130000	0	3000

Maximum From Table:

20000

130000

Minimum of these Maximum Regrets = 20000

Decision : Small Inventory