A shop that sells a variety of fitness apparel needs to place an order of a part

Question

A shop that sells a variety of fitness apparel needs to place an order of a particular brand of swimsuits for the upcoming summer season. The order volumes being considered are large and small, and the demand levels for the swim season for this brand can be strong, moderate, or weak The accompanying decision table shows the payoffs for all combinations of order sizes and demand levels. Complete parts a through e below. a. Choose the best order size or swimsuits using the maximax criterion. The is the best alternative based on the maximax criterion because its payoff is the of all the actions. b. Choose the best order size of swimsuits using the maximin criterion. The is the best alternative based on the maximin criterion because its payoff is the of all the actions. c. Choose the best order size of swimsuits using the equally likely criterion. The is the best alternative based on the equally likely criterion because its payoff is the of all the actions. d. Choose the best order size of swimsuits using the minimax regret criterion. The is the best alternative based on the minimax regret criterion because its payoff is the of all the actions. e. Choose the best order size of swimsuits using the Hurwicz criterion with alpha = 0.3. The is the best alternative based on this Hurwicz criterion because its weighted average. $, is the of all the actions.

Explanation / Answer

Solution

The given pay-off figures alongwith certain computations are presented in the table below:

Decision

Alternative

Pay –off ($) under States of Nature

Row

Max

Row

Min

Demand

Strong

Moderate

Weak

Large order

11000

4000

- 9000

11000

- 9000

Small order

6000

1000

- 2000

6000

- 2000

Now, to work out solution,

Part (a)

Since maximum of row max = 10000, decision under maxi-maxi criterion is

‘large order’ ANSWER

Part (b)

Since maximum of row min = - 2000, decision under maxi-min criterion is

‘small order’ ANSWER

Part (c)

Under equally likely criterion, each demand state has an equal probability of 1/3.

Hence, EMV for Large order = (10000 + 4000 - 9000)/3 = 2000 and EMV for Small order = (6000 + 1000 - 2000)/3

= 1667.

Since 2000 > 1667, decision is ‘large order’ ANSWER

.Part (d)

Regret for a decision alternative under a particular state of nature = maximum pay-off for the decision alternative - pay-off for the particular state.

Regret Table is given below:

Decision

Alternative

Regret ($) under States of Nature

Row

max

Demand

Strong

Moderate

Weak

Large order

0

7000

20000

20000

Small order

0

5000

8000

8000

Since 8000 < 20000, decision under mini-max regret criterion is

‘small order’ ANSWER

Decision

Alternative

Pay –off ($) under States of Nature

Row

Max

Row

Min

Demand

Strong

Moderate

Weak

Large order

11000

4000

- 9000

11000

- 9000

Small order

6000

1000

- 2000

6000

- 2000

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