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EMGT 501 HW Solutions Chapter 12 - SELF TEST 9 Chapter 12 - SELF TEST 18 12-9 a. b. c. d. e. f. 12-18 a. b. e. Chapter 14 Decision Analysis Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis

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EMGT 501 HW Solutions Chapter 12 - SELF TEST 9 Chapter 12 - SELF TEST 18

12-9 a. b. c. d.

e. f.

12-18 a. b.

e.

Chapter 14 Decision Analysis Problem Formulation Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information Computing Branch Probabilities

Problem Formulation A choice issue is portrayed by choice options, conditions of nature, and coming about adjustments. The choice options are the distinctive conceivable systems the leader can utilize. The conditions of nature allude to future occasions, not under the choice's control producer, which may happen. Conditions of nature ought to be characterized so they are totally unrelated and on the whole comprehensive.

Influence Diagrams An impact chart is a graphical gadget demonstrating the connections among the choices, the chance occasions, and the results. Squares or rectangles delineate choice hubs. Circles or ovals portray chance hubs. Jewels portray result hubs. Lines or circular segments interfacing the hubs demonstrate the course of impact.

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 settlements for all blends of choice options and conditions of nature is a result table . Adjustments can be communicated as far as benefit , cost , time , separation or whatever other fitting measure.

Decision Trees A choice tree is an ordered representation of the choice issue. Every choice tree has two sorts of hubs; round hubs compare to the conditions of nature while square hubs relate to the choice choices.

The branches leaving every round hub speak to the diverse conditions of nature while the branches leaving every square hub speak to the distinctive choice choices. Toward the end of every appendage of a tree are the adjustments accomplished from the arrangement of branches making up that appendage.

Decision Making without Probabilities Three normally utilized criteria for choice making when likelihood data in regards to the states' probability of nature is occupied are: the hopeful approach the moderate approach the minimax misgiving methodology.

Optimistic Approach The idealistic methodology would be utilized by a hopeful leader. The choice with the biggest conceivable result is picked. On the off chance that the result table was as far as expenses, the choice with the least cost would be picked.

Conservative Approach The traditionalist methodology would be utilized by a preservationist leader. For every choice the base result is recorded and afterward the choice comparing to the most extreme of these base settlements is chosen. (Thus, the base conceivable result is boosted .) If the result was as far as expenses, the most extreme expenses would be resolved for every choice and afterward the choice relating to the base of these greatest expenses is chosen. (Thus, the most extreme conceivable expense is minimized .)

Minimax Regret Approach The minimax misgiving methodology requires the development of a misgiving table or an open door misfortune table . This is finished by ascertaining for every condition of nature the contrast between every result and the biggest result for that condition of nature. At that point, utilizing this misgiving table, the most extreme misgiving for every conceivable choice is recorded. The choice picked is the one relating to the most extreme's base second thoughts .

Example Consider the accompanying issue with three choice options 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

Example: Optimistic Approach An idealistic chief would utilize the hopeful (maximax) approach. We pick the choice that has the biggest single worth in the result table. Most extreme Decision Payoff d 1 4 d 2 3 d 3 5 Maximaxdecision Maximax result

Example: Optimistic Approach Formula Spreadsheet

Example: Optimistic Approach Solution Spreadsheet

Example: Conservative Approach A moderate leader would utilize the preservationist (maximin) approach. List the base result for every choice. Pick the choice with the most extreme of these base adjustments. Least Decision Payoff d 1 - 2 d 2 - 1 d 3 - 3 Maximin choice Maximin result

Example: Conservative Approach Formula Spreadsheet

Example: Conservative Approach Solution Spreadsheet

Example: Minimax Regret Approach For the minimax subtracting so as to misgive methodology, first process a misgiving table every result in a section from the biggest result in that segment. In this illustration, in the first section subtract 4, 0, and 1 from 4; and so forth. The subsequent misgiving table is: s 1 s 2 s 3 d 1 0 1 d 2 4 2 0 d 3 0 2

Example: Minimax Regret Approach For every choice rundown the greatest misgiving. Pick the choice with the base of these qualities. Most extreme Decision Regret d 1 d 2 4 d 3 Minimax choice Minimax lament

Example: Minimax Regret Approach Formula Spreadsheet

Example: Minimax Regret Approach Solution Spreadsheet

Decision Making with Probabilities Expected Value Approach If probabilistic data in regards to the conditions of nature is accessible, one may utilize the normal quality (EV) approach . Here the normal return for every choice is figured by summing the result's results under every condition of nature and the likelihood of the particular 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 aggregate of weighted adjustments 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 estimation. 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

Expected Value Approach Formula Spreadsheet

Expected Value Approach Solution Spreadsheet

Expected Value of Perfect Information Frequently data is accessible which can enhance the likelihood gauges for the conditions of nature. The normal estimation of impeccable data (EVPI) is the increment in the normal benefit that would come about if one knew with conviction which condition of nature would happen. The EVPI gives an upper bound on the normal estimation of any specimen or review data .

Expected Value of Perfect Information EVPI Calculation Step 1: Determine the ideal return relating to every condition of nature. Step 2: Compute the normal estimation of these ideal returns. Step 3: Subtract the EV of the ideal choice from the sum decided in step (2).

Expected Value of Perfect Information Calculate the normal worth for the ideal result for every condition of nature and subtract the EV of the ideal choice. EVPI= .4(10,000) + .2(18,000) + .4(21,000) - 14,000 = $2,000

Expected Value of Perfect Information Spreadsheet

Risk Analysis Risk examination helps the chief perceive the distinction between: the normal estimation of a choice option, and the result that may really happen The danger profile for a choice option demonstrates the conceivable adjustments for the choice option alongside their related probabilities.

Risk Profile Model C Decision Alternative .50 .40 .30 Probability .20 .10 5 10 15 20 25 Profit ($thousands)

Sensitivity Analysis Sensitivity investigation can be utilized to decide how changes to the accompanying inputs influence the suggested choice option: prob