QM Spring2017 - TUTORIAL - Additional Problems - Chapter 3 Decision Table - SOLUTION

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Vietnam International University (VNU) HCMC INTERNATIONAL UNIVERSITY (IU) Semester 02, Academic Year 2016 - 2017 ------o0o------ Page 1 of 8 Course: Quantitative Methods for Business (BA168IU) | Lecturer: Mr. Nguyen Minh Tuan Paper Title: TUTORIAL MATERIAL 02 (Chapter 03: Decision Analysis | Part 1: Decision Table) TUTORIAL MATERIAL 02 SOLUTION TO ADDITIONAL PROBLEMS (Chapter 03: Decision Analysis | Part 01: Decision Table) PART I: DECISION TABLE PROBLEM 1: Even though independent gasoline stations have been having a difficult time, Susan Solomon has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table: SIZE OF FIRST STATION GOOD MARKET ($) FAIR MARKET ($) POOR MARKET ($) Small 50,000 20,000 10,000 Medium 80,000 30,000 20,000 Large 100,000 30,000 40,000 Very large 300,000 25,000 160,000 For example, if Susan constructs a small station and the market is good, she will realize a profit of $50,000. (a)What is the maximax decision? (b)What is the maximin decision? (c)What is the equally likely decision? (d)What is the criterion of realism decision? Use an α value of 0.8.(e)What is the minimax regret decision? (f)Given that the probabilities of good, fair, and poor market are 0.3, 0.4, and 0.3, respectively, what is the best decision based on the EMV approach? (g)What is the maximum amount that should be paid for a perfect forecast of the economy? Solution to Problem 01: SIZE OF FIRST STATION GOOD MARKET ($) FAIR MARKET ($) POOR MARKET ($) Maximum In Rows Minimum In Rows Weighted Averages Rows Averages EMV Small 50,000 20,000 50,000 -10,000 38,000 20,000 20,000 Medium 80,000 30,000 80,000 -20,000 60,000 30,000 30,000 Large 100,000 30,000 100,000 -40,000 72,000 30,000 30,000 Very large 300,000 25,000 300,000 -160,000 208,000 55,000 52,000 Probability 0.3 0.4 0.3 (a)The maximax decision is to construct a very large size station; (b)The maximin decision is to construct a small size station; (c)The equally likely decision is to construct a very large size station; (d)The criterion of realism decision is to construct a very large size station; Opportunity Loss Table:
Vietnam International University (VNU) HCMC INTERNATIONAL UNIVERSITY (IU) Semester 02, Academic Year 2016 - 2017 ------o0o------ Page 2 of 8 Course: Quantitative Methods for Business (BA168IU) | Lecturer: Mr. Nguyen Minh Tuan Paper Title: TUTORIAL MATERIAL 02 (Chapter 03: Decision Analysis | Part 1: Decision Table) SIZE OF FIRST STATION GOOD MARKET ($) FAIR MARKET ($) POOR MARKET ($) Maximum In Rows Small 250,000 10,000 0 250,000 Medium 220,000 0 10,000 220,000 Large 200,000 0 30,000 200,000 Very large 0 5,000 150,000 150,000

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