Question #1 You are a project engineer (PE) who must assist a decision maker (DM) compare five construction projects A, B, C, D, and E and choose the best one to bid on. Each project has been evaluated in terms of the following attributes: Cost x1, Time to Completion X2 and Quality Rating X3 as shown in the following table: Projects Cost(X1) Completion(x2) Quality(x3) A 10 19 B 12 15 3 20 17 2 D 14 25 4 E 15 27 5 X1 is measured in millions of dollars X2 is measured in months X3 the higher index indicates better quality (i.e., 5 is the best) a) Suppose (1) Less cost is preferred to more cost; (2) Shorter completion times are preferred to longer; and (3) Higher quality is preferred to lower quality when the other two attribute levels are held fixed. Which, if any, projects could be eliminated according to our notions of Pareto Optimality? b) The DM feels that {X2, X3} is Preferentially Independent (PI) of X1. What does this mean in plain English? c) The DM's conditional preferences in the {X2, X3} consequence space (assuming Xi is fixed) are such that: (Hint: Graph the Relationships) (19, 1) is indifferent to 25, 3) (15, 3) is indifferent to (15, 3) (17, 2) is indifferent to (20,3) (25, 4) is indifferent to (21,3) (27,5) is indifferent to (19, 3) Given this information, can you eliminate any further projects as non-contenders for the DM's consideration? d) The DM feels that each month is saved on a project of quality 3 is worth $150,000. Which project is best? Question #1 You are a project engineer (PE) who must assist a decision maker (DM) compare five construction projects A, B, C, D, and E and choose the best one to bid on. Each project has been evaluated in terms of the following attributes: Cost x1, Time to Completion X2 and Quality Rating X3 as shown in the following table: Projects Cost(X1) Completion(x2) Quality(x3) A 10 19 B 12 15 3 20 17 2 D 14 25 4 E 15 27 5 X1 is measured in millions of dollars X2 is measured in months X3 the higher index indicates better quality (i.e., 5 is the best) a) Suppose (1) Less cost is preferred to more cost; (2) Shorter completion times are preferred to longer; and (3) Higher quality is preferred to lower quality when the other two attribute levels are held fixed. Which, if any, projects could be eliminated according to our notions of Pareto Optimality? b) The DM feels that {X2, X3} is Preferentially Independent (PI) of X1. What does this mean in plain English? c) The DM's conditional preferences in the {X2, X3} consequence space (assuming Xi is fixed) are such that: (Hint: Graph the Relationships) (19, 1) is indifferent to 25, 3) (15, 3) is indifferent to (15, 3) (17, 2) is indifferent to (20,3) (25, 4) is indifferent to (21,3) (27,5) is indifferent to (19, 3) Given this information, can you eliminate any further projects as non-contenders for the DM's consideration? d) The DM feels that each month is saved on a project of quality 3 is worth $150,000. Which project is best
