Modeling Inventory
(Deterministic View)
John H. Vande Vate
Spring 2007
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Types of Inventory
• Deterministic Inventory
– Pipeline Inventory: Inventory in transit
– Cycle Inventory:
• Goods accumulating for transit
• Goods delivered and waiting for processing
• Stochastic Inventory (later)
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Illustrative Example
• Develop a distribution strategy to minimize
inventory and transportation costs
• Purpose:
– Outline issues covered in outbound logistics
– The importance of transportation in the supply
chain
– Illustrate costs and investments
– Always do a quick analysis first, then refine
it.
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Overview
• Products:
– Computers: CPU, Monitor, Keyboard
– Televisions: TV and Console
• Stores
– 100 across the US
– Sell 10 TVs and 10 computers per day
– 250 days/year
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We assume weightComponents
not
cube determines vehicle
capacity
Truck holds 30,000
lbs
Computers
TV/Monitor
Cost
$300
$400
Console
$100
Weight
5 lbs
10 lbs
30 lbs
Green Bay
Indianapolis Denver
From
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Initial Strategies to Consider
• All direct shipments in full truckloads
• Consolidate in Indianapolis. All
shipments in full truckloads
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Simplification
• Shipments on the order of 1,000 miles
Gre e n Bay
De nve r
Indianapolis
Distances
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What Costs?
•
•
•
•
•
•
Transportation
Pipeline inventory – inventory in transit
Inventory at Plants
Inventory at Stores
Handling
…
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Direct:Transportation Cost
• How many shipments/year?
–
–
–
–
Green Bay
Indianapolis
Denver
Total
100*2,500/6,000 = 41.67
100*5,000/3,000 =166.67
100*2,500/1,000 = 250
~ 460
100 stores * Annual Store Demand /Items to fill a truck
Items to fill a truck = Cap. of truck/Weight of Item
– Green Bay
– Indianapolis
– Denver
30,000/5 = 6,000
30,000/10 = 3,000
30,000/30 = 1,000
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What Costs?
• Direct
– Transportation ~
• $1/mile*1,000 miles/trip*460 trips/year = $460,000/year
–
–
–
–
–
Pipeline inventory
Inventory at Plants
Inventory at Stores
Handling
…
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Pipeline Inventory
• How long are goods in transit?
– 1,000 miles at 50+ miles per hour
– 2 days +
• How much inventory is in transit on
average?
• Imagine we send the items one-at-a-time
• How many items in the pipe?
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Pipeline Inventory
• One Day worth of sales at a Store
– 10 TVs at $400+$100 each = $5,000
– 10 Computers at $300+$400 = $7,000
– Total $12,000 per day per Store
• Two days of system-wide sales:
– 2 days * $12,000/Store/day * 100 stores = $2,400,000
– Carrying cost 15% of $2,400,000 = $360,000
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What Costs?
• Direct
– Transportation ~
• $1/mile*1,000 miles/trip*460 trips/year = $460,000/year
– Pipeline inventory
• $2,400,000 in capital
• $360,000 in annual carrying costs
–
–
–
–
Inventory at Plants
Inventory at Stores
Handling
…
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Inventory at the Plants
• Two Extremes
– Simultaneous shipments
– Staggered shipments
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Simultaneous Shipments
• A truckload of computers from Green Bay
has 6,000 computers in it
• A Store sells 2,500 per year
• So we only need to replenish the Stores
every 6,000/2,500 = 2.4 years
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Inventory at Green Bay
• Simultaneous Shipments
600,000
2.4 years
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Simultaneous shipments
– Green Bay ships once every 2.4 years
• Inventory is 1.2 years demand or 300,000 CPUs
• Inventory value is $90,000,000
• Inventory carrying cost is $13,500,000
– Denver ships 2.5 times per year
• Inventory is 20% of annual demand or 50,000 Consoles
• Inventory value is $5,000,000
• Inventory carrying cost is $750,000
– Indianapolis ships 1.6 times per year
• Inventory is 500,000/3.2 or about 150,000 items
• Inventory value is $60,000,000
• Inventory carrying cost is $9,000,000
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Why Not?
• What are problems with simultaneous
shipments?
• When are simultaneous shipments likely?
• What alternatives?
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Inventory at Green Bay
• Staggered Shipments
6,000
~6 days
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What Costs?
• Inventory at Plants
– Simultaneous Shipments
•
•
•
•
Green Bay
Denver
Indianapolis
Total
Capital
Carrying Cost
$90 million
$ 5 million
$60 million
$155 million
$13.5 million
$ .75 million
$ 9.0 million
$23.25 million
– Staggered Shipments (divide by 100!)
Capital
•
•
•
•
Green Bay
$900 K
Denver
$ 50 K
Indianapolis $600 K
Total
$1.55 million
Carrying Cost
$135 K
$ 7.5 K
$ 90 K
$232.5 K
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What Costs?
• Direct
– Transportation ~
• $1/mile*1,000 miles/trip*460 trips/year = $460,000/year
– Pipeline inventory
• $2,400,000 in capital
• $360,000 in annual carrying costs
– Inventory at Plants – Staggered Shipments
• $1.55 million in capital
• $232.5 K in annual carrying costs
– Inventory at Stores
– Handling
– …
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DC Inventory from Green Bay
6,000
~2.4 years
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Inventory at Stores
• At the Stores?
– ½ truckload or 3,000 CPUs at $300 each: $900,000
– ½ truckload or 1,500 Monitors at $400 each: $600,000
– ½ truckload or 500 Consoles at $100 each: $ 50,000
$1,550,000
Carrying cost: 15% of $1,550,000 or $232,500
Total Carrying cost at the Stores: $23,250,000!
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What Costs?
• Direct
– Transportation ~
• $1/mile*1,000 miles/trip*460 trips/year = $460,000/year
– Pipeline inventory
• $2,400,000 in capital
• $360,000 in annual carrying costs
– Inventory at Plants – Staggered Shipments
• $1.55 million in capital
• $232.5 K in annual carrying costs
– Inventory at Stores
• $155 million in capital
• $23.25 million in carrying costs
– Handling
– …
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Total Cost & Capital Direct
Costs
• Transportation Costs:
$
• Pipeline Inventory
$
• Inventory Costs at Plants: $
• Inventory Costs at Stores: $
Total: $
Capital Required:
• Pipeline Inventory
$
• Inventory Costs at Plants: $
• Inventory Costs at Stores: $
Total: $
460,000
360,000
232,500
23,250,000
24,302,500!
2,400,000
1,550,000
155,000,000
158,950,000!
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Consolidation
• Strategy 2: Assemble Products in
Indianapolis and distribute by truckload
from there
• What will happen to costs?
–
–
–
–
–
Transportation
Pipeline
At plants
At Indianapolis Warehouse/Cross Dock
At Stores\s
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Via Indianapolis
Gre e n Bay
De nve r
Indianapolis
Facts
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What Costs?
• Transportation
– To Indianapolis
– From Indianapolis to Stores
• Pipeline inventory
– To Indianapolis
– From Indianapolis to Stores
•
•
•
•
•
Inventory at Plants
Inventory at Indianapolis Cross Dock
Inventory at Stores
Handling
…
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Indirect: Transportation
• To Indianapolis
–
–
–
–
Green Bay 400 miles* 42 trips = 16,800
Indianapolis
0 miles*167 trips =
~ 0
Denver
1,100 miles*250 trips = 275,000
Total
$291,800
• From Indianapolis to Stores
– Same as total transport before, we are moving
the same goods the same distance (roughly
1,000 miles to each Store)
$460,000
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What Costs?
• Transportation
– To Indianapolis
– From Indianapolis to Stores
$291,800
$460,000
• Pipeline inventory
– To Indianapolis
– From Indianapolis to Stores
•
•
•
•
•
Inventory at Plants
Inventory at Indianapolis Cross Dock
Inventory at Stores
Handling
…
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Pipeline Inventory
• To Indianapolis
– From Green Bay 400 miles ~ 1 day
• 1,000 per day at $300 each ~ $300,000 capital
• 15% of $300,000 is $45,000 carrying cost
– From Denver 1,100 miles ~ 2 days
• 2 days at 1,000 per day at $100 each ~ $200,000 capital
• 15% of $200,000 is $30,000 carrying cost
– Total
• Capital $500,0000
• Carrying Cost $ 75,0000
• From Indianapolis to Stores
– Same as before 2 days of sales
– Capital
$2,400,000
– Carrying Cost
$ 360,000
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What Costs?
• Transportation
– To Indianapolis
– From Indianapolis to Stores
$291,800
$460,000
• Pipeline inventory
– To Indianapolis
• Capital
• Carrying Cost
$500,000
$ 75,000
– From Indianapolis to Stores
• Capital
• Carrying Cost
•
•
•
•
•
$2,400,000
$ 360,000
Inventory at Plants
Inventory at Indianapolis Cross Dock
Inventory at Stores
Handling
…
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Inventory at Plants
• Same as before
– Green Bay holds ½ of a truckload
– Denver holds ½ of a truckload
– Assume Indianapolis holds ½ of a truckload
for delivery to the cross dock
– Capital
$1,550,000
– Carrying Cost
$ 232,500
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What Costs?
• Transportation
– To Indianapolis
– From Indianapolis to Stores
$291,800
$460,000
• Pipeline inventory
– To Indianapolis
• Capital
• Carrying Cost
$500,000
$ 75,000
– From Indianapolis to Stores
• Capital
• Carrying Cost
$2,400,000
$ 360,000
• Inventory at Plants
– Capital
– Carrying Costs
$1,550,000
$ 232,500
• Inventory at Indianapolis Cross Dock
• Inventory at Stores
• Handling
• …
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Inventory at Cross Dock
Receiving
Shipping
WIP
CPUs, Monitors, Consoles
Computers & TVs
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Inventory at Indianapolis Cross
Dock
• Receiving from the Plants
– ½ a truckload of CPUs
– ½ a truckload of Monitors
– ½ a truckload of Consols
Capital
$1,550,000
Carrying Cost $ 232,500
• Shipping to the Stores
– ½ a truckload of Computers and TVs
• WIP – like Pipeline inventory
– How long does the process take?
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What’s in a Truck
• Of Computers and TVs?
• In the same mix as demand
–
–
–
–
–
–
1:1 computers to TVs
X computers in a truck
Weight of the computers 15X lbs
Weight of the TVs 40X lbs
15X + 40X = 30,000 lbs
X = 30,000/55 = 545
• A full truck of finished goods has
– 545 computers and 545 TVs
– 545 CPUs, 545 Consoles and 1090 Monitors
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Inventory at Indianapolis
Cross Dock
• Receiving from the Plants
– ½ a truckload of CPUs
– ½ a truckload of Monitors
– ½ a truckload of Consols
Capital
$1,550,000
Carrying Cost $ 232,500
• Shipping to the Stores
– ½ a truckload of Computers and TVs
•
•
•
•
•
273 CPUs at $300 each or
273 Consoles at $100 each or
545 Monitors at $400 each or
Total
Carrying cost
$ 81,900
$ 27,300
$218,000
$327,200
$ 49,080
• WIP – like Pipeline inventory
– How long does the process take?
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Inventory at Stores
• Inventory at a Store:
– Visited by truck 4.6 times per year
– Same as before
– So inventory costs at Stores are the same
as before, right?
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Wrong! Magic?
Product
TV
Computer
Value
$ 500.00
$ 700.00
Number
per year
2,500
2,500
Number per
shipment
545
545
Inventory
Carrying
Average
Average Value
Inventory
of Inventory
Cost
273 $
136,500 $
20,475
273 $
191,100 $
28,665
Total: $
49,140
• Total Inventory Carrying Cost at Stores:
$4,914,000
compared with
$23,250,000
under earlier strategy. Explain!
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The Difference
Product
TV
Computer
Value
$ 500.00
$ 700.00
Part
CPU
Monitor/Keyboard
Console
Number
per year
2,500
2,500
Value
$300
$400
$100
Number
per year
2500
5000
2500
Number per
shipment
543
543
Number per
shipment
6,000
3,000
1,000
Inventory
Average
Average Value
Carrying
Inventory
of Inventory
Cost
272 $
135,869.57 $ 20,380.43
272 $
190,217.39 $ 28,532.61
Total: $ 48,913.04
Average
Inventory
3,000
1,500
500
Average Value
of Inventory
$
900,000.00
$
600,000.00
$
50,000.00
Total:
Inventory
Carrying Cost
$ 135,000.00
$ 90,000.00
$
7,500.00
$ 232,500.00
Explain?
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With Consolidation
– Transportation Costs:
$
751,800
– Inventory Costs at Stores: $ 4,891,300
– Inventory Costs at Plants: $
513,900
Total: $
6,757,000
Without Consolidation
– Transportation Costs:
$
460,000
– Inventory Costs at Stores: $ 23,250,000
– Inventory Costs at Plants: $
232,500
Total: $ 23,942,500!
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Comparison
Direct
Capital
Transportation
To Indianapolis
From Indianapolis to stores
Pipeline Inventory
To Indianapolis
From Indianapolis to stores $
Inventory at Plants
$
Inventory at Cross Dock
Receiving
Shipping
Inventory at stores
$
Total
$
Cost
$
$
Consolidation
Capital
Cost
460,000
2,400,000 $
1,550,000 $
$
360,000 $
232,500 $
155,000,000 $
158,950,000 $
$
$
23,250,000 $
24,302,500 $
$
$
291,800
460,000
500,000 $
2,400,000 $
1,550,000 $
75,000
360,000
232,500
1,550,000
327,600
32,760,000
39,087,600
$
$
$
$
232,500
49,140
4,914,000
6,614,940
Invest some of the $120 million in the cross dock
Spend some of the $18 million on handling
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Summary
• Deterministic Inventory
– Pipeline
– Cycle
– WIP
•
•
•
•
•
Pipeline from Days in transit * Value/Day
Cycle from half of shipment
WIP like pipeline
Value of consolidation
Quick & Dirty analysis first
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Deterministic Supply Chain
Design
• Next time: should we be shipping in full
truckloads?
• Later, different kinds of cross docks
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