# solution

Romeo head, owner of Wanky, Sweet Shoes must place orders with an athletic shoe manufacturer 6 months prior to the time the shoes go on the shelf. Specifically, Ravi must decide on October 1st how many pairs of the manufacturerâ€™s newest â€œMud Puppyâ€ model to order for sale during the upcoming 2022 spring/summer season. This popular model costs the store \$88. per pair. Furthermore, each pair can be sold to customers at \$175 per pair. Any pairs unsold at the end of the summer season will be sold in a closeout sale next fall for \$74 per pair. The probability distribution of consumer demand for these shoes during the upcoming season has been estimated as follows:
Demand Probability
140 0.05
165 0.23
190 0.35
215 0.31
240 0.06
Romeo also knows from experience that if their stores are stocked out (i.e., no more inventory) and the customer wants it, he will lose business from other related products because customers will shop at his competitors in the future and probably never return. He quantifies lost sales to be valued at \$33.00 per pair whenever customer demand for this shoe exceeds his supply.

Help Romeo determine the right number of pairs of Mud Puppies to order for the upcoming year by answering the questions below. The manufacturer will take orders only for multiples of 10. Assuming the demand and costing information above is accurate, answer the following questions* by developing a spreadsheet model using Excel (DO NOT use paper and pencil for this question):
Construct a payoff matrix.
a) What decision should be made according to the EMV decision rule?
b) What decision should be made according to the maximax decision rule?
c) What decision should be made according to the maximin decision rule?
d) What decision should be made according to the minimax regret decision rule?
e) What decision should be made according to the EOL decision rule?
f) What is the very most that Romeo should be willing to pay to obtain a forecast of customer demand that is 100% accurate?
g) Which decision rule would you recommend Romeo use? Provide a clear explanation why you are recommending a particular decision rule.

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