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

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

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

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

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

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

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

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

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

The General Model

Our Model

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

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

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

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

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

Results Small Problems

Results Small Problems

Solution Times (minutes) Small Problems

Results Larger Problems

Results Larger Problems

Solution Times (minutes) Larger Problems

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

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

Thank You