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Homework Sol Due 10-3 Cutting Stock Col Gen

# Homework Sol Due 10-3 Cutting Stock Col Gen - Homework...

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Unformatted text preview: Homework Cutting Stock Problem Solve this cutting stock problem two different ways: (1) Formulate and solve using a SOLVER such as CPLEX or Excel. (2) Solve this formulation via the large scale approach I did in class: max ggB‘l P — 0 st (8,10,12):£+c=30 nonnegative integers Problem Data: Lengths: (8",10",12") Stock length: 30” Demands: (250, 210, 140) respectively for the lengths (8", 10", £2”) MGR/LP (Revised 1/93} Date: 10/ 5/11 Time: 14:55:03 H:\MORLPS~1\Cghwll.lpe MODEL DESCRIPTION *‘k**‘k***9¢**~k****************************-k-k~k1ir-k-k*****+ min 2 = 6xl+4x2+2x3+0x4+2X5+6X6+0X7 st 3x1+2x2+2x3+lx4+1X5+0x6+0x7 3 250 0xl+1x2+0x3+1x4+2X5+0x3+3x7 = 210 0x1+0x2+1x3+1x4+0x5+2x6+0x7 m 140 "nonneg" 'k*k'k*iv**~k***~k****************~k1':icieskzkicir-k-k‘k‘k-k‘k‘k-k‘k'k‘k‘k'k‘ki' Simplex Method Tableau: 5 BASIS Z X1 X2 X3 X4 X5 X6 X7 Artifl ArtifZ Artif3 SOL. Z 00 -O 00 0 00 —0 00 0 00 0 00 -10 00 X2 0.00 2.00 1.00 l 00 0 00 0 00 —0 67 ~l 00 0.67 “0.33 —0 33 50 00 X5 0 00 —l.00 0.00 -l 00 0 00 1 00 -0 67 2 00 —0.33 0.67 —0 33 10.00 X4 0 00 0.00 0.00 l 00 1.00 0 00 2 00 0 00 0.00 0.00 l 00 140 00 “AA Optimal Solution AAA Z e 220.0000 X1 = 0.0000 X2 = 50.0000 X3 = 0.0000 X4 = 140.0000 X5 : 10.0000 X6 = 0.0000 X7 = 0.0000 HW Due 10-4-2011 Cutting Stock Problem File: colgenl 1.mle in 620 models PT 3 0 0 2 1 0 2 0 I 1 1 I l 2 0 0 0 2 0 3 0 patterns pat: 1 P= {3,0,0} waste 6 skien: 30 wt: 6 pet: 2 P={2, 1,0} waste 4 skien: 30 wt: 4 pat: 3 P= {2, 0, 1} waste 2 sklen: 30 wt: 2 pat: 4 P:{1,1,1} waste 0 sklen: 30 wt: 0 pat: 5 P: { 1,2,0} waste 2 sklen: 30 wt: 2 pat: 6 P= {0,0,2} waste 6 sklen: 30 wt: 6 pat: 7 P: {0, 3, 0} waste 0 sklen: 30 wt: 0 _________________ 1 ________________________ B XB: {8,9,10} Wm Q/J‘wm/Q’ XB: {250.000, 210.000, 140.000} 1 CB: {100010001000} - atom/9,5111%, 1:0»? «”1“?! cost: 600000.000 max: {1000.000,1000.000,1000.000} — C st { 8, 10, 12} +0: 30 or 0 z: {I000.000,1000.000,1000.000} maxv: 3000.000 maxi: 4 newi: 4 G” __ best P: { 1, 1, 1} c: 0 sk len: 30 val: 3000.000 {gazing (“i/V ﬁgguﬂmtuﬁ 107 entering var x 1 Pattern: { 1, 1, 1} waste: 0 Aj: { 1.000, 1.000, 1.000} ratios: { 250.000, 210.000, 140.000} ratio: 140.000 100: 3 1eavevariab1e10c: 3 _________________ 2 --__-__-_,___________-__ B 1.000 0.000 1.000 0.000 1.000 1.000 0.000 0.000 1.000 Binv 1.000 0.000 ~1.000 0.000 1.000 -1.000 0.000 0.000 1.000 XB: { 8, 9, 1} KB: { 110.000, 70.000, 140.000} CB: { 1000, 1000, 0} cost: 180000.000 max: {1000.000,1000.000,-2000.000} — c st{8,10,12} +0: 30 or 0 z: {1000.000,1000.000,—2000.000} maxv: 3000.000 maxi: 7 newi: 7 best P: {0, 3, 0} c: 0 sklen: 30 val: 3000.000 entering var x 2 Pattern: {0, 3,0} waste: 0 Aj: { 0.000, 3.000, 0.000} ratios:{ 0.000, 23.333, 0.000} ratio: 23.333 100: 2 leave variable 100: 2 _________________ 3 ___________________--,-_ B 1.000 0.000 1.000 0.000 3.000 1.000 0.000 0.000 1.000 Binv 1.000 0.000 -1.000 0.000 0.333 -0.333 0.000 0.000 1.000 KB: {8, 2,1} ' XB: { 110.000, 23.333, 140.000} CB: { 1000, 0,0} cost: 110000.000 max: {1000.000, 0.000,-1000.000} -C St{8,10,12} +6: 30 or 0 2: {1000.000, 0.000,—1000.000} maxv: 2994.000 maxi: 1 newi: 1 best P: {3, 0, 0} c: 6 SR len: 30 val: 2994.000 entering var x 3 Pattern: { 3, O, 0} waste: 6 Aj: { 3.000, 0.000, 0.000} ratios: { 36.667, 0.000, 0.000} ratio: 36.667 100: 1 leave variable loo: 1 _________________ 4 ___-______-_-_-_:_______ B 3.000 0.000 1.000 0.000 3.000 1.000 0.000 0.000 1.000 Binv 0.333 0.000 -0.333 0.000 0.333 —0.333 0.000 0.000 1.000 X13: {3, 2, 1} XB: { 36.667, 23.333, 140.000} CB: {6, 0, 0} cost: 220.000 max: { 2.000, 0.000, —2.000} -c st{8,10, 12} +c= 30 or 0 Z:{ 2.000, 0.000, -2.000} maXV: 0 maxi: 0 opt has been found WW‘ ”WM-.94» -,_H,;.;,1:‘.;.A¢_ 7. ...
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