Module9 Handouts

Module9 Handouts - 8/13/2010...

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8/13/2010 1 Transportation Problem Supply Less than Demand Cleveland i=1 5000 Bedford i=2 5000 Boston j=1 6000 2 3 6 Chicago j=2 4000 York i=3 2500 St Louis j=3 2000 Lexington j=4 1500 2 5 4 5 Transportation Problem Cleveland i=1 5000 Bedford i=2 5000 Boston j=1 6000 2 3 6 Chicago j=2 4000 York i=3 2500 St Louis j=3 2000 Lexington j=4 1500 2 5 4 5 1000 Dummy i=4 Supply 0 0 0 0 Work Assignment Problem Worker Project/Client 123 1 Brya 10 h 15 h 9h Bryan 10 hr 15 hr 9 hr 2 Rachel 9 hr 18 hr 5 hr 3 John 6 hr 14 hr 3 hr
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8/13/2010 2 Transportation Representation of Work Assignment Problem 1:Bryan 1 Project 10 9 15 1 1 1:Rachel 1:John 1 Project 1 Project 6 18 9 5 3 14 3 2 3 2 Supply =1 Demand = 1 Formulation of Work Assignment Problem Formulation/Solution of Work Assignment Problem 11 12 13 21 22 23 31 32 33 11 12 13 21 22 23 31 32 33 10 15 9 9 18 5 6 14 3 . . .1 1 .2 1 .3 1 Min X X X X X X X X X st CX X X ++ + + ++≤ ++ ≤ Could be = 1 if # workers = # of jobs but “ ” if # workers exceed number of jobs. 11 21 31 12 22 32 13 23 33 .4 1 .5 1 .6 1 CX X X CX X X X X ++= Solution: X 12 =1, X 23 =1, X 31 =1 Cost/Time =15+5+6=26
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8/13/2010 3 Transportation Representation of Work Assignment Problem More Workers than Projects 1:Bryan 1:Rachel 1 Project 1 Project 10 9 15 18 9 2 1 2 1 Supply =1 Demand = 1 1:John 1 Project 6 5 3 14 3 3 1:Bonnie 5 12 4 4 Objective MIN 10X11+15X12+9X13+9X21+18X22+5X23+6X31+14X32+3X33+5X41+12X42+4X43 S.T . 1) 1X11+1X12+1X13<1 2) 1X21+1X22+1X23<1 3) 1X31+1X32+1X33<1 4) 1X41+1X42+1X43<1 5) 1X11+1X21+1X31+1X41=1 6) 1X12+1X22+1X32+1X42=1 7) 1X13+1X23+1X33+1X43=1 Solution to Modified Assignment Problem Objective Function Value = 23.000 Variable Value Reduced Costs X11 0.000 2.000 X12 0.000 0.000 X13 0.000 4.000 X21 0.000 1.000 X22 0.000 3.000 X23 1.000 0.000 X31 1.000 0.000 X32 0.000 1.000 X33 0.000 0.000 X41 0.000 0.000 X42 1.000 0.000 X43 0.000 2.000 Shortest Route Problem 7 7 5 3 1 2 9 3 5 4 6 2 Supply =1 Demand =1 6 4 3 3 18 X 25 = 1 if shortest route includes arc from 2 to 5, 0 if not. Node 1 is the origin node Node 2 is the destination node All other nodes are transshipment nodes. Numbers above arcs are distances
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8/13/2010 4 Table for Formulation of Shortest Route Problem 12 13 4 3 32 25 52 35 53 46 67 57 56 65 791 8 3 #5544 33622.
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Module9 Handouts - 8/13/2010...

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