1. Use More Soap Building Supply Chain Models Fixed Costs Aggregation
Transportation Costs
Inventory Costs
Basic Model Building

2. Fixed Costs Capital costs Operating costs
Investments in depreciable assets
buildings
equipment
patents
Operating costs
Recurring expenses
labor
rent
fuel

3. Different Animals $4,000,000 to expand a plant
Annual operating expenses
Handling costs
Transportation costs
Ordering costs
Do not mix

4. Cost of Capital Use Cost of Capital Careful about “fixed” costs
Opportunity Cost
Financing Cost, etc.
Careful about “fixed” costs

5. Aggregation Aggregating Products Families or baskets
Products with similar characteristics

6. Aggregating Customers
By segment
Commercial
Consumer
etc.
Geographically
Census Tract
ZIP Code
3-digit ZIP
State
Territory

7. Calculating Transport Costs
Regression against past costs
Depend on
Distance
Location
Order size!

8. Calculating Transport Costs
Regression against past costs
Depend on
Distance
Location
Order size!

9. A Classic Trap Aggregating Large and Small Customers Total Cost
Average Shipment
Large Shipment
Small Shipment
Shipment Size

10. A Classic Trap Aggregating Large and Small Customers
Cost of Average Shipment
Total Cost
Average Cost of Shipment
Average Shipment
Large Shipment
Small Shipment
Shipment Size

11. Aggregate Transport Costs
Average of shipment costs
Not cost of average shipment

12. What Problems? Changing Channels
Must re-cost many shipments and average
Easier to Cost a single average shipment

13. Inventory Typical Model Pull Model
Inventory grows as sqrt of Throughput
Pull Model
Inventory depends on
Shipment sizes
Number of channels

14. Modeling Traditional Inventory
Throughput

15. Approximating the curve
Requires integer variables to force solver to take all the expensive Rapid Increase before any of the inexpensive Slow Increase
Inventory
Rapid Increase
Slow Increase
Break
Throughput
Max

16. How that works Throughput = CWT of throughput
Rapid = CWT of throughput incurring high inventory cost (up to Break)
Slow = CWT of throughput beyond Break incurring low inventory cost
IsRapidFull = Binary variable indicating which region we are in
IsRapidFull = 0 means Throughput is less than Break
IsRapidFull = 1 means Throughput is more

17. Constraints Throughput = Slow + Rapid Rapid <= Break
Rapid >= Break*IsRapidFull
Slow <= (Max-Break)*IsRapidFull
Cost = High Cost * Rapid + Low Cost * Slow

18. Modeling Pull Inventory
Count the number of Channels
Need Integer Variable for each channel
IsChannelUsed = 1 if used, 0 otherwise
Volume on Channel <= IsChannelUsed*Bound
The smaller the bound, the better this works (typically).

19. Reality Probably some combination
“Safety Stock” increases with additional distribution centers
More smaller centers = more safety stock
Quadratic relationship
Pull inventory depends on channels and modes