1. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory [1] Dr: Galal I. Elabd Business Administration Department Alexandria University E-mail : galalelabd@yahoo.com 1 Decision Theory

2. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Introduction :- Decision theory is a popular field of study which provides an insightful framework for statistically analyzing decision characterized by uncertain environment. Decision theory includes different decision tools, that help decision makers in solving problems. Decision Theory 2

3. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Some types tools in decision theory [1] – State of risk 1-1 : Expected Monetary Value. 1-2 : Value of Perfect Information. 1-3 : Decision Tree. 2-1 : Maximax Criteria. [2] – State of risk 2-2 : Maximini Criteria. 3-1 : Equally likely Criteria. Decision Theory 3

4. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 4 Fundamentals of Decision Theory Regardless of the complexity of a decision or sophistication of the technique used to analyze the decision, all decision makers faced with alternatives and state of nature. The following notation will be used in explaining decision theory :- 1-Terms: a)- Alternative : A Course of action or strategy that may be chosen by a decision maker ( for example :go or not go to the lecture of QBA). b)- State of Nature : A Situation over which the decision maker has little or no control (for example: weather tomorrow).

5. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 5 2-Symbles used in decision tree: a)- A decision node from which one of several alternatives may be selected. b)- A state of nature node out of which one state of nature will occur.

6. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 6 Example(1-1) XYZ company is investigating the possibility of producing and marketing hi Tec computers. Undertaking this project would require the construction of either a large or small manufacturing plant. The market of hi Tec computers could be either favorable or unfavorable. XYZ co., has the option of not developing the new product line at all. The following table indicats profits in case market situations. [1-1] Expected Value [1]-Decision Tools Under Risk

7. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 7 States of Nature Alternatives UnfavorableFavorable $-180000$200000Large plant $-20000$100000Small plant $0 Do nothing 0.60.4 Payoff table

8. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 8 Required 1-Determine the expected value of each alternative and the optimal.? 2-What the cost of perfect information.? Solution Expected value of an alternative is sum of profit or cost in each state weighted by probabilities

9. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 9 E.M.V Of large plant = 200000 x 0.6 + (180000) x 0.4 = $ 48000 E.M.V Of Small plant = 100000 x 0.6 + (20000) x 0.4 =$ 52000 E.M.V Of Small plant = 0 x0.6 + 0 x 0.4 = $0

10. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 10 Optimal Alternative is to construct a small plant which maximize profit of XYZ Co.,

11. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 11 [2] Value of a Perfect Information VPI EVPI is the sum of the better alternative in each state of nature weighted by its probability. 1)- compute expected value of perfect information. EVPI = $200000 x 0.6 + $0 x 0.4 = $120000

12. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 12 VPI = EVPI – EMV = $120000 - $ 52000 = $70000 2)- Compute the Value of Perfect Information - VPI. The maximum Value of Perfect Information is $ 70000.

13. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 13 [3] Decision Tree Favorable 0.6 Unfavorable 0.4 Favorable 0.6 Unfavorable 0.4 $200000 $-180000 $100000 $-20000 $0 Large plant Small plant Do nothing

14. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 14 [2]-Decision Tools Under Uncertainty [2-1] Maximax [2-2] Maximax This criterion finds an alternative that maximize The maximum outcome for every alternative. a)- find the maximum outcome within every alternative. b)- pick the alternative with the maximum number. This criterion finds an alternative that maximize The minimum outcome for every alternative. a)- find the minimum outcome within every alternative. b)- pick the alternative with the maximum number.

15. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 15 States of Nature Alternatives UnfavorableFavorable $-180000$200000Large plant $-20000$100000Small plant $0 Do nothing [2-3] Maximax This criterion finds an alternative with the highest average outcome. a)- Calculate the average outcome for in every alternative. b)- pick the alternative with the maximum number. Example(1-2)

16. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 16 Required 1-find the optimal alternative according to Maximax.? 3-find the optimal alternative according to equally likely.? 2-find the optimal alternative according to Maximini.? Solution Row Average Minimum In Row Maximum In Row State of Nature Alternatives UnfavorableFavorable $10000$-180000$200000$-180000$200000Large Plant $40000$-20000$100000$-20000$100000Small Plant $0 Do Nothing

17. Course Title: Qantitative Business Analysis - Dr:Galal I. Elabd http://Khobaraa.tripod.com Decision Theory 17 My best wishes for you Next week will meet again