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1 KPP KPP

2 Transportation method A quantitative approach for cost effective allocation of resources from multiple sources to multiple destinations. In this course we deal with three different methods: - Least Cost Method, LCM - Vogel s Approximation Method, VAM - Modified Transportation Method, MOI KPP

3 The initial problem Factory C=00 Factory C= Factory C=80 istributor A =0 istributor B =0 istributor C = istributor =0 KPP

4 The initial problem Factory C=00 Factory C= Factory C=80 istributor A =0 istributor B =0 istributor C = istributor =0 KPP

5 The initial problem Factory C=00 Factory C= Factory C=80 Cost = Cost = Cost = Cost = Cost = Cost = istributor A =0 istributor B =0 istributor C = istributor =0 KPP

6 Factory C=00 Factory C= Factory C=80 The initial problem istributor A =0 How to allocate the products from the three istributor B different factories to the four =0 different distributors in the most cost effective manner? istributor C = istributor =0 KPP

7 The initial tableau C istributors KPP

8 The Least Cost Method C istributors Step : Identify the cell with the lowest cost. KPP 8

9 The Least Cost Method istributors C Step : Identify the cell with the lowest cost. Step : Allocate as much capacity as possible to the identified cell Note that you can not allocate more capacity to each row than the total amount for that Factory. Neither can you allocate more capacity to each column than the total demand for that istributor. Step : Repeat steps and until all capacity is allocated to meet the demand. KPP

10 The Least Cost Method istributors C Step : Calculate the total cost by multiplying each allocation with its specific cost. Cost= 0x + x + x + x + 0x + 0x = KPP 0

11 Vogel s Approximation Method C istributors = - = - = Step : For each row and column, find the difference between the two lowest shipping costs. KPP

12 Vogel s Approximation Method C istributors = - = - = Step : For each row and column, find the difference between the two lowest shipping costs. Step : In the row or column with the highest difference, allocate as much demand as possible to the cell with the lowest cost. KPP

13 Vogel s Approximation Method C istributors = - = - = Step : If a capacity is fully used, or a demand fully satisfied, that row or column is finished. KPP

14 Vogel s Approximation Method istributors C = - = - = Step : Now we repeat steps - but without the finished column, and itterate until all capacity is allocated. KPP

15 Vogel s Approximation Method istributors C Step : Calculate the total cost by multiplying each allocation with its specific cost. Cost= 8x + x + 0x + x + 0x + 0x = 8 KPP

16 Modified istribution Method istributors C Step : Make an initial allocation with the North-West corner rule. KPP

17 Modified istribution Method istributors C U i 0 V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables U i, and V j. Set U to 0 KPP

18 Modified istribution Method istributors C U i 0 - V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables U i, and V j. Set U to 0 Step : If X>0; C ij = U i + V j KPP 8

19 Modified istribution Method istributors C U i 0 - V j Step : Make an initial allocation with the North-West corner rule. Step : Introduce the variables U i, and V j. Set U to 0 Step : If X>0; C ij = U i + V j Step : Calculate the shadow cost. If X = 0, then C ij = C ij U i - V j KPP

20 Modified istribution Method istributors C U i 0 - 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 0

21 Modified istribution Method istributors C U i 0 - 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 + 0x + x + 0x + 0x = 8 KPP

22 Questions? Next lecture on Thursday 0-- Layout, Line balancing KPP

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