Inventory Vehicle Routing

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Inventory Vehicle Routing

• Adapted from.
• Ann Campbell
• Lloyd Clarke
• Martin Savelsbergh
• Industrial Systems Engineering
• Georgia Institute of Technology

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Vehicle Routing Decisions

• Based on customers orders
• Which plant serves each customer
• Which vehicle makes the delivery
• What route the vehicle travels

?
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Vendor Managed Inventory

• Customers do not place orders
• Vendor monitors customers use of product
• Vendor controls customers inventory
• Determines when to deliver
• Determines how much to deliver

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Advantages

• For vendor
• more opportunities for savings
• however, problem becomes more difficult
• For customer
• one less worry if you trust your vendor

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Conventional Inventory Management -- Day 1
MICHIGAN
Detroit
LAKE ERIE
Cleveland
OHIO
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Conventional Inventory Management -- Day 2
MICHIGAN
Detroit
LAKE ERIE
Cleveland
OHIO
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Vendor Managed Inventory

• Customer
• trusts the vendor to manage the inventory
• Vendor
• monitors customers inventory
• customers call/fax/e-mail
• remote telemetry units
• set levels to trigger call-in
• controls inventory replenishment decides
• when to deliver
• how much to deliver
• how to deliver

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Vendor Managed Inventory -- Day 1
MICHIGAN
Detroit
LAKE ERIE
Cleveland
OHIO
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Vendor Managed Inventory -- Day 2
MICHIGAN
Detroit
LAKE ERIE
Cleveland
OHIO
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Inventory Routing

• Chemical Industry
• air products distribution
• Petrochemical industry
• gas stations
• Automotive Industry
• parts distribution

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Praxairs Business

• Not an airline!
• Air products
• harvest the sky
• produce nitrogen, oxygen, argon, hydrogen,
  helium, etc.

Oxygen
Nitrogen
Argon
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Praxairs 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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Praxairs 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

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Whats 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 policy
• p(j) probability a stock out first occurs on
  day j
• Does this make sense?
• p p(1) p(2) p(d-1) The probability of
  stock out
• S 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 policy
• pS (1-p)c
• p(1) 2p(2) dp(d)
• p(d) 1-p

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Average Cost per Day
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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)

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Example I
A
B

• 300 hour period
• Choices
• deliver customers separately
• deliver customers together

5 miles
10 miles
10 miles
depot
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Example I

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

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Example I
A
B

• 300 hour period
• Customers separate
• 3 deliveries each customer
• 60 miles each customer
• 120 miles total
• Customers combined
• 5 deliveries total
• 25 miles each delivery
• 125 miles total

5 miles
10 miles
10 miles
depot
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Example I
A
B

• 300 hour period
• Choices
• deliver customers separately
• deliver customers together

2 miles
10 miles
10 miles
depot
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Long Term Objectives

• Avoid outages
• Minimize transportation costs
• Performance measures
• /mile
• /volume
• volume/mile
• outage/delivery

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Short Term Decisions

• Today, deliver to customers that need a delivery
• Tomorrow, may not have enough capacity

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Short Term Decisions

• Today, deliver to customers in need
• Also, deliver to anyone near by and top-off the
  customers inventory space

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Using Customer Information

• Reactive Approach
• Customer inventory space
• Customer current inventory
• Proactive Approach
• Customer usage rate