11

Modeling Inventory(Deterministic View)

John H. Vande Vate

Spring 2007

22

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)

33

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.

44

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

55

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

66

Initial Strategies to Consider

• All direct shipments in full truckloads

• Consolidate in Indianapolis. All shipments in full truckloads

77

Simplification

• Shipments on the order of 1,000 miles

F

F

F

Green Bay

Indianapolis Denver

Distances

88

What Costs?

• Transportation

• Pipeline inventory – inventory in transit

• Inventory at Plants

• Inventory at Stores

• Handling

• …

99

Direct:Transportation Cost

• How many shipments/year?– Green Bay

– Indianapolis

– Denver

– Total100 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

100*2,500/6,000 = 41.67

100*5,000/3,000 =166.67

100*2,500/1,000 = 250

~ 460

1010

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– …

1111

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?

1212

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

1313

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– …

1414

Inventory at the Plants

• Two Extremes– Simultaneous shipments– Staggered shipments

1515

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

1616

Inventory at Green Bay

• Simultaneous Shipments

600,000

2.4 years

1717

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

1818

Why Not?

• What are problems with simultaneous shipments?

• When are simultaneous shipments likely?

• What alternatives?

1919

Inventory at Green Bay

• Staggered Shipments

6,000

~6 days

2020

What Costs?

• Inventory at Plants– Simultaneous Shipments

Capital Carrying Cost

• Green Bay $90 million $13.5 million• Denver $ 5 million $ .75 million• Indianapolis $60 million $ 9.0 million• Total $155 million $23.25 million

– Staggered Shipments (divide by 100!) 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

2121

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– …

2222

DC Inventory from Green Bay

6,000

~2.4 years

2323

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!

2424

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– …

2525

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

2626

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

2727

Via Indianapolis

F

F

F

Green Bay

Indianapolis Denver

Facts

2828

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• …

2929

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

3030

What Costs?

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

• Pipeline inventory – To Indianapolis– From Indianapolis to Stores

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

3131

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

3232

What Costs?• Transportation

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

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

3333

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

3434

What Costs?• Transportation

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

• 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• …

3535

Inventory at Cross Dock

Receiving Shipping

CPUs, Monitors, Consoles

Computers & TVsWIP

3636

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

3737

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

3838

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• 545 Monitors at $400 each or $218,000• Total $327,200• Carrying cost $ 49,080

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

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

3939

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?

4040

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!

4141

The Difference

Product Value Number per year

Number per shipment

Average Inventory

Average Value of Inventory

Inventory Carrying

CostTV 500.00$ 2,500 543 272 135,869.57$ 20,380.43$ Computer 700.00$ 2,500 543 272 190,217.39$ 28,532.61$

Total: 48,913.04$

Part Value Number per year

Number per shipment

Average Inventory

Average Value of 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?

4242

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!

4343

Comparison

Capital Cost Capital CostTransportation

To 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

4444

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

4545

Deterministic Supply Chain Design

• Next time: should we be shipping in full truckloads?

• Later, different kinds of cross docks