Choice Examination.

Choice ANALYSIS

Decision Analysis with probabilities Decision Making without Probabilities Decision Making with Probabilities

Payoff Tables The outcome coming about because of a particular blend of a choice option and a condition of nature is a result . A table indicating adjustments for all blends of choice options and conditions of nature is a result table . Settlements can be communicated as far as benefit , cost , time , separation or some other proper measure.

Example Consider the accompanying issue with three choice choices and three conditions of nature with the accompanying result table speaking to benefits: States of Nature s 1 s 2 s 3 d 1 4 - 2 Decisions d 2 0 3 - 1 d 3 1 5 - 3

Decision Making with Probabilities Expected Value Approach If probabilistic data in regards to the conditions of nature is accessible, one may utilize the normal worth (EV) approach . Here the normal return for every choice is ascertained by summing the result\'s results under every condition of nature and the likelihood of the individual condition of nature happening. The choice yielding the best expected return is picked.

Expected Value of a Decision Alternative The normal estimation of a choice option is the whole of weighted settlements for the choice option. The normal worth (EV) of choice option d i is characterized as: where: N = the quantity of conditions of nature P ( s j ) = the likelihood of condition of nature s j V ij = the result comparing to choice elective d i and condition of nature s j

Example: Burger Prince Burger Prince Restaurant is considering opening another eatery on Main Street. It has three different models, each with an alternate seating limit. Burger Prince estimates that the normal number of customers every hour will be 80, 100, or 120. The result table for the three models is on the following slide.

Payoff Table Average Number of Customers Per Hour s 1 = 80 s 2 = 100 s 3 = 120 Model A $10,000 $15,000 $14,000 Model B $ 8,000 $18,000 $12,000 Model C $ 6,000 $16,000 $21,000

Expected Value Approach Calculate the normal quality for every choice. The choice tree on the following slide can help with this figuring. Here d 1 , d 2 , d 3 speak to the choice options of models A, B, C, and s 1 , s 2 , s 3 speak to the conditions of nature of 80, 100, and 120.

Decision Tree Payoffs .4 s 1 10,000 s .2 15,000 s 3 .4 d 1 14,000 .4 s 1 8,000 d 2 1 .2 3 s 2 18,000 s 3 d 3 .4 12,000 .4 s 1 6,000 4 s .2 16,000 s 3 .4 21,000

Expected Value for Each Decision Choose the model with biggest EV, Model C. EMV = .4(10,000) + .2(15,000) + .4(14,000) = $12,600 d 1 2 Model An EMV = .4(8,000) + .2(18,000) + .4(12,000) = $11,600 d 2 Model B 1 3 d 3 EMV = .4(6,000) + .2(16,000) + .4(21,000) = $14,000 Model C 4