Inventory Vehicle Routing

Adapted from….Ann CampbellLloyd ClarkeMartin Savelsbergh

Industrial & Systems EngineeringGeorgia Institute of Technology

Vehicle Routing Decisions

Based on customers’ ordersWhich plant serves each customerWhich vehicle makes the deliveryWhat route the vehicle travels?

Vendor Managed Inventory

Customers do not place ordersVendor monitors customers’ use of

productVendor controls customers’

inventory Determines when to deliver Determines how much to deliver

4

Advantages

For vendor more opportunities for savings however, problem becomes more

difficultFor customer

one less worry if you trust your vendor

OHIO

MICHIGANLAKE ERIEDetroit

Cleveland

Conventional Inventory Management -- Day 1

OHIO

MICHIGANLAKE ERIEDetroit

Cleveland

Conventional Inventory Management -- Day 2

7

Vendor Managed InventoryCustomer

trusts the vendor to manage the inventory

Vendor monitors customers’

inventorycustomers call/fax/e-mailremote telemetry unitsset levels to trigger call-in

controls inventory replenishment & decides

when to deliverhow much to deliverhow to deliver

OHIO

MICHIGANLAKE ERIEDetroit

Cleveland

Vendor Managed Inventory -- Day 1

OHIO

MICHIGANLAKE ERIEDetroit

Cleveland

Vendor Managed Inventory -- Day 2

Inventory Routing

Chemical Industry air products distribution

Petrochemical industry gas stations

Automotive Industry parts distribution

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Praxair’s Business

Not an airline!

Air products “harvest the sky”

produce nitrogen, oxygen, argon, hydrogen, helium, etc.

OxygenOxygen

NitrogenNitrogen

ArgonArgon

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Praxair’s Business Plants worldwide

44 countries

USA 70 plants

South America 20 plants

Product classes packaged products

bulk products

lease manufacturing equipment

Distribution 1/3 of total cost attributed to

distribution

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Praxair’s BusinessBulk products

Distribution 750 tanker trucks

100 rail cars

1,100 drivers

drive 80 million miles per year

Customers 45,000 deliveries/month to 10,000 customers

Variation 4 deliveries/customer/day to

1 delivery/customer/2 months

Routing varies from day to day

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VMI Implementation at Praxair

Convince management and employees of new methods of doing business

Convince customers to trust vendor to do inventory management

Pressure on vendor to perform - Trust easily shaken

Praxair currently manages 80% of bulk customers’ inventories

Demonstrate benefits

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VMI Implementation at Praxair

Praxair receives inventory level data via telephone calls: 1,000 per day fax: 500 per day remote telemetry units: 5,000 per day

Forecast customer demands based on historical data customer production schedules customer exceptional use events

Logistics planners use decision support tools to plan whom to deliver to when to deliver how to combine deliveries into routes how to combine routes into driver schedules

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Benefits of VMI at Praxair

Before VMI, 96% of stockouts due to customers calling when tank was already empty or nearly empty

VMI reduced customer stockouts

0

5

10

Ja

n

Ma

r

Ma

y

Ju

ly

Se

pt

No

vafter 2 yrs

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What’s needed to make VMI work

Information management is crucial to the success of VMI inventory level data historical usage data planned usage schedules planned and unplanned exceptional usage

Forecast future demand Decision making: need to decide on a regular (daily)

basis whom to deliver to when to deliver how to combine deliveries into routes how to combine routes into driver schedules

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Separately stock each customer

The every d-day policyp(j) = probability a stock out first occurs on

day jDoes this make sense?p = p(1) + p(2) + … + p(d-1) The

probability of stock outS = cost to serve in case of stock out

(expedited service)c = cost to serve otherwise

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How often to serve?

Average daily cost of d-day policypS + (1-p)c

p(1) + 2p(2) + … dp(d)

p(d) = 1-p

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Average Cost per Day40.000

20.769

14.386

11.216

9.333

8.0957.227

6.591 6.111 5.742 5.455 5.230 5.055 4.921 4.821 4.750 4.706 4.689 4.714 4.686

-

5.000

10.000

15.000

20.000

25.000

30.000

35.000

40.000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Days between deliveries

Example I

Delivery vehicle capacity - 1200 m3

Customer A capacity 1500 m3

usage 12 m3/hr delivery every 100 hrs (~4 days)

Customer B capacity 800 m3

usage 8 m3/hr delivery every 100 hrs (~4 days)

Example I

300 hour periodChoices:

deliver customers separately

deliver customers together

depot

A B5 miles

10 miles

10 miles

Example I

Combined customer usage 20 m3/hr delivery every 60 hr (~2.5 days)

Example I

300 hour periodCustomers separate

3 deliveries each customer

60 miles each customer 120 miles total

Customers combined 5 deliveries total 25 miles each delivery 125 miles total

depot

A B5 miles

10 miles

10 miles

Example I

300 hour periodChoices:

deliver customers separately

deliver customers together

depot

A B2 miles

10 miles

10 miles

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Long Term Objectives

Avoid outagesMinimize transportation costsPerformance measures

$/mile $/volume volume/mile outage/delivery

Short Term Decisions

Today, deliver to customers that need a delivery

Tomorrow, may not have enough capacity

Short Term Decisions

Today, deliver to customers in needAlso, deliver to anyone near by and

“top-off” the customer’s inventory space

Using Customer Information

Reactive Approach Customer inventory space Customer current inventory

Proactive Approach Customer usage rate