1 1 Transportation & Supply Chain Costs John H. Vande Vate Spring, 2001.
Transcript of 1 1 Transportation & Supply Chain Costs John H. Vande Vate Spring, 2001.
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Transportation & Supply Chain Costs
John H. Vande Vate
Spring, 2001
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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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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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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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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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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
88Time
Cum
ulat
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num
ber
of it
ems
Cumul
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e Pr
oduc
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Cumul
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e D
eman
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kth item
produced
consumedshipped
received
In transit
nth item
Constant DemandConstant Demand
In transit
In transit
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of it
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In transit
Constant Demand
Item-hours waiting
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• Assumption: – Ship all that’s produced
• 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
Inventory at Origin
Item-hours waiting
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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
1212Time
Cum
ulat
ive
num
ber
of it
ems
Cumul
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oduc
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In transit
Apparent Contradiction
Max. Inv. at Origin
Max. Inv. at Destination
“The maximum accumulation at the
destination is the same as it is at the origin”
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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?
1919Did we save the company $130 mil/yr? Did we save the company $130 mil?
Before & After
$150 mil.RevenuesExpenses
$130 mil
$20 mil.
RevenuesExpenses
What did we save the company?
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Analogy
What would you pay to reduce the minimum balance you must hold in
your checking account?
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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– ...
• Origin ZIP (3 digit)• Destination ZIP (3 digit)
Base Rate
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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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LTL Rates
fixedVariable
Tot
al C
ost
Volume Shipped
Total = fixed + variable*volume
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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– 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’22 + 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
0
2,000
4,000
6,000
8,000
10,000
12,000
0
100
200
300
400
500
600
700
800
900
1,000
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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
0
2,000
4,000
6,000
8,000
10,000
12,000
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
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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
0
2,000
4,000
6,000
8,000
10,000
12,000
$-
$0.50
$1.00
$1.50
$2.00
$2.50
$3.00
$3.50
$4.00
$4.50
$5.00