Location Case Study Shanghai GM Service Parts Part II

1. Location Case StudyShanghai GM Service PartsPart II John H. Vande Vate Spring 2006 1

2. Service a primary driver Product has relatively high value The transportation network is likely Schedule Driven, (e.g. daily deliveries) Alternative is Load Driven (deliver whenever there’s enough demand for a full truckload) For now, let’s assume 5 days a week Schedule Driven Transport 2

3. Mileage Number of lanes Cost of Transportation So?! 3

4. Where the parts come from 4

5. Where they go… 5

6. Schedule, not capacity drives transport Handling fees are “nominal” … Assumptions 6

7. Consolidation should Have no effect On inventory at supplier On inventory at dealerships Create some inventory at the DCs Add to pipeline inventory Assumption: Each lane creates inventory equal to half the value of its average shipment Inventory 7

8. Consequences • Inventory depends on the lanes not just the number of DCs • Trade-offs are • Capital cost of DCs & • Additional inventory at DCs vs • Savings in Freight Consolidation • We are ignoring pipeline effects as they are probably small. 8

9. The ALT Heuristic now has Flow problem: Determine how goods move from suppliers to dealers (e.g., what do we run through DCs) Location problem: Determine where to put the DCs Comment: This is still a heuristic and by no means the only possibility. Mechanical Consequences An MIP Convex Opt. 9

10. Multi-Commodity Network Flow Supply (Scaled to weekly value) Supplies from each province are a commodity, e.g., supplies from Heilongjiang Demand (Scaled to weekly value) Assume demand is the same everywhere (i.e., 1% of the value of parts comes from Heilongjiang so 1% of the value of demand for parts in each province is for parts from Heilongjiang.) The Network Supply Provinces direct to Dealers Supply Provinces to DCs DCs to DCs DCs to dealers The Flow Problem 10

11. If you send flow (of any product) from one location to another, you pay for daily shipments you create inventory at the destination Note the transportation costs does NOT depend on how much flow you send, just whether you send any at all, so…. The Cost Structure Consolidate! 11

12. Pay inventory carrying cost of ½ the value of average shipment on each lane WEEKLY holding rate e.g., 0.004 = 20%/50 weeks Value of average shipment of product Flow[fromnode, tonode, product]/5 Inventory Cost Number of shipments/week Value of a weeks shipments 12

13. Model the flows Flow[fromnode, tonode, product] is how much of a given “product” we send directly from “fromnode” to “tonode” UseLane[fromnode, tonode] is the BINARY variable indicating whether or not we send flow of any product from “fromnode” to “tonode” Cost: To get weekly transport cost 5*CostPerMile*Distance*UseLane Add those up across all the lanes Modeling the Cost Cost of each shipment Do we ship that way or not Shipments per week 13

14. Constraints to ensure the meaning Method #1: For each (fromnode, tonode) BigEnoughNumber*UseLane[fromnode, tonode] >= sum{(fromnode, tonode) in EDGES, product in PRODUCTS} Flow[fromnode, tonode, product]; Method #2: For each (fromnode, tonode, product) Supply[product]*UseLane[fromnode, tonode] >= Flow[fromnode, tonode, product]; Which is better? Don’t Forget 14

15. Fixed Charge Network Flow Problem Typically difficult to solve LP Relaxation is far from the MIP CPLEX adds cuts to close this gap These are constraints implied by the integer variables Caution 15

16. Just like before Fix the transportation network and change the locations of the dcs 5*CostPerMile*Distance*UseLane Re-Locating The DC’s This changes as we move the DCs This is fixed for now 16

17. Read the Supplier Locations and %’s Read the Province Locations and %’s Read the current DC locations and whether they are open Some additional parameters param CostPerMile default 2; param HoldingRate default 0.004; param WeeklyVolume default 17500000; The Data Need that to balance inventory and transport 17

18. The Model & Script 18

19. Running the Model 19

20. The Solution 20

21. The Solution 21

22. Equipment Balance Vehicles cycling among the DCs Vehicles traveling back and forth between Supplier Province and DC Single Sourcing (even though we didn’t insist on it) Advantages 22

23. Every day?! It’s a 7 day trip What should we consider next? 23

24. Add a set of FREQUENCIES E.g., 1, 3, or 5 times per week Expanded the variables UseLane[fromnode, tonode, frequency] That let’s us capture the cost: Frequency*Distance*UseLane… Flow[fromnode, tonode, product, frequency] That let’s us capture inventory HoldingRate*Flow [fromnode, tonode, product, frequency]/(2*frequency) Frequency! 24

25. You have to conserve product at a DC, but you don’t have to conserve frequency Product from Heilongjiang comes in weekly, but goes out daily Our estimate of inventory is pretty rough at the DCs but it’s good at the Provinces 3 Frequency options mean the model is 3X as large….that really slows things down. Some Comments 25

26. Where’s to Use Frequency There are also other reasons for high frequency 26

27. Geographic Details Provincial demand not all centered on the capital. The split to DCs may not match the assignment of the capitals Transportation Cost Details May be savings from round trips May have capacity issues on some lanes … What’s happening to the effort? What’s happening to the impact? What Next? 27

28. No Class February 21st Review for the exam Work on your projects In Class Exam on February 23rd Covers lectures through today Open-book, open-notes YOUR OWN WORK What’s Next For Us? 28

29. Two kinds of answers possible Unambiguous AMPL-like formation Excel formulation (less preferred but acceptable) See the example http://www2.isye.gatech.edu/~jvandeva/Classes/6203/SolverAndExam.htm Modeling Questions 29

30. BMW Case Study Modeling Variability Impact of Improved Forecasting Impact of Increased Frequency Managing Variability in Supply Do not miss this After the Exam 30