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
• Satish Ukkusuri
• 20th International Symposium of Transportation
  and Traffic Theory
• Noorwijk, Netherlands
• July 2013

2
Outline

1. Introduction
2. Problem
3. Methodology
4. Numerical Results
5. Conclusion
6. 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. The Indispensable 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

(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 Carriers
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
3
4
 
 
 
9
1. Introduction

• Economies of consolidation (scale and density)
  LTL

 
 
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

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

V 1
V 2
V 3
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
  lt in 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 BB 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 BB 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
BB node (active)
BB 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
cij 0 1 2 3 4 5 6 7 8
0 99.0 3.0 7.0 5.0 1.0 1.0 7.0 5.0 3.0
1 3.0 99.0 3.0 7.0 5.0 1.0 5.0 1.0 7.0
2 7.0 3.0 99.0 3.0 7.0 5.0 1.0 1.0 5.0
3 5.0 7.0 3.0 99.0 3.0 7.0 1.0 5.0 1.0
4 1.0 5.0 7.0 3.0 99.0 3.0 5.0 7.0 1.0
5 1.0 1.0 5.0 7.0 3.0 99.0 7.0 3.0 5.0
6 7.0 5.0 1.0 1.0 5.0 7.0 99.0 3.0 3.0
7 5.0 1.0 1.0 5.0 7.0 3.0 3.0 99.0 7.0
8 3.0 7.0 5.0 1.0 1.0 5.0 3.0 7.0 99.0
24
4. Numerical Results (LTL)
Min. Cost Deployment Bundles Time (sec) Time (sec) Time (sec) Gap ()
Min. Cost Deployment Bundles Deep-first search Strategy 1 Strategy 2 Gap ()
5 1 50 13 0-1-2-3-4-0 (1,3),(2,4) 0.203 0.171 0.313 0.0
5 1 40 13 0-1-2-3-4-0 (1,3),(2,4) 0.188 0.188 0.406 0.0
5 1 20 21 0-1-3-2-4-0 (1,3),(2,4) 1.640 0.734 0.531 0.0
5 2 50 30 0-1-3-0-2-4-0 (1,3),(2,4) 1.063 1.125 0.265 0.0
5 2 40 30 0-1-3-0-2-4-0 (1,3),(2,4) 1.094 1.078 0.203 0.0
5 2 20 30 0-1-3-0-2-4-0 (1,3),(2,4) 0.891 0.672 0.235 0.0
7 1 50 11 0-5-1-2-6-3-4-0 (1,3),(2,4),(5,6) 0.359 0.234 0.281 0.0
7 1 40 15 0-5-1-6-2-3-4-0 (1,3),(2,4),(5,6) 2.609 8.062 1.718 0.0
7 1 20 31 0-5-6-1-3-2-4-0 (1,3),(2,4),(5,6) 1.937 4.688 5.859 0.0
7 2 50 28 0-2-4-0-5-1-6-3-0 (2,4),(1,3),(5,6) 23.124 13.469 4.390 0.0
7 2 40 28 0-2-4-0-5-1-6-3-0 (2,4),(1,3),(5,6) 16.734 16.109 4.781 0.0
7 2 20 32 0-1-3-0-5-6-2-4-0 (1,3),(2,4),(5,6) 7.390 7.109 6.000 0.0
7 3 50 45 0-1-3-0-2-4-0-5-6-0 (1,3),(2,4),(5,6) 15.344 3.985 1.812 0.0
7 3 40 45 0-1-3-0-2-4-0-5-6-0 (1,3),(2,4),(5,6) 14.203 13.406 1.813 0.0
7 3 20 45 0-1-3-0-2-4-0-5-6-0 (1,3),(2,4),(5,6) 5.484 3.719 1.125 0.0
9 1 50 13 0-5-1-7-6-2-3-8-4-0 (1,3),(2,4),(5,6),(7,8) 19.203 37.265 12.188 0.0
9 1 40 13 0-5-1-7-6-2-3-8-4-0 (1,3),(2,4),(5,6),(7,8) 7.094 53.656 10.531 0.0
9 1 20 31 0-5-6-7-1-8-3-2-4-0 (1,3),(2,4),(5,6),(7,8) 53.312 103.359 55.406 0.0
9 2 50 26 0-2-4-0-5-1-7-6-3-8-0 (2,4),(1,3),(5,6),(7,8) 574.012 219.905 113.172 0.0
9 2 40 26 0-2-4-0-5-1-7-6-3-8-0 (2,4),(1,3),(5,6),(7,8) 383.779 214.186 174.281 0.0
9 2 20 30 0-1-7-3-8-0-5-6-2-4-0 (1,3),(7,8),(5,6),(2,4) 5.812 36.406 130.657 0.0
9 3 50 43 0-2-4-0-5-1-6-3-0-7-8-0 (2,4),(1,3),(5,6),(7,8) 2148.677 254.654 397.782 0.0
9 3 40 43 0-2-4-0-5-1-6-3-0-7-8-0 (2,4),(1,3),(5,6),(7,8) 1267.945 270.67 413.016 0.0
9 3 20 43 0-1-7-3-8-0-2-4-0-5-6-0 (2,4),(1,3),(7,8),(5,6) 205.436 91.984 138.625 0.0
9 4 50 60 0-1-3-0-2-4-0-5-6-0-7-8-0 (1,3),(2,4),(5,6),(7,8) 692.870 91.375 58.084 0.0
9 4 40 60 0-1-3-0-2-4-0-5-6-0-7-8-0 (1,3),(2,4),(5,6),(7,8) 503.496 101.702 77.581 0.0
9 4 20 60 0-1-3-0-2-4-0-5-6-0-7-8-0 (1,3),(2,4),(5,6),(7,8) 260.092 59.71 39.563 0.0
25
4. Numerical Results

• TL Scenario 3
• Comparison

Min. Cost Deployment Bundles Time (sec) Gap ()
9 1 43 0-1-3-2-4-5-6-7-8-0 (1,3),(2,4),(5,6),(7,8) 14.000 0.00
9 2 42 0-1-3-2-4-0-5-6-7-8-0 (1,3),(2,4),(5,6),(7,8) 25.266 0.00
9 3 47 0-1-3-0-5-6-2-4-0-7-8-0 (1,3),(2,4),(5,6),(7,8) 113.172 0.00
9 4 60 0-1-3-0-2-4-0-5-6-0-7-8-0 (1,3),(2,4),(5,6),(7,8) 78.188 0.00
Opt. for Bundle No. lanes LTL operation LTL operation LTL operation   TL operation TL operation TL operation   LTL min margin
Opt. for Bundle No. lanes Deployment Total cost Cost per lane   Deployment Total cost Cost per lane   LTL min margin
LTL (1,3),(5,6),(7,8) 3 0-5-1-7-6-3-8-0 11.00 3.67   0-5-6-1-3-7-8-0 35.00 11.67   24.01
LTL (1,3),(5,6) 2 0-5-1-6-3-0 13.00 6.50   0-5-6-1-3-0 25.00 12.50   12
TL (1,3),(2,4) 2 0-1-2-3-4-0 13.00 6.50   0-1-3-2-4-0 21.00 10.50   8
TL (5,6),(7,8) 2 0-5-7-6-8-0 13.00 6.50   0-5-6-7-8-0 21.00 10.50   8
TL (5,6),(2,4) 2 0-5-2-6-4-0 13.00 6.50   0-5-6-2-4-0 17.00 8.50   4
TL / LTL (1,3),(2,4),(5,6),(7,8) 4 0-5-1-7-6-2-3-8-4-0 13.00 3.25   0-1-3-2-4-5-6-7-8-0 43.00 10.75   30
TL / LTL (1,3) 1 0-1-3-0 15.00 15.00   0-1-3-0 15.00 15.00   0
TL / LTL (2,4) 1 0-2-4-0 15.00 15.00   0-2-4-0 15.00 15.00   0
TL / LTL (5,6) 1 0-5-6-0 15.00 15.00   0-5-6-0 15.00 15.00   0
TL / LTL (7,8) 1 0-7-8-0 15.00 15.00   0-7-8-0 15.00 15.00   0
26
5. Conclusion

• Research shows benefits of considering in-vehicle
  consolidation (LTL) in the construction of bids
• Numerical results show that consolidated bids
  (LTL) dominate non-consolidated ones (TL)
• LTL carriers can submit bids with prices that are
  less than or equal to the costs of TL carriers
• Savings increase as the capacity of 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