Question:
Red Fish Blue Fish is an outdoor waterfront eatery in Victoria's Inner Harbour that serves a variety of daily seafood dishes. Each day, Barry Schmelly, the owner of Red Fish Blue Fish must decide how many salmon to purchase from the local fisherman. Salmon costs him $4.45 per pound and is sold at an average price of $16.95 per pound (across the many salmon dishes he serves each day). To maintain his reputation for fresh seafood dishes, any leftover salmon is sold to a local cannery for $2.50 per pound. Barry is also aware that any unmet customer demand for fresh salmon will cost him as patrons will go to another eatery on the Harbour to eat fresh salmon and may potentially impact future sales. He quantifies lost sales and damaged customer goodwill to be $5.00 per pound whenever demand for salmon exceeds his supply. Historically, his daily demand for salmon is:
Daily Demand (in pounds) 20 25 30 35 40 45 50 55 60 65 70 75
Probability 0.02 0.05 0.06 0.10 0.12 0.13 0.17 0.13 0.09 0.06 0.04 0.03
Help Barry determine how many pounds of salmon to order each day by answering the questions below. Assume the demand/costing information provided is accurate and that Barry can order exact salmon weights represented in the table above.
a. Construct a payoff matrix.
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 EMV decision rule?
e. What decision should be made according to the minimax regret decision rule?
f. What decision should be made according to the EOL decision rule?
g. How much should the Barry be willing to pay to obtain a demand forecast that is 100% accurate?
h. Which decision rule would you recommend for Barry to use? Provide a clear explanation why you are recommending a particular decision rule.