Iterated Local Search for a Vehicle Routing Problem with

Synchronization Constraints

Nacima Labadie

, Christian Prins

and Yanyan Yang

LOSI, University of Technology of Troyes, CS42060, 10004, Troyes Cedex, France

CGS, Mines ParisTech, 60 Boulevard Saint Michel, 75272, Paris Cedex 06, France

Keywords:

Vehicle Routing, Synchronization Constraints, Iterated Local Search.

Abstract:

This paper deals with vehicle routing problem (VRP) with synchronization constraints. This problem consists

in determining a least-cost set of routes to serve customers who may require several synchronized visits. The

main contribution of the paper is: 1) it presents a deﬁnition and a classiﬁcation of different types of syn-

chronization constraints considered in the VRP literature; 2) it describes a variant of vehicle routing problem

with synchronization constraints which is formulated as a mixed integer programming model; 3) ﬁnally, it

provides a constructive heuristics and an iterated local search metaheuristic to solve the considered problem.

The performance of the proposed approaches is evaluated small and medium sized instances.

1 INTRODUCTION

The vehicle routing problem (VRP) was introduced

by Dantzig and Ramser in 1959 (Dantzig and Ramser,

1959). It is a fundamental planning problem in the

ﬁeld of transportation, distribution and logistics. This

combinatorial optimization problem consists in seek-

ing routes for a set of vehicles, to perform a set of

tasks in a network. During the past half century there

has been a vast amount of literature and research

on the VRP and its variants, complete surveys can

be found in Desaulniers and Desrosiers (Desaulniers

et al., 2002), Berbeglia and Cordeau (Berbeglia et al.,

2007), and Parragh et al. (Parragh et al., 2008).

A recently arising and hot extension of VRP

is the vehicle routing problem with synchronization

constraints (VRPS). Drexl (Drexl, 2011) deﬁned the

VRPS as a VRP exhibiting additional synchronization

requirements in spatial, temporal, and load aspects, he

gave a recent review of VRPS and deﬁned the VRPS

as a vehicle routing problem where more than one ve-

hicle may or must be used to fulﬁl a task. However,

there are some problems which require more than one

vehicle to fulﬁl a task but are not synchronization

problems, like split delivery VRP. Thus we propose a

simpler deﬁnition of the VRPS: ”A VRPS is a vehicle

routing problem where there exists at least one vertex

requiring simultaneous visits of vehicles, or succes-

sive visits resulting from precedence constraints”.

The fundamental difference between the VRP and

VRPS is that in the VRPS the routes are interdepen-

dent. It means that a change in one route may have

effects on other routes because of the synchronization

constraints while a change in one route does not af-

fect any other route in the standard VRP. In the worst

case, a change in a VRPS route may lead all the other

routes infeasible.

Due to the spatial, temporal, and load aspects,

Drexl (Drexl, 2011) classiﬁes the VRPSs into ﬁve

categories: Task synchronization, operation synchro-

nization, Movement synchronization, Load synchro-

nization and Resource synchronization. However, we

propose a classiﬁcation according to two synchro-

nization types based on our deﬁnition, simultaneous

synchronization and precedence synchronization. In

the simultaneous synchronization (SS), the vertex re-

quires at least two visits, simultaneously or in a nar-

row time window while in the precedence synchro-

nization (PS) the vertex requires several successive

visits with or without time windows.

The literature on routing problems with synchro-

nization constraints is relatively scattered. For the

case of simultaneous synchronization we can ﬁnd

the paper of Ioachim and J. Desosiers (Ioachim and

Desosiers, 1999) which describes an aircraft ﬂeet

assignment and routing problem with synchroniza-

tion constraints. In this problem, the authors pro-

pose the synchronization constraints from so-called

same-departure-time requirements: the same identi-

ﬁer ﬂights have to depart at the same time every day

257

Labadie N., Prins C. and Yang Y..

Iterated Local Search for a Vehicle Routing Problem with Synchronization Constraints.

DOI: 10.5220/0004837502570263

In Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems (ICORES-2014), pages 257-263

ISBN: 978-989-758-017-8

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

during a week which induces a simultaneous syn-

chronization problem. To solve the problem, the

authors proposed a branch-and-price using a multi-

commodity ﬂow formulation. Common real applica-

tions of routing with synchronization are home health

care and hospital systems. Bertels and Fahle (S. Ber-

tels, 2006) considered a problem with hard roster-

ing constraints like qualiﬁcation requirements or work

time limitations, and soft constraints like preference

of serving time, preference of patients and prefer-

ence of nurses. Some tasks may need cooperation of

nurses which leads to simultaneous synchronization.

The objective is to minimize the total cost and max-

imize patients/staff satisfaction. The authors develop

a combined constraint programming and tabu search

method which produces good solutions within short

time. Bredstrom and Ronnqvist (Bredstrom and Ron-

nqvist, 2008) also consider home care staff schedul-

ing where may be two or more staff members would

be required to accomplish a task (such as two nurses

for bathing elderly person). The objective function

is a weighted sum of preferences, traveling time and

balancing variables. In this work, a MIP formula-

tion is proposed and a heuristic that iteratively solves

restricted MIP problems is used to improve the best

known feasible solutions. Inc (Braysy et al., 2009)

three communal routing problems with synchroniza-

tion are described: the organization of home care,

transportation of the elderly and home meal delivery

in Finland. In the home care nurse problem, personnel

has a maximum number of working hours per day and

different levels of education and different skills qual-

iﬁed to perform different services. Each customer in

a given service area are allocated to a given team and

workers typically work exclusively in their own team.

Each customer requires several visits within a given

interval time. The objective is to maximize the work-

ing hours and the workers’ preferences while taking

into account the regulation for breaks.

Amaya et al. (Amaya et al., 2007), (Amaya et al.,

2010) study the capacitated arc routing problem with

reﬁll points (CARP-RP) of road marking problem in

Canada. In this problem, there are two vehicles, a

painting vehicle serving the road and a tank vehicle

to reﬁll the painting vehicle. The painting vehicle can

only be reﬁlled by the tank vehicle but at any road

junction and both vehicles are originally located and

end their routes at the depot. In the ﬁrst paper, af-

ter each reﬁll the tank vehicle must return to the de-

pot which makes the synchronization constraint much

simpler. The objective is to determine the vehicle

routes simultaneously both for the painting vehicle

and the tank vehicle to minimize the total traveling

cost. To solve the problem, the authors propose an

integer programming model and develop a cutting-

plane algorithm applied to solve instances involving

20 to 70 nodes and 50 to 595 arcs.

The second publication extends the problem by

since there is no need for the tank vehicle to return

to the depot each time after the replenishment. The

authors upgrade their previous IP model and develop

a heuristic method based on the route-ﬁrst-cluster-

second principle. However, due to the construction

of the network, the heuristic does not need to con-

sider the synchronization constraints. Salazar-Aguilar

et al. (Salazar-Aguilar et al., 2013) consider a sim-

ilar road marking problem where several capacitated

vehicles are used to paint lines on roads instead of

only one in the two previous studies, and a tank ve-

hicle is also used to replenish the painting vehicles.

The objective is to determine routes and schedules for

the painting and replenishment vehicles to minimize

the makespan: the duration of the longest route. The

authors developed an adaptive large neighbourhood

search (ALNS) metaheuristic to solve this problem.

In the constructive procedure, routes of painting ve-

hicles have been generated, the potential reﬁll nodes

on each of them are identiﬁed and the route of the

replenishment vehicle is then constructed by means

of a GRASP ensuring the synchronization constraints.

Moreover, the authors improve the ALNS by combin-

ing seven destroy/repair operators.

Applications with similar nature are developed in

(Salazar-Aguilar et al., 2012). These authors pro-

posed a synchronized arc routing for snow plowing

operations in Canada. In this problem, streets require

plowing operations in one or two direction and each

direction has one to three lanes. All lanes belong-

ing to the same segment in the same direction must

be plowed simultaneously and each lane can only be

served by one vehicle at a time. There is a ﬂeet of

snow plowing vehicles originally located at a depot.

The objective is to determine a set of routes to min-

imize the duration of the longest route (makespan)

while all street must be plowed.

Few studies deal with precedence synchroniza-

tion: in Kim et al. (Kim et al., 2010), a combined

manpower-vehicle routing problem with multi-staged

services is studied. In this problem, the workers can

only be moved to the customers by vehicles and cus-

tomers demand several visits of different workers in

a predeﬁned sequence. The objective is to minimize

the total cost of the vehicle routing. To solve the

problem, the authors develop a simple constructive

heuristic and a particle swarm optimization (PSO).

A home health care staff scheduling problem is stud-

ied in (Rasmussen et al., 2012), the authors consider

staffs with different qualiﬁcations where both patients

ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems

258

and staffs have time windows, all visits are associated

with priorities and each patient has his own preferred

carer. A branch-and-price algorithm using Dantzig-

Wolfe decomposition is used to solve the problem

where the aim is to minimize a weighted sum of three

criteria: the number of uncovered visits, the total trav-

eling cost and the sum of preferences. A similar prob-

lem was studied in a previous work from Dohn et al.

(Dohn et al., 2009). In this study, the authors pro-

pose a vehicle routing problem with time windows

and precedence constraints. Each customer demands

a sequence of visits in a given time window. The ob-

jective is to minimize the total travel distance. The

authors developed a column generation approach to

solve the problem.

The remainder of this paper is organized as fol-

lows. Section 2 describes the studied vehicle rout-

ing problem with simultaneous synchronization con-

straints, and proposes a mixed integer programming

formulation of the problem. The solution approaches

that we developed are described in Section 3. Com-

putational results are presented in Section 4, followed

by conclusions in Section 5.

2 PROBLEM DESCRIPTION AND

MATHEMATICAL MODEL

This work is dedicated a special case of vehicle rout-

ing problem with simultaneous synchronization con-

straints and is motivated by real applications occur-

ring in home health care systems or services sector.

In these ﬁelds, some customers may require a service

which must be accomplished by more than one per-

son because the personnel constituting a staff has not

the same competencies.

Formally, the studied problem can be deﬁned

in an undirected graph G = (V, E) with a node-set

V = {0, 1, 2, , n, n + 1} and an edge-set E. Nodes 0

and n + 1 are special nodes called initial resp. ﬁnal

depots; while the other vertices correspond to cus-

tomers. Each edge e = [i, j] is associated with a travel

cost c

and a traversal duration T

. It is assumed that

these times satisfy the triangle inequality. The initial

depot 0 offers a set of possible services P = {1, 2, , r}

to customers. Each customer demands a subset of ser-

vices speciﬁed by a vector U

= (v

, v

, , v

) where

equals to 1 if customer i demands the service p ∈ P

(P = {1, ..., r}, 0 otherwise. Services required by

the same customer should all start simultaneously and

have a common time duration D

. Each customer has

its available time window [α

, β

] where α

is the ear-

liest start time of service at the customer i and β

the latest start time at the customer i.

A limited number V of vehicles in H =

...

offering services are originally lo-

cated at the depot 0. Each vehicle k ∈ H

is qualiﬁed

to perform a unique service p in the set P. [α

, β

]

is the available time for all the vehicles which means

that all vehicles can only leave the initial depot at α

and must return to the ﬁnal depot before β

The problem consists in building a set of routes

starting at the initial depot 0 and ending at the ﬁnal

depot n + 1, such that each vehicle route doesn’t ex-

ceed the maximal imposed duration, each customer is

provided the required services and each of these ser-

vices must start at the same time (when there is at

least two services needed) within the customer’s time

window. Each kind of service must be accomplished

by the corresponding qualiﬁed vehicle (team). This

study considers the minimization of overall cost of

edges crossed by the vehicles.

The problem can be modeled as a linear mixed in-

teger program using the following decision variables:

binary variables x

i jk

equal to 1 if and only if the vehi-

cle k visits the node i then leaves to node j, real vari-

ables a

, t

and w

indicating respectively the arrival

time of vehicle k at customer i, the starting time of

service at customer i if visited by vehicle k, and the

waiting time at customer i if visited by vehicle k.

The objective is to minimize the total cost (1). All

customers’ demands must be satisﬁed (2). Constraint

(3) requires each vehicle to leave and return at the de-

pot. (4) ensure the continuity of the routes. If a vehi-

cle is set to travel between two customers, there has to

be enough time between the two visits (5). All time

windows must be respected (6). (7) imply the syn-

chronization constraints. (8) deﬁne the service start

time equal to the sum of the arrival time and the wait-

ing time. The remaining constraints of the model ﬁx

the nature of the decision variables.

3 RESOLUTIONS APPROACH

To solve the problem, an iterative local search (IlS)

framework is proposed. The general procedure of the

implemented ILS (see Algorithm 1) starts by gener-

ating an initial solution (with a constructive heuristic

) which is then improved by a local search proce-

dure (LS). The current best solution is considered as

the starting one in the ILS. Each iteration of the al-

gorithm considers the best current solution which is

then perturbed to generated neighbor solutions later

improved by Local Search (LS). If the new solution

is better than the current best solution, this later is

updated for the next steps. More details about the

method can be found in (Loureno et al., 2003).

IteratedLocalSearchforaVehicleRoutingProblemwith

SynchronizationConstraints

259

minz =

∑

i∈V

∑

j∈V

∑

k∈H

i j

· x

i jk

(1)

subject to

∑

k∈H

∑

j∈V\{0}

i jk

= v

∀i ∈ V \ {0, n + 1}, ∀p ∈ P (2)

∑

j∈V\{0,n+1}

0 jk

∑

j∈V\{0,n+1}

jn+1k

= 1 ∀k ∈ H (3)

∑

j∈V\{0}

i jk

∑

j∈V\{n+1}

jik

∀i ∈ V \ {0, n + 1}, ∀k ∈ H (4)

+ (T

i j

+ D

) · x

i jk

≤ a

+ β

· (1 − x

i jk

) ∀i, j ∈ V, ∀k ∈ H (5)

∑

j∈V

i jk

≤ t

≤ β

∑

j∈V

i jk

∀i ∈ V \ {0, n + 1}, ∀k ∈ H (6)

· v

∑

k∈H

= v

· v

∑

k∈H

∀i ∈ V, ∀p

, p

∈ P, p

6= p

(7)

= a

+ w

∀i ∈ V, ∀k ∈ H (8)

i jk

∈ {0, 1} ∀i, j ∈ V, ∀k ∈ H

, w

∈ R

∀i ∈ V, ∀k ∈ H (9)

Algorithm 1: General structure of the IlS.

GenerateInitialSolution (S

)

∗

:= LS(S

)

BestSol := S

∗

for k := 1 to k

max

SChild := Perturb(S

∗

);

NewSol := LS(SChild)

if z(NewSol) < z(BestSol) then

BestSol := NewSol

end if

end for

3.1 Constructive Heuristic

A constructive heuristic called Simple-Append is pro-

posed to generate an initial solution. In this algorithm,

a permutation of all customers is transformed to a fea-

sible schedule. Here the initial permutation is a list of

the customers sorted by their earliest completion time

, i ∈ V \{0, n+1} in a non-descending order. at

each iteration j of the algorithm, the customer in the

position j from the permutation is selected, then the

set of vehicles which can service the corresponding

customer before the end of its time window is com-

puted. If there are more than one possible vehicle, the

vehicle that have the least travel cost is selected. If

there are insufﬁcient vehicles to service the customer,

the solution is unfeasible. Services at each customer

are scheduled to start when all required vehicles have

arrived. If this occurs earlier than the earliest starting

time of service, a waiting time must be considered for

each needed vehicle and starting time of service is set

to the beginning of customer time window.

3.2 Perturbation Procedure

The perturbation procedure has a role of the diversi-

ﬁcation in the ILS. To move from one feasible solu-

tion to neighboring solutions, neighbors of the current

permutation are found by using a Relocate operator.

First, all the routes are concatenated then randomly

chosen customers are selected and their position po-

sition is changed randomly in the permutation. The

neighbor detailed solutions are then constructed by

the Simple-Append heuristic.

3.3 Local Search

The Local Search procedure used in the ILS contains

two main procedures: the ﬁrst one is based on 2-opt

move executed on a single route. The second one is

the k-exchange moves including three types of move-

ments that involve two routes. In local search proce-

dure, the service start time at the customers requiring

synchronization visits are ﬁxed like in the input solu-

tion. The 2-opt procedure removes and replaces two

arcs in a tour and reorders vertices. The k-exchange

moves offer the possibility of improving the assign-

ment decisions of customers to routes. Three basic

k-exchange neighborhoods for the VRP (see (Savels-

bergh, 1992)) relocating vertices between two routes

are tested, the ﬁrst one is the relocate operator that

removes one customer from a route and insert it in a

ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems

260

different tour, the second one is the exchange oper-

ator that swaps the positions of two customers from

two different routes. The last one is the 2-opt

∗

oper-

ator applied to different routes. The neighborhoods

exploration requires O(n

) by reducing the computa-

tional effort of time windows violation to O(1) thanks

to the feasibility checks of (Savelsbergh, 1985).

4 NUMERICAL RESULTS

A set of test instances has been extended from the

data set proposed by Bredstrom and Ronnqvist (Bred-

strom and Ronnqvist, 2008). In these new instances,

the customers’ demands are randomly generated but

the information including the distance matrix, time

windows, and the time duration of routes remains the

same as in (Bredstrom and Ronnqvist, 2008). Table 1

describes the used instances, column 2 gives the num-

ber of customers |N|, the total number of vehicles |K|

and the number of synchronized visits |P

syn

| are pro-

vided in the two last columns.

Table 1: The used benchmark.

Instances |N| |K| |P

syn

1 8 3 1

2 8 3 2

3 8 4 2

4 12 5 1

5 12 5 2

6 12 5 3

7 18 5 2

8 18 5 4

9 45 14 8

10 45 16 5

The mathematical models have been implemented

in the software GUSEK, and the heuristic and meta-

heuristic algorithms haven been coded in C

lan-

guage. The results are shown in Tables 2, 3, 4. All

experiments have been carried out on a 3.00 GHz, In-

tel(R) Core(TM) 2Duo processor PC, running under

Windows XP with 1.96 GB of RAM.

Note that in the Simple-Append heuristic, a list

of customers sorted by earliest ﬁnish time is used to

get the initial solution in the ILS. LS-2OPT indicates

the local search with 2-opt procedure, LS-REL, LS-

EXCH, LS-2OPT

∗

stand for the local search moves

when two routes are involved and respectively the

Relocate, Exchange, 2-opt

∗

operator is used. The

maximum number of iterations K

max

is set to 1000.

Column Imp. in Table 4 computes the improvement

achieved by the ILS compared to the initial input so-

lution obtained with Simple-Append.

Table 2: Computational results-Part I.

GUSEC Simple-Append

File Obj CPU(s) Obj CPU(s)

1 217 6.2 222 0.031

2 224 24.4 224 0.047

3 207 1.7 208 0.031

4 390 5427 402 0.031

5 446 0.047

6 462 0.031

7 340 0.031

8 388 0.047

9 856 0.047

10 959 0.031

Av. 0.0374

Table 3: Computational results-Part II.

LS-2OPT LS-REL LS-EXCH

File Obj CPU(s) Obj CPU(s) Obj CPU(s)

1 222 0.047 222 0.047 222 0.047

2 224 0.031 224 0.031 224 0.047

3 207 0.047 207 0.047 207 0.047

4 402 0.063 393 0.047 393 0.047

5 446 0.063 446 0.047 442 0.047

6 462 0.047 462 0.047 458 0.047

7 340 0.047 333 0.047 334 0.047

8 387 0.063 377 0.047 387 0.047

9 823 0.047 778 0.047 781 0.047

10 941 0.094 929 0.094 916 0.094

Av. 0,0549 0,0501 0,0517

Table 2 reports that GUSEK only performs well

with small instances and cannot solve problems from

12 customers and 2 synchronization visits. Further-

more, we can see that Simple-Append with a list of

customers sorted by earliest ﬁnish time used as the

initial permutation has a really good performance

with a convergence error less than 5% and a much

smaller computation time.

Table 3 shows that the 2-opt local search move in-

volving a single route has not big improvement on the

results compared to the initial input solution obtained

by Simple-Append. It is due to the fact that in the

local search method, we ﬁx to the same value the ser-

vice start time of the synchronization visits as in the

input solution. In this case, the improvement of as-

signment decisions is much more effective than the

improvement of routing decisions as shown in the ta-

ble. Moreover, the same operator involving two dif-

ferent routes turns out to be the most powerful move-

ment among the three moves involving more than one

route.

Finally, Table 4 shows that ILS can reach the opti-

mum on small instances and has a much smaller com-

putation time. For the larger instances, ILS has reachs

a maximum improvement of 16% when compared to

the initial solutions.

IteratedLocalSearchforaVehicleRoutingProblemwith

SynchronizationConstraints

261

Table 4: Computational results-Part III.

LS-2OPT

∗

ILS

File Obj CPU(s) Obj CPU(s) Imp.

1 222 0.031 217 0.106 0.0225

2 224 0.047 224 0.104 0

3 207 0.047 207 0.108 0.00480

4 393 0.047 390 0.125 0.0298

5 442 0.047 436 0.138 0.0224

6 458 0.047 452 0.135 0.0216

7 333 0.063 333 0.139 0.0205

8 387 0.047 361 0.163 0.069

9 741 0.047 718 0.203 0.161

10 884 0.047 844 0.25 0.119

Av. 0.047 0.1471 0.047255491

5 CONCLUSIONS

This paper provides a quick review of routing prob-

lem with synchronization constraints studied in the

literature. It considers a particular case of vehicle

routing problem with simultaneous synchronization

constraints where a service centre (the depot) offers

several types of services and customers may demand

more than one service to be provided simultaneously.

To solve this NP-hard problem, a mixed integer pro-

gramming model minimizing the total travel cost has

been proposed. Furthermore, a constructive heuris-

tics and a metaheuristic based on local search have

been developed. Computational experiments are car-

ried out on 10 instances which are extended from

the benchmark initially proposed by (Bredstrom and

Ronnqvist, 2008). The experimental results obtained

by solving the MIP model with GUSEK solver show

that only instances with less than 12 customers and 2

synchronization visits can be solved optimally.

The constructive heuristic has shown quick solu-

tions with all the testing instances with up to 45 cus-

tomers and 15 synchronization visits. To improve the

results, four local search operators have been tested

and embedded within an Iterative Local Search (ILS)

framework. The ILS has reached the optimum for the

small instances solved by GUSEK very quickly. For

the other instances, the ILS achieves a maximum im-

provement of 16% when compared to the initial input

solutions. Future work would be dedicated to improv-

ing the local search especially by designing moves

more suitable for handling the synchronization con-

straints. The problem studied in this paper uses the

minimization of the total travel cost as objective func-

tion, another interesting direction for future research

could consider other criteria like the overall waiting,

work balancing.

REFERENCES

Amaya, A., Langevin, A., and Trpanier, M. (2007). The

capacitated arc routing problem with reﬁll points. Op-

erations Research Letters, 35:45 –53.

Amaya, A., Langevin, A., and Trpanier, M. (2010). A

heuristic method for the capacitated arc routing prob-

lem with reﬁll points and multiple loads. Journal of

the Operational Research Society, 61:1095–1103.

Berbeglia, G., Cordeau, J.-F., Gribkovskaia, I., and Laporte,

G. (2007). Static pickup and delivery problems: A

classiﬁcation scheme and survey. TOP, 15:1–31.

Braysy, O., Dullaert, W., and Nakari, P. (2009). The po-

tential of optimization in communal routing problems:

case studies from ﬁnland. Journal of Transport Geog-

raphy, 17:484 – 490.

Bredstrom, D. and Ronnqvist, M. (2008). Combined vehi-

cle routing and scheduling with temporal precedence

and synchronization constraints. European Journal of

Operational Research, 191:19–31.

Dantzig, G. B. and Ramser, J. H. (1959). The truck dis-

patching problem. Management Science, 1:80–91.

Desaulniers, G., Desrosiers, J., Erdmann, A., Solomon, M.,

and Soumis, F. (2002). Vrp with pickup and deliv-

ery. In Toth, P. and Vigo, D., editors, The vehicle

routing problem, volume 9, pages 225–242. SIAM

Monographs on Discrete Mathematics and Applica-

tions, Philadelphia, PA.

Dohn, A., Rasmussen, M. S., and Larsen, J. (2009). The

vehicle routing problem with time windows and tem-

poral dependencies. volume 1. DTU Management En-

gineering, Copenhagen.

Drexl, M. (2011). Synchronization in vehicle routing: A

survey of vrps with multiple synchronization con-

straints. Technical Report LM.

Ioachim, I. and Desosiers, J. (1999). Fleet assignment and

routing with schedule synchronization constraints.

European Journal of Operational Research, 119:75 –

90.

Kim, B., Koo, J., and Park, J. (2010). The combined

manpower-vehicle routing problem for multi-staged

services. Expert Systems with Applications, 37:8424–

8431.

Loureno, H., Martin, O., and Thomas, T. (2003). Iter-

ated local search. In Hillier, F. S., Glover, F., and

Kochenberger, G., editors, Handbook of Metaheuris-

tics, volume 57 of International Series in Operations

Research & Management Science, pages 320–353.

Springer New York.

Parragh, S., Doerner, K., and Hartl, R. (2008). A survey on

pickup and delivery problems. Journal f ¨ur Betrieb-

swirtschaft, 58:21–51.

Rasmussen, M. S., Justesen, T., Dohn, A., and Larsen, J.

(2012). The home care crew scheduling problem:

Preference-based visit clustering and temporal depen-

dencies. European Journal of Operational Research,

219:598–610.

S. Bertels, T. F. (2006). A hybrid setup for a hybrid

scenario: combining heuristics for the home health

ICORES2014-InternationalConferenceonOperationsResearchandEnterpriseSystems

262

care problem. Computers and Operations Research,

33:2866 – 2890.

Salazar-Aguilar, M. A., Langevin, A., and Laporte, G.

(2012). Synchronized arc routing for snow plow-

ing operations. Computers and Operations Research,

39:1432 – 1440.

Salazar-Aguilar, M. A., Langevin, A., and Laporte, G.

(2013). The synchronized arc and node routing prob-

lem: Application to road marking. Computers and

Operations Research, 40:1708 – 1715.

Savelsbergh, M. W. P. (1985). Local search in routing prob-

lems with time windows. Annals of Operations Re-

search, 4:285–305.

Savelsbergh, M. W. P. (1992). The vehicle routing prob-

lems with time windows: Minimizing route duration.

INFORMS Journal on Computing, 4:146–154.

IteratedLocalSearchforaVehicleRoutingProblemwith

SynchronizationConstraints

263