1. Demand Allocation Example
Single product
Two plants p1 and p2
Plant P1 has an annual capacity of 200,000 units.
Plant p2 has an annual capacity of 60,000 units.
The two plants have the same production costs.
There are two warehouses w1 and w2 with identical warehouse handling costs.
There are three markets areas c1,c2 and c3 with demands of 50,000, 100,000 and 50,000, respectively.

2. Example

3. Example: Distribution Network$0
D = 50,000 $3
Cap = 200,000 $4 $6 $5
D = 100,000 $2 $4 $1 $2
Cap = 60,000 $2
D = 50,000
Production costs are the same, warehousing costs are the same

4. Traditional Approach #1: Assign each market to closest WH
Traditional Approach #1: Assign each market to closest WH. Then assign each plant based on cost.
D = 50,000
Cap = 200,000
$5 x 140,000
D = 100,000
$2 x 50,000
$1 x 100,000
$2 x 60,000
Cap = 60,000
$2 x 50,000
D = 50,000
Total Costs = $1,120,000

5. Traditional Approach #2: Assign each market based on total landed cost$0
D = 50,000 $3
Cap = 200,000
P1 to WH1 $3
P1 to WH2 $7
P2 to WH1 $7
P2 to WH 2 $4 $4 $6 $5
D = 100,000 $2
P1 to WH1 $4
P1 to WH2 $6
P2 to WH1 $8
P2 to WH 2 $3 $4 $1 $2
Cap = 60,000 $2
D = 50,000
P1 to WH1 $6
P1 to WH2 $7
P2 to WH1 $10
P2 to WH 2 $4

6. Traditional Approach #2: Assign each market based on total landed cost$0
D = 50,000 $3
Cap = 200,000
P1 to WH1 $3
P1 to WH2 $7
P2 to WH1 $7
P2 to WH 2 $4 $4 $6 $5
D = 100,000 $2
P1 to WH1 $4
P1 to WH2 $6
P2 to WH1 $8
P2 to WH 2 $3 $4 $1 $2
Cap = 60,000 $2
D = 50,000
P1 to WH1 $6
P1 to WH2 $7
P2 to WH1 $10
P2 to WH 2 $4
Market #1 is served by WH1, Markets 2 and 3
are served by WH2

7. Traditional Approach #2: Assign each market based on total landed cost
$0 x 50,000
D = 50,000
$3 x 50,000
Cap = 200,000
P1 to WH1 $3
P1 to WH2 $7
P2 to WH1 $7
P2 to WH 2 $4
$5 x 90,000
D = 100,000
P1 to WH1 $4
P1 to WH2 $6
P2 to WH1 $8
P2 to WH 2 $3
$1 x 100,000
$2 x 60,000
Cap = 60,000
$2 x 50,000
D = 50,000
P1 to WH1 $6
P1 to WH2 $7
P2 to WH1 $10
P2 to WH 2 $4
Total Cost = $920,000

8. What is the LP?

9. What is the LP?

10. Demand Allocation Model
Which market is served by which plant?
Which supply sources are used by a plant?
xij = Quantity shipped from plant site i to customer j
5-10

11. The Optimal Strategy Table 2 Distribution strategy
Facility P1 P2 C1 C2 C3
Warehouse W1
140000
50000
90000 W2
60000
10000
50000
The total cost for the optimal strategy is 740,000.

12. A real example: much more complex problem, the current Network
Inbound: $ ,000
Outbound: $ 2,930,000
Inv Cost: $13,291,000
WH Fixed: $ 1,875,000
Total: $18,947,000

13. A real example: Optimal Network
Inbound: $ ,000
Outbound: $ 5,900,000
Inv Cost: $ 7,679,000
WH Fixed: $ ,000
Total: $14,987,000
$4 Million Savings