IE383_Assignment4_sol

IE383_Assignment4_sol - IE 383 Assignment 4 solution Some...

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IE 383 Assignment 4 solution Some steps are omitted, but you should show your steps in your homework solutions. Problem 1 a) This is a minimax problem w/o consideration of travel frequency. Because we are required to solve this problem graphically, we should use diamond method and we can use the following formula to double check our graphical solution but not substitute for it. The graph is omitted. X Y X + Y Y - X Main office 50 10 60 -40 Nurse room 55 45 100 -10 Doctor room 35 45 80 10 Supplies room 30 25 55 -5 File room 75 25 100 -50 C1 = min (x i + y i ) 55 C2 = max (x i + y i ) 100 C3 = min (-x i + y i ) -50 C4 = max (-x i + y i ) 10 C5 = max (C2-C1,C4-C3) 60 X Y Point 1 52.5 32.5 Point 2 45 25 Optimal point is any point on the line connected by the points 1 & 2. b) Maximum travel distance = C5/2 = 30 or you can solve it from the graph. c) This is a minisum problem that utilizes rectilinear distance w/ consideration of travel frequency (weight). We can solve the problem by using median condition method. X Y W Main office 50 10 25 Nurse room 55 45 35 Doctor room 35 45 30 Supplies room 30 25 12 File room 75 25 15 Sum 117
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Sum of W= 117 Sum of W/2 = 58.5 X W Cul W 30 12 12 35 30 42 50 25 67 55 35 102 75 25 127 Y W Cul W 10 25 25 25 27 52 45 65 117 Therefore the optimal point is at (50, 45)
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