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

Vehicle Routing Decisions Based on customers’ orders zWhich plant serves each customer zWhich vehicle makes the delivery zWhat route the vehicle travels ?

Vendor Managed Inventory zCustomers do not place orders zVendor monitors customers’ use of product zVendor controls customers’ inventory yDetermines when to deliver yDetermines how much to deliver

4 Advantages zFor vendor ymore opportunities for savings yhowever, problem becomes more difficult zFor customer yone less worry if you trust your vendor

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

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

7 Vendor Managed Inventory zCustomer ytrusts the vendor to manage the inventory zVendor ymonitors customers’ inventory xcustomers call/fax/e- mail xremote telemetry units xset levels to trigger call-in ycontrols inventory replenishment & decides xwhen to deliver xhow much to deliver xhow to deliver

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

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

Inventory Routing zChemical Industry yair products distribution zPetrochemical industry ygas stations zAutomotive Industry yparts distribution

11 Praxair’s Business zNot an airline! zAir products y“harvest the sky” yproduce nitrogen, oxygen, argon, hydrogen, helium, etc. Oxygen Nitrogen Argon

12 Praxair’s Business zPlants worldwide y44 countries yUSA 70 plants ySouth America 20 plants zProduct classes ypackaged products ybulk products ylease manufacturing equipment zDistribution y1/3 of total cost attributed to distribution

13 Praxair’s Business Bulk products zDistribution y750 tanker trucks y100 rail cars y1,100 drivers ydrive 80 million miles per year zCustomers y45,000 deliveries/month to 10,000 customers zVariation y4 deliveries/customer/day to y1 delivery/customer/2 months zRouting varies from day to day

14 VMI Implementation at Praxair zConvince management and employees of new methods of doing business zConvince customers to trust vendor to do inventory management zPressure on vendor to perform - Trust easily shaken zPraxair currently manages 80% of bulk customers’ inventories zDemonstrate benefits

15 VMI Implementation at Praxair zPraxair receives inventory level data via ytelephone calls: 1,000 per day yfax: 500 per day yremote telemetry units: 5,000 per day zForecast customer demands based on yhistorical data ycustomer production schedules ycustomer exceptional use events zLogistics planners use decision support tools to plan ywhom to deliver to ywhen to deliver yhow to combine deliveries into routes yhow to combine routes into driver schedules

16 Benefits of VMI at Praxair zBefore VMI, 96% of stockouts due to customers calling when tank was already empty or nearly empty zVMI reduced customer stockouts

17 What’s needed to make VMI work zInformation management is crucial to the success of VMI yinventory level data yhistorical usage data yplanned usage schedules yplanned and unplanned exceptional usage zForecast future demand zDecision making: need to decide on a regular (daily) basis ywhom to deliver to ywhen to deliver yhow to combine deliveries into routes yhow to combine routes into driver schedules

18 Separately stock each customer zThe every d-day policy zp(j) = probability a stock out first occurs on day j zDoes this make sense? zp = p(1) + p(2) + … + p(d-1) The probability of stock out zS = cost to serve in case of stock out (expedited service) zc = cost to serve otherwise

19 How often to serve? zAverage 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

Example I zDelivery vehicle capacity m 3 zCustomer A ycapacity 1500 m 3 yusage 12 m 3 /hr ydelivery every 100 hrs (~4 days) zCustomer B ycapacity 800 m 3 yusage 8 m 3 /hr ydelivery every 100 hrs (~4 days)

Example I z 300 hour period z Choices: ydeliver customers separately ydeliver customers together depot AB 5 miles 10 miles

Example I zCombined customer yusage 20 m 3 /hr ydelivery every 60 hr (~2.5 days)

Example I z 300 hour period z Customers separate y3 deliveries each customer y60 miles each customer y120 miles total z Customers combined y5 deliveries total y25 miles each delivery y125 miles total depot AB 5 miles 10 miles

Example I z 300 hour period z Choices: ydeliver customers separately ydeliver customers together depot AB 2 miles 10 miles

26 Long Term Objectives zAvoid outages zMinimize transportation costs zPerformance measures y$/mile y$/volume yvolume/mile youtage/delivery

Short Term Decisions zToday, deliver to customers that need a delivery zTomorrow, may not have enough capacity

Short Term Decisions zToday, deliver to customers in need zAlso, deliver to anyone near by and “top- off” the customer’s inventory space

Using Customer Information zReactive Approach yCustomer inventory space yCustomer current inventory zProactive Approach yCustomer usage rate