Question 1:
Harry R.M. Pitts, the Director of Legal of Council of Vancouver, will have to make a number of tough decisions in the upcoming fiscal year due to the Federal government's austerity measures to cut spending across all provincial government agencies. The legal agency he oversees must implement cost cutting programs during the upcoming fiscal year by modifying either personnel or professional work practices. The director has identified 3 acceptable alternatives to deal with the cost cutting measures. One is to reassign present staff members to new duties, another is to let go (i.e., fire) several staff members, and the third is to redesign current work practices. An unknown factor is the caseload for the upcoming year, which will directly impact the amount of savings to the agency.
Harvey estimates that if he reassigns staff, the savings to the agency will be $135, $95 or $35 (in thousands of dollars respectively) depending on the upcoming caseload being "moderate", "high" or "very high". Likewise, if he fires legal staff members, the additional savings to the agency will be $90,000 regardless of the variation in caseload in the upcoming year. And lastly, if he redesigns the current work practices, the additional savings/costs to the agency will be $125, $100 or -$15 (in thousands of dollars respectively) depending on the upcoming caseload being "moderate", "high" or "very high".
Harvey has estimated caseload probabilities for the upcoming year to be 0.40 for "moderate", 0.40 for "high" and 0.20 for "very high".
Using paper and pencil only, neatly create the Payoff Table and determine Harvey's optimal decision using the following decision criteria:
a) Maximax
b) Maximin
c) Expected Monetary Value
d) Minimax Regret
e) Expected Opportunity Loss
Question 2:
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.