1. IE 8580 Module 2: Transportation in the Supply Chain
Lecture 2.3:
Transportation Network Models

2. Capacitated Plant Location Model
Where do you place plants to serve customers?
Plants in each region?
Plants in a few regions?
Conflicting factors
Transportation and avoiding duties vs. reducing economies of scale
There are fixed and variable costs
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3. Capacitated Plant Location Model
Market 1
Plant 2
Market 2 … …
Plant n
Market m
Fixed annual cost to keep a plant open
Cost per unit to transport
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4. Variables and Parameters
n = number of potential plants
m = number of markets
Dj = annual demand in market j
Ki = maximum capacity in plant i
fi = annualized fixed cost of plant i
cij = cost to produce and ship 1 unit from factory i to market j
Decision variables
yi = 1 if plant i is open; 0 otherwise
xij = quantity shipped from factory i to market j
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5. … … Graphically… c11, x11 K1, f1, y1 Plant 1 Market 1 D1 c12, x12
Kn, fn, yn
Plant n
cnm, xnm
Market m Dm
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6. Mathematical Model
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7. Flow Allocation Model
Brownfield design in which the locations of the plants, warehouses, and customers are known and fixed.
The possible modes of transportation are fixed and the costs are deterministic
How do you allocate the flow of materials to meet customer demand with minimum cost?
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8. Plants, warehouses, and customers are fixed
Flow Allocation Model
Plant 1
Warehouse 1
Customer 1
Plant 2
Warehouse 2
Customer 2 … … …
Plant I
Warehouse J
Customer K
Plants, warehouses, and customers are fixed
Demand and capacities known
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9. Two-Stage Transportation Problem
xij = flow from plant i to warehouse j
yjk = flow from warehouse j to customer k
cij = cost to ship one unit from i to j
c’jk = cost to ship one unit from j to k
Si = capacity of plant i
Dk = demand of customer k
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10. Two-Stage Transportation Problem
c11, x 11
c’11, y 11 D1 S1
Plant 1
Warehouse 1
Customer 1 S2
Plant 2
Warehouse 2
Customer 2 D2 … … … SI
Plant I
Warehouse J
Customer K DK
cIJ, x IJ
c’JK, x JK
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11. Network Flow Model
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12. This is how you get the minimum cost we discussed last time!
Single product, two plants, two warehouses, 3 customers
Plant capacities: 140,000 and 60,000
Customer demands: 50,000, 100,000, and 50,000
Unit distribution costs ($) P1 P2 C1 C2 C3 W1 4 3 5 W2 2 1
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13. It’s the same problem from before!50 3
140
Customer 1 4 5 5
Plant 1
W/H 1
100 2 4 1
Customer 2 2 2 60 50
Plant 2
W/H 2
Customer 3
IE 8580, 13

14. Mathematical Model (Long Form)
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15. Locating Plants and Warehouses Simultaneously
c1hi Fi
c2ie fe
c3ej
Supplier 1
Plant 1
Warehouse 1
Market 1 S1 K1 W1 D1
Supplier 2
Plant 2
Warehouse 2
Market 2 S2 K2 W2 D2 … … … …
Supplier l
Plant n
Warehouse t
Market m SI Kn We Dm
x1hi
yPi
x2ie
yWe
x3ej
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16. Mathematical Model
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