Georgia Institute of Technology The Supply Chain and Logistics Institute

AN INVENTORY ROUTING CASE STUDY

Praxair
INTRODUCTION
The Inventory Routing Problem (IRP) is concerned with the repeated distribution of a set of products from several facilities to a set of customers over a given planning horizon. The facilities produce these products at given rates and have ample storage capabilities for the products. The customers consume products at a given rate and have limited storage capabilities. A fleet of vehicles is available at each of the facilities as well as a set of drivers. The objective is to minimize the overall costs during the planning period.
 
The following data has been collected for two real-life instances of the IRP.
*If you have any questions or comments, please direct them to Martin Savelsbergh at Georgia Tech.
 
CUSTOMERS
1. ID an identifier for each customer - such as a business name or city where it is located.
2. X longitude coordinate.
3. Y latitude coordinate.
4. OPENTIME time a customer starts using product each day (using a 24 hour clock, like all times).
5. CLOSETIME time a customer stops using product each day.
6. OPENWINDOW time a customer is able to start receive deliveries each day.
7. CLOSEWINDOW time a customer stops being able to receive deliveries each day.
8. FIXEDSTOP fraction of an hour required to make a stop at a customer, not including fill time.
9. MATEVEHCLASS type of vehicle able to make delivery at a customer (not enforced).
10. PRODUCTID type of product that is used by a customer (limit of one currently).
11. PRODMEAN mean rate at which customer uses product per hour when time is between open time and close time.
12. PRODSTDEV standard deviation of this usage rate (not used).
13. PRODCAPACITY the limit on how much inventory of a product can be held at a customer.
14. PRODSS "safety stock" for inventory of a product. It is often set so that when inventory falls below this level, this is a trigger to plan a delivery to the customer.
15. PRODINV initial inventory of product at a customer.
16. PRODSOCOST when customer runs out of product, this is the "cost" per unit that the customer would have used if sufficient resources were available.
 
DRIVERS
1. DRIVERID an identifier for each driver.
2. HOMEBASE home plant associated with a driver.
3. OPENWINDOW time a driver can start driving each day (not enforced).
4. CLOSEWINDOW time a driver must return to the home plant each day (not enforced).
5. REGTIMEWAGE wages earned per hour of regular time work.
6. OVERTIMEWAGE wages earned per hour of overtime work.
7. MATEVEHDRIV type of vehicle that a driver is able to drive (not enforced).
 
FACILITIES
1. ID an identifier for each plant such as the city where it is located.
2. X longitude coordinate.
3. Y latitude coordinate.
4. OPENTIME time plant starts producing (the same for all products currently).
5. CLOSETIME time plant stops producing (the same for all products currently).
6. FIXEDSTOP fraction of an hour required to make a stop at a plant while driver is on a tour, not including reload time.
7. FAILUREPARM parameter for describing frequency of failure in production process (not used).
8. MATEVEHCLASS type of vehicle that is able to pick up product from a plant (not used).
 
PRODUCTS
1. ProductID an identifier for each product.
2. FillRate number of units of product per hour that can be pumped into a vehicle at the plant.
3. DispenseRate number of units of product per hour that can be dispensed from a vehicle to a customer.
 
FACPRODUCTS
1. ID unique record number representing a plant/product pair.
2. FACILITYID an identifier for a plant, must match an ID on FACILITIES worksheet.
3. PRODUCTID an identifier for a product, must match a ProductID on PRODUCTS worksheet.
4. PRODRATE number of units of the product that is produced per hour while plant is producing.
5. PRODINV initial inventory at a plant of a product.
6. PRODCAP limit on amount of inventory of a product that can be maintained at a plant.
 
VEHICLES
1. VEHICLEID identifier for each vehicle.
2. HOMEBASE home facility associated with a vehicle.
3. MAXVOLUME limit on amount of product that a vehicle can hold.
4. SPEED speed at which vehicle drives on average, used to compute travel times.
5. FIXEDCOST cost charged for using a vehicle during the time horizon.
6. COSTMILE cost charged per mile driven on a vehicle.
7. PRODUCTID an identifier for a product, must match a ProductID on PRODUCTS worksheet.
8. MATEVEHDRIV "type" of vehicle (not used).
9. VEHFAILPARM parameter for describing frequency of failure in delivery process (not used).
 
INSTANCE
1. INSTANCEID identifier for instance.
2. TIMEHORIZON number of days game will be played.
3. DRIVLIMIT driving below this limit will be charged regular wage, above this will be charged overtime wage.
4. USAGECHINT (not used)
5. STOPOPEN (not used)
6. STOPCLOSE (not used)
 
View/Download the Data in Microsoft Excel 97 format

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The following basic questions related to the inventory routing can be investigated:

1. How would you decide which customers should receive a delivery on a day to make sure none of them would run out of product? Would you just look at current inventory or would you look at distance from the plant as well?

2. Which customers do you think would be good choices to be on a route together? What factors would you use to make such a decision?

3. If you were a planner trying to make a schedule for these customers, is there any other information that you think would be helpful?

4. If you were making a schedule for delivering to these customers, how far do you think you would plan ahead to make sure you wouldn't let anyone run out of product? 1 day? 2 days? Why?

5. For a given dataset, which appears to drive the total cost more - stockout cost, driver costs, or vehicle costs? For each of these, if it represented the only cost involved, how would this change your delivery policy?

6. Time horizon is listed as a characteristic of the instance. How do you think strategy would be different if time horizon was 3 days versus 33 days? Why?

7. How do small delivery time windows for customers complicate the problem? Do small windows for using product really affect things?

8. Do you think it would make the problem easier or harder if all customers had product capacity the same size as vehicle capacity? Why?

9. If you consider the stochastic information about customer usage rate, such as customer specific standard deviation, would this change your answer to question 1, and if so, how?

10. If safety stock is used as a signal to start planning a delivery to a given customer, how would you suggest setting this level? What factors would you consider besides usage rate?

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