Modeling Inventory (Deterministic View)

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Modeling Inventory(Deterministic View)

John H. Vande VateSpring 2008

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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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Components

Computers TV/Monitor ConsoleCost $300 $400 $100

Weight 5 lbs 10 lbs 30 lbs

From Green Bay Indianapolis Denver

We assume weight not cube determines vehicle

capacityTruck holds 30,000 lbs

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Current Situation• All direct shipments in full truckloads

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Simplification • Shipments on the order of 1,000 miles

F

F

F

Green Bay

Indianapolis Denver

Distances

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What Costs?

• Transportation• Pipeline inventory – inventory in transit• Inventory at Plants• Inventory at Stores• Handling• …

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Transportation Costs• Estimate number of shipments/year

– Annual Demand (in units)/Units per TruckUnits per Truck = TL Capacity (in lbs) Weight of Unit– CPU: 6,000 = 30,000/5– Monitor: 3,000 = 30,000/10– Console: 1,000 = 30,000/30

• Estimate cost per shipment $/mile * Average Miles per shipment

• The product gives total cost

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Direct:Transportation Cost

• How many shipments/year?– Green Bay– Indianapolis– Denver– Total100 stores * Annual Store Demand /Items to fill

a truck

100*2,500/6,000 = 41.67100*5,000/3,000 = 166.67100*2,500/1,000 = 250

~ 460

Why 5,000?

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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• Little’s Law• L = WNumber of items in the pipe (L) = Rate the items arrive (Time each item spends in the pipe (W)• It doesn’t matter how they arrive

– One at a time– In parcels– In Truck loads– …

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Pipeline Inventory

• How long are goods in transit?– 1,000 miles at 50+ miles per hour– 2 days +

• How fast do they arrive?– Rate of sales

• Let’s calculate $ in the pipe instead of items

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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

• The $ in the pipe: $2.4 million!– That’s ALWAYS there.

• Carrying cost 15% of $2,400,000 = $360,000 per year– We pay that each year

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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 Green Bay• (Perfectly) Staggered Shipments

6,000

~6 days

Why ~6 days?

Inve

ntor

y

Time

Average Inventory?

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Inventory in Green Bay

• 3,000 units (Half a truck load)• $300 per unit• $900,000 in inventory• 15% capital charge => $135,000 in

carrying costs

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What Costs?

• Inventory at Plants– Perfectly Staggered Shipments

– Capital Carrying Cost

• Green Bay $900 K $ 135 K• Denver $ 50 K $ 7.5 K• Indianapolis $600 K $ 90 K• Total $1.55 million $ 232.5 K

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– Transportation ~ • $460,000/year


– Inventory at Plants – Staggered Shipments• $1.55 million in capital• $232.5 K in annual carrying costs

– Inventory at Stores– Handling– …

2020

Store Inventory from Green Bay

6,000

~2.4 years

Why ~2.4 years?

Inve

ntor

y

Time

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Inventory at Stores

• At EACH Store?– 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

$1,550,000Carrying cost: 15% of $1,550,000 or $232,500Total Capital at the Stores: $155 millionTotal Carrying cost at the Stores: $23,250,000!

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– Transportation ~ • $460,000/year


– 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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Costs• Transportation Costs: $ 460,000• Pipeline Inventory $ 360,000• Inventory Costs at Plants: $ 232,500• Inventory Costs at Stores: $ 23,250,000

Total: $ 24,302,500!Capital Required: • Pipeline Inventory $ 2,400,000• Inventory Costs at Plants: $ 1,550,000• Inventory Costs at Stores: $ 155,000,000

Total: $ 158,950,000!

Total Cost & Capital Direct

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Return on Capital• Return on Capital = Pre-tax Profit Capital Employed = Pre-Tax Profit * Revenues Revenues Capital Employed = Profit Margin * SPEED• How to improve Return on Capital?• What’s our SPEED?

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SPEED• Revenues: Well Cost of Goods, we don’t have

selling prices….• $12,000/day per store• $1.2 million per day• 250 days means $300 million• Capital Employed: $159 million (not counting the

cost of the stores, the factories, and anything else we own)

• Speed is 1.89 = 300/159, i.e., each year we generate $1.89 in revenue for every $1 invested.

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Your Job is…

• As newly hired VP of SC, your job is to improve:– profitability and– capital utilization

• Suggestions?

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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

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Via Indianapolis

F

F

F

Green Bay

Indianapolis Denver

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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– To Indianapolis $291,800– From Indianapolis to Stores $460,000

• Pipeline inventory – To Indianapolis– From Indianapolis to Stores


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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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• Pipeline inventory – To Indianapolis

• Capital $500,000• Carrying Cost $ 75,000

– From Indianapolis to Stores• Capital $2,400,000• Carrying Cost $ 360,000


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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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• Pipeline inventory – To Indianapolis

• Capital $500,000• Carrying Cost $ 75,000

– From Indianapolis to Stores• Capital $2,400,000• Carrying Cost $ 360,000

• Inventory at Plants– Capital $1,550,000– Carrying Costs $ 232,500

• Inventory at Indianapolis Cross Dock• Inventory at Stores • Handling• …

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Inventory at Cross Dock

Receiving Shipping

CPUs, Monitors, Consoles

Computers & TVsWIP

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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

• Shipping to the Stores– ½ a truckload of Computers and TVs

• WIP – like Pipeline inventory– How long does the process take?

Capital $1,550,000Carrying Cost $ 232,500

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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

• Shipping to the Stores– ½ a truckload of Computers and TVs

• 273 CPUs at $300 each or $ 81,900• 273 Consoles at $100 each or $ 27,300• 546 Monitors at $400 each or $218,400• Total $327,600• Carrying cost $ 49,140

• WIP – like Pipeline inventory– How long does the process take?

Capital $1,550,000Carrying Cost $ 232,500

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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 Value Number per year

Number per shipment

Average Inventory

Average Value of Inventory

Inventory Carrying

CostTV 500.00$ 2,500 545 273 136,500$ 20,475$ Computer 700.00$ 2,500 545 273 191,100$ 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 Value Number per year

Number per shipment

Average Inventory


Inventory Carrying

CostTV 500.00$ 2,500 545 273 136,500.00$ 20,475.00$ Computer 700.00$ 2,500 545 273 191,100.00$ 28,665.00$

Total: 49,140.00$

Part Value Number per year

Number per shipment

Average Inventory


Inventory Carrying Cost

CPU $300 2500 6,000 3,000 900,000.00$ 135,000.00$ Monitor/Keyboard $400 5000 3,000 1,500 600,000.00$ 90,000.00$ Console $100 2500 1,000 500 50,000.00$ 7,500.00$

Total: 232,500.00$

Explain?

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With Consolidation– Transportation Costs: $ 751,800– Pipeline Inventory: $ 435,000– Inventory Costs at Stores: $ 4,914,000– Inventory Costs at Plants: $ 232,500– Inventory Costs at XDock: $ 281,640

Total: $ 6,614,900Without Consolidation

– Transportation Costs: $ 460,000– Pipeline Inventory: $ 360,000– Inventory Costs at Stores: $ 23,250,000– Inventory Costs at Plants: $ 232,500

Total: $ 24,302,500!

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ComparisonCapital Cost Capital Cost

TransportationTo Indianapolis -$ 291,800$ From Indianapolis to stores 460,000$ 460,000$

Pipeline InventoryTo Indianapolis 500,000$ 75,000$ From Indianapolis to stores 2,400,000$ 360,000$ 2,400,000$ 360,000$

Inventory at Plants 1,550,000$ 232,500$ 1,550,000$ 232,500$ Inventory at Cross Dock

Receiving 1,550,000$ 232,500$ Shipping 327,600$ 49,140$

Inventory at stores 155,000,000$ 23,250,000$ 32,760,000$ 4,914,000$ Total 158,950,000$ 24,302,500$ 39,087,600$ 6,614,940$

Direct Consolidation

Invest some of the $120 million in the cross dock

Spend some of the $18 million on handling

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SPEED

• With consolidation our SPEED (with the same caveats) is

• $300 million/$39 million = 7.69!• We generate $7.69 in revenue for every $1

invested• That give us a lot more room to play with

margin and still have a high return on capital

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For Future Reference• Consolidation illustrates two situations

– 1-to-1 shipments• E.g. from Green Bay to Indianapolis XDock• Inventory at Green Bay Inventory of CPUs in Indianapolis

– 1-to-Many shipments• E.g., from XDock to stores• Inventory at XDock Inventory at a SINGLE store

• The point: Inventory at the origin of a 1-to-Many system has a smaller impact than in a 1-to-1 system…we will see this next time.

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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, how to reduce inventory in stores• Reducing inventory in stores is a powerful way to

improve return on capital – Wal-Mart has more than 2,300 supercenters in the US– Reducing inventory in each one by a mere $10K frees

$23 million in capital.

Modeling Inventory (Deterministic View)

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