1. Project #1 Optimization Model
John H. Vande Vate
Spring, 2001 1

2. Careful about Words... Plants can ship to
DCs (direct) or
The Warehouse (indirect)
All combined shipments come from the warehouse (not the Indiana plant). 2

3. Without Optimization For each DC there are 4 options:
All parts direct
All parts via Indianapolis warehouse
Green Bay & Indianapolis ship via warehouse
Denver & Indianapolis ship via warehouse
Easy to calculate which of these is cheaper …. 3

4. But...
Ignoring the inventory implications at the plants and warehouse for indirect shipments
Why? 4

5. Not per DC 5

6. Inventory at the Warehouse6

7. Approaches Inbound: Half a truckload Outbound: ?
The problem of different headways
Estimates:
Average Headway
(too small and hard to model)
Maximum Headway
(too large, easy to model) 7

8. What’s right? Aware of the need for estimation
Explain and understand the estimates you use
Evaluate the quality empirically
The real story? 8

9. Time How much does indirect shipment add to the time to market?
Production
Production
Demand 9

10. EOQ How to calculate the optimal shipment size? Is the cost per unit:
Distance/Q + Interest Rate*Value or
Distance/Q + Interest Rate*Value/2? 10

11. Actually, Neither Want to minimize This is not separable… Cost of
Inventory at Plant: S Qi2/(2SQi)
Inventory at the DCs: SQi/2
Transportation: Sdistance*D’/Qi
This is not separable… 11

12. Approximation Approximate inventory at Plant by Average Q/2
If n DCs are served directly,
EOQ = (2*fixed*Annual Demand/ci)*n/(n+1)
So, the better approximation appears to be
(2*fixed*Annual Demand/ci)
Unless n is very small, e.g., 1 or 2 12

13. Without Optimization
Ignore inventory at the plants and at the warehouse
Calculate best strategy at each dc
All Direct: $4.5 million
Only Denver via Indianapolis: $4.1 million
Only GB via Indianapolis: $3.5 million
All via Indianapolis: $3.0 million
Best at each DC: $3.0 million 13

14. Conclusions Optimal solution will supply most dcs via Indianapolis
EOQ for Direct shipments might be closer to
(fixed*Annual Demand/ci) 
(2*fixed*Annual Demand/ci)*n/(n+1)
EOQ for shipments via Indianapolis might be closer to
(2*fixed*Annual Demand/ci) 14

15. Overview Sets Parameters PLANTS DCS
OPTIONS: All direct, none direct, ...
Parameters
Distances
EOQs
for direct shipments and
each option via the warehouse 15

16. Variables Select an option for each dc
Whether or not each plant ships to the warehouse
Optionally, indicate whether or not each plant serves each dc directly (can be inferred from the option chosen.
Maximum Shipment Value from each plant and from the warehouse to calculate inventory costs 16

17. Objective Transportation Costs Inventory Costs
Carrying cost for 1/2 the appropriate EOQ at the DCs
1/2 the maximum value of a shipment at the plants and the warehouse
Carrying cost of 1/2 a truckload at the warehouse for each plant that ships to the warehouse. 17

18. Constraints Select a single option at each dc
Whether or not each plant ships to the warehouse
Calculate the maximum shipment value from each plant
Calculate the maximum shipment value from the warehouse 18