Transportation & Supply
Chain Costs
John H. Vande Vate
Spring, 2001
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1
Two Primary Types
• Moving (change of place)
– Handling
• loading
• unloading
• ...
– Transportation
• Holding (change of time)
– from production to consumption (goods)
– from investment to revenue ($)
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2
Holding Cost
• Rent (Fixed)
– Cost of the space
– Handling equipment
– Maintenance
• Waiting or Holding Costs (Variable)
– (Opportunity) Cost of capital tied up in
goods
– Shrinkage, Spoilage
– Obsolescence
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3
System Costs
•
•
•
•
Including those we don’t bear
These are the costs the ultimate customer sees
These costs influence our competitiveness
Supply Chain Management
– Examples?
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4
Holding Costs
• Uses of Inventory
– Cycle Stock
• consequence of batching or to avoid
changeovers
– Anticipatory Inventory
• storing capacity for peak period
• advance purchasing to exploit discounts
– Safety Stock
• buffer against variability in lead-time demand
– Pipeline Inventory
• Goods in transit
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Our Focus
– Cycle Stock
• As influenced by transportation
– awaiting shipment
– shipment awaiting sales
– Anticipatory Inventory
– Safety Stock
• buffer against variability in
– lead-time
– demand
– Pipeline Inventory
• Goods in transit
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6
Constant Demand
– Cycle Stock
• As influenced by transportation
– awaiting shipment
– shipment awaiting sales
– Anticipatory Inventory
– Safety Stock
• buffer against variability in
– lead-time
– demand
– Pipeline Inventory
• Goods in transit
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7
Constant
ConstantDemand
Demand
In transit
In transit
nth item
kth item
In transit
consumed
shipped
produced
Time
received
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8
Constant Demand
In transit
Item-hours waiting
Time
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9
Inventory at Origin
• Assumption:
– Ship all that’s produced
•
•
•
•
•
Item-hours waiting
Item-hours waiting = Area
Area = (base * height)/2
Area = (headway*shipment size)/2
Avg. Waiting time per item = headway/2
Maximum Inventory =
Production Rate*Maximum Headway
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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?
• Do not turn anything in, just give a
clear explanation if called on next class
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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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Rent or “Fixed” costs
• Fixed vs Sunk costs
– Sunk Costs: Money already spent that cannot be
influenced by the decisions in question
• Capital investments in real estate, buildings,
equipment,…
• IGNORE
– Fixed Costs: If we are considering liquidating
capital investments or making additional
investments.
• DON’T COMPARE WITH OPERATING COST
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Rent or Fixed Costs
• Grow with the maximum inventory
• Probably economies of scale
• Only appropriate if
– Space is leased or
– Strategic planning for facility investments
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Holding Costs
• Cost per Unit
– ci = holding cost per item per year
– Typically the product of
» a “cost of funds” rate i
» the cost or value of an item
• Total Holding Cost
– ci *(Item-years in inventory)
– ci (Annual production rate*Time from production to consumption)
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Finer View
• Inventory at the source
– ci (Average inventory at the source)
• Pipeline Inventory
– ci (Average inventory in transit)
– ci (Annual Demand)(Avg. transit time in yrs)
• Inventory at the destination
– ci (Average inventory at the destination)
– ci typically larger here -- we invested in
handling and transportation
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Basic Understanding
• Our Example in Class reduced
inventory value by $130 million
• How do we account for those savings?
What are they worth?
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Before & After
Expenses
$150 mil.
Revenues
$130 mil
Expenses
Revenues
$20 mil.
mil/yr? 19
What
didsave
we the
savecompany
the company?
Did we
$130 mil?
19
Analogy
What would you pay to reduce the
minimum balance you must hold in
your checking account?
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20
Transportation Costs
•
•
•
•
•
•
Parcel
LTL - less than truckload
Truckload
Rail car
Unit train
...
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LTL Rates
• Freight Class
• Weight range
–
–
–
–
–
0-500lbs
500-1000 lbs
1000-5000 lbs
5000-1000 lbs
...
Base Rate
• Origin ZIP (3 digit)
• Destination ZIP (3 digit)
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What is the Rate?
•
•
•
•
Bundled rates
Exchanges
Combinatorial bidding
….
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Concave
• fixed origin, destination and class
• Increasing in weight
• Increasing at a decreasing rate
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fixed
Total Cost
LTL Rates
Volume Shipped
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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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Shipment Size
• Fix the range
– e.g. 1,000-5000 lbs
• Transportation Cost
– fixed + variable * volume
• Inventory
– ci $/item/year
– item in inventory for (roughly)
volume/Annual demand
• Cost per item
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– ci (volume/Annual demand) + fixed/ volume + variable
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EOQ
• Cost per item
– ci (volume/Annual demand) + fixed/ volume + variable
• Shipment Size
– volume = (fixed*Annual Demand/ci)
• Assume you can handle from here….
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Handle from here
•
•
•
•
If EOQ falls in range...
If EOQ exceeds range…
If EOQ falls below range…
etc.
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Variability
• Pull strategies, e.g, (s, S) or continuous
review policies
– When inventory (on hand and on order)
drops to s, order S.
– s consists of
• expected lead time demand +
• safety stock
– protection against variability in lead time demand
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Common Model
• Demand modeled as a diffusion process
– rate D’(items per year)
– index of dispersion  (items)
– In a period of length t
• Demand is normally distributed
• mean is D’t
• variance is D’t
• Lead time taken as normally distributed
– mean tm
– variance 2
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Lead Time Demand
• Expected Lead time Demand
– D’tm
• Variance in Lead time Demand
– D’22 + D’tm
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Classical Approach
• Set safety stock to 2 or 3 standard deviations
in lead time demand
• This increases average inventory by 2 or 3
standard deviations in lead time demand
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Alternate Approach
• Expedite
– ce constant cost per unit expedited (e.g.,
next day air)
• Need to calculate f(s)
– Expected number of items expedited per
regular order if we set the reorder point at
s (treat this as fixed)
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Expediting vs Safety Stock
12,000
1,000
900
10,000
800
700
8,000
600
6,000
500
400
4,000
300
200
2,000
100
0
0
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Expediting
• Transportation
– fixed + variable*volume + cef(s)
• Inventory
– ci(volume + Safety Stock)/Annual Demand
• EOQ formula for volume
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Shipment Size vs Safety Stock
12,000
4,000
3,500
10,000
3,000
8,000
2,500
6,000
2,000
1,500
4,000
1,000
2,000
500
0
0
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How important was this?
• The major influence of expediting is to
– Change the shipment size?
– Change the reorder point?
– ….
• We want to trade off
– Costs of expediting vs
– ???
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How to go about this?
• Previous method finds best shipment
size for each re-order point s: S(s)
• The best cost at reorder point s:
– cost (s, S(s))
• Search for the best value of s
• Why does shipment size matter?
• Does this raise an issue with f(s), the
expected number expedited per regular
shipment if the reorder point is s?
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Cost vs Safety Stock
12,000
$5.00
$4.50
10,000
$4.00
$3.50
8,000
$3.00
6,000
$2.50
$2.00
4,000
$1.50
$1.00
2,000
$0.50
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0
$-
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