Rule-based Price Discovery Methods in Transportation Procurement Auctions

1. Rule-based Price Discovery Methods in Transportation Procurement Auctions Jiongjiong Song Amelia Regan Institute of Transportation Studies University of California, Irvine INFORMS Revenue Management Conference 2004

2. Outline • Introduction to Procurement Auctions • The Business Rule based Bid Analysis Problem • Shippers’ business considerations • An integer programming model • Our solution methodologies • Construction heuristics and Lagrangian heuristics • Experimental results • Conclusion and extensions

3. Procurement Auctions • Combinatorial auction • An allocation mechanism for multiple items • Multiple items put out for bid simultaneously • Bidders can submit complicated bids for any combinations of items • Unit auction • Packages are pre-defined and are mutually exclusive • Applications in freight transportation • Freight transportation exhibits economies of scope • Shippers gain more benefits to bundle lanes • Carriers dislike this combinatorial auction idea

4. Procurement Auctions • Combinatorial auction • Complicated optimization problems for both shippers and carriers • Shippers lose control over bundles, carriers have more freedom • Unit auction • Shippers gain control • Carriers have much simpler pricing problem to solve • Shippers still have a difficult optimization problem to solve

5. Business Considerations • If price is the sole reason for assigning bids – the unit auction problem is simple to solve • However, shippers have additional considerations • Caplice and Sheffi (2003) identify the primary considerations for the trucking industry case

6. Business Considerations • Minimum/maximum number of winning carriers (core carriers) • Favor of Incumbents • Backup concerns • Minimum/maximum coverage • Threshold volumes • Complete regional coverage

7. Business Considerations • Performance factors – these are necessary to ensure that high priced carriers don’t “Lose the auction but win the freight”

8. Our Model • We include the following: • maximum / minimum number of winning carriers • maximum / minimum coverage • incumbent preference • performance factors (penalty cost)

9. Our Model • We assume that: • backup considerations • regional coverage • Can be taken care of in pre-processing and pre-screening steps

10. The General Model

11. Our Model

12. Our Model

13. Cost # of Carriers Relationship between procurement costs and number of winners Our Model • Our objective function problem minimizes total procurement costs including the bid prices and the penalty costs to manage multiple carrier accounts

14. Our Model • The penalty cost can also be used to capture the shipper’s favoring of specific carriers at the system level • incumbents have a zero penalty cost and non-incumbents have a positive penalty cost • This could be extended to specific packages • Though we model the maximum and minimum volume constraints at the system level, these could be applied at the regional or facility level

15. Our Model • Even with the simplification of some business constraints to the network level this problem can easily be shown to be NP-Complete • Solving problems of reasonable size (thousands of lanes, hundreds of carriers) using exact methods is not feasible • CPLEX failed to solve such as a case in two days with a moderately fast computer

16. Our Solution Approach • Simple construction techniques based on the relationship between our problem and the capacitated facility location problem • MDROP and MADD for Modified DROP and ADD • Lagrangian Relaxation • Constraint (4) is relaxed (a lane is only assigned to a single carrier) • Network flow based algorithms to solve the relaxed problem

17. Test Data • Input data for each problem includes: • Each carrier’s bid prices for each lane • penalty cost for each carrier • minimum and maximum number of lanes if this carriers is a winner • minimum and maximum number of winners • a carrier’s bid price is randomly distributed between 10 and 100 • the penalty cost is randomly distributed between 0 and 3% of total bid prices

18. Results • Small Problems

19. Results • Small Problems

20. Solution Times (minutes) • Small Problems

21. Results • Larger Problems

22. Results • Larger Problems

23. Solution Times (minutes) • Larger Problems

24. Conclusion • We show that unit auctions with side constraints can be solved in reasonable time and with a high degree of confidence • The Lagrangian Relaxation solution method could be used to make final decisions while the heuristics (or improved versions of these) could be used to conduct sensitivity analysis

25. Extensions • Shippers may have additional or more complicated business rules • As optimization tools improve, requirements will increase • Eventually, pure combinatorial auctions (for large shippers and large carriers) may be feasible and preferable – we are working to solve bidding and winner determination problems for those auctions

26. Thank You