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Lineare Optimierung - integer Simplex- Zuschnittproblem

Autor:hawe

cutting-stock problem - simplex integer programm

An order for 30 pieces of length 2, 10 pieces of length 3 and 20 pieces of length 4 is to be cut from stock lengths 5, 6, and 9 with costs respectively of 6, 7, and 10 D,E,F,G,H,I,J Zuschnitt-Muster, D1:J1 standard längen auf Lager (Cutting pattern, stock length) Spreadsheet calculation table Simplex linear integer prgramm
  1. X Input tableau transfer from Spreadsheet
  2. make Start Tableau for Dual Simplex program (dual simplex minimize programm) doing simplex steps until cost row (last) all elements positiv
  3. make minimum number col x5 integer delete col x5 in input tableau (1.) and subtract units produced x5 in row 1 input cost 3x6=18 in Z
  4. make Dual Simplex Tableau doing simplex steps until cost row (last) all elements positiv
  5. Puuh, remaining cutting pattern are integers
  6. transfer to spreadsheet row 6
Zuschnitt
  • x1=1 - 5 m Standard - 1 Einheit verwendet
  • x4=11
  • x5=3 - 6 m Standard - 14 Einheiten
  • x6=9 - 9 m Standard - 9 Einheiten
  • Kosten 173+3 x 7=194 für 24 Einheiten
wxMaxima minimize_lp( x1*6+x2*6+x3*7+x4*7+x5*7+x6*10+x7*10,[ x1+x4+3*x5+x6 >= 30, x1+2*x3+x6 >= 10, x2+x4+x6+2*x7 >= 20, x5=6 ]), nonegative_lp=true, numer; [182.0,[x7=4.0,x2=0,x3=0,x6=10,x5=6,x4=2,x1=0]] Kosten minimize_lp( x1*0+x2+x3*0+x4*0+x5*0+x6*0+x7*1,[ x1+x4+3*x5+x6 >= 30, x1+2*x3+x6 >= 10, x2+x4+x6+2*x7 >= 20, x5=3 ]), nonegative_lp=true, numer; [0.0,[x7=0,x2=0,x3=0,x6=9.0,x5=3,x4=11.0,x1=1.0]] Verschnitt x1*6+x2*6+x3*7+x4*7+x5*7+x6*9+x7*9,x7=0,x2=0,x3=0,x6=9.0,x5=3,x4=11.0,x1=1.0; 185.0 Kosten goolge spreadsheet: Grundlagen Simplex-Algorithmus simplex.js

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