Inventory Vehicle Routing

1. Inventory Vehicle Routing Adapted from…. Ann Campbell Lloyd Clarke Martin Savelsbergh Industrial & Systems Engineering Georgia Institute of Technology

2. Vehicle Routing Decisions Based on customers’ orders • Which plant serves each customer • Which vehicle makes the delivery • What route the vehicle travels ?

3. 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

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

5. Conventional Inventory Management -- Day 1 MICHIGAN Detroit LAKE ERIE Cleveland OHIO

6. Conventional Inventory Management -- Day 2 MICHIGAN Detroit LAKE ERIE Cleveland OHIO

7. 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 Vendor Managed Inventory

8. Vendor Managed Inventory -- Day 1 MICHIGAN Detroit LAKE ERIE Cleveland OHIO

9. Vendor Managed Inventory -- Day 2 MICHIGAN Detroit LAKE ERIE Cleveland OHIO

10. Inventory Routing • Chemical Industry • air products distribution • Petrochemical industry • gas stations • Automotive Industry • parts distribution

11. Praxair’s Business • Not an airline! • Air products • “harvest the sky” • produce nitrogen, oxygen, argon, hydrogen, helium, etc. Oxygen Nitrogen Argon

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. Average Cost per Day

21. 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)

22. Example I A B • 300 hour period • Choices: • deliver customers separately • deliver customers together 5 miles 10 miles 10 miles depot

23. Example I • Combined customer • usage 20 m3/hr • delivery every 60 hr (~2.5 days)

24. 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

25. Example I A B • 300 hour period • Choices: • deliver customers separately • deliver customers together 2 miles 10 miles 10 miles depot

26. Long Term Objectives • Avoid outages • Minimize transportation costs • Performance measures • $/mile • $/volume • volume/mile • outage/delivery

27. Short Term Decisions • Today, deliver to customers that need a delivery • Tomorrow, may not have enough capacity

28. Short Term Decisions • Today, deliver to customers in need • Also, deliver to anyone near by and “top-off” the customer’s inventory space

29. Using Customer Information • Reactive Approach • Customer inventory space • Customer current inventory • Proactive Approach • Customer usage rate