2. Jodi wants to lease a new car and start a part time business to give people c

Question

2. Jodi wants to lease a new car and start a part time business to give people car rides. She has contacted three automobile dealers for pricing information. Each dealer offered Jodi a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The three dealers provided the details about the monthly lease cost, the mileage allowance, and the cost for additional miles.

Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 15,000 miles per year, or 20,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each option are given below:

Dealer       10000 Miles             15000 Miles       20000 Miles

   A                 $10000                  $10000               $ 8000

   B                 $ 7500                     $11000               $10500

   C                 $ 8500                      $ 9000                $ 8800

Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria.

a. Maximax

b. Maximin

c. Equal likelihood

d. Minimax regret criterion.

Explanation / Answer

Maximax:

This criterion says that we select the alternative which has highest payoff available.

Here, since the maximum payoff available is 11000 from dealer B for 15000 miles we will lease from Dealer B since the payoff is highest.

Maximin:

Here we look at the minimum payoff for each dealer and select the highest pay off among them.

Dealer A minimum payoff = 8000 for 20000 miles.

Dealer B minimum payoff = 7500 for 10000 miles.

Dealer C minimum payoff = 8500 for 10000 miles.

Highest among these is 8500 payoff, hence we select Dealer C in Maximin criteria.

Equal likelihood:

Assuming equal probability for driving 10000 miles, 15000 miles and 20000 miles per year we calculate the expected profit for leasing from all three dealers.

Hence, probability = 1/3

dealerA:

expected profit = 10000*1/3 + 10000*1/3 + 8000*1/3

= 3333.33 + 3333.33 + 2666.67

= 9333.33

Dealer A expected profit = $9333.33

Dealer B:

Expected profit = 7500*1/3 + 11000*1/3 + 10500*1/3

= 2500 + 3666.67 + 3500

= 9666.67

Dealer B expected profit = $9666.67

Dealer C:

Expected profit = 8500*1/3 + 9000*1/3 + 8800*1/3

= 2833.33 + 3000 + 2933.33

= 8766.66

Dealer C expected profit = $8766.66

Here we find that maximum expected payoff is for Dealer B with $9666.67

Hence we choose Dealer B in equal likelihood criteria.

Minimax regret:

This criteria minimizes the maximum regret.

Here we find the miximum profit for each decision and subtract that with the other payoffs in the same decision to find the regret in each decision. Then select the maximum regret for each decision. Once we have the miximum regret we select the regret which is least among them.

Here for dealer A: maximum profit = 10000 for 10000 miles and 15000 miles.

regret for 20000 miles = 10000 - 8000 = 2000

regret for 10000 and 15000 miles = 10000 - 10000 = 0

the regret is tabulated as follows for all decisions:

Dealer A maximum regret = 2000

Dealer B maximum regret = 3500

Dealer C maximum regret = 500

Minimum of these is 500 for Dealer C.

Hence we choose Dealer C for this criterion.

Dealer 10000 miles 15000 miles 20000 miles A 0 0 2000 B 3500 0 500 C 500 0 200

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