1. Transportation & Supply Chain Costs: Answers to Questions
John H. Vande Vate
Spring, 2001 1

2. Assignment #1 (Group)
How does the average inventory at the origin compare with the common estimate:
Average Shipment Size/2 or
Production Rate * Average Headway/2? 2

3. Analysis Item Hours from one headway Total Item Hours Total Time
headway*shipment size/2
headway*(headway*Rate of Demand)/2
headway2*Rate of Demand/2
Total Item Hours
sum (hi2*D’)/2
Total Time
sum hi
Average Items in Inventory
sum (hi2*D’)/[2*sum(hi)] 3

4. Production Rate * Average Headway/2?
Average Inventory
sum (hi2*D’)/[2*sum(hi)]
How does this compare with
Production Rate * Average Headway/2?
i.e., with Avg(h)*D’/2?
How does sum(hi2)/sum(hi) compare with Avg(h)? 4

5. How does sum(hi2)/sum(hi) compare with Avg(h)?
Some extremes
There’s just one headway
Headways are 0 and H
More general
(h12 + h22)/(h1+h2) ? (h1+h2)/2
2(h12 + h22) ? (h1+h2)2
(h1-h2)2 ? 0 5

6. Conclusion
If there is variation in the headways then the average number of items in inventory is greater than estimated from the average headway
Why? 6

7. (Un)Common Sense
Inventories associated with longer headways are not only larger, they are also around longer. 7

8. Apparent Contradiction
Time
Cumulative number of items
Cumulative Production
Cumulative Demand
In transit
Apparent Contradiction
“The maximum accumulation at the destination is the same as it is at the origin”
Max. Inv. at Destination
Max. Inv. at Origin 8

9. Assignment #2 Explain this apparent contradiction.
Is Daganzo just plain wrong?
Can we calculate the maximum inventory at the destination?
What about the average inventory? 9

10. Explanation Daganzo is right is we also assume that
Shipment arrives when customer inventory reaches 0
What does this say about transit times, etc.? 10

11. Average Inventories at Destination
How to calculate this when transit time varies?
Inventory at Origin + Pipeline + Destination = Total Inventory 11

12. Maximum Inventory It is a random variable Bound it
Calculate a distribution
Tail Probabilities
... 12

13. Assignment #3 E(f(x))  f(E(x))
Avg. Cost of Shipment  Cost of Avg. Shipment
Assignment 3: What relationship is there between
Avg. Cost of Shipment
Cost of Avg. Shipment? 13

14. LTL Rates Total Cost Volume Shipped Cost of Avg. Shipment Avg. Cost of14
Customer 1
Volume Shipped
Customer 2

15. Conclusion
Typically the Cost of the Average Shipment Overestimates the Average Cost of a shipment.
Calculating the Average Cost of a shipment is more tedious.
Get Average Cost of Shipment from averages for each segment 15