An Iterative Request Exchange Mechanism for Carrier Collaboration

in Less than Truckload Transportation

Xiaohui Lyu

1,2

, Haoxun Chen

and Nengmin Wang

Industrial Systems Optimization Laboratory, Charles Delaunay Institute and UMR CNRS 6281,

University of Technology of Troyes, 12 rue Marie Curie, CS 42060, 10004 Troyes, France

School of Management, Xi’an Jiaotong University, 710049, NO.28 Xianning Road, Xian Shaanxi, China

Keywords: Carrier Collaboration, Less than Truckload Transportation, Combinatorial Auctions, Request Exchange,

Pickup and Delivery.

Abstract: In carrier collaboration, multiple carriers form an alliance and exchange some of their transportation

requests to improve the overall profit of the alliance and the individual profit of each carrier. In this paper,

we propose a mechanism for the request exchange with limited information sharing among the carriers. In

each round of the mechanism, each carrier first outsources multiple bundles of requests with the

corresponding transfer payments and then insources bundles of requests from other carriers. The auctioneer

reassigns bundles of requests among carriers based on the outsourcing bundles and insourcing bundles of

requests. The auction mechanism iterates until a certain criterion is met. Numerical experiments on

randomly generated instances show that our iterative request exchange mechanism can provide high quality

solutions.

1 INTRODUCTION

Road freight transportation is a backbone of trade

and commerce. Trucks and vans move more than 14

billion tonnes of goods per year, delivering 75% of

all goods carried over land in Europe (ACEA, 2016).

However, according to statistics from the

Department for Transport in UK (2017), the average

empty running of trucks in 2015 in the UK reached

28.6%. Similarly, the vehicle utilization rate was

64% in 2015 in the UK. To reduce transportation

costs by eliminating empty back-hauls and raising

vehicle utilization rates, shippers and carriers can

form an alliance to optimize their transportation

operations by consolidating or exchanging their

transportation requests to minimize their

transportation costs or to maximize their profits.

In this paper, we focus on carrier collaboration,

in which an alliance with multiple carriers who

provide similar transportation services is formed to

exchange transportation requests among them to

increase profit and to optimize the utilization of

transportation resources. In carrier collaboration,

before request exchange (reassignment), carriers

offer transportation requests to other carriers that

cannot be integrated efficiently into their routing

plans and acquire requests from other carriers that

are complementary to their existing requests

(Krajewska and Kopfer, 2006; Bolduc et al., 2008;

Krajewska and Kopfer, 2009; Liu et al., 2010; Dai

and Chen, 2011; Defryn et al., 2015; Li, Rong, and

Feng, 2015; Li, Chen, and Prins, 2016; Gansterer

and Hartl, 2016). In the literature, there are two

planning approaches for collaborative transportation

problem: centralized planning approach and

decentralized planning approach. In a centralized

planning approach, a centralized decision maker

with complete information about all carriers

determines the optimal reassignment of requests

among those players to minimize the total

transportation cost or to maximize the total profit. In

the literature adopting a centralized planning

approach, different kinds of multi-depot vehicle

routing problem need to be solved to reassign

requests among carriers ( Dai and Chen, 2009; Audy

et al., 2011; Sprenger and Monch, 2012; Yilmaz and

Savasaneril, 2012; Lyu et al., 2018). In a

decentralized planning approach, request exchange

among carriers is usually realized by an auction with

limited information sharing among them. In auction-

based mechanisms, many researches focus on

Lyu, X., Chen, H. and Wang, N.

An Iterative Request Exchange Mechanism for Carrier Collaboration in Less than Truckload Transportation.

DOI: 10.5220/0007368602990306

In Proceedings of the 8th International Conference on Operations Research and Enterprise Systems (ICORES 2019), pages 299-306

ISBN: 978-989-758-352-0

299

combinatorial auction (Berger and Bierwirth, 2010;

Dai et al., 2014; Wang and Kopfer, 2014a, 2014b; Li,

Rong, and Feng, 2015; Chen et al., 2009; Lai et al.,

2017; Chen, 2016). Combinatorial auctions take

advantage of complementarities, in which requests are

not traded individually but are combined to bundles.

Except for combinatorial auction, a double-auction

mechanism (Özener, Ergun, and Savelsbergh, 2011;

Xu et al., 2016) and a combinatorial clock-proxy

exchange mechanism (Chen, 2016) are also proposed

to solve carrier collaboration problem. As carriers are

not willing to share their confidential cost

information, we adopt a decentralized collaborative

transportation planning approach to solve the carrier

collaboration problem.

In this study, we focus on the design of an auction

mechanism to solve the carrier collaboration problem

in less-than truckload transportation with pickup and

delivery requests. An iterative request exchange

mechanism with limited sharing of transportation cost

information is proposed. In each iteration, each carrier

as a seller first provides multiple bundles of requests

to offer and determines their corresponding transfer

payments. This decision problem is referred to as

outsourcing bundles selection problem. Each carrier

as a buyer then determines which bundles of requests

to acquire from one or multiple carriers. This problem

is called insourcing bundles selection problem. Here,

a carrier outsources a bundle of requests means that it

offers this bundle to other carriers and a carrier

insources a bundle of requests means that it acquires

this bundle from other carriers. Based on the offers

and demands submitted by all carriers, the mechanism

reassigns (exchanges) some bundles of requests

among carriers by solving a winner determination

problem. The request exchange process iterates until a

certain criterion is met. In each iteration, each carrier

updates its outsourcing bundles of requests based on

the feedback from previous iterations. Numerical

experiments show that this iterative request exchange

mechanism significantly outperforms a combinatorial

auction mechanism in the literature.

The main contribution of this paper is in three

aspects: (1) To increase collaboration potentials, each

carrier can outsource multiple bundles of requests to

other carriers and each carrier can insource (acquire)

more than one bundles of requests from multiple other

carriers in our exchange mechanism. (2) In the

mechanism, each carrier updates the outsourcing price

of each request based on the feedback from previous

iterations and thus selects different bundles of

requests to outsource in each iteration. (3) Numerical

experiments show that our mechanism significantly

outperforms the combinatorial auction proposed in

Berger and Bierwirth (2010).

The rest of the paper is organized as follows.

Problem description and the iterative request

exchange mechanism are described in Section 2. In

Section 3, we describe decision problems appeared in

the mechanism. In Section 4, numerical experiments

to evaluate the mechanism are reported with the

analysis of computational results. Section 5 concludes

this paper with remarks for future research directions.

2 PROBLEM DESCRIPTION AND

MECHANISM DESIGN

In this paper, we consider a carrier collaboration

problem in less-than truckload transportation.

Multiple carriers participate in a collaborative

transportation network. Each carrier has a set (fleet)

of homogeneous vehicles. Before collaboration, each

carrier has a set of pickup and delivery requests

provided by shippers. Each request is specified by a

pair of pickup and delivery locations, a

pickup/delivery quantity, and two time windows for

pickup and delivery respectively. Serving each

request will generate a revenue paid by a shipper.

With collaboration, each carrier can outsource part of

its own requests to other carriers and acquire some

requests from other carriers in order to increase its

individual profit.

We design an iterative request exchange

mechanism for LTL carrier collaboration. The general

structure of our mechanism is sketched in Algorithm

1. In this mechanism, each carrier sequentially

decides the requests to outsource (sell) as a seller and

the requests to insource (buy) as a buyer. The

mechanism then matches the offers and the demands

of all carriers and reassigns some bundles of requests

among them by solving a winner determination

problem (WDP) with limited information sharing.

The iterative request exchange mechanism terminates

when a certain stopping criterion is satisfied.

Note that each carrier updates its outsourcing

bundles of requests based on the feedback from

previous iterations.

To well explore the collaboration potential, the

selection of outsourcing requests plays an important

role in our iterative mechanism. To increase

collaboration possibilities by allowing carriers to

have more flexibility to select requests to outsource,

we adopt the minimum profit margin, to influence

whether a request is selected as an outsourcing

request. According to Dai and Chen (2011), the min-

ICORES 2019 - 8th International Conference on Operations Research and Enterprise Systems

300

Algorithm 1: Procedure of the request exchange

mechanism.

Each carrier determines bundles of outsourcing

requests

Each carrier determines bundles of insourcing

requests

The auctioneer solves the WDP problem to

reassign bundles of requests among carriers

If the offers of all carriers match the demands

of all carriers

Update the individual profit and request

set of each carrier

Else

Update the bundles of outsourcing

requests by each carrier, and go to Step2

While (the stopping criterion is not satisfied)

imum profit margin for a carrier represents its

profitability expectation for each request in

percentage of the request’s price provided by a

supplier.

Each carrier prefers to outsource the requests

whose marginal cost is higher than the price paid by

a shipper (Berger and Bierwirth, 2010; Li, Rong,

and Feng, 2015; Gansterer and Hartl, 2016). In order

to make the requests with high marginal costs

attractable to other carriers, each carrier can set the

initial value of the minimum profit margin to a small

value, which represents a low profitability

expectation of his requests. Each carrier adjusts the

value of the minimum profit margin based on the

matching results of offers and demands determined

by the auction mechanism. If there is no demand

from other carriers for the outsourcing requests

offered by a carrier and the carrier does not acquire

any request from other carriers, the carrier increases

the value of its minimum profit margin. Otherwise,

the same value of the minimum profit margin is

preserved for the next iteration.

In this iterative request exchange mechanism, the

transfer payment for a bundle of requests is the

money collected by the auctioneer from the

outsourcing carrier and then paid to the insourcing

carrier of this bundle after the exchange of this

bundle between the two carriers. A rule for

determining the transfer payment is specified before

the auction.

In order to make a bundle of requests more

attractive to other carriers, we introduce a profit

sharing mechanism which allows a carrier to share

part of the profit it can gain from outsourcing a

bundle of requests with another carrier who

insources this bundle, in the determination of the

transfer payment of this bundle. This profit sharing

can make carriers able to identify more profitable

request exchanges (Özener, Ergun, and Savelsbergh,

2011). This makes our determination of transfer

payment different from that of Dai and Chen (2010).

With the minimum profit margin and profit

sharing, the transfer payment for each bundle of

requests includes two parts. The first part consists of

the maximum profit margin of each outsourcing

request that a carrier is willing to offer to another

carrier for serving it. The second part is the

percentage of profit gain that each carrier is willing

to share with another carrier when outsourcing a

bundle of requests.

In the next section, we will present the decision

problem for the selection of outsourcing bundles of

requests (Section 3.1) and the decision problem for

the selection of insourcing bundles of requests

(Section 3.2), for each carrier in each iteration of the

auction and the winner determination problem

(Section 3.3) for the auctioneer.

3 DECISION PROBLEMS IN

REQUEST EXCHANGE

In this section, we present the outsourcing bundles

selection problem, the insourcing bundles selection

problem, and the winner determination problem

(WDP). The first two problems are solved by each

carrier and the WDP is solved by the auctioneer in

each iteration of the request exchange mechanism.

3.1 Outsourcing Bundles Selection

In this stage, each carrier needs to select multiple

requests to outsource to other carriers from its

current request set. We adopt the idea of minimum

profit margin in Dai and Chen (2011) to select

outsourcing requests. Dai and Chen (2011) defined

the minimum profit margin of a carrier as the

carrier’s profitability expectation. This problem of

selecting requests to outsource is a pickup and

delivery problem with selective requests, time

windows, and profits, which can be modeled as a

mixed integer programming problem.

After selecting the requests to outsource, each

carrier composes multiple outsourcing bundles of

requests to exploit synergies between requests. The

set of outsourcing requests for each carrier is

constructed by the requests which each carrier

decides to outsource. Each outsourcing bundle of

requests is composed by a number of different

requests in the set of outsourcing requests.

Each carrier calculates its profit gain for outsourc-

An Iterative Request Exchange Mechanism for Carrier Collaboration in Less than Truckload Transportation

301

ing each bundle of requests composed. The profit gain

is computed by the difference of the total profit

required to serve all the requests including and

excluding this bundle of requests. Each carrier selects

a bundle of requests with the positive profit gain to

outsource to make sure that after outsourcing this

bundle of requests, its profit will not be decreased.

The transfer payment for each outsourcing bundle of

requests is computed as described in Section 2.

Different from Berger and Bierwirth (2010), Dai

and Chen (2011) and Gansterer and Hartl (2016), we

propose multiple bundles of requests to outsource in

order to increase collaboration possibilities. However,

from a practical point of view, offering all possible

bundles is not manageable, since the number of

outsourcing bundles of requests grows exponentially

with the number of outsourcing requests. When the

number of outsourcing requests in the outsourcing set

is large, we limit the number of outsourcing bundles

of requests. We rank the outsourcing bundles of

requests based on the profit gain and select the first

number of NR bundles.

3.2 Insourcing Bundles Selection

Before determining the bundles of requests to

insource by each carrier, the auctioneer reveals all

information about outsourcing bundles of requests

and their transfer payments to all carriers in the

alliance. Each carrier insources bundles of requests

that complement to their current set of requests.

Once a bundle of requests is insourced by the

carrier, the transfer payment of this bundle is paid

to this carrier.

Each carrier selects multiple bundles of

requests to acquire (insource) from one or multiple

carriers. This decision problem is modeled as a

mixed integer programming problem. The

following assumptions are made for this decision

problem:

1) In each round of the auction, each outsourcing

bundle of requests can only be insourced (acquired)

by one carrier.

2) Once each carrier decides to insource one bundle

of requests, it must serve all of the requests in this

bundle by its own vehicles.

3) In each round of the auction, each carrier can

insource at most one bundle of requests from any

other carrier.

The insourcing bundles selection problem can also

be formulated as a mixed integer programming

problem.

After solving the insourcing bundles selection

problem, each carrier constructs its set of

insourcing bundles of requests. This set is composed

of one or multiple outsourcing bundles of other

carriers. The profit gain for this set of insourcing

bundles of requests is the difference between the total

profits obtained by serving the requests including and

excluding all the requests in the set of insourcing

bundles respectively.

3.3 Winner Determination

In our request exchange mechanism, there is an

auctioneer (coordinator) who solves a WDP to

reassign (exchange) some bundles of requests among

carriers to improve their overall operational

efficiency. Because carriers may be competitors, they

are not willing to share their confidential information,

such as the profit gain or transportation cost after

outsourcing or insourcing a bundle of requests.

Because of this, when the auctioneer determines

winning carriers and winning bids in the stage of

requests reassignment, the only information available

is the outsourcing bundles of requests and the

insourcing bundles submitted by each carrier.

In our iterative request exchange mechanism, the

exchange rules are defined as follows:

1) In each round of the auction, each carrier can only

be a seller or a buyer, but not both.

2) Each carrier can insource only one bundle of

requests from any other carrier.

3) The goal of the auction is to maximize the number

of bundles of requests to be exchanged among carriers

in each round.

Let

be the set of carriers involved in the

auction. Each carrier

Ml

submits a set of

outsourcing bundles of requests

and a set of

insourcing bundles of requests

to the auctioneer in

a round.

BO 

is an outsourcing bundle of requests

in the set

for each carrier

Ml

Based on the information provided by all carriers,

the mechanism reassigns (exchanges) some bundles

of requests among them by solving a winner

determination problem. The WDP model with

incomplete information is formulated as follows:

Notations

The set of carriers in the alliance

The set of outsourcing bundles of

requests for each carrier

Ml 

Each outsourcing bundle of requests for

each carrier

BOMl  ,

The set of outsourcing requests by all the

carriers

ICORES 2019 - 8th International Conference on Operations Research and Enterprise Systems

302

The set of insourcing bundles of requests

for each carrier

Ml 

Ri,



The binary parameter indicating

whether request

is included in the set

of requests

RR 

Decision Variables

wOl

Binary variable which equals to 1 if

andonly if carrier l M is assigned to be

aseller and a bundle of requests Ol Bl

isoutsourced by the carrier l M

wIl

Binary variable which equals to 1 if

andonly if carrier l M is assigned to be

abuyer and carrier l M insources the setof

bundles of requests Il .

The objective function (1) maximizes the total

number of bundles of requests to be exchanged in

each round of auction. Constraints (2) mean that if a

request is outsourced, this request must be insourced

by other carriers. Constraints (3) and (4) ensure that

each request can only be outsourced by at most one

bundle and insourced by at most one carrier.

Constraints (5) ensure that each carrier cannot be a

seller or a buyer in the same time. Constraints (6)

and (7) define the variables.

Based on the offers and demands of bundles of

requests submitted by all carriers, the auctioneer

reassigns (exchanges) some bundles of requests

among carriers by solving the WDP. After solving

the WDP, carriers exchange some bundles of

requests based on the decision making of the

auctioneer. Based on the results of WDP, each

carrier updates its outsourcing bundles of requests in

the same way as described in Section 2.

4 COMPUTATIONAL STUDY

In this section, we evaluate the performance of the

proposed iterative request exchange mechanism. The

proposed approach was coded in C++. Numerical

experiments were carried out on a computer with an

Intel Core i5-3210M CPU and 4.0 GB of RAM

under the Microsoft Windows 7 operating system.

4.1 Test Instances

Firstly, two sets of 10 small instances were

randomly generated. Each instance has three carriers

and each carrier with two vehicles at its own vehicle

depot has 3 or 5 requests. The capacity of each

vehicle is 20 units. The coordinates of all nodes in

the transportation network of each instance are

generated in the same way as in Chen (2016). The

distance between any two nodes is their Euclidean

distance and it is assumed that the traveling time

between any two nodes coincides with their

distance. The profit of each request is set to

],[2 dnodepnode

, which depends on the distance

from the pickup location to the delivery location of

the request (Chen 2016). For easy reference, each

instance is named with the format SerialNumber—

NumberOfRequest. For example, the instance 0-9

has the serial number 0 and 9 requests in the carrier

alliance.

4.2 Evaluation of the Request

Exchange Mechanism

We use the two sets of instances introduced in

Section 4.1 to evaluate the performance of our

request exchange mechanism by comparing it with a

centralized planning approach. In the centralized

planning approach, a decision-maker with complete

information of all carriers determines the optimal

reassignment of requests among carriers with the

objective of maximizing the total profit. Moreover,

we compare our iterative exchange mechanism with

the single request auction and the combinatorial

auction of Berger and Bierwirth (2010) on

benchmark instances.

All mixed integer programming models

involved in individual planning, centralized planning

and our iterative request exchange mechanism were

)max(

 





 





Ml BO

(1)

Subject to:

Ml lmMm IO

IOr

Ml BO





   

  



 



Rr

(2)



 

 



Ml BO



(3)



  

  



Ml lmMm IO



(4)

1



MlBO

 ,

(5)

}1,0{



MlBO

 ,

(6)

}1,0{



Ml 

(7)

An Iterative Request Exchange Mechanism for Carrier Collaboration in Less than Truckload Transportation

303

solved by calling the MIP solver of CPLEX 12.6.

The parameters used in our iterative request

exchange mechanism include the initial value of the

minimum profit margin, the percentage of profit

sharing, the step size for the increase of the

minimum profit margin in each round of the auction

and the maximum number of outsourcing bundles

for each carrier in each round. For simplicity, the

values of these parameters are set the same for each

carrier, which are 0, 0.5, 0.1, and 100, respectively.

The comparison results of our iterative request

exchange mechanism with the centralized planning

approach on the randomly generated instances are

given in Table 1, where p

IRE

and p

denotes the total

profit of all carriers generated by our iterative

request exchange mechanism (IRE) and the

centralized planning approach (CP) respectively,

CPU is the computation time in seconds and Gap

denotes the relative gap between the profits obtained

by IRE and CP. Gap is defined as follows:

%100*)(

CPIRECP

pppGap 

(8)

Table 1: Comparison results on randomly generated

instances.

Instance

No.

IRE

Gap

IRE

CPU

1-9

271.28

91.18

271.28

0.95

0.00

2-9

281.62

8.48

281.62

0.25

0.00

3-9

256.20

16.45

256.20

1.64

0.00

4-9

350.06

69.65

350.06

1.45

0.00

5-9

179.71

11.74

179.71

0.44

0.00

6-9

320.59

121.60

320.59

1.89

0.00

7-9

274.52

18.18

274.52

0.38

0.00

8-9

216.28

9.91

216.28

0.48

0.00

9-9

239.59

12.30

239.59

0.97

0.00

10-9

427.61

81.34

427.61

0.56

0.00

1-15

257.27

410.21

274.27

294.89

6.20

2-15

213.73

414.18

213.73

213.69

0.00

3-15

206.03

592.55

206.03

563.33

0.00

4-15

254.15

1304.23

256.93

1727.36

1.08

5-15

202.09

85.46

211.36

220.09

4.39

6-15

523.50

503.25

523.50

3682.44

0.00

7-15

226.87

568.22

226.87

340.66

0.00

8-15

322.30

113.46

340.28

164.78

5.28

9-15

358.77

962.8

366.31

763.91

2.06

10-15

232.29

347.63

232.29

271.83

0.00

From Table 1, we find that our iterative request

exchange mechanism can find an optimal solution

for most instances except for the instances 1-15, 4-

15, 5-15, 8-15 and 9-15.

The comparison results of our iterative request

exchange mechanism (IRE) with the two auction

mechanisms proposed in Berger and Bierwirth

(2010) on the thirty benchmark instances are given

in Table 2, where p

SRA

, p

and p

IRE

denotes the total

profit of all carriers generated by the single request

auction (SRA), the combinatorial auction (CA) and

our iterative request exchange mechanism (IRE)

respectively. Imp denotes the improvement of our

iterative request exchange mechanism with respect

to one of two auctions of Berger and Bierwirth

(2010). Imp

I-S

and Imp

I-C

are defined as follows:

%100*)(

IRESRAIRESI

pppImp 



(9)

%100*)(

IRECAIRECI

pppImp 



(10)

Table 2: Comparison results on instances in Berger and

Bierwirth (2010).

Instance

No.

SRA

IRE

Imp

I-S

Imp

I-C

16.00

164

216

24.07

210

253

17.00

187

0.00

149

0.00

190

209

9.09

237

300

21.00

218

229

4.80

142

159

10.69

A10

230

289

20.42

273

328

16.77

187

236

20.76

164

231

29.00

247

294

303

18.48

2.97

226

231

282

19.86

18.09

198

280

29.29

176

240

26.67

213

340

37.35

137

169

183

25.14

7.65

O10

184

286

35.66

268

320

16.25

0.00

272

187

373

27.08

49.87

265

367

27.79

158

227

30.40

189

403

53.10

307

378

439

30.07

13.90

283

491

42.36

288

417

483

40.37

13.66

259

258

355

27.04

27.32

I10

314

237

398

21.11

40.45

Avg

23.25

21.54

From Table 2, we find that our iterative request

exchange mechanism can achieve better solutions

than the two auctions in Berger and Bierwirth (2010)

with the average improvement of 23.25% and 21.54%

respectively. This shows our mechanism

significantly outperforms those of Berger and

Bierwirth (2010).

ICORES 2019 - 8th International Conference on Operations Research and Enterprise Systems

304

5 CONCLUSIONS

We have proposed an iterative request exchange

mechanism for carrier collaboration with pickup and

delivery requests in less-than truckload

transportation. Numerical experiments show that our

mechanism can obtain high quality solutions and

outperforms the combinatorial auction proposed by

Berger and Bierwirth (2010). Future research may

focus on developing efficient and effective

algorithms to solve the outsourcing requests

selection and the insourcing requests selection

problems to improve the effectiveness of our

mechanism. Moreover, we may consider new

characteristics in carrier collaboration in less than

truckload transportation, such as the dynamic arrival

of requests in the carrier alliance.

ACKNOWLEDGEMENTS

The research presented in this paper is supported by

French National Research Agency (ANR) under the

project ANR-14-CE22-0017 entitled “Collaborative

Transportation in Urban Distribution”, the PHC CAI

YUANPEI project with project number 36690WJ,

the Key Project of National Natural Science

Foundation of China under Grant 71732006, the

National Natural Science Foundation Project of

China 71572138,71390331,71371150,71401132.

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