Transcript
Page 1: Benefits of in-vehicle consolidation in less than  truckload  freight transportation operations

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

operations

Rodrigo Mesa-ArangoSatish Ukkusuri

20th International Symposium of Transportation and Traffic TheoryNoorwijk, Netherlands

July 2013

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Outline

1. Introduction

2. Problem

3. Methodology

4. Numerical Results

5. Conclusion

6. Questions/Comments

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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.

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1. Introduction

• Economic mechanism attractive for consolidation?

• Combinatorial Auctions

– Successful implementations (6)(7)(8)(9)(10):

(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.

- 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

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• Combinatorial Auctions in Freight Transportation

Shipper

(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

WinnerDeterminationProblem(11) (12)(13)(14)

1. Introduction

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• 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)

1. Introduction

(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

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1. Introduction• Routes, costs and prices…

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1. Introduction• Economies of scope [TL]

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1. Introduction• Economies of consolidation (scale and density) [LTL]

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• 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

1. Introduction

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Objective fun: Minimize total traversing cost

Each node visited once

All vehicles are used

Vehicle flow conservation

Sub-tour elimination

( , )

min vij ij

v V i j A

c x

1;    'vij

v V j N

x i N

;    ;v vji ij

j N j N

x x i N v V

0 1;   v

jj N

x v V

1;    ';vij

i M j M

x M M N v V

• MIP Formulation for m-PDVRP (1/2)

Binary variables{1,0};    , ;vijx i j N v V

2. Problem

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Objective fun: Minimize total traversing cost( , )

min vij ij

v V i j A

c x

• MIP Formulation for m-PDVRP (2/2)

Demand Satisfaction constraint (Deliveries)

Demand Satisfaction constraint (Pickups)

Payload flow conservation

Vehicles leave the depot empty and return empty

Loads only on traversed links without exceeding vehicle capacity

Non-negative continuous variables

, ;    ; 'ri v riji

v V j N

l p r N i N

, ;    ; 'is v is

ijv V j N

l p s N i N

, , ;    ';  , \ ;rs v rs v

ji ijj N j N

l l i N r s N i v V

, ,1 10      0;    '; , \ ;rs v rs vi il and l i N r s N i v V

, ;    , ';rs v vij ij

r N s N

l x Q i j N v V

, 0;    , , , ,rs vijl i N j N r N s N v V

2. Problem

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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.

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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

IP Linear Relaxation

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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

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3.2. Dantzig Wolfe dec. + col. gen.

Each node visited once

All vehicles are used

Vehicle flow conservation

Sub-tour elimination

1;    'vij

v V j N

x i N

;    ;v vji ij

j N j N

x x i N v V

0 1;   v

jj N

x v V

1;    ';vij

i M j M

x M M N v V

Binary variables{1,0};    , ;v

ijx i j N v V

VRP deployment (t)

( )v vij ij t t

t T

x x

1  t

t T

0 t

Convex combination

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3.2. Dantzig Wolfe dec. + col. gen.

0 1

23

10

23

0 1

23

t = 2 t = 2

10

23

0 1

23

t = 3 t = 3

010

23

1

23

0 1

23

t = 1 t = 1 t = 1

|V| = 1 |V| = 2 |V| = 3

• Examples of deployments of trucks

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Objective fun: Minimize total traversing costmin t tt T

c

Demand Satisfaction constraint (Deliveries)

Demand Satisfaction constraint (Pickups)

Payload flow conservation

Vehicles leave the depot empty and return empty

Loads only on traversed links without exceeding vehicle capacity

Non-negative continuous variables

;    ; 'ri riji

j N

l p r N i N

;    ; 'is is

ijj N

l p s N i N

;    ';  , \rs rs

ji ijj N j N

l l i N r s N i

1 10      0;    '; , \rs rsi il and l i N r s N i

;    , 'rsij ijt t

r N s N t T

l Q a i j N

0;    , , ,rsijl i N j N r N s N

3.2. Dantzig Wolfe dec. + col. gen.

Vehicles leave the depot empty and return empty1 10      0;    '; , \rs rsi il and l i N r s N i

( )ij

0( )

• Master problem (MP): Generates t as needed(MP)

Non-negativity0  t t T

1tj N

Convexity Constraint

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3.2. Dantzig Wolfe dec. + col. gen.

Objective fun: Minimize reduced cost

Each node visited once

All vehicles are used

Vehicle flow conservation

Sub-tour elimination

*

0( , )

min vij ij ij

v V i j A

c c x

1;    'vij

v V j N

x i N

;    ;v vji ij

j N j N

x x i N v V

1 1;   v

jj N

x v V

1;    ';vij

i M j M

x M M N v V

Binary variables{1,0};    , ;v

ijx i j N v V

• Each Solution generates a column t, {x0j0,…,xi0

v}, that is associated with a variable t in the MP

(Sub-P)

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3.2. Branch-and-price

Solve MP

Add new column to poolSolve Sub-P

Set Sub-P costsUpdate arcs and costs

No

Root B&B Node (Active)

Column GenerationYes

Select B&B node and set as inactive

Terminate node by infeasibility

Terminate node by solution

Terminate node by bound

Branch

Active nodes?

No

Stop

Set node as inactive

Update incumbent solution

Column Generation Column Generation

B&B node (active) B&B node (active)

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3.3. Acceleration strategies

• Originally depth-first search– Finding initial incumbent solution (upper bound): Time

consuming

• 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

• Strategy 1: Fast initial upper bound

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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

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4. Numerical Results

5

71

0

2

6

84 3

Scenario 3

10 2010

20

5

1

0

2

6

4 3

Scenario 2

10 20

20

1

0

2

4 3

Scenario 1

10 20

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 3.01 3.0 99.0 3.0 7.0 5.0 1.0 5.0 1.0 7.02 7.0 3.0 99.0 3.0 7.0 5.0 1.0 1.0 5.03 5.0 7.0 3.0 99.0 3.0 7.0 1.0 5.0 1.04 1.0 5.0 7.0 3.0 99.0 3.0 5.0 7.0 1.05 1.0 1.0 5.0 7.0 3.0 99.0 7.0 3.0 5.06 7.0 5.0 1.0 1.0 5.0 7.0 99.0 3.0 3.07 5.0 1.0 1.0 5.0 7.0 3.0 3.0 99.0 7.08 3.0 7.0 5.0 1.0 1.0 5.0 3.0 7.0 99.0

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4. Numerical Results (LTL)

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4. Numerical Results

• TL + Scenario 3

• Comparison

Opt.for

BundleNo.lanes

LTL operation   TL operation  LTLminmargin

DeploymentTotalcost

Cost perlane

  DeploymentTotalcost

Cost perlane

 

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   24.01LTL {(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   12TL {(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   8TL {(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   8TL {(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   4TL / 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   30TL / LTL {(1,3)} 1 0-1-3-0 15.00 15.00   0-1-3-0 15.00 15.00   0TL / LTL {(2,4)} 1 0-2-4-0 15.00 15.00   0-2-4-0 15.00 15.00   0TL / LTL {(5,6)} 1 0-5-6-0 15.00 15.00   0-5-6-0 15.00 15.00   0TL / LTL {(7,8)} 1 0-7-8-0 15.00 15.00   0-7-8-0 15.00 15.00   0

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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

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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!

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6. Questions - Comments


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