Modified Distribution Method

Transcription

1 istributors C 8 Step : Make an initial allocation with the North-West corner rule. KPP

2 istributors C 8 V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to KPP

3 istributors C 8 V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j X> means that you have assigned capacity to a cell C ij : The cost for moving capacity from V j to KPP

4 istributors C 8 V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Since we set U = and C, = ; then V has to be KPP

5 istributors C 8 V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Since we set U = and C, = ; then V has to be KPP

6 istributors C 8 - V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Since V = and C, = ; then U has to be - KPP

7 istributors C 8 - V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Since U = - and C, = ; then V has to be KPP

8 istributors C 8 - V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Since V = and C, = ; then U has to be KPP 8

9 istributors C 8 - V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Since U = and C, = ; then V has to be KPP

10 istributors C V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables, and V j. Set U to Step : If X>; C ij = + V j Step : Calculate the shadow cost. If X =, then C ij = C ij - V j KPP

11 istributors The most C negative C ij V j Step : Transfer the largest quantity possible to the cell that has the most negative C ij while creating a loop that satisfies the demand and capacity of each column and row. Except for the empty cell with a negative C ij the cells in the loop should contain quantities. KPP

12 C The most negative C ij istributors V j Step : Transfer the largest quantity possible to the cell that has the most negative C ij while creating a loop that satisfies the demand and capacity of each column and row. Except for the empty cell with a negative C ij the cells in the loop should contain quantities. As seen above, the factory s capacity of is distributed to distributor () and distributor (). So we have to re-distribute as much capacity as possible to distributor where we have the negative C ij. KPP

13 C The most negative C ij istributors V j Step : Transfer the largest quantity possible to the cell that has the most negative C ij while creating a loop that satisfies the demand and capacity of each column and row. Except for the empty cell with a negative C ij the cells in the loop should contain quantities. So, we can re-distribute capacity from either distributor () or distributor (). But we then have to balance the matrix by re-assigning capacity between demands in the two other rows. KPP

14 istributors C V j Step : Transfer the largest quantity possible to the cell that has the most negative C ij while creating a loop that satisfies the demand and capacity of each column and row. Except for the empty cell with a negative C ij the cells in the loop should contain quantities. We may not move any capacity to cells that have no quantities assigned already! KPP

15 istributors C V j Step : Transfer the largest quantity possible to the cell that has the most negative C ij while creating a loop that satisfies the demand and capacity of each column and row. Except for the empty cell with a negative C ij the cells in the loop should contain quantities. So, in this example, the only way to get a ballanced matrix is to move material according to the green arrows above! The maximum capacity that can be moved is the lowest of the two quantities at the root of the arrows (). KPP

16 istributors C 8 V j Now, a new distribution matrix is achieved. Set U to and calculate the new shadow costs. KPP

17 istributors C 8 - V j Step : Repeat steps - until there are no negative C ij. Step : Calculate the total cost by multiplying each allocation with its specific cost. Cost= x + x + x + x + x + x = 8 KPP

18 Questions? Next lecture on Thursday -- Layout, Line balancing KPP 8