HW7_solution

HW7_solution - Homework 7 solution 1 P 372 10 Supply = Auditor1 Auditor2 Auditor3 = 480 Supply Points Point1 A1 = 160 Point2 A2 = 160 Point3 A3 =

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Unformatted text preview: Homework 7 solution 1. P. 372 # 10 Supply = Auditor1 + Auditor2 + Auditor3 = 480 Supply Points: Point1 : A1 = 160 ; Point2 : A2 = 160 ; Point3 : A3 = 160 Demand Points: Point1 : P1 = 130 ; Point2 : P2 = 140 ; Point3 : P3 = 160 Total Supply = 480 Total Demand = 430 So we add dummy demand of 480 430 = 50 Table Auditor2 Auditor3 Auditor1 130 2. P. 371 # 1 Supply = 40 + 30 = 70 Demand = 30 + 30 + 30 = 90 So we add dummy supply point equal to 90 70 = 20, with cost equal to the shortage cost for that customer. Table Warehouse1 Warehouse2 Dummy 30 10 30 0 90 20 80 30 0 20 30 0 Custormer1 15 10 Custormer2 35 50 40 10 110 Custormer3 25 40 0 30 0 20 0 Project1 120 140 160 140 Project2 150 130 140 160 Project3 190 120 150 50 Dummy 0 0 0 160 160 160 Initial BFS: X11=30, X12=10, X22=20, X23=10, X33=20; X13=X21= X31=X32=0. 3. P. 371 # 2 Because the warehouses can purchase extra units for $100/unit, we must update our supply and demand points as below: Supply Points: Point 1 = Warehouse 1 (S1=40) Point 2 = Warehouse 2 (S2=30) Point 3 = Warehouse 1 for extra units (S3=9040=50) Point 4 = Warehouse 2 for extra units (S4=9030=60) Demand Points: Point 1 = Customer 1 (d1=30) Point 2 = Customer 2 (d2=30) Point 3 = Customer 3 (d3=30) So we add dummy demand point equal to (40+30+50+60)(30+30+30) = 90 with cost equal to $0 Table Warehouse1 Warehouse2 30 10 30 0 115 110 20 135 150 30 20 0 0 30 20 0 20 140 60 90 60 Custormer1 15 10 Custormer2 35 50 Custormer3 10 125 30 0 25 40 Dummy 0 0 0 0 40 10 0 30 10 0 20 0 60 Extra of W1 Extra of W2 Initial BFS: X11=30, X12=10, X22=20, X23=10, X33=20, X34=30, X44=60; X13= X14=X21=X24= X31= X32= X41= X42= X43=0. 4. P. 371 # 3 Supply Points: Point 1 = Month 1 RT (S1=200), Point 2 = Month 1 OT (S2=100) Point 3 = Month 2 RT (S3=200), Point 4 = Month 2 OT (S4=100) Point 5 = Month 3 RT (S5=200), Point 6 = Month 3 OT (S6=100) Point 7 = Month 4 RT (S7=200), Point 8 = Month 4 OT (S8=100) Point 9 = Month 5 RT (S9=200), Point 10 = Month 5 OT (S10=100) Point 11 = Month 6 RT (S11=200), Point 12 = Month 6 OT (S12=100) Demand Points: Point1 = Month 1 (d1=200), Point2 = Month 2 (d1=260) Point3 = Month 3 (d1=240), Point4 = Month 4 (d1=340) Point5 = Month 5 (d1=190), Point6 = Month 6 (d1=150) Total Supply = 200*6+100*6=1800 Total Demand=200+260+240+340+190+150=1380 So we need to add a dummy demand point equal 1800 1380 = 420 with cost equal to $0 Mont h 1 7 200 11 M M M M M M M M M M 200 0 Mont h 2 8 0 12 100 7 160 11 M M M M M M M M 200 160 0 Mont h 3 9 13 8 40 12 100 7 100 11 M M M M M M 240 200 100 Mont h 4 10 14 9 13 8 100 12 100 7 140 11 M M M M 340 240 140 Mont h 5 11 15 10 14 9 13 8 60 12 100 7 30 11 M M 190 130 30 Mont h 6 12 16 11 15 10 14 9 13 8 150 12 7 11 150 Dumm y 0 0 0 0 0 0 0 0 0 20 0 100 0 200 0 100 420 400 300 100 Table Month 1 RT Month 1 OT Month 2 RT Month 2 OT Month 3 RT Month 3 OT Month 4 RT Month 4 OT Month 5 RT Month 5 OT Month 6 RT Month 6 OT 200 0 10 0 200 40 1 200 10 0 10 0 10 0 200 60 10 0 200 20 170 10 0 20 0 10 0 Initial BFS: X11=200, X12=0, X22=100, X32=160, X33=40, X43=100, X53=100, X54=100, X64=100, X74=140, X75=60, X85=100, X95=30, X96=150, X97=20, X10,7=100, X11,7=200, X12,7=100 Otherwise Xi,j=0 for 1 i 12; 1 j 7 ...
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This note was uploaded on 02/10/2010 for the course IEOR 3600 taught by Professor Chudnovsky during the Spring '09 term at Columbia.

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