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Transportation Model
TRANSPORTATION MODELTRANSPORTATION MODEL
Requirements - List of origins and each one’s capacity. List of destinations and each one’s demand. Unit cost of shipping.
Assumptions - Items to be shipped are homogeneous. Shipping cost per unit is the same. Only one route between origin and destination. Demand and supply is equal.
TRANSPORTATION MODEL SCENARIOTRANSPORTATION MODEL SCENARIO
D(demand)
B(demand)
C(demand)
A(demand)
1(supply)
2(supply)
3(supply)
A TRANSPORTATION TABLEA TRANSPORTATION TABLEWarehouse
4 7 7 1100
12 3 8 8200
8 10 16 5150
450
45080 90 120 160
A B C D
1
2
3
FactoryFactory 1can supply 100units per period
Total supplycapacity perperiod
Total demandper period
Demand
Warehouse B can use 90 units per period
NETWORK PRESENTATIONNETWORK PRESENTATION
Transportation problem can be represented as a network. Circles represent origins and destinations, and the arcs between them represent the decision variables, i.e. the amounts shipped.
Supply Origin
DemandDestination
D1
D2
D3
410
6
816
6
14 1810
100
300
300
200
300
200
S1
S2
S3
LINEAR PROGRAMMING FORMULATIONLINEAR PROGRAMMING FORMULATION
Let xij be unknown number of units shipped from origin i to destination j (i,j = 1,2,3)
x11 + x21 + x31 > 200x12 + x22 + x32 > 300x13 + x23 + x33 > 200
Demand constraintsSupply constraints
x11 + x12 + x13 < 100x21 + x22 + x33 < 300x31 + x32 + x33 < 300
min z = 4x11 + 10x12 + 6x13 + 8x21 + 16x22 + 6x23
+ 14x31 + 18x32 + 10x33
st.
xij > 0
Non-negative constraints
TRANSPORTATION PROBLEMTRANSPORTATION PROBLEM
Des Moines(100 units)capacity
Cleveland(200 units)required
Boston(200 units)required
Evansville(300 units)capacity
Ft. Lauderdale(300 units)capacity
Albuquerque(300 units)required
From(Sources)
To(Destinations)
Albuquerque Boston ClevelandDes Moines
Evansville
Fort Lauderdale
$5
$8
$9
$4
$4
$7
$3
$3
$5
TRANSPORTATION PROBLEMTRANSPORTATION PROBLEM
Des Moines(D)
Evansville(E)
Ft Lauderdale(F)
WarehouseReq.
Albuquerque(A)
Boston(B)
Cleveland(C)
FactoryCapacity
5 4 3
3
57
48
9
UNIT SHIPPING COST: 1 UNIT, FACTORY TO UNIT SHIPPING COST: 1 UNIT, FACTORY TO WAREHOUSEWAREHOUSE
Des Moines(D)
Evansville(E)
Ft Lauderdale(F)
WarehouseReq.
Albuquerque(A)
Boston(B)
Cleveland(C)
FactoryCapacity
300 200 200 700
300
300
100
TOTAL DEMAND & TOTAL SUPPLYTOTAL DEMAND & TOTAL SUPPLY
Des Moines(D)
Evansville(E)
Ft Lauderdale(F)
WarehouseReq.
Albuquerque(A)
Boston(B)
Cleveland(C)
FactoryCapacity
300 200 200 700
300
300
1005 4 3
3
57
48
9
TRANSPORTATION TABLETRANSPORTATION TABLE
• Start in the upper left-hand cell and allocate units to shipping routes as follows:
– Exhaust the supply (factory capacity) of each row before moving down to the next row.
– Exhaust the demand (warehouse) requirements of each column before moving to the next column to the right.
– Check that all supply and demand requirements are met.
NORTH - WEST CORNER METHOD NORTH - WEST CORNER METHOD
Des Moines(D)
Evansville(E)
Ft Lauderdale(F)
WarehouseReq.
Albuquerque(A)
Boston(B)
Cleveland(C)
FactoryCapacity
300 200 200 700
300
300
1005 4 3
3
57
48
9
100
200 100
100 200
NORTH - WEST CORNER METHOD (CONTD.) NORTH - WEST CORNER METHOD (CONTD.)
Total = $4,200
Des Moines(D)
Evansville(E)
Ft Lauderdale(F)
WarehouseReq.
Albuquerque(A)
Boston(B)
Cleveland(C)
FactoryCapacity
2000
700
800
5005 4 3
3
57
48
9
500
600 200
400 300
400 900 700
Total Cost: 10,200
LEAST COST METHOD LEAST COST METHOD
Des Moines(D)
Evansville(E)
Ft Lauderdale(F)
WarehouseReq.
Albuquerque(A)
Boston(B)
Cleveland(C)
FactoryCapacity
2000
700
800
5005 4 3
3
57
48
9
100
800
400 900 700
Total Cost: 9,100
400
700
SAME EXAMPLE WITH NWM SAME EXAMPLE WITH NWM
EXCEL TEMPLATE EXCEL TEMPLATE