MGMT 2012- Introduction to Quantitative MethodsGroup Assignment -Graded Assignment Two S1- 2016-17- Due November 26th - 10 percent Final Grade Students should note that this assignment should submitted in a Word document. Question 1A A CEO of a multihospital system is planning to expand operations into various states. It will take several years to get certificate of need (CON) approvals so that the new facilities can be constructed. The eventual cost (in millions of dollars) of building a facility will differ among states, depending upon finances, labor, and the economic and political climate. An outside consulting firm estimated the costs for the new facilities as based on declining, similar, or improving economies, and the associated probabilities as shown in the Table below. Decision alternatives Declining Same Kentucky 22.00 19.00 Improving 15.00 Maryland 19.00 18.50 18.00 North carolina 19.50 17.00 15.50 Tennesee 23.00 17.00 14.00 Virginia 25.00 21.00 13.00 (a) Which alternative should the firm choose under the maximax criterion? (1 mark) (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (2 marks) (d) Which option should the firm choose with the Hurwicz criterion with = 0.4? (2 marks) (e) Using a minimax regret approach, what alternative should the firm choose? (4 marks) (f) Economists have assigned probabilities of 0.25, 0.40, and 0.35 to the possible economic climate of (1 mark) declining, same and improving respectively. Using expected monetary values, what option should be chosen and what is that optimal expected value? (4 marks) (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (3 marks) (h) Use the alternative method to verify EVPI (3 marks) Question 1B Assume now that the pay offs are profits answer the following: (a) (b) (c) (d) (e) (f) g) h) Using an optimistic approach (maximax), which option would you choose? 1 mark Using a pessimistic approach (maximin), which option would you choose?1 mark If you are a LaPlace decision maker, which option would you choose? 2 marks If you are a Hurwicz decision maker, which option would you choose with = 0.4?1 mark Using a minimax regret approach, which option would you choose? 4 marks Using the same probabilities of 0.25, 0.4, and 0.35 for possible economic climates respectively, which decision alternative will maximise the expected profit? What is the expected annual profit associated with that recommendation? 4 marks What is the most the firm should be willing to pay to obtain further (perfect) information (EVPI)? 3 marks Use the alternative method to verify EVPI (3 marks Question 2 CWD Inc is considering entering the snowplowing business for the coming winter season. CWD can purchase either a snowplow blade attachment for the station's pick-up truck or a new heavy-duty snowplow truck. CWD has analyzed the situation and believes that either alternative would be a profitable investment if the snowfall is heavy. Smaller profits would result if the snowfall is moderate, and losses would result if the snowfall is light. The following profits have been determined. CWD is willing to pay $50 for additional information on the weather which can be normal or unreasonable. Heavy, s1 Moderate, s2 Light, s3 Blade Attachment, d1 3500 1000 -1500 New Snowplow, d2 7000 2000 -9000 0.4 0.3 0.3 Decision Alternatives Probability Conditional Probability For A Given State of Nature Test Results Heavy Moderate Light Normal 0.7 0.8 0.9 Unreasonable 0.3 0.2 0.1 That is P (N/H) =0.7; P (N/M) =0.8, P(N/L) =0.9, P (U/H) =0.3; P (U/M) =0.2, P(U/L) =0.1 After you have computed the revised probabilities round to two decimal places a) Construct the appropriate decision tree to help CWD make the appropriate decisions. This tree must be constructed in logical order with labels and net payoffs ( 5 marks ) It also includes the revised probabilities (5 marks) (10 marks) b) Fold back the decision tree (5 marks) to determine the best strategy for CWD; you must state this strategy (1 mark). What is the final expected profit?( 1 mark)(7 marks) c) What is the expected value of sample information(EVSI)- the most that should be paid to seismic testing firm for the test?( 1 mark) d) Calculate the expected value of perfect information (EVPI)- the most that should be paid to an expert for perfect prediction of the uncertain outcomes.(1 mark) e) What is the efficiency of sample information?(1 mark) Question 3 Data collected on patient days in a hospital over the past 12 months are shown in the following table. a) Using a weight of .50 for the most recent observation, .30 for the second most recent, and .20 for third most recent, compute a three-month weighted moving average for the time series. Compute the MAD, MSE and MPE for this method.( six marks) b) Use exponential smoothing with a smoothing constant of 0.30 to forecast the patient days. Assume that last period's forecast for month 1 is equal to actual to begin the procedure. Which method do you think is best? Is this an improvement over the weighted average- use MAD only ( Six marks) c) Use regression analysis to estimate the line of best fit -use the manual method with the formulas shown below.( eight marks) Question 4 Consider the following project where times are in weeks Activity Times and Predecessors Activity Immediate predecessor Optimistic Time (a) Most Likely Time (m) Pessimistic time (b) Variance A - 6 8 9 .25 B - 9 12 15 1.00 C A,B 4 6 11 1.36 D B 3 4.5 6 .25 E A 1 2 3 .11 F C 1 3 5 .44 G E,F 5 6 10 .69 H D,F 2 3 4 .11 I G,H 1 1 1 .00 J I 2 3 7 .69 When decimal places are not integer, you are not permitted to round off to integers. Use two decimal places for non-integer times. Required a) Draw the activity net work for this problem (6 marks) b) Determines the expected times of each activity. ( 1 mark) c) Determines the activity schedule(ES, EF,LS, and LF ) as well as slack.( optional: It is recommended that you show the results in a table) 7 marks d) Determines and state the critical path for this project. This must be based on you work in c) and not by inspection.(1 marks) e) What are the expected times and variance of the project?(2 marks) f) What is the probability the project will take between 30 and 32 weeks?(3 marks