Delicatessen Catering Co. provides catering services for weddings, reunions, bus

Question

Delicatessen Catering Co. provides catering services for weddings, reunions, business functions, and a variety of other social events. Delicatessen is thinking of hiring more staff to keep up with rising demand. This would require purchasing more equipment and vehicles to ensure these staff can do their jobs. Determine what choice they should make using the Hurwicz ( = 0.7 and = 0.4) and equal likelihood criteria. What are the expected values?

Decision Increased demand Decreased demand Hire staff $25,040 -$18,950 Do not hire $5,650 $4,970

Explanation / Answer

Hurwicz Principle

It stipulates that a decision maker’s view may fall somewhere between the extreme pessimism of the maximin principle and the extreme optimism of the maximax principle. This principle provides different levels of optimism or pessimism, by defining the coefficient of optimism, , which ranges from 0 to 1. An = 0 indicates extreme pessimism, while = 1 indicates extreme optimism. Hurwicz principle suggests that the decision maker must select an alternative that maximizes:

H = × (maximum payoff of strategy) + (1 ) × (minimum payoff of strategy)

Decision

Increased demand

Decreased demand

Maximum

Minimum

Average

H ( = 0.4)

H ( = 0.7)

Hire staff

$25,040

($18,950)

$25,040

($18,950)

$3,045

($1,354.0)

$11,843.0

Do not hire

$5,650

$4,970

$5,650

$4,970

$5,310

$5,242.0

$5,446.0

According to = 0.4,

H for alternative Hire = [(0.4 x $25,040) + (0.6 x -18,950)] = -$1,354

H for alternative do not Hire = [(0.4 x $5,650) + (0.6 x 4,970)] = $5,242

H ( = 0) = Maximize [-$1,354, $5,242] = $5,242

According to the Hurwicz Principle, with coefficient optimism = 0.4, the alternative of not hiring yields maximum expected value, thus Delicatessen should not hire more staff.

According to = 0.7,

H for alternative Hire = [(0.7 x $25,040) + (0.3 x -18,950)] = $11,843.0

H for alternative do not Hire = [(0.7 x $5,650) + (0.3 x 4,970)] = $5,446.0

H ( = 0) = Maximize [$11,843.0, $5,446.0] = $11,843

According to the Hurwicz Principle, with coefficient optimism = 0.7, the alternative of hiring yields maximum expected value, thus Delicatessen should hire more staff.

Equal Likelihood Principle

Laplace principle is based on a simple philosophy that if there is uncertainty about various events, then treat them as equally probable to occur, that is, each state of nature or chance event is assigned an equal probability. It is also known as equal probabilities criterion. In this assumption, the expected value or average payoff for each course of action or strategy is determined and the strategy with the highest mean value is adopted.

EV of alternative hiring = [(0.5 x $25,040) + (0.5 x -18,950)] = $3,045

EV of alternative do not Hire = [(0.5 x $5,650) + (0.5 x 4,970)] = $5,310

EV according to equal likelihood = maximize [$3,045, $5,310] = $5,310

According to the equal likelihood Principle, the alternative of not hiring yields maximum expected value, thus Delicatessen should not hire more staff.

Decision

Increased demand

Decreased demand

Maximum

Minimum

Average

H ( = 0.4)

H ( = 0.7)

Hire staff

$25,040

($18,950)

$25,040

($18,950)

$3,045

($1,354.0)

$11,843.0

Do not hire

$5,650

$4,970

$5,650

$4,970

$5,310

$5,242.0

$5,446.0

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