11

Transportation & Supply Chain Costs

John H. Vande Vate

Spring, 2001

22

Two Primary Types• Moving (change of place)

– Handling• loading

• unloading

• ...

– Transportation

• Holding (change of time)– from production to consumption (goods)– from investment to revenue ($)

33

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

44

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?

55

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

66

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

77

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

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produced

consumedshipped

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nth item

Constant DemandConstant Demand

In transit

In transit

99Time

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In transit

Constant Demand

Item-hours waiting

1010

• 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

1111

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

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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”

1313

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?

1414

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

1515

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

1616

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)

1717

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

1818

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?

2020

Analogy

What would you pay to reduce the minimum balance you must hold in

your checking account?

2121

Transportation Costs

• Parcel

• LTL - less than truckload

• Truckload

• Rail car

• Unit train

• ...

2222

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

2323

What is the Rate?

• Bundled rates

• Exchanges

• Combinatorial bidding

• ….

2424

Concave

• fixed origin, destination and class

• Increasing in weight

• Increasing at a decreasing rate

2525

LTL Rates

fixedVariable

Tot

al C

ost

Volume Shipped

Total = fixed + variable*volume

2626

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?

2727

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

2828

EOQ

• Cost per item– ci (volume/Annual demand) + fixed/ volume + variable

• Shipment Size– volume = (fixed*Annual Demand/ci)

• Assume you can handle from here….

2929

Handle from here

• If EOQ falls in range...

• If EOQ exceeds range…

• If EOQ falls below range…

• etc.

3030

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

3131

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

3232

Lead Time Demand

• Expected Lead time Demand– D’tm

• Variance in Lead time Demand– D’22 + D’tm

3333

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

3434

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)

3535

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

3636

Expediting

• Transportation– fixed + variable*volume + cef(s)

• Inventory– ci(volume + Safety Stock)/Annual Demand

• EOQ formula for volume

3737

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

3838

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– ???

3939

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?

4040

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