Transportation & Supply Chain
Costs:
Answers to Questions
John H. Vande Vate
Spring, 2001
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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?
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Analysis
• Item Hours from one headway
– 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)]
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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)?
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2
sum(hi )/sum(hi)
How does
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
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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?
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(Un)Common Sense
• Inventories associated with longer
headways are not only larger, they are
also around longer.
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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
In transit
Time
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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?
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Explanation
• Daganzo is right is we also assume that
– Shipment arrives when customer
inventory reaches 0
– What does this say about transit times,
etc.?
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Average Inventories at Destination
• How to calculate this when transit time
varies?
• Inventory at Origin + Pipeline +
Destination = Total Inventory
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Maximum Inventory
•
•
•
•
•
It is a random variable
Bound it
Calculate a distribution
Tail Probabilities
...
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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?
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LTL Rates
Total Cost
Cost of
Avg. Shipment
Avg. Cost of
Shipment
Avg. Shipment
Customer 1
Volume Shipped
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Customer
2
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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
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