Benefits of in-vehicle consolidation in less than truckload freight transportation operations

1. Benefits of in-vehicle consolidation in less than truckload freight transportation operations Rodrigo Mesa-Arango SatishUkkusuri 20th International Symposium of Transportation and Traffic Theory Noorwijk, Netherlands July 2013

2. Outline • Introduction • Problem • Methodology • Numerical Results • Conclusion • Questions/Comments

3. 1. Introduction • Trucking: Important economic sector (1) • US GDP: $ 14,499 billion dollars • For hire transportation: $ 403 billion dollars • Trucking: $ 116 billion dollars • Air:$ 63 billion dollars • Rail:$ 15 billion dollars • Externalities - Emissions - Safety - Congestion - Asset deterioration • Mitigation: Increasing vehicle utilization(2)(3)(4)(5) (1) U.S. Department of Transportation (2012). National transportation statistics (2) Sathaye, et al, The Environmental Impacts of Logistics Systems and Options for Mitigation, 2006 (3) Organisation for Economic Co-Operation and Development. Delivering the Goods-21st Century Challenges to Urban Goods Transport. 2003. (4) European Commission, Directorate-General for Energy and Transport. Urban Freight Transport and Logistics. European Communities. 2006. (5) Transport for London. London Freight Plan – Sustainable Freight Distribution: A Plan for London. 2007.

4. 1. Introduction • Economic mechanism attractive for consolidation? • Combinatorial Auctions • Successful implementations (6)(7)(8)(9)(10): - Home Depot Inc. - Staples Inc. - Wal-Mart Stores Inc. - Reynolds Metal Company - K-Mart Corporation - Ford Motor company - The Limited - Compaq Computer Corporation - Sears Logistics Services (6) Elmaghraby, and Keskinocak. Combinatorial Auctions in Procurement. 2002. (7) De Vries, and Vohra. Combinatorial Auctions: A Survey. 2003. (8) Moore, et al. TheIndispensable Role of Management Science in Centralizing Freight Operations at Reynolds Metals Company. 1991 (9) Porter, et al. The First Use of a Combined-Value Auction for Transportation Services. 2002. (10) Sheffi, Y. Combinatorial Auctions in the Procurement of Transportation Services. 2004.

5. 1. Introduction • Combinatorial Auctions in Freight Transportation Shipper Winner Determination Problem (11) (12)(13)(14) (11) Caplice and Sheffi. Combinatorial Auctions for Truckload Transportation. 2006. (12) Sandholm. Algorithm for Optimal Winner Determination in Combinatorial Auctions. 2002 (13) Abrache, et al. Combinatorial auctions. Annals of Operations Research. 2007 (14) Ma, et al. A Stochastic Programming Winner Determination Model for Truckload Procurement Under Shipment Uncertainty. 2010

6. 1. Introduction • Bidding advisory models • Truckload (TL) operations(15)(16)(17)(18)(19) • Direct movements • Economies of scope(20)(21)(22)(23) • Less-Than-Truckload (LTL) operations? • Consolidated movements • Economies of scope, scale, density(20)(21)(22)(23) (15) Song, and Regan. Combinatorial Auctions for Transportation Service Procurement, The Carrier Perspective. 2003, (16) Song, and Regan. Approximation Algorithms for the Bid Construction Problem in Combinatorial Auctions for the Procurement of Freight Transportation Contracts. 2005, (17) Wang, and Xia. Combinatorial Bid Generation Problem for Transportation Service Procurement. 2005 (18) Lee, et al. A Carrier’s Optimal Bid Generation Problem in Combinatorial Auctions for Transportation Procurement. 2007 (19) Chang. Decision Support for Truckload Carriers in One-Shot Combinatorial Auctions. 2009 (20) Caplice, and Sheffi. Combinatorial Auctions for Truckload Transportation. 2006 (21) Caplice. An Optimization Based Bidding Process: A New Framework for Shipper-Carrier Relationship. 1996 (22) Jara-Diaz. Transportation Cost Functions: A Multiproducts Approach. 1981 (23) Jara-Diaz. Freight Transportation Multioutput Analysis. 1983

7. 1. Introduction • Routes, costs and prices…

8. 1. Introduction • Economies of scope [TL] 1 2 1 2 1 2 k h h h k 4 3 4 3 4 3

9. 1. Introduction • Economies of consolidation (scale and density) [LTL] 1 2 1 2 1 2 k h h h k 4 3 4 3 4 3

10. 1. Introduction • This research • Show Benefits for carries • In-vehicle consolidation • Bidding construction • Freight Transportation combinatorial auctions • Use • Multi-commodity one-to-one pick up and delivery vehicle routing problem (m-PDVRP) to find optimal LTL bundles. • Compare against optimal bundles obtained for TL carriers

11. 2. Problem • MIP Formulation for m-PDVRP (1/2) Objective fun: Minimize total traversing cost Each node visited once All vehicles are used Vehicle flow conservation Sub-tour elimination Binary variables …

12. 2. Problem • MIP Formulation for m-PDVRP (2/2) Objective fun: Minimize total traversing cost … Demand Satisfaction constraint (Deliveries) Demand Satisfaction constraint (Pickups) Payload flow conservation Loads only on traversed links without exceeding vehicle capacity Vehicles leave the depot empty and return empty Non-negative continuous variables

13. 3. Methodology • Branch-and-price(24)(25) • Branch-and-bound • Dantzig-Wolfe and Column generation • Master Problem • Sub - problem (24) Barnhart, et al. 1998. Branch-and-price: Column generation for solving huge integer programs. (25) Desaulniers, et al. 1998. A unified framework for deterministic time constrained vehicle routing and crew scheduling problems.

14. 3.1 Branch-and-bound • Branch-and-Bound • Solve linear relaxation of IP • Terminate (fathom) a node • Infeasibility \ Bound \ Solution • Branch • Stop when all nodes are terminated • Branch-and-Price • Dantzig Wolfe Decomposition • Column Generation LP0 LP1 LP2 Linear Relaxation IP

15. 3.2. Dantzig Wolfe dec. + col. gen. • MIP has special structure appropriate for decomposition • Master Problem (MP) • Linear Program • Controls column generation process • Requests columns from the Sub problem • Integer variables are represented as convex combination of the columns generated by the Sub problem • Sub Problem • Integer program • Generates columns • Set of integer variables with common structure

16. 3.2. Dantzig Wolfe dec. + col. gen. Each node visited once All vehicles are used Vehicle flow conservation Sub-tour elimination Binary variables … Convex combination VRP deployment (t)

17. 3.2. Dantzig Wolfe dec. + col. gen. • Examples of deployments of trucks 0 1 0 1 0 1 0 1 |V| = 1 |V| = 2 |V| = 3 t = 1 t = 1 t = 1 3 2 3 2 3 2 3 2 0 1 0 1 t = 2 t = 2 3 2 3 2 0 1 0 1 t = 3 t = 3 3 2 3 2

18. 3.2. Dantzig Wolfe dec. + col. gen. • Master problem (MP): Generates lt as needed (MP) Objective fun: Minimize total traversing cost Demand Satisfaction constraint (Deliveries) Demand Satisfaction constraint (Pickups) Payload flow conservation Loads only on traversed links without exceeding vehicle capacity Vehicles leave the depot empty and return empty Non-negative continuous variables Vehicles leave the depot empty and return empty Convexity Constraint Non-negativity

19. 3.2. Dantzig Wolfe dec. + col. gen. • Each Solution generates a column t, {x0j0,…,xi0v}, that is associated with a variable ltin the MP (Sub-P) Objective fun: Minimize reduced cost Each node visited once All vehicles are used Vehicle flow conservation Sub-tour elimination Binary variables

20. 3.2. Branch-and-price Root B&B Node (Active) Solve MP Update arcs and costs Set Sub-P costs Add new column to pool Solve Sub-P No Column Generation Yes Active nodes? Select B&B node and set as inactive Terminate node by infeasibility Set node as inactive No Terminate node by bound Update incumbent solution Terminate node by solution Branch B&B node (active) B&B node (active) Column Generation Column Generation Stop

21. 3.3. Acceleration strategies • Originally depth-first search • Finding initial incumbent solution (upper bound): Time consuming • Strategy 1: Fast initial upper bound • Strategy 2: Continuous increment to lower bound • Strategy 1 replace Step 3 as follows • Find branch-and-bound node with current lowest solution and fathom it, repeat

22. 4. Numerical Results • Implementation • Java • Branch-and-Bound • Interactions in Column Generation • Set Sub-P • Update MP • Network Management • Information/Updates: Nodes, Links, Tours • ILOG CPLEX • MP LP Solution • Sub-P IP Solution

23. 4. Numerical Results Scenario 1 Scenario 2 1 7 1 1 10 10 2 2 2 20 20 5 5 20 0 0 0 6 6 4 4 4 3 3 3 Scenario 3 8 10 10 20 20

24. 4. Numerical Results (LTL)

25. 4. Numerical Results • TL + Scenario 3 • Comparison

26. 5. Conclusion • Research shows benefits of considering in-vehicle consolidation (LTL) in the construction of bids • Numerical results show that consolidated bids (LTL) dominatenon-consolidated ones (TL) • LTLcarriers can submit bids with prices that are less than or equal to the costs of TL carriers • Savings increase as the capacityof trucks increases • Low transportation costs potentially reduce shipper procurement cost • In-vehicle consolidation (as defined in this research) integrates the flexibility of TL (economies of scope) to the economies of scales/density of LTL

27. 5. Conclusion • Future research • Understanding the tradeoff between low price and delivery times (as well as other attributes of the carrier) for shippers • Econometric techniques • Segmented pricing policies • Acceleration of the solution methodology • Parallel computing • Hybrid-metaheuristics • Consideration of stochastic demand • Development of a robust biding advisory model that incorporates these features. • Analysis of positive/negative externalities associated to large trucks at a macroscopic level • Thank you!

28. 6. Questions - Comments