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Transportation Simplex Method

Transportation Simplex Method. Transportation Simplex Method. If the problem is unbalanced, balance it Use one of the methods described in section 7.2 to find a bfs

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Transportation Simplex Method

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  1. Transportation Simplex Method

  2. Transportation Simplex Method • If the problem is unbalanced, balance it • Use one of the methods described in section 7.2 to find a bfs • Use the fact that u1=0 and ui+ vj =cij for all basic variable to find the [u1 u2 … um v1 v2 …vn] for the current bfs • If ui + vj – cij ≤ 0 for all nonbasic variable, then the current bfs is optimal. If this is not the case, enter the variable with the most positive ui + vj – cijinto the basis using pivot procedure. This yield a new bfs • Using the new bfs, return to step 3 and 4

  3. For maximization problem replace 4 by 4’ 4’. If ui + vj – cij≥ 0 for all nonbasic variable, then the current bfs is optimal. If this is not the case, enter the variable with the most negative ui + vj – cij into the basis using pivot procedure.

  4. Bagaimanamelakukan Pivot dalamMasalahTransportasi • Tentukanvariabel yang harusmasuksebagai basis • Temukan loop (pastihanyaadasatu loop) yang berkaitandengan entering variable danbeberapa basic variable • Hitunghanyasel yang adadalam loop. Labelisel yang ditemukanpadalangkah 2 mulaidari entering variable: yang merupakanbilangangenapkitalabelisebagaiselgenapdan yang merupakanbilanganganjilkitalabelisebagaiselganjil. • Temukanselganjil yang memilikinilaiterkecil (sebutnilaiinisebagai. Variabelpadaseliniakanmeninggalkan basis. Turunkannilaidarisetiapselganjildantingkatkannilaisetiapselgenap

  5. Definition An ordered sequence of at least four different cells is called loop if • Any two consecutive cells lie in either the same row or same column • No three consecutive cells lie in the same row or column • The last cell in the sequence has a row or column in common with the first cell in the sequence

  6. Example Powerco Problem using North West Corner Method 35 10 20 20 10 10

  7. Basic Variable x11=35 x21=10 x22=20 X23=20 x33=10 x34=30 Hitung[u1 u2u3v1 v2v3 v4] dari u1 = 0 ui+ vj =cijuntuksemua basic variable x11u1+v1=c11=8 v1= 8 x21u2+v1=c21=9 u2=1 x22u2+v2=c22=12 v2=11 x23u2+v3=c23=13 v3=12 x33u3+v3=c33=16 u3=4 x34u3+v4=c34=5 v4=1

  8. Hitung ij= ui+vj– cijuntuksemuanonbasic variable 12 = 0 +11 – 6 = 5 13 = 0 +12 -10 = 2 14 = 0 +1 – 9 = -8 24 = 1 +1 – 7 =-5 31 = 4 +8 – 14 = -2 2 = 4 +11 – 9 = 6 Terdapat yang positif. 2 paling positifsehingga x32masuksebagai basis Gunakanprosedur looping Loop yang mencakup x32danbeberapa basic variabeladalah (3,2) – (3,3) – (2,3) – (2,2)

  9. 35 10 20 20 10 10

  10. Odd cell : (3,3) dan (2,2) X33 =10 x22 = 20   = 10 X33 dan x22dikurangi 10, x32dan x23ditambah 10 SehinggadidapatTabel 2

  11. 35 10 10 30 30 10

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