A Hybrid Genetic and Simulation Annealing Approach for a

Multi-period Bid Generation Problem in Carrier Collaboration

Elham Jelodari Mamaghani, Haoxun Chen and Christian Prins

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

University of Technology of Troyes, Troyes 10004, France

Keywords: Carrier Collaboration, Bid Generation, Periodic Vehicle Routing Problem, Pickup and Delivery, Profit.

Abstract: In this article, a new vehicle routing problem appeared in carrier collaboration via a combinatorial auction

(CA) is studied. A carrier with reserved requests wants to determine within a time horizon of multi periods

(days) which requests to serve among a set of selective requests open for bid of the auction to maximize its

profit. In each period, the carrier has a set of reserved requests that must be served by the carrier itself. Each

request is specified by a pair of pickup and delivery locations, a quantity, and two time windows for pickup

and delivery respectively. The objective of the carrier is to determine which selective requests may be

served in each period in addition of its reserved requests and determine optimal routes to serve the reserved

and selective requests to maximize its total profit. For this NP-hard problem, a mixed-integer linear

programming model is formulated and a genetic algorithm combined with simulated annealing is proposed.

The algorithm is evaluated on instances with 6 to 100 requests. The computational results show this

algorithm significantly outperform CPLEX solver, not only in computation time but also in solution quality.

1 INTRODUCTION

In collaborative logistics, carriers may exchange

some of their transportation demands in order to

improve their profitability (Hernández et al., 2011).

In this article, we consider collaboration among

multiple carriers through exchanging some of their

requests. The goal of this collaboration is to

maximize the total profit of all carriers and generate

more profit for each carrier. The carrier

collaboration is usually realized in two steps. The

first step is the re-assignment of a part of requests

called selective requests among carriers and the

second step is the sharing of the profit among

carriers (Dai et al., 2015).

Combinatorial Auction (CA) is an approach for

request re-assignment among carriers. In a multi-

round CA, in each round (iteration), the service price

for each selective request is updated by an

auctioneer (Dai et al., 2014). Each carrier determines

which selective requests to serve in addition to its

reserved requests to maximize its own profit by

solving a bid generation problem. In real world

applications, carriers usually plan their pickup and

delivery operations and use of vehicle resources in

advance (several days ago) and in a rolling horizon

way (Wang et al., 2014), (Wang et al., 2015). This

requires that each carrier considers multiple periods

(days) when it determines which transportation

requests to bid and serve in each period (day).

Moreover, requests open for bid (requests to be

exchanged among carriers) may span across multiple

periods (days). That is, instead of fixing a day for

serving each of the requests, each request is allowed

to be served within a service day window consisting

of multiple consecutive days. An important

application of multi-period BGP is in e-commerce.

For example, goods ordered on-line by a customer

on Monday is asked to deliver to the home of the

customer within three days from Tuesday to

Thursday. This gives rise to a multi-period

combinatorial auction (CA) problem. In this article,

a multi-period Bid Generation Problem (BGP) for a

carrier is considered. In the problem, there are two

different types of requests, reserved requests of the

carrier and selective requests. The carrier is

committed by contracts with its shippers to serve all

reserved requests by itself. The selective requests are

offered by other carriers and are opened for bid by

the carrier. Each request is specified by a pair of

pickup and delivery locations, a pickup/delivery

quantity, and two time windows for pickup and

Mamaghani, E., Chen, H. and Prins, C.

A Hybrid Genetic and Simulation Annealing Approach for a Multi-period Bid Generation Problem in Carrier Collaboration.

DOI: 10.5220/0007369203070314

In Proceedings of the 8th International Conference on Operations Research and Enterprise Systems (ICORES 2019), pages 307-314

ISBN: 978-989-758-352-0

307

delivery, respectively. The pickup/delivery time

window of a request specifies the earliest and the

latest time at which the pickup/delivery operation of

the request must be performed in each period. In

addition, each selective request has a period window

which specifies the earliest period and the latest

period between which the request must be served.

Moreover, each selective request is associated with a

profit that is the price for serving the request

provided by a shipper. By considering multiple

periods in CA, the carrier can plan its transportation

operations in advance and in a rolling-horizon way.

A carrier must make two important decisions in its

BGP: Which requests are chosen to bid and serve

within their service period windows and how the

routes are constructed to maximize its total profit.

This leads to a new periodic pickup and delivery

problem with time windows, profits and reserved

requests. According to Wang and Kopfer (2014), the

presented problem is NP-hard and it is impossible to

get an optimal solution for large instances by using a

commercial solver like CPLEX. Hence, a hybrid

approach combined genetic algorithm and simulated

annealing (GASA) is proposed to solve the problem.

The numerical results demonstrate the proposed

algorithm can find a good feasible solution in a

reasonable computation time for large instances.

The rest of the paper is organized as follows.

Section 2 is devoted to literature review. A detailed

description of a mathematical model is given in

Section 3. In section 4, the GASA algorithm is

described. In section 5, detailed numerical results of

solving the model by GASA and CPLEX solver on

instances is presented and compared. The final

section concludes this paper with some remarks for

future research.

2 LITERATURE REVIEW

Collaborative Transportation Management (CTM) is

achieved through the horizontal collaboration

between multiple shippers or carriers by either

sharing transport capacities or transportation orders.

With the collaboration, all actors involved can

improve their profitability by eliminating empty

backhauls and raising vehicle utilization rates (Dai

and Chen, 2011). (D’Amours and Rönnqvist, 2010)

present a survey of previous contributions in the

field of collaborative logistics. Indeed, efficient

utilization of vehicle capacity and reducing the

number of vehicles through carrier collaboration is

noticeable in Less than Truck Load (LTL)

transportation. With this type of collaboration,

operation efficiency will increase (Hernández et al.,

2011). The considered problem in the current paper

is a bid generation problem with multi periods in

collaborative transportation. The bid generation

problem (BGP) which is considered from the

perspective of each carrier is the request selection

problem and a key decision problem for auction-

based decentralized planning approaches in CTP.

(Lee et al., 2007) study the carrier’s optimal BGP in

combinatorial auctions for transportation

procurement in TL (truckload) transportation.

Carriers employ vehicle routing models to identify

sets of lanes to bid for based on the actual routes.

(Buer, 2014) proposes an exact strategy and two

heuristic strategies for bidding on subsets of

requests. The model proposed in this paper is a

multi-period extension of the model proposed in (Li

et al., 2016). Both of them assume the BGP of a

carrier, but the BGP considered in this paper

involves multi periods. There are two interesting

studies in multiple periods BGP: (Wang et al.,

2014), (Lau et al., 2007). In these papers, each

carrier considers multiple periods (days) when it

determines which transportation requests to bid and

serve in each period (day). Moreover, requests open

for bid may span across multiple periods (days).

Other works related to ours include studies on the

Team Orienting Problem (TOP). Multiple vehicle

routing problem with profits is called Team

Orienting Problem (TOP) (Chao et al., 1996) focus

on the TOP by considering multiple tour maximum

collection problem and multiple tour VRP with

profits. (Yu et al., 2010) utilize a simulated

annealing algorithm to solve a capacitated location

routing problem.

3 PROBLEM DESCRIPTION AND

MATHEMATICAL MODEL

In this problem, we consider a carrier who wants to

determine which requests to bid (select) among all

requests open for bid (offered by all carriers) in a

combinatorial auction to maximize its own profit by

solving a bid generation problem. Since the carrier

plans its transportation operations in advance and in

a rolling horizon way as mentioned in the

introduction, this bid generation problem involves

multiple periods. We consider the problem in the

less-than-truck load transportation, where each

transportation request is a pickup and delivery

request with time windows, two types of requests-

reserved requests and selective requests are

involved, and each request is associated with a profit

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

308

which is the revenue provide by a shipper to serve

the request. Formally, the multi-period bid

generation problem can be defined on a directed

graph

(,)GNE

where N is the set of all nodes

comprising all pickup, delivery nodes and the depot

node of the carrier and E is the set of edges. The

node set is defined as

{0,..., 2 1}Nn





, where n

represents the number of requests, 0 and 2n+1 both

denote the depot of the carrier, i and n + i represent

the pickup point and the delivery point of request i =

1, 2, …, n. Let  denote the set of nodes excluding

the depot node. The set of periods denoted by .In

the problem, the carrier has a finite fleet of

homogenous vehicles whose index set is given by





1,2, … ,



where VK is the maximum

number of vehicles. The capacity of each vehicle is

denoted by Q and the load of each vehicle cannot

exceed its capacity. 



and 



are the travelling time

and the transportation cost from node i to node j,

respectively. We assume 







. The set of pickup

and delivery nodes of all requests are denoted by



1,2, … ,



and 



1,..,2, respectively.

Each request i has its pickup node i and its delivery

node n+i. The demand of the pickup node of request

i is denoted by d

, while the demand of the delivery

node of the same request is denoted by d

i+n

, d

i+n

= -

. The delivery node of each request must be visited

after its pickup node on the same route. The set of

all requests is denoted by R, where

R=

⋃











⋃





. 



is the set of reserved

requests that must be served in period l, 



is the set

of selective requests and H is the set of periods.

Each selective request has a service period window

and two time windows. The service period window

determines which periods the selective request can

be served, and the two time windows determine at

which times in each period the pickup node and the

delivery node of the request can be visited by a

vehicle that serves the request. Both selective and

reserved requests are associated with two time

windows, whereas only selective requests are

associated with a service period window (the period

in which each reserved request must be served is

pre-specified). The time window of pickup node i

and delivery node i+n

of request i are denoted by

[



,l

] and [



,



], respectively. The service

period window for each selective request i is

represented by [



,



]. Each reserved request i  



must be served in its pre-specified period l, l  H.

The maximum duration of each route is limited by.

The multi-period bid generation problem can be

formulated as a mixed-integer linear programing

model. In the model, parameters 











used to formulate linearly the time window

constraints. The decision variables of the model

include binary variables, 



and 



and real

variables 



and 



are defined as follows.

1 if and only if vehicle k

visits directly node j after node i in period h

0 else

ijkh













1 if and only if request i is served by

vehicle k in period h

0 else

ikh













arrival time of vehicle k at node i in period h

Load of vehicle k when it leaves node i in period h

ikh



The problem can be formulated as the following

mixed integer-programming model:

max

i ikh ij ijkh

iRkKhH kNiNjNhH

py cx

  





 

Subject to:

0 ( ),

jikh ijkh

jNji jNji

xiPD

kKhH

 



 



(1)

jkh

kKhHjPj









(2)

,2 1, ,

,21

in kh

kKhHiDi n



    







(3)

1 ,

ikl rl

yiRlH



 



(4)



ikh s

hELkK

yiR







(5)

,,0

, ,

jn ih ikh

jNji

yiPkK











(6)

,,21

, ,

ijkh ikh

jNji n

yiPkK

 







(7)

,,,

, ,

ikh i n i i n k h

Ut U iPkK



 



(8)

(1 )

,, ,

jkh ikh ij ijkh ij ijkh

UUtxBM x

ij N k K h H

  

 

(9)

(1 )

i ikh ikh i ikh ij

ey U l y BM

iN kKhH





   



(10)

(1 ) ,

ikh ij ij ijkh

UtBM x TiW

kKhH

   

 

(11)

A Hybrid Genetic and Simulation Annealing Approach for a Multi-period Bid Generation Problem in Carrier Collaboration

309

(1 )

,, ,

jkh ikh j j ijkh

CV CV d CV x

ij N k K h H

 



(12)

max{0, } min{ , }

i N, k K, h H

iikh i

dCV QQd 

  

(13)

{0,1} , , ,

ijkh

ij N k K h H

(14)





0 , ,

0 ,

ikh s i i

ikh rl

yforanyiRhEL

and

yforanyiRhl





(15)

0 , ,

ikh

UiNkKhH 

(16)

0 , ,

ikh

CV i N k K h H 

(17)

The objective function represents the total profit of

the carrier, which is equal to the difference between

the total payments of serving requests in all periods

and the total transportation cost. Constraint (1)

ensures that when a vehicle arrives at a node in a

period, it must leave from the node in the same

period. Constraints (2) and (3) signify that each

vehicle leaves its depot in a period must return to the

depot in the same period. Equation (4) implies that

each reserved request must be served in its pre-

specified period. Equation (5) indicates that each

selective request can be served in a period within its

service period window or not served. Constraints (6)

and (7) guarantee if a request is served in a period,

its delivery node must be visited after its pickup

node with the same vehicle in the same period.

Equations (8)-(11) specify time window constraints

on the pickup and delivery nodes of each request,

and the constraint on the maximum duration of each

route. Constraints (12)-(13) ensure vehicle capacity

constraints. Equations (14)-(17) describe the

variables.

4 METAHEURISTIC APPROACH

TO SOLVE MULTI-PERIOD

BID GENERATION PROBLEM

The Multi-Period Bid Generation Problem based on

Pickup and Delivery with Time Windows, reserved

requests and profits is NP-hard (Wang and Kopfer,

2014a) and special case of vehicle routing problem.

Consequently, it is required to enforce metaheuristic

algorithms to solve the problem. GASA is a

metaheuristic algorithm used to solve the problem.

4.1 Initial Solution Construction

Procedure

In the proposed hybrid genetic algorithm with

simulated annealing (GASA), the size of population

determines the number of initial solutions to

construct. The initial solutions are constructed in the

following three ways:

1. Only the reserved requests are served. All

reserved requests are sorted in the decreasing

order of their profits and the reserved request

with the highest profit is firstly served. All

reserved requests must be served in this case.

2. All reserved requests are served firstly and then

selective requests are served. Both types of

requests are sorted in the decreasing order of

their profits and the reserved request with the

highest profit is served at first. After serving all

reserved requests, selective requests are served in

the decreasing order of their profits within their

service period windows. In this case, all selective

requests must be served.

3. All reserved requests must be served first and

selective requests are served only if its assigned

period is not zero. That is, if the period assigned

to the request is zero, it will be not served.

If the probability of choosing each of the three ways

to construct an initial solution is denoted by

12 3

, and





, respectively, then

123





4.2 Hybrid Genetic Algorithm with

Simulated Annealing (GASA)

One of the well-known metaheuristic algorithms

inspired from the nature is Genetic Algorithm (GA)

that is suggested by (Holland and H., 1992). Another

well-known metaheuristic algorithm is Simulated

Annealing (SA) that accepts a worse solution with a

probability. Actually, diversification of search space

is included in the algorithm by decreasing the

probability of accepting worse solution. We apply

hybrid algorithm of GA and SA that is called GASA

to prevent GA from premature convergence. All

components of GASA for multi-period CT with

pickup and delivery and time window will be

explained in the rest of this section. In each iteration

of GASA, the profit is updated thanks to the

obtained profit in the latest generation. SA is applied

on each solution of the present population. Each

solution is selected with a probability based on a

simulated annealing procedure.

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

310

Simulated Annealing in GASA

Simulated Annealing gives a chance to worse

solutions, which accepts a worse new solution with a

probability. The new solution acceptance probability

is given by 



















/

where 









is the

objective value of the new solution and 







is the

objective value of the current solution and 



















. The acceptance probability depends on both

the profit decrease 











 and the temperature

parameter  which is decreased at each iteration.

The temperature reduction is performed by

multiplying  with a cooling factor ∈ 0,1. To

attain a slow cooling, the cooling factor must be set

close to one. At the beginning of the GASA

algorithm, the temperature parameter is set to



and a solution with profit 30% lower than that of the

initial solution is accepted with a given

possibility. In GASA, to produce the next

generation solutions, at the end of each GA iteration,

the solutions generated by crossover and mutation

are sorted and merged with the current population.

GASA utilizes the SA rule to determine whether

each solution in the sorted list becomes a solution

(chromosome) in the next generation.

4.2.1 Solution Representation in GASA

The chromosome of multi-period BGP is defined by

three vectors , and . Vector  is included all

pickup nodes and delivery nodes and its dimension

is |



| as the index of each request is the same as

its pickup node index in three vectors. The size of

vector  is equal to the number of all requests, and

each component of vector  indicates the period

assigned to a request. Since a selective request is not

compulsory to be served, if it is not profitable, it will

not be served. Vector  is similar to vector  and the

dimension of  is equal to the number of all

requests. In vector , each component indicates the

index of the vehicle serving a request. An extra

period is introduced to indicate a selective request is

not served. The extra period is referred to period 0.

4.2.2 Operators of GASA

The proposed chromosome has three vectors which

two of them have same structure. Therefore, two

different crossover and mutation operators are

applied.

Crossover Operator of Vector

A single point crossover is suitable to the solution

structure with permutation specification. In the

suggested chromosome to GASA, vector  has a

permutation structure and single point crossover is

used without need to use any extra operation to

make its produced offspring’s chromosomes

feasible. In fact, by using single point crossover, it is

prevented from creating repetition genes. To

generate the first offspring after chosen the

crossover point randomly in the vector , all genes

of first parent chromosome before the crossover

point are sequentially transferred and creates the first

part of the offspring’s chromosome. To generate the

genes after the crossover point, in the beginning, all

genes of second parent are compared with the first

part of first offspring chromosome. All non-

repetitive genes of the second parent are transferred

to construct the rest gens of first offspring and

complete the chromosome of first offspring. This

approach of gene selection in the opposite direction

is done to produce second offspring.

Crossover operator of vector and 

According to the structure of vector  and ,

uniform crossover is suitable crossover operator. At

first, a mask vector with the same size of parents is

created with zero and one genes. The value of each

offspring’s gene is generated according to the value

of mask vector and the same indexed gene of parent.

The gene of first parent is transferred to the first

offspring gene with the same index if the mask gene

is one and the gene of second parent is transferred to

first offspring if the mask gene is zero. To produce

second offspring, the gene of second offspring has

the same value of first parent when the mask vector

gene with the same index is zero and the value of

second offspring gene is chosen from second parent

if the value of mask in the same index is one.

Mutation over Vector 

To have a diversified feasible solution, a mutation

operation with the following two steps is suitable to

the permutation structure vector .

1) Choose randomly two genes of vector 

2) Choose randomly one of the relocation, swap and

reversion operations and execute the selected

operation on the selected genes.

 Swap Operator

Select two components of vector  and swap

their positions in the vector.

 Reversion Operator

Selects two components of vector  and

reverse the order of the components between

the selected components.

 Relocation Operator

Select two components in vector  and

A Hybrid Genetic and Simulation Annealing Approach for a Multi-period Bid Generation Problem in Carrier Collaboration

311

relocates one of them to the front of another

component.

Mutation over Vectors and 

The mutation over vector is proceeded in three

steps. At first, the number of mutated genes of

vector  is determined randomly and illustrated by .

The number of mutated genes are obtained in the

following step: The primer step is generating

randomly integer number  between 1 and dim [],

as dim [] is the number of genes in vector  where

VK is the maximum number of vehicles. This

number is multiplied by a mutation rate , leading to

. By rounding  to the least integer number

larger than or equal to , the number  is obtained.

In the second step, from ,  genes are randomly

selected. Finally, for each selected gene of Z, an

integer number is randomly generated between 1 and

VK, and the gene in  is changed to this value. The

mutation over vector  is the same as mutation

operation over vector  with a difference in third

step. In vector , for each chosen gene, an integer

number is randomly generated between 0 and 

where  is the maximum periods and the selected

gene in  is changed to this value. After the

mutation, an offspring chromosome is modified

from the parent chromosome with new values in

some elements.

5 EXPERIMENTAL RESULTS

To evaluate the performance of the proposed

metaheuristic algorithm, we applied it to solve

instances of taken from (Li et al., 2016) with the

same reserved requests and the selective requests,

and compared them with the MILP solver of CPLEX

12.6 in terms of profit and computation time. We

consider there are 5 periods and each period has its

own reserved requests according to the random

function. Note that for the instances more than

20requests it was impossible to solve the MILP

model optimally by CPLEX after 2 hours.

5.1 Parameter Setting

The values of some parameters of the algorithm are

determined empirically and are given in Table 1.

The values of other parameters are tuned by using

the Taguchi method (Semioshkina and Voigt, 2006)

are given in Table 2.

Table 1: Parameter values of GASA determined

empirically.

Parameter Description Value

SubIt

Number of

iteration of SA

110



Mutation rate 0.26

Table 2: Parameter values of GASA determined by

Taguchi.

Methodology Parameter Description Value

Npop

Size of

population

150

nIt

Number of

iterations

800

Crossover

probability

0.6

Mutation

probability

0.05

5.2 Test Results

After the parameters calibration, we executed the

GASA algorithm and CPLEX on all instances. For

CPLEX, since the considered carrier collaboration

problem is NP-hard (Wang and Kopfer, 2014b) it is

very time consuming to solve optimally large size

instances. For this reason, we set a maximum

running time for CPLEX to solve large size instance.

The time limitation is 2 hours. Our proposed

algorithm is compared with CPLEX based on the

criterions defined in Table 3, where Obj

GASA

and is

the profits of the studied problem obtained by the

algorithm, respectively; UB

MILP

and LB

MILP

are the

upper bound and the lower bound of the objective

value of the problem obtained by CPLEX in a preset

computation time.

Table 3: Criterions used for comparison of GASA and

Cplex.

Criterion Descri

tion

Gap



The relative gap between



and



, defined as



LB



Gap



The relative gap between



and

Obj



, defined as





Obj





The computation results are given in Table 4 and

Table 5. From Table 4, we can see, for small

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instances, CPLEX and GASA could find an optimal

solution. However, for some 8 requests instances

and CPLEX could not even find a feasible solution

in a preset computation time, whereas GASA could

find a feasible solution for all instances. So we

compare the solutions obtained by GASA based on a

relative gaps with the upper bound obtained by

CPLEX, i.e., using the above-mentioned criteria.

GASA can find an optimal solution for 6 requests

instances, it can find a solution with the relative

profit gap smaller than 0.34% for 8 request instances

and 4.50% for 10 request instances. For instances

with 20 requests, GASA can find a solution with the

gap smaller than 6.98%. For instances with 30

requests, GASA can find a solution with the gap

smaller than 10.31%. For instances with 40 and 50

requests, GASA can find a solution with the gap

smaller than 11% and 13.2% sequentially. For the

instances with 100 requests, GASA can find a

solution with the gap smaller than 16.4%. From the

results, we can see our proposed algorithms perform

much better than CPLEX in terms of running time

for medium and large instances.

Table 4: Computational results of GASA and CPLEX –

part one.

Instance LB

MILP

Profit

GASA

6-3-3 256.5254 265.5254 265.5254

8-4-4 512.015 514.731 514.682

10-5-5a 909.810 984.660 974.614

10-5-5c 974.001 1028.626 1019.693

10-3-7

1157.164 1257.153 1248.267

10-3-7f - 1210.611 1183.689

20-10-10a - 2619.785 2473.626

20-10-10c - 3815.445 3651.975

20-5-15

1832.804 2015.517 1991.431

20-5-15e - 2568.903 2462.24

30-15-15c - 7432.469 7003.483

30-10-20

- 6629.284 6263.02

30-20-10g - 11214.73 10452.39

40-20-20a - 12065.1 11103.11

40-15-25

- 12205.41 109481.51

40-25-15g - 11115.574 99794.391

50-25-25a - 23781.93 21105.171

50-20-30

- 22083.155 19206.231

50-20-30f - 20495.213 18004.147

100-50-50a - 88406.782 75606.06

100-50-50b - 90722.467 78110.724

100-25-75

- 112103.589 93850.223

100-25-75f - 90686.991 75815.239

100-75-25g - 93663.471 78945.834

100-75-25h - 82124.016 70237.949

Table 5: Computational results of GASA and CPLEX –

part two.

Instance

Gap

GASA

(%)

Gap

MILP

(%)

CPU

GASA

CPU

ILP

6-3-3 0 0 85.117

67.64

8-4-4 0.009 0.333 100.794

93.36

10-5-5a 0.512 7.61 184.342 500

10-5-5c 0.869 5.311 173.110 500

10-3-7

0.469 7.733 186.185 500

10-3-7f 0.729 2.003 177.961 500

20-10-10a 5.579 - 331.511 3600

20-10-10c 4.284 - 351.836 3600

20-5-15

1.195 9.065 326.537 3600

20-5-15e 4.1520 - 322.419 3600

30-15-15c 5.771 - 547.992 3600

30-10-20

5.524 - 5213.14 3600

30-20-10g 6.797 - 546.232 3600

40-20-20a 7.973 - 825.753 7200

40-15-25

10.297 - 844.225 7200

40-25-15g 10.007 - 819.471 7200

50-25-25a 11.255 - 1719.124 7200

50-20-30

13.027 - 1696.439 7200

50-20-30f 12.154 - 1690.491 7200

100-50-50a 14.479 - 2725.955 10800

100-50-50b 13.901 - 2728.801 10800

100-25-75f 16.398 - 2759.854 10800

100-75-25g 15.713 - 2916.492 10800

100-75-25h 14.473 - 2891.837 10800

6 CONCLUSIONS

In this article, a new vehicle routing problem

appeared in collaborative logistics, the multi period

pickup and delivery problem with time windows,

reserved requests and selective, is considered. By

solving this problem, a carrier determines which

transportation requests to serve in a combinatorial

auction. This problem has a new feature that each

selective request has a service period window

besides time windows to visit its pickup and delivery

points. We have proposed a hybrid metaheuristic

algorithm to solve the model. Numerical

experiments on benchmark instances show that the

algorithm can obtain optimal solutions for small

instances and much better solutions for medium to

large instances than CPLEX. CPLEX cannot find

even a feasible solution for such instances in a preset

computation time.

ACKNOWLEDGEMENT

This work is supported by the ANR (French

National Research Agency) under the project

A Hybrid Genetic and Simulation Annealing Approach for a Multi-period Bid Generation Problem in Carrier Collaboration

313

ANR-14-CE22-0017 entitled “Collaborative

Transportation in Urban Distribution”.

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