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Chapter 2

PROCESS SYSTEMS FOR

MANUFACTURINGLOGISTIC PLANNING & DESIGN

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Chapter 2

LOGISTIC PLANNING & DESIGN

Transportation Problems

allocation of raw materials purchased from

various suppliers.

delivery of finished goods produced from various

factories to various distribution center.

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Suppliers Manufacturers Warehouses &Distribution Centers

Customers

Material Costs

TransportationCosts

TransportationCosts

Transportation

CostsInventory CostsManufacturing Costs

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Chapter 2


Linear Programming Models

presents a matrix of:

1- Quantities required at the sinks (market).

2- Unit cost transportation from each source

(factory).

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Chapter 2


Linear Programming Models (continue)

DistributorsPlants

D1 D2 D3 Plantcapacity

P1 $ $ $ Q1P2 $ $ $ Q2

P3 $ $ $ Q3

P4 $ $ $ Q4

Demand X1 X2 X3

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Chapter 2



Three ways:

1-Northwest Corner Ruleallocating to (1,1) cell as much as is needed

for sink 1(distributor 1) or as much as it can be

supplied from source 1 (plant 1).

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Chapter 2



DistributorsPlants


P1 $max(X1,Q1)

$ $ Q1

P2 $ $ $ Q2P3 $ $ $ Q3

P4 $ $ $ Q4

Demand X1 X2 X3

1-Northwest Corner Rule (example)

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Chapter 2



1-Northwest Corner Rule (continue)

if the needed of sink 1 is satisfied, no

assignment to any other cell in the 1stcolumn.

move to the (1,2) cell of the 1st row and

allocate min (a1b1, b2) to this cell; and so on.

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Chapter 2



DistributorsPlants


P1 $ (X1) $ min(Q1-X1,X2) $ Q1

P2 $ $ $ Q2

P3 $ $ $ Q3

P4 $ $ $ Q4

Demand X1 X2 X3

1-Northwest Corner Rule (continue)

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Chapter 2



2-Least unit transportation cost

starting with a combination of factory and

market having least unit transportation cost.

quantity required is allocated in this cell as

much as is needed.

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Chapter 2



DistributorsPlants


P1 $ $ $ Q1

P2 $ $ $ Q2

P3 $ min$max(X2,Q3)

$ Q3

P4 $ $ $ Q4

Demand X1 X2 X3

2-Least unit transportation cost (example)

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Chapter 2



2-Least unit transportation cost

no assignment is needed to any other cell in

this row when all products are exhausted OR all

demands are satisfied.

the same process is continued for 2nd, 3rd,

least unit transportation cost.

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Chapter 2



DistributorsPlants


P1 $ $ $ Q1

P2 $ $ min$

max(X3,Q2)

Q2

P3 $ min$max(X2,Q3)

$ Q3

P4 $ $ $ Q4

Demand X1 X2 X3

2-Least unit transportation cost (example)

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Chapter 2



3-VAM (Vogels Approximation Method)

in each row OR each column, calculate the

difference between 2nd least and the least

transportation cost.

assign a cell with the least transportation

cost that having THE GREATEST DIFFERENCE.

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Chapter 2



DistributorsPlants


P1 Diff.$ Diff.$ Diff.$ Q1

P2 Diff $ Diff $ Diff $ Q2

P3 Max. Diff.$ Diff.$ Diff.$ Q3

P4 Diff $ Diff $ Diff $ Q4

Demand X1 X2 X3

3- VAM (Vogels Approximation Method)

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EXAMPLE

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Example (continue):

Periodically, shipments are made from the three plants to four

distribution warehouses located in USA; Texas, New Jersey, Chicago,

South Dakota. Over the next month, it has been determined that these

warehouses should receive the following companys production as

shown in Table 2 below.

Warehouse Total Shipment Quantity

(in 1000 unit)

Texas 80

New Jersey 78

Chicago 47

South Dakota 55

Chapter 2


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Question

What is the optimum total costfor the

transportations from plants to warehouses?

Chapter 2


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Solution

Step 2: Select the lowest shipment cost.WAREHOUSES Anticipate

d

Production quantity

FACTORIES Texas Chicago NewJersey SouthDakota

California 250 420 380 280 45

Ireland 1,280 990 1,440 1,520 120

Thailand 1,550 1,420 1,660 1,730 95

TotalShipment

quantity

80 78 47 55

Chapter 2


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SolutionStep 3: Select and write the minimum quantity betweenproduction and shipment at the column of the minimum shipment cost.

WAREHOUSES Anticipated

Productionquantity

FACTORIES Texas Chicago NewJersey

SouthDakota

California 250(45)

420 380 280 45

Ireland 1,280 990 1,440 1,520 120

Thailand 1,550 1,420 1,660 1,730 95

TotalShipment

quantity

80 78 47 55

Chapter 2


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Solution

Step 4: Draw a line through the row (in this example, the 1strow)WAREHOUSES Anticipated

ProductionquantityFACTORIES Texas Chicago NewJersey

SouthDakota

California 250(45)

420 380 28045

Ireland 1,280 990 1,440 1,520 120

Thailand 1,550 1,420 1,660 1,730 95

TotalShipment

quantity

80 78 47 55

Chapter 2


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Solution

Step 6: Select the lowest quantity between production andshipment.

WAREHOUSES AnticipatedProduction

quantityFACTORIES Texas Chicago NewJersey SouthDakota

California 250(45)

420 380 28045

Ireland 1,280 990

(78)

1,440 1,520 120

Thailand 1,550 1,420 1,660 1,730 95

TotalShipmentquantity

80 78 47 55

Chapter 2


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NOTES

At this point, no more can be shipped out to

Chicago. Then, draw a line through the 2nd

column.

Chapter 2


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SolutionStep 7: Draw a line across the column (in this example, across 2nd

column. WAREHOUSES AnticipatedProduction

quantityFACTORIES Texas Chicago NewJersey SouthDakota

California 250(45)

420 380 28045

Ireland 1,280 990

(78)

1,440 1,520 120

Thailand 1,550 1,420 1,660 1,730 95


80 78 47 55

Chapter 2


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quantityFACTORIES Texas Chicago New Jersey South

DakotaCalifornia 250

(45)420 380 280

45

Ireland 1,280(35)

990(78)

1,440 1,520 120

Thailand 1,550 1,420 1,660(47)

1,730 95


80 78 47 55

Result the minimum quantity for Ireland/Texas is selected.

Chapter 2


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NOTES

At this point, no more can be shipped out to

Texas. Then, draw a line through the 1st

column.

Chapter 2


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Dakota

California 250(45)

420 380 28045

Ireland 1,280(35)

990(78)

1,440(7)

1,520 120

Thailand 1,550 1,420 1,660(47 7 = 40)

1,730 95


80 78 47 55

Result the minimum quantity for Thailand/New Jersey isselected.

Chapter 2


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quantityFACTORIES Texas Chicago New

JerseySouthDakota

California 250(45)

420 380 28045

Ireland 1,280(35)

990(78)

1,440(7)

1,520 120

Thailand 1,550 1,420 1,660(40) 1,730(95 - 40 = 55) 95


80 78 47 55

Result the quantity for Thailand/South Dakota iscalculated.

Chapter 2


Ch t 2

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DakotaCalifornia 250

(45)420 380 280

45

Ireland 1,280(35)

990(78)

1,440(7)

1,520 120

Thailand 1,550 1,420 1,660(40)

1,730(55)

95


80 78 47 55

Overall Result

Chapter 2


Ch t 2

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Thus, the optimum shipment quantities for each factory to warehouses

for next month are:

California-Texas= 45; no shipment to other warehouses.

Ireland-Texas = 35

Ireland-Chicago = 78

Ireland-New Jersey = 7

No shipment from Ireland to South Dakota.

Thailand-New Jersey = 40

Thailand-South Dakota = 55

No shipment from Thailand to Texas and Chicago.

Chapter 2


BMFG_3113_Ch2_Part4

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