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Program Overview
Wednesday Sep. 27th Thursday Sep. 28th Friday Sep. 29th
SESSION 2: SESSION 6:
9:00-10:40 CONTINUOUS LOCATION NETWORK/TERRITORY
PLANNING
10:40-11:10 Coffee break Coffee break
Invited Speaker: Invited Speaker:
11:10-12:30 Pierre Bonami James Campbell
SESSION 3: SESSION 7:
12:30-13:45 ROUTING PROBLEMS HUB LOCATION
13:45-14:30 Locat. Network Meeting
LUNCH
14:30-15:30 LUNCH
SESSION 4:
15:30-17:10 APPLICATIONS
17:10-17:40 REGISTRATION Coffee break
17:40-18:10 OPENING SESSION SESSION 5:
DISCRETE LOCATION
18:10-19:20 SESSION 1:
DISCRETE LOCATION
19:20-19:50
21:00 Welcome Reception DINNER
PROCEEDINGS OF
THE VIII INTERNATIONAL WORKSHOP
ON LOCATIONAL ANALYSIS AND
RELATED PROBLEMS (2017)
Edited by
Marta Baldomero-Naranjo
Inmaculada Espejo-Miranda
Luisa I. Martínez-Merino
Antonio M. Rodríguez-Chía
Diego Ruiz-Hernández
ISBN:978-84-697-5263-0
.
Preface
The International Workshop on Locational Analysis and Related Problems
will take place during September 27-29, 2017 in Segovia (Spain). It is or-
ganized by the Spanish Location Network and Location Group GELOCA
(SEIO). GELOCA is a working group on location belonging to the Statistics
and Operations Research Spanish Society. The Spanish Location Network
is a group of more than 100 researchers distributed into 16 nodes corre-
sponding to several Spanish universities. The Network has been funded
by the Spanish Government.
Every year, the Network organizes a meeting to promote the communi-
cation between its members and between them and other researchers, and
to contribute to the development of the location field and related problems.
Previous meetings took place in Málaga (September 14-16, 2016), Barcelona
(November 25-28, 2015), Sevilla (October 1-3, 2014), Torremolinos (Málaga,
June 19-21, 2013), Granada (May 10-12, 2012), Las Palmas de Gran Canaria
(February 2-5, 2011) and Sevilla (February 1-3, 2010).
The topics of interest are location analysis and related problems. It in-
cludes location, networks, transportation, routing, logistics models, as well
as, exact and heuristic solution methods, and computational geometry, among
others.
The organizing committee.
vi Preface
Scientific committee:
Emilio Carrizosa (U. de Sevilla)
Ángel Corberán (U. Valencia)
Elena Fernández (U. Politécnica de Cataluña)
Alfredo Marín (U. de Murcia)
Juan A. Mesa (U. de Sevilla)
Blas Pelegrín Pelegrín (U. de Murcia)
Justo Puerto (U. de Sevilla, España)
Antonio M. Rodríguez Chía (U. de Cádiz)
Diego Ruiz Hernández (Colegio Universitario de Estudios Financieros)
Organizing committee:
Marta Baldomero Naranjo (U. de Cádiz)
Inmaculada Espejo Miranda (U. de Cádiz)
Luisa Isabel Martínez Merino (U. de Cádiz)
Belén Palop del Río (U. de Valladolid)
Dolores Rosa Santos Peñate (U. de Las Palmas de Gran Canaria)
Contents
Preface v
Program 1
Invited Speakers 7
Some recent advances in mixed-integer nonlinear optimization 9
P. Bonami
Strategic design of drone delivery systems 11
J.F. Campbell
Abstracts 13
Routing vehicle fleets during disaster relief 15
E. Barrena, D. Canca and F.A. Ortega
The periodic rural postman problem with irregular services 17
E. Benavent, Á. Corberán, D. Lagannd F. Vocaturo
The multi-period service territory design problem 19
M. Bender, J. Kalcsics, A. Meyer, S. Nickel, and M. Pouls
On the location of separating hyperplanes with `p-norms mar-
gins 21
V. Blanco, J. Puerto, and A.M. Rodríguez-Chía
Territorial districting models for the reorganization of postal ser-
vices 23
vii
viii CONTENTS
G. Bruno, M. Cavola, A. Diglio, and C. Piccolo
A bilevel approach for the single-source capacitated facility lo-
cation problem with customer’s preferences 25
H.I. Calvete, C. Galé, J.F. Camacho-Vallejo, and M.S. Casas-Ramírez
Blackout risk mitigation by using distributed gas turbine gen-
eration. An application to the electrical Spanish distribution
network. 27
D. Canca, Á. Arcos-Vargas, and F. Nuñez
Energy-efficient timetables. 29
D.C. Ortíz, and A. Zarzo
A matheuristic for the rapid transit network design problem with
elastic demand 31
D. Canca, A. De-Los-Santos, G. Laporte, and J.A. Mesa
Uncertainty in building times: identifying critical facilities in a
dynamic location problem 33
J. Dias
Inducing universal access to privately- managed social-interest
goods via location decisions 35
J. Elizalde, A. Erro, and D. Ruiz-Hernández
Some heuristic methods for the p-median problem with maxi-
mum distance constraints 37
A. Esteban Pérez, and J. Sáez-Aguado
On location and vessel fleet composition for offshore wind farm
maintenance 39
A. Gutierrez, E.M.T. Hendrix, G. Ortega, D. Haugland, E.E. Halvorsen-Weare
The mobile facility location problem 41
M. Landete
Some criteria for locating sensors in a wind turbine blade 43
M.C. López-de-los-Mozos,J.A. Mesa, D. Ruiz-Hernández, and C.Q. Gómez-Muñoz
Tree of hubs location problem with upgrading 45
A. Marín
CONTENTS ix
A stochastic multi-period covering model 47
A. Marín, L. Martínez-Merino, A. M. Rodríguez-Chía, and F. Saldanha-da-Gama
Supply chain complexity and the network design : Location does
matter! 49
M.B.C. Menezes, and D. Ruiz-Hernández
Heuristics for the stochastic uncapacitated r-allocation p-hub me-
dian problem 51
J. Peiró, Á. Corberán, R. Martí and F. Sandanha-da-Gama
Profiling the inherent complexity of different facility location
strategies 53
J.M. Pinar-Pérez, D. Ruiz-Hernández, and M. Menezes
Approval voting problem under the k-centrum criterion 55
D. Ponce, J. Puerto, F. Ricca, and A. Scozzari
The ordered median tree of hubs location problem 57
M.A. Pozo, J. Puerto, and A.M. Rodríguez-Chía
Location theory and some physical principles in a nutshell 59
J. Puerto
The periodic vehicle routing problem with driver consistency 61
I. Rodríguez-Martín, J.J. Salazar-González, and H. Yaman
The effect of products’ short lifecycle on network design 63
D. Ruiz-Hernández, M.B.C. Menezes, and O. Allal-Cheriff
Facilities delocation in the retail sector 65
M. Sierra-Paradinas, A. Alonso-Ayuso, and J.F. Rodríguez-Calo
PROGRAM
Wednesday September 27th
17:10-17:40 Registration
17:40-18:10 Opening Session
18:10-19:50 Session 1: Discrete Location
A bilevel approach for the single-source capacitated facility location
problem with customer’s preferences
H.I. Calvete, C. Galé, J.F. Camacho-Vallejo, and M.S. Casas-Ramírez
Approval voting problem under the k-centrum criterion
D. Ponce, J. Puerto, F. Ricca, and A. Scozzari
A stochastic multi-period covering model
A. Marín, L.I. Martínez-Merino, A. M. Rodríguez-Chía, and F. Saldanha-
da-Gama
The mobile facility location problem
M. Landete
21:00 Welcome Reception
4
Thursday September 28th
9:00-10:40 Session 2: Continuous Location
Some criteria for locating sensors in a wind turbine blade
M.C. López-de-los-Mozos,J.A. Mesa, D. Ruiz-Hernández, and C.Q.
Gómez-Muñoz
Territorial districting models for the reorganization of postal services
G. Bruno, M. Cavola, A. Diglio, and C. Piccolo
On the location of separating hyperplanes with `p-norms margins
V. Blanco, J. Puerto, and A.M. Rodríguez-Chía
Location theory and some physical principles in a nutshell
J. Puerto
10:40-11:10 Coffee break
11:10-12:30 Invited Speaker: Pierre Bonami
Some recent advances in mixed-integer nonlinear optimization
P. Bonami
12:30-13:45 Session 3: Routing
Routing vehicle fleets during disaster relief
E. Barrena, D. Canca, and F.A. Ortega
The periodic rural postman problem with irregular services
E. Benavent, Á. Corberán, D. Laganà, and F. Vocaturo
The periodic vehicle routing problem with driver consistency
I. Rodríguez-Martín, J.J. Salazar-González, and H. Yaman
13:45-15:30 Lunch
15:30-17:10 Session 4: Applications
Energy-efficient timetables
D.C. Ortíz, and A. Zarzo
On location and vessel fleet composition for offshore wind farm main-
tenance
5
A. Gutierrez, E.M.T. Hendrix, G. Ortega, D. Haugland, E.E. Halvorsen-
Weare
Blackout risk mitigation by using distributed gas turbine generation.
An application to the electrical Spanish distribution network.
D. Canca, Á. Arcos-Vargas, and F. Nuñez
Inducing universal access to privately-managed social-interest goods
via location decisions
J. Elizalde, A. Erro, and D. Ruiz-Hernández
17:10-17:40 Coffee break
17:40-19:20 Session 5: Discrete Location
Profiling the inherent complexity of different facility location strate-
gies
J.M. Pinar-Pérez, D. Ruiz-Hernández, and M. Menezes
Uncertainty in building times: identifying critical facilities in a dy-
namic location problem
J. Dias
Some heuristic methods for the p-median problem with maximum
distance constraints
A. Esteban Pérez, and J. Sáez-Aguado
Facilities delocation in the retail sector
M. Sierra-Paradinas, A. Alonso-Ayuso, and J.F. Rodríguez-Calo
21:00 Dinner
6
Friday September 29th
9:00-10:40 Session 6: Network/Territory design
A matheuristic for the rapid transit network design problem with
elastic demand
D. Canca, A. De-Los-Santos, G. Laporte, and J.A. Mesa
Supply chain complexity and the network design: Location does mat-
ter!
M.B.C. Menezes, and D. Ruiz-Hernández
The effect of products’ short lifecycle on network design
D. Ruiz-Hernández, M.B.C. Menezes, and O. Allal-Cheriff
The multi-Period service territory design problem
M. Bender, J. Kalcsics, A. Meyer, S. Nickel, and M. Pouls
10:40-11:10 Coffee Break
11:10-12:30 Invited Speaker: James F. Campbell
Strategic design of drone delivery systems
J.F. Campbell
12:30-13:45 Session 7: Hub Location
Tree of hubs location problem with upgrading
A. Marín
The ordered median tree of Hubs location problem
M.A. Pozo, J. Puerto, and A.M. Rodríguez-Chía
Heuristics for the stochastic uncapacitated r-allocation p-hub median
problem
J. Peiró, Á. Corberán, R. Martí, and F. Sandanha-da-Gama
13:45-14:30 Location Network Meeting
14:30-15:30 Lunch
INVITED SPEAKERS
VIII Workshop on Locational Analysis and Related Problems 2017 9
Some recent advances in mixed-integer
nonlinear optimization
Pierre Bonami1
1Laboratoire d’Informatique Fondamentale de Marseille Aix Marseille Université/ IBM,
France, pierre.bonami@es.ibm.com
Mixed Integer Nonlinear Optimization is the optimization of a nonlin-
ear function over a feasible set described by nonlinear functions and in-
tegrality constraints. We will review some of the main algorithmic tech-
niques that are employed in commercial solvers. We will focus in particu-
lar on two recent works that address global solution of non-convex mixed
integer optimization problems: cuts from the binary quadric polytope and
maxclique inequalities.
10
VIII Workshop on Locational Analysis and Related Problems 2017 11
Strategic design of drone delivery systems
James F. Campbell1
1College of Business Administration, University of Missouri – St. Louis, USA,
campbell@umsl.edu
Home delivery by drones as an alternative to traditional delivery by
trucks is attracting considerable attention from major retailers and service
providers (Amazon, UPS, Google, DHL, Wal-mart, etc.), as well as from
startups. While drone delivery may offer considerable economic savings,
the fundamental issue of how best to deploy drones for home delivery is
not well understood. Operations Research has a long tradition in analyz-
ing location, logistic and routing problems and drone delivery provides
some new opportunities for research. This presentation first provides an
overview of drone delivery systems and highlights research opportuni-
ties, especially using drones is conjunction with trucks. Then we present a
strategic analysis for the design of truck-drone delivery systems using con-
tinuous approximation modeling techniques to derive general insights. We
formulate and optimize models that consider hybrid truck-drone delivery
(where truck-based drones make deliveries simultaneously with trucks),
truck-only delivery and drone delivery from depots. Results show that
truck-drone hybrid delivery can be very economically advantageous in
many settings, especially in more rural areas and with multiple drones per
truck, but that the benefits depend strongly on the relative operating costs
and marginal stop costs. Results also examine locating depots for drones,
especially to achieve high service levels.
ABSTRACTS
VIII Workshop on Locational Analysis and Related Problems 2017 15
Routing vehicle fleets during disaster relief∗
Eva Barrena,1David Canca,2and Francisco A. Ortega3
1Universidad de Granada, ebarrena@ugr.es
2Universidad de Sevilla, dco@us.es
3Universidad de Sevilla, riejos@us.es
Last mile in the humanitarian logistics management refers to the sup-
ply of relief items from the local distribution centres to the disaster area.
Some estimations suggest that as much as 80%of the expenditure of aid
agencies lies on logistics. Therefore, humanitarian logistics management
need to be efficiently and effectively planned in their relevant components
(facility location, inventory management, transportation management, dis-
tribution management, etc.) at the strategic, tactical and operational levels.
The problem addressed in this paper consists of designing routes for vehi-
cles among nodes that receive an available quantity of goods (depots called
local distribution centers –LDCs-) and others that have a demand of those
goods, simultaneously choosing the most adequate types of vehicles and
determining the flow of the aid along a time horizon. For that reason, we
consider the possibility of interaction between the different LCDs in terms
of transferring goods to be supplied and allocating vehicles for transporta-
tion.
∗This research has been partially supported by the Spanish Ministry of Economy and Com-
petitiveness through grant MTM2015-67706-P (MINECO/FEDER, UE). This support is grate-
fully acknowledged.
16
VIII Workshop on Locational Analysis and Related Problems 2017 17
The periodic rural postman problem with
irregular services
Enrique Benavent,1Ángel Corberán,1Demetrio Laganà, 2and Francesca
Vocaturo2
1DEIO, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain, en-
rique.benavent@uv.es
angel.corberan@uv.es
2DIMEG, Università della Calabria, via Pietro Bucci Cubo 41/C, 87036 Arcavacata di
Rende (CS), Italy, demetrio.lagana@unical.it
francesca.vocaturo@unical.it
Periodic routing problems consist of designing vehicle routes for all the
days of a given time horizon, or planning period, in order to meet specific
service requirements of a subset of arcs in a given graph, which usually
represents an street or road network. Generally, a required arc does not
need a service on every day, but must be serviced at least once (or a speci-
fied number of times) over the time horizon. In some practical applications
the required frequency of services may be irregular; for instance, some arcs
must be serviced twice during the first five days of a week and once during
the weekend; in addition, the days for service may vary from one week to
the other.
In this talk, we deal with the periodic rural postman problem with ir-
regular services (PRPPIS) in which some links of a mixed graph must be
traversed a specified number of times in some given time horizon sub–
periods. The aim is to design a set of least-cost tours, one for each period
in the horizon, that satisfy the service requirements. Some practical appli-
cations of the problem can be found in road maintenance operations and
road network surveillance.
In order to solve the PRPPIS, we propose a mathematical model and a
branch-and-cut algorithm. In the solution framework, constraints ensur-
ing connectivity and other valid inequalities are identified by using spe-
cific separation procedures. Some valid inequalities consider the particular
nature of the PRPPIS. We show the effectiveness of the solution approach
through an extensive experimental phase.
18
VIII Workshop on Locational Analysis and Related Problems 2017 19
The multi-period service territory design
problem
Matthias Bender,1Jörg Kalcsics,2Anne Meyer,1Stefan Nickel,1,3and
Martin Pouls1
1Department of Logistics and Supply Chain Optimization, Research Center for Information
Technology (FZI), Karlsruhe, Germany
2School of Mathematics, University of Edinburgh, Edinburgh, Scotland
3Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Ger-
many, stefan.nickel@kit.edu
Classical sales or service territory design problems consist of grouping
customers into larger clusters, which are called territories or districts, such
that some relevant planning criteria, e.g., compactness and balance, are
met [2]. In each district, a service provider, e.g., a salesperson or service
technician, is responsible for providing services at the customers’ sites. In
many cases, these services must be provided several times during a given
planning horizon, which extends the classical problem to a multi-period
setting.
The main contributions of this talk are the following:
We introduce a new problem, which we call the Multi-Period Service
Territory Design Problem (MPSTDP) ( [1] ). Despite its high practical
relevance, it has not been studied in the literature before.
We formally define the scheduling subproblem, i.e., the subproblem
dealing with the assignment of service visits to the weeks and days of
the planning horizon, as a mixed integer linear programming model.
We propose a heuristic solution approach for the scheduling sub-
problem. The approach is capable of considering the relevant plan-
ning requirements of practical settings. It involves the repeated solu-
tion of an integer programming model, which can easily be extended
by additional planning requirements.
20
We present a column generation formulation of the resulting schedul-
ing problem and propose an exact branch-and-price algorithm. Our
method incorporates specialized acceleration techniques, such as a
fast pricing heuristic and a symmetry handling strategy. The latter
aims to reduce the symmetry inherent to the model by fixing vari-
ables and thereby eliminating symmetric solutions from the search
tree.
We perform extensive computational experiments on real-world in-
stances and on instances that were derived from real-world data by
varying the values of some parameters. The results show that the
new approach produces high-quality solutions and outperforms so-
lution methods of existing software products.
References
[1] Matthias Bender, Anne Meyer, Jörg Kalcsics, and Stefan Nickel. “The mul-
tiperiod service territory design problem – An introduction, a model and a
heuristic approach.” Transportation Research Part E: Logistics and Transporta-
tion Review, 96:135–157, 2016.
[2] Jörg Kalcsics.“ Districting problems”. In Gilbert Laporte, Stefan Nickel,
and Francisco Saldanha da Gama, editors, Location Science, pages 595–622.
Springer International Publishing, 1 edition, 2015.
VIII Workshop on Locational Analysis and Related Problems 2017 21
On the location of separating hyperplanes
with `p-norms margins
Víctor Blanco,1Justo Puerto,2and Antonio M. Rodríguez-Chía3
1Universidad de Granada, vblanco@ugr.es
2Universidad de Sevilla, puerto@us.es
3Universidad de Cádiz, antonio.rodriguezchia@uca.es
In this work we present new results on the determination of a hyper-
plane that separate two classes of given data. We deal with the problem of
obtaining such a hyperplane when the goal is to minimize the `p-margin
(with rational p≥1) between the two classes. We provide valid non-linear
mathematical programming formulations for the problem involving the
minimization of homogenous polynomials over linear regions. The for-
mulation allows us to manage the use of transformations of the data and
the resolution of the problem without using the specific knowledge of the
transformation but some properties about it. Some methodologies for solv-
ing the problem in practice are provided.
Introduction
We are given a set of dquantitative measures about nindividuals. The
dmeasures about each individual i∈ {1, . . . , n}are identified with the
vector xi·∈Rd. Each observation is also classified into a class in {−1,1},
being yi∈ {−1,1}the class of the ith observation, for i= 1, . . . , n.
The goal of this work is to find a hyperplane H={z∈Rd:ωtz+b= 0}
that minimizes the misclassification of data to their own class.
22
By using a classical result in [2], the problem can be formulated as:
ρ∗= minkωkq
q+C
n
X
i=1
ξi
s.t. yi(ωtxi·+b)≥1−ξi,∀i= 1, . . . , n,
ξi≥0,∀i= 1, . . . , n.
where qis such that 1
p+1
q= 1 and Cis a constant. This problem allows
an equivalent reformulation as a second-order cone programming prob-
lem.
By using Lagrangian duality, we prove that the above problem can be
equivalently reformulated as a set of nonlinear optimization problems where
only multivariate homogeneous polynomials of certain degree rare in-
volved.
In case we consider a transformation, Φ : Rd→RD, which maps the
data to a higher dimensional space, better separation schemes can be de-
rived. We prove that applying the same methodologies, we can obtain
minimal separating hyperplanes without the explicit knowledge of Φ. We
determine sufficient conditions on Φnecessary for obtaining the separat-
ing hyperplanes and derive a methodology to classify outsample data.
These characterizations involve the use of tools borrowed from real higher-
dimensional tensor rank-one decomposition [1].
Finally, we detail how to solve the dual separating hyperplane problem
using the Theory of Moments and SDP Relaxations [3].
References
[1] Comon, P., Golub, G., Lim, L-H Mourrain, B. (2008). Symmetric tensors and sym-
metric tensor rank. SIAM Journal on Matrix Analysis and Applications 30(3),
1254–1279.
[2] Mangasarian, O.L. (1999). Arbitrary-norm separating plane. Operations Research
Letters 24 (1–2), 15–23.
[3] Lasserre J. B. (2001). Global Optimization with Polynomials and the Problem of Mo-
ments, SIAM Journal on Optimization 11, 796-817.
VIII Workshop on Locational Analysis and Related Problems 2017 23
Territorial districting models
for the reorganization of postal services
Giuseppe Bruno,1Manuel Cavola,1Antonio Diglio1and Carmela
Piccolo1
1Department of Industrial Engineering, University of Naples Federico II
Piazzale Tecchio, 80 – 80125, Naples, Italy
(giuseppe.bruno, antonio.diglio,carmela.piccolo)@unina.it,manuelcavola@live.com
In the last years, postal services were interested by profound changes due
to different factors. In particular, the progressive substitution of conven-
tional letters by electronic forms of communication (e-substitution), led to
a drastic decrease of volumes of classic postal mails and to a consequent
reduction of revenues [3]. In order to effectively face these changes, postal
companies are responding by adapting their logistic systems. In this con-
text, we address several problems related to the reorganization of mail col-
lection and delivery service, in collaboration with the Italian Postal Service
Provider (Poste Italiane S.p.A.).
Usually, two types of mails may be distinguished: priority and ordinary
mails, that have to be delivered within one and two days respectively. For
ordinary mails, mailboxes represent the access points of users to the logis-
tic network. Mails contained in the mailboxes are picked up by dedicated
operators, moved to Distribution Centers (DC) for sorting operations, and
transported to final destinations. Usually the time span devoted to collec-
tion is very limited, as all the subsequent activities (sorting, distribution,
delivery) need to be performed within strict deadlines. Then, the number
of employed operators and routes strongly depends on the number and on
the position of mailboxes over the study region. As the mails volumes have
drastically reduced, Poste Italiane is interested in reducing the number of
mailboxes, in order to improve service efficiency. However, as the postal
service is labeled as "essential", in pursuing this objective it is obliged to
satisfy contraints imposed by specific authorities on users accessibility.
In order to tackle the problem, we refer to the class of Districting Problems
24
(DP), that aim at partitioning a given territory in a fixed number of sub-
areas, named districts [7]. The reference territory is usually divided into
basic units, that have to be grouped so as constraints on dimension and
topology of single districts are satisfied. DPs are suitable to describe prob-
lems related to the organization of public services, in which the goal is
to design sub-areas for facilities’ service provision [5, 6]. Within such lit-
erature stream, some contributions deal with the problem of modifying
existing district maps, as a consequence of facility closure or relocation (re-
districting problems) [2,4].
In the case under analysis, the reference territory is divided into census
tracks, already grouped in districts, each associated to a single mailbox.
In such partition, it has been reasonably assumed that users refer to the
closest postal box. Once a subset of mailboxes are closed, users have to be
reassigned to the closest active mailbox in the neighborhood of their resi-
dence. The problem consists in deciding how many and which mailboxes
have to be closed in order to minimize the management costs of the service
and guaranteeing a good and equitable service level to users [1].
We tested the proposed models on the case of the urban area of the city
of Bologna (Italy), where 272 mailboxes are located to serve about 400.000
inhabitants. Obtained solutions provide useful indications for supporting
decision makers in the rationalization of the described process.
References
[1] Barbati, M., Piccolo, C. (2016). Equality measures properties for location problems.
Optimization Letters, 10(5), 903-920.
[2] Bruno, G., Genovese, A., Piccolo, C. (2017). Territorial amalgamation decisions in
local government: Models and a case study from Italy. Socio-Economic Planning
Sciences, 57, 61-72.
[3] Çetiner, S., Sepil, C., Süral, H. (2010).Hubbing and routing in postal delivery sys-
tems. Annals of Operations Research, 181(1), 109-124.
[4] De Assis, L. S., Franca, P. M., Usberti, F. L. (2014). A redistricting problem ap-
plied to meter reading in power distribution networks. Computers and Operations
Research, 41, 65-75.
[5] Ferland, J. A., Guénette, G. (1990). Decision support system for the school districting
problem. Operations Research, 38(1), 15-21.
[6] Hanafi, S., Freville, A., Vaca, P. (1999). Municipal solid waste collection: an effective
data structure for solving the sectorization problem with local search methods. INFOR:
Information Systems and Operational Research, 37(3), 236-254.
[7] Kalcsics, J., Nickel, S., Schroder, M. (2005). Towards a unified territorial design
approach – Applications, algorithms and GIS integration. TOP, 13(1):1–74.
VIII Workshop on Locational Analysis and Related Problems 2017 25
A bilevel approach for the single-source
capacitated facility location problem with
customer’s preferences ∗
Herminia I. Calvete, and Carmen Galé,1
José-Fernando Camacho-Vallejo, and Martha-Selene Casas-Ramírez2
1Universidad de Zaragoza, Spain,
herminia@unizar.es, cgale@unizar.es
2Universidad Autónoma de Nuevo León, México,
jose.camachovl@uanl.edu.mx, martha.casasrm@uanl.edu.mx
Location models are among the main optimization models in facility plan-
ning. At the strategic level of decision making, the decisions remain un-
changed for a long time. So, to decide where to locate the facilities is one
of the most critical decisions in logistics. The facility location problem is
a well-known combinatorial optimization problem. It consists of selecting
the location of a set of facilities from a finite set of potential sites to meet
customer demand. The location problem considered in this work is single
source model, that is to say, each customer is served from a single facility.
Moreover, a capacity constraint is added to the model to limit the number
of customers which can be allocated to each facility. Finally, other crucial
aspect to be considered is the choice of the optimization criterium for allo-
cating customers to facilities.
In the literature, the customer allocation problem has been solved con-
sidering alternative criteria in the objective function according to different
perspectives ( [1], [2], [3] and [4]). In this paper, the customers’ preferences
regarding the selection of facilities are taken into account. Once the facili-
ties are located, the customers are allocated to their preferred facility while
holding the capacity constraints. In order to solve the conflict that arises
when several customers prefer the same open facility and its capacity is
∗This research work has been funded by the Spanish Ministry of Economy, Industry and
Competitiveness under grant ECO2016-76567-C4-3-R.
26
insufficient to serve all of them, we assume a cooperative behavior of the
customers.
A bilevel problem is proposed to model this system. In the upper level
the leader decides on the facilities which will be located. In the lower level
the allocation problem is solved. The leader’s objective function consists of
minimizing the overall costs for opening the facilities and serving the cus-
tomers. Concerning the lower level problem, we establish a set of ordered
preference values for every customer in which the lowest value is associ-
ated with the most preferred facility. Then, the optimization criteria of the
lower level problem is to minimize the sum of the preferences. Moreover,
we assume an optimistic approach when solving the bilevel problem, i.e.
in case of multiple optima in the lower level problem the best option for
the leader is selected.
An analysis exploiting some particularities of the problem leads to a re-
formulation as a single level optimization problem. Small instances of this
model can be solved using usual optimization tools. A genetic algorithm is
developed for solving instances which cannot be solved to optimality in a
reasonable computational time. A numerical experimentation is conducted
to test the performance of the heuristic algorithm. Benchmark instances by
Holmberg for the single source capacity facility location problem are con-
sidered and suited for the problem introduced in this work. The number
of customers in these instances ranges from 20 to 90 and the number of po-
tential locations ranges from 10 to 30. A new set with larger instances has
also been randomly generated.
References
[1] Caramia, M., and Mari, R. (2016). “A decomposition approach to solve a bilevel
capacitated facility location problem with equity constraints”, Optimization
Letters, Vol. 10(5), 997–1019.
[2] Ho, S.C. (2015). “An iterated tabu search heuristic for the Single Source Capac-
itated Facility Location Problem”, Applied Soft Computing, Vol. 27, 169–178.
[3] Teixeira, J.C., and Antunes, A.P. (2008). “A hierarchical location model for pub-
lic facility planning”, European Journal of Operational Research, Vol. 185(1),
92–104.
[4] Vasilév, I.L., Klimentova, K.B., and Kochetov, Y.A. (2009). “New lower bounds
for the facility location problem with clients’ preferences”, Computational
Mathematics and Mathematical Physics, Vol. 49(6), 1010–1020.
VIII Workshop on Locational Analysis and Related Problems 2017 27
Blackout risk mitigation by using
distributed gas turbine generation.
An application to the electrical Spanish
distribution network.∗
David Canca,1Ángel Arcos-Vargas,2and Fernando Nuñez3
1Universidad de Sevilla, dco@us.es
2Universidad de Sevilla, aarcos@us.es
3Universidad de Sevilla, fnunuezh@us.es
The aim of this paper consists on analysing the economic aspects of the
mitigation of network power at risk by locating the appropriate gas tur-
bines at risk points. We propose two different Mixed Integer Programming
optimization models. The first one considers the existence of a global net-
work agreement among generation companies and distributor in order to
cover at least partially all the points at risk. The second one considers an
unregulated framework where distributed generators have full freedom
to choose locations among those proposed by the distribution company
and to select the most convenient turbine models. In both cases the mod-
els consider the temporal deployment of risk mitigation. Since electricity
distribution is a regulated activity, we study the impact of a possible reg-
ulated remuneration that encourage generators to install the appropriate
generation power at the specific points at risk. We illustrate the proposed
approach by solving the case of power at risk in a big scenario concerning
approximately the half of the Spanish distribution network.
∗This research has been partially supported by the Spanish Ministry of Economy and Com-
petitiveness through grant MTM2015-67706-P (MINECO/FEDER, UE). This support is grate-
fully acknowledged.
28
VIII Workshop on Locational Analysis and Related Problems 2017 29
Energy-efficient timetables.∗
David C. Ortíz,1and Alejandro Zarzo2
1Departamento de Organización Industrial y Gestión de Empresas I (Industrial Engineer-
ing and Management Science), Universidad de Sevilla, Spain, dco@us.es
2Departamento de Matemáticas del Área Industrial, E.T.S. Ingenieros Industriales, Uni-
versidad Politécnica de Madrid, Spain, and Instituto Carlos I, Universidad de Granada,
Granada, Spain, alejandro.zarzo@upm.es
A methodology to design timetables with minimum energy consump-
tion in Rapid Railway Transit Networks is presented. Using an empirical
description of the train energy consumption as a function of running times,
the timetable design problem is modelled as a Mixed Integer Non-Linear
optimization problem (MINLP) for a complete two-way line. In doing so,
all the services in both directions along a certain planning horizon are con-
sidered while attending a known passengers’ demand. The MINLP for-
mulation, which depends on train loads, is fully linearised supposing train
loads are fixed. A sequential Mixed Integer Linear (MILP) solving proce-
dure is then used to solve the timetabling optimization problem with un-
known train loads. The proposed methodology emphasizes the need of
considering all the services running during the planning horizon when
designing energy-efficient timetables, as consequence of the relationship
among train speeds, frequency and fleet size of each line. Moreover, the
convenience of considering the energy consumption as part of a broad ob-
jective function that includes other relevant costs is pointed out. Otherwise,
passengers and operators could face up to an increase in the whole cost and
a decrease in the quality of service. A real data scenario, based on the C-2
∗This research work was supported by the Ministry of Economy and Competitiveness of
Spain and the European Regional Development Fund (ERDF) under grant MTM2015-67706-P.
The second author (AZ) also acknowledge partial financial support from the Ministry of Econ-
omy and Competitiveness of Spain and the European Regional Development Fund (ERDF)
under grant MTM2014-53963-P, from Junta de Andalucía through the Excellence Grant P11-
FQM-7276 and the research group FQM-020, and from Technical University of Madrid (re-
search group TACA).
30
Line of the Madrid Metropolitan Railways, is used to illustrate the pro-
posed methodology and to discuss the differences between the minimum-
energy solutions and those obtained when considering operation and ac-
quisition costs.
Keywords: Railway Rapid Transit, Timetabling, Energy consumption, Mixed
Integer Non-Linear Programming, Sequential MILP procedure
VIII Workshop on Locational Analysis and Related Problems 2017 31
A matheuristic for the rapid transit
network design problem with elastic
demand
David Canca,1Alicia De-Los-Santos,2, Gilbert Laporte3and Juan A.
Mesa,4
1Department of Industrial Engineering and Management Science, University of Seville,
Spain, dco@us.es
2Department of Statistic, Econometrics, I.O. And Business Organization, University of
Cordoba, Spain, aliciasantos@uco.es
3Canada Research Chair in Distribution Management. HEC Montreal, Canada.
gilbert.laporte@cirrelt.ca
4Department of Applied Mathematics II, University of Seville, Spain. jmesa@us.es
In this work, we propose a matheuristic for the integrated Railway Rapid
Transit Network Design and Line Planning problem. The network design
problem incorporates costs relative to the network construction and pro-
poses a set of candidate lines whereas the line planning problem deter-
mines the best combination of frequencies and train capacities for the set
of lines taking into account rolling stock, personnel and fleet acquisition
costs. We consider the existence of an alternative transportation mode com-
peting with the railway system for each origin-destination pair. Passengers
choose their transportation mode according to their own utility. Due to the
problem complexity and the impossibility of solving the problem on realis-
tic size scenarios, we develop a matheuristic combining an Adaptive Large
Neighborhood Search (ALNS) algorithm and an transit assignment model.
At each iteration, in an cooperative way, the ALNS solves the network de-
sign problem and the assignment model is in charge of the line planning
problem. As consequence of the non-linear nature of the assignment prob-
lem, in order to guarantee optimality at each iteration, a full-linearisation
of the inner model is also presented.
32
VIII Workshop on Locational Analysis and Related Problems 2017 33
Uncertainty in building times:
identifying critical facilities in a dynamic
location problem
Joana Dias2
1INESCC, CeBER, Faculty of Economics, University of Coimbra, Av. Dias da Silva, 165,
3004512 Coimbra, Portugal joana@fe.uc.pt
In dynamic location problems, most of the times, the decisions that are con-
sidered in the mathematical models are where and when to locate facilities.
It is assumed that deciding when to open will deterministically determine
when to begin all the necessary procedures to guarantee that the facility is
indeed opened at the desired time period. These procedures can include
property acquisition, infrastructure construction, having human and ma-
terial resources prepared, among other things. In this work, uncertainty
associated with this “building time” is explicitly assumed. The decisions
are now where to locate facilities and when to begin building these facili-
ties. As time and cost compromises are usually present, the decision maker
can decide to increase costs in order to decrease the uncertainty associated
with the building times. It is possible to identify critical facilities: the ones
in which it is worth investing to guarantee that there are no delays in their
opening times.
Keywords: dynamic location, uncertainty, scenarios, building time, critical facil-
ities
1. Introduction
Most of the times, there are several activities that have to be executed be-
fore a facility is ready to be used. There are situations where the facility
has to be built, infrastructures have to be created and resources have to
be assigned. Opening a facility is usually a project that has to be planned,
executed, and that takes time. More often than not, there can be delays.
Most of the times, there is uncertainty related with the time lag between
34
beginning to prepare a facility to be open and having it ready to have as-
signed clients. In the present work, a dynamic location problem will be de-
scribed, where the uncertainty associated with the time to “build” a facility
is explicitly considered. Uncertainty is represented by resorting to scenar-
ios. It is assumed that the location decisions are taken at the beginning of
the planning horizon and cannot be changed from that point forward. The
assignment variables can be optimized in each time period. Moreover, the
decision maker has the possibility of increasing the cost associated with the
opening of a given facility in order to decrease the uncertainty related with
its building time (by assigning more resources to its preparedness process,
for instance).
2. Mathematical Model
The most obvious way of formulating this problem is by using a non-
linear formulation, where the building times are decision variables them-
selves that will determine the possible values of the assignment variables.
It is, however, possible to also devise a mixed integer linear programming
problem resorting to additional auxiliary variables and constraints. It is
even possible to consider different levels of investment, with different con-
sequences in the corresponding building times, representing the compro-
mises that exist between building time and costs. Facilities which are ad-
vantageous to invest in order to decrease/eliminate the uncertainty associ-
ated with their building times can be considered as critical facilities, in the
sense that it is worth spending more to guarantee that they are operational
in the expected time period.
3. Conclusion
In this problem, the uncertainty associated with the building time of facil-
ities in a dynamic location problem is considered. It is possible to develop
a mixed integer linear programming problem that represents this prob-
lem. Computational experiments are being done, with the purpose of: 1.
Understanding how the model can be used to illustrate the time vs cost
compromises and its relation with the identification of critical facilities; 2.
To assess the possibility of solving large instances of this problem by using
a general solver, and to reach a conclusion regarding the need to develop
a (meta)heuristic procedure. Different objective functions could be consid-
ered, like minimizing the maximum regret, or multiobjective approaches
could be devised.
VIII Workshop on Locational Analysis and Related Problems 2017 35
Inducing universal access to privately-
managed social-interest goods via
location decisions
Javier Elizalde, 1Amaya Erro, 2Diego Ruiz-Hernández 3,4
3University College for Financial Studies, Department of Quantitative Methods, Leonardo
Prieto Castro 2, 28040, Madrid, Spain d.ruiz@cunef.edu
1Universidad de Navarra, Campus Arrosadía, 31006, Pamplona, Spain
2Universidad Pública de Navarra, Campus Universitario, Edificio Amigos, 31009, Pam-
plona, Spain
4Supply Chain and Complexity Lab, KEDGE Business School
There exist a largen number of services for which the public authority may
have an interest in guaranteeing universal access. Examples, among many
others, are health and education services and the delivery of water, elec-
tricity and postal services to the households. Some of these services, such
as water, electricity and post, are most often natural monopolies, with one
single firm in the most efficient market structure. Moreover, those services
are directly delivered to the final consumer and therefore the universal pro-
vision of the service is independent –from the point of view of the final
consumer– of the location of the sources.
However, in other cases, such as education, health, and community ser-
vices, ease of access plays a central role in the universal provision of the
service. Several approaches have been taken to analyse the problem of find-
ing the optimal location of a service in order to guarantee total population
coverage; with efforts coming from disciplines as diverse as economics, ge-
ography and operational research. Among the recent articles dealing with
the location of education centres we can refer the work of Ewing et al. [2]
and Pal [5]; regarding the location of health and emergency services we can
cite Daskin and Dean [1]; and Günes and Nickel [3].
In the present work, given that some of these services are provided in
facilities where the individuals have to commute to, we use a theoretical
36
model of spatial monopoly. A choice that, moreover, allows us to better
illustrate the problem of partial vs full provision. The firm providing the
service is assumed to private, emphasising the need of public intervention
for guaranteeing universal access. We focus on two public policies that can
be used by the government in order to influence the level of access and
prices, namely, fixing a universal price with free location, or allowing for
price discrimination with public dictation of the location of the facilities.
Given that in most of our work’s appplication areas of the population is
concentrated in urban areas, we base our analysis on the framework devel-
oped by Hwang and Mai [4]. Additionally, given that our goal is to anal-
yse the effect of different policies on universal access rather than on total
output, we depart from the assumption of elastic demand functions con-
sidering instead that demand is completely inelastic, up to certain reser-
vation value, to the price of the good. As with this assumption each indi-
vidual consumes either zero or one unit of the good, universal access takes
place when the price charged to each agent, plus the transportation cost in-
curred, is less than the reservation value, which garantees the consumption
by each customer.
Our results predict that the allowance for price discrimination ensures
universal access more often. When this happens, the facilities are located in
the most populated cities, and the inhabitants from other places are com-
pensated for their journeys through a lower price. Full provision is more
likely when the commuting population is more numerous, is located closer
to the source and transport is cheaper. Public regulation of location tends
to induce intermediate locations or positive consumer surplus but it does
not improve the likelihood of full coverage.
References
[1] Daskin, M. S., and Dean, L. K. (2005). Location of health care facilities. Opera-
tions research and health care, 43-76.
[2] Ewing, R., Schroeer, W., and Greene, W. (2004). School location and stu-
dent travel analysis of factors affecting mode choice. Transportation Research
Record: Journal of the Transportation Research Board, (1895), 55-63.
[3] Güne ¸s, E. D., and Nickel, S. (2015). Location problems in healthcare. In Location
Science (pp. 555-579). Springer International Publishing.
[4] Hwang, H., and Mai, C. C. (1990). Effects of spatial price discrimination on
output, welfare, and location. The American Economic Review, 80(3), 567-575.
[5] Pal, S. (2010). Public infrastructure, location of private schools and primary
school attainment in an emerging economy. Economics of Education Review,
29(5), 783-794.
VIII Workshop on Locational Analysis and Related Problems 2017 37
Some heuristic methods for the p-median
problem with maximum distance constraints
Adrián Esteban Pérez∗,1Jesús Sáez-Aguado2
1Universidad de Valladolid, Valladolid, Spain, adrianesteban@live.com
2Departamento de Estadística e Investigación Operativa, Universidad de Valladolid, Val-
ladolid, Spain, jsaez@eio.uva.es
Abstract. In this work we study the p-median problem with maximum dis-
tance constraints (PMPDC) which is a variant of the classical p-median
problem (PMP). (PMPDC) appeared first time in [3] and it is a problem of
interest in facility location. To our knowledge, the last study about heuris-
tic methods for (PMPDC) is [1] based on Lagrangian relaxation. First of all,
we provide some different formulations for (PMPDC). Note that (PMP) is
a NP-hard problem, so adding the maximum distances constraints does
not modify this complexity, but the problem is computationally more diffi-
cult. A first formulation is to consider the (PMP) with the following simple
approach, based on modify the distance matrix:
d0
ij =(dij ,if dij ≤si
M, if dij > si
where dij is the distance between demand point iand facility site j,siis
the the maximum distance limit between a demand point iand any facility
site and Mis a big value.
So we can transform (PMPDC) in a (PMP) with distance matrix modified.
In a first look, (PMPDC) can be seen like a (PMP) but this formulation has
a big problem: the heuristic methods for (PMP) frequently provide infeasi-
ble solutions and the quality of solutions depends of the value of big-M(
[1]).
∗Corresponding author
38
We give other formulation, based on adding to (PMP) the maximum dis-
tance constraints and without modifying the distance matrix. Different heuris-
tic procedures for the (PMPDC) problem are developed. First, a Lagrangian
relaxation algorithm which differs from the existing in [1] is developed.
Second, we apply a new approach, based on the GRASP methodology ad-
dapted to (PMPDC) from (PMP) [2].
In addition, we study in depth the relation between the feasibility of (PMPDC)
and the parameters pand maximum distance limits providing an analytic-
geometric characterization.
Finally, in order to compare the different methods, two data sets have been
used. The first set contains data from several real problems of medical as-
sistance in Castilla & León, in Spain. The second data set contains some
problems which are randomly generated (with bigger sizes than the first
data set). We solve them very efficiently and we compare the obtained re-
sults with the exact solution computed with XPRESS.
Keywords: Facility location, p-median problem, Lagrangian relaxation, GRASP.
References
[1] Choi, I.-C. and Chaudhry, S.S. (1993). "The p-median problem with max-
imum distance constraints: a direct approach", Location Science, Vol. 1 No. 3,
235-43.
[2] Resende M., Werneck, R.F. (2003). "On the Implementation of a Swap-
Based Local Search Procedure for the p-Median Problem". In R.E. Ladner
(ed.), Proceedings of the Fifth Workshop on Algorithm Engineering and Experiments
(ALENEX’03), SIAM, 119-127.
[3] Toregas, C., Swain, R.W., ReVelle, C.S. and Bergman, L. (1971). "The
location of emergency service facilities". Operations Research. Vol. 19 (6), 1971,
363-73.
VIII Workshop on Locational Analysis and Related Problems 2017 39
On location and vessel fleet composition
for offshore wind farm maintenance∗
Alejandro Gutiérrez Alcoba,1Eligius M.T. Hendrix,1Gloria Ortega,2
Dag Haugland,3Elin E. Halvorsen-Weare 4
1Computer Architecture, Universidad de Málaga agutierrez@ac.uma.es;eligius@uma.es
2Informatics, Almería University, gloriaortega@ual.es
3Department of Informatics, Bergen University, dag.haugland@uib.no
4Department of Maritime Transport Systems, MARINTEK, Norway,
elin.halvorsen-weare@marintek.sintef.no
Maintenance provides a large part of the cost of an offshore wind farm.
Several models have been presented in literature to optimize the fleet com-
position of the required vessels. A drawback such models is that they are
based on perfect information on weather and incidences to schedule for
the coming year. Our research question is what will happen to the fleet
composition if the practical scheduling is simulated by using heuristics.
1. Maintenance of offshore wind farms
The offshore wind energy industry is expected to continue its growth ten-
dency in the near future. The European Wind Energy Association expects
in its Central Scenario by 2030 a total installed capacity of 66 GW of off-
shore wind in the UE [1]. Offshore wind farms (OWFs) are large scale in-
frastructures, requiring large fleets able to perform operations and mainte-
nance (O&M) activities on the installed turbines. The O&M cause a large
part of the costs of running an OWF installation up to one third of the OWF
∗Alejandro Gutierrez-Alcoba is a fellow of the Spanish FPI programme, granted by the Min-
istry of Economy, Industry and Competitiveness. This paper has been supported by The Span-
ish Ministry (TIN2015-66680) and Seneca Foundation (19241/PI/14) of the Murcia region, in
part financed by the European Regional Development Fund (ERDF).
40
costs, see [5]. Moreover, the fleet makes the installations depend on non-
renewable energy resources. Therefore, optimising the efficiency of the re-
sources used for the O&M activities of an OWF becomes extremely impor-
tant in order to make them economically viable and to reduce CO2 emis-
sions.
Recent deterministic and stochastic model formulations for vessel com-
position and maintenance optimization can be found in [2] and [3]. A re-
cent literature review on DSS for OWF’s is given by [4].
This basis of our investigation is a scenario based MILP model which
like the models in [3] and [6] decide on the fleet composition. All these
models evaluate the value of the vessel composition and base selection
based on scheduling with perfect information; the weather conditions and
breakdowns happening during a scenario of a year is known beforehand.
Such a procedure underestimates the maintenance costs for a practical sit-
uation.
The research question is whether the composition may be affected a lot
when maintenance scheduling is done in a more practical heuristic way
given the practical information available.
References
[1] European Wind Energy Association. Wind energy scenarios for 2030.
http://www.ewea.org/fileadmin/files/library/publications/reports/EWEA-
W ind-energy-scenarios-2030.pdf. Accessed: 2016-12-14.
[2] Christian Gundegjerde, Ina B. Halvorsen, Elin E. Halvorsen-Weare, Lars Mag-
nus Hvattum, and Lars Magne Nonås. A stochastic fleet size and mix model
for maintenance operations at offshore wind farms. Transportation Research Part
C: Emerging Technologies, 52:74 – 92, 2015.
[3] Elin E. Halvorsen-Weare, Christian Gundegjerde, Ina B. Halvorsen, Lars Mag-
nus Hvattum, and Lars Magne Nonås. Vessel fleet analysis for maintenance
operations at offshore wind farms. Energy Procedia, 35:167 – 176, 2013.
[4] Matthias Hofmann. A review of Decision Support Models for offshore wind
farms with an Emphasis on Operation and Maintenance Strategies. Wind Engi-
neering, 35:1–16, 2011.
[5] Brian Snyder and Mark J. Kaiser. Ecological and economic cost-benefit analysis
of offshore wind energy. Renewable Energy, 34(6):1567 – 1578, 2009.
[6] Magnus Stålhane, Hanne Vefsnmo, Elin E. Halvorsen-Weare, Lars Magnus
Hvattum, and Lars Magne Nonås. Vessel fleet optimization for maintenance
operations at offshore wind farms under uncertainty. Energy Procedia, 94:357
– 366, 2016. 13th Deep Sea Offshore Wind R&D Conference, EERA Deep-
Wind’2016.
VIII Workshop on Locational Analysis and Related Problems 2017 41
The mobile facility location problem
Mercedes Landete1
1Universidad Miguel Hernández, 03202, Elche, Spain, landete@umh.es
The Mobile Facility Location Problem (MFLP) is the problem of re-locating
a set of existing facilities and re-allocating all the customers so that the
total cost of the movements is minimized. The re-location of facilities in
a stochastic network which minimizes the expected travel time have been
widely studied in the literature. However, the stochastic approach and the
MFLP differ in two regards: firstly, the MFLP considers the initial location
of the facilities, and thus the initial allocation of customers, as an input;
secondly the objective function is the total movement cost instead of an
expected total cost. The MFLP was introduced in [1]. Later, Halper et al.
[2] presented a local heuristic and Raghavan and Sahin [3] considered the
extension with capacitated facilities.
This work introduces two different set packing formulations for the
problem. One formulation is for the case in which re-locating costs and
re-allocating costs are proportional to distances and the another is for the
general costs case. Valid inequalities and optimality conditions for each
of the formulations are introduced. Computational results show the per-
formance of both formulations as well as the performance of the different
families of valid inequalities.
References
[1] Friggstad Z., Salavatipour, MR. (2011). “Minimizibg movement in mobile facil-
ity location problem,” ACM Trans Algorithms 7(3):30.
[2] Halper,R. and Raghavan,S. and Sahin,M. (2015). “Local search heuristics for the
mobile facility location problem,” Computers and Operations Research 210–
223.
[3] S. Raghavan and M. Sahin and F.S. Salman (2016). “The capacitated mobile
facility location problem,” Working paper, University of Maryland.
42
VIII Workshop on Locational Analysis and Related Problems 2017 43
Some criteria for locating sensors in a wind
turbine blade
M.Cruz López-de-los-Mozos,1Juan A. Mesa,2Diego Ruiz-Hernández,
3and Carlos Q. Gómez-Muñoz,4
1Department of Applied Mathematics I, University of Seville, Spain, mclopez@us.es
2Department of Applied Mathematics II, University of Seville, Spain, jmesa@us.es
3Department of Quantitative Methods, University College for Financial Studies, Madrid,
Spain, d.ruiz@cunef.edu
4Department of Business Management, University of Castilla-La Mancha, Ciudad Real,
Spain, carlosquiterio.gomez@uclm.es
Using acoustic sensors for detecting the location of a breakage on a wind
turbine blade reduces the associated maintenance cost. The triangulation
method developed in [1] is based on strategically placing three acoustic
sensors in the surface of the blade section to approach the location of a
randomly generated crack. Assuming the hypothesis made in [1], among
them approximating the section blade by a planar surface (a rectangle),
the question of how locating the three sensors is closely related with the
accuracy of the approximation.
In this work we explore several criteria for locating acoustic sensors
in a section of the wind turbine blade in order to apply the triangulation
method to detect a breakdown in the surface of the blade.
Taking into account the experimental results obtained from the simula-
tion of the method in the laboratory, we have considered several problems.
Let Ωdenote the rectangle, and let Σ = {Si, i = 1, . . . , p} ⊂ Ωdenote
a set of psensors. We have considered a demand continuously distributed
over Ω, with uniform distribution in the first two cases.
1. p-min-max-max criterion. For p= 3, the problem is to find Σ⊂Ω
minimizing the maximum distance from the point in Σfurthest from
44
all points in Ω:
min
Σ⊂Ω,|Σ|=3 τ(Σ) = min
Σ⊂Ω,|Σ|=3 max
S∈Σmax
X∈Ωd(S, X)
s.t. min
Si,Sj∈Σ, Si6=Sj
d(Si, Sj)≥δ > 0
2. Maximum area criterion with sensors range threshold Although in
the laboratory the sensors cover the overall blade section, there are
several blade sizes. In this case we have considered a sensors range
threshold ∆>0, meaning that for X∈Ω, if d(X, Si)>∆then Si
does not receive the acoustic signal from X. Let A(conv(Σ)) be the
area of the convex hull of Σ. The second problem is
max
Σ⊂Ω,|Σ|=3 A(conv(Σ))
s.t. d(S, X)≤∆,∀X∈Ω,∀S∈Σ
3. Maximum area criterion with regional fault distribution The geo-
metrical form make the edges of the wind turbine blade (trailing and
leading edges) more susceptible to damage, in particular the trail-
ing edge. Thus, we have considered three zones in Ω, with different
breaking probability. Let Ωi, i = 1,...,3be three consecutive rectan-
gles in Ωsuch that a side of Ω1coincides with the trailing edge, and a
side of Ω3coincides with the leading edge Let 0< w1≤min{w2, w3},
with W=
3
X
i=1
wi, and let wi/W be the probability of a fault in Ωi,
i= 1,...,3. The third problem is
max
Σ⊂Ω,|Σ|=3 F(Σ) := 1
W
3
X
i=1
wiA(Ωi∩conv(Σ))
The second phase of this work (still open) consists in incorporating these
elements in a cooperative cover model, as the one proposed in [2]
References
[1] Gómez Muñoz, C. and García Márquez, F. (2016). A new fault location approach
for acoustic emission techniques in wind turbines. Energies , 9(1):40.
[2] Berman, O., Drezner, Z. and Krass, D. (2010). Cooperative cover location problems:
The planar case. IIE Transactions 42 (3): 232–246.
VIII Workshop on Locational Analysis and Related Problems 2017 45
Tree of hubs location problem
with upgrading ∗
Alfredo Marín1
1Departamento de E. e Investigación Operativa, Universidad de Murcia, amarin@um.es
The Tree of Hubs Location Problem (THLP) was introduced for the first
time in [2]. Since then, it has received much attention in the specialized
literature. The THLP is a single-allocation hub location problem where p
hubs have to be located on a network and connected by means of a (non-
directed) tree. Then each non-hub node must be connected (allocated) to a
hub and all the flow between nodes must use these connections to circulate,
i.e., excepting the arcs that connect each non-hub node with its allocated
hub, the arcs that route the flows must be links connecting hubs. There is
a per unit transportation cost associated with each arc. The objective is to
minimize the operation costs of the system.
On the other hand, many variants of the Minimum Spanning Tree Prob-
lem are being explored, among them the Spanning Tree Problem with up-
grading (STPU), see e.g. [1]. Here the cost (length, weight) associated to
each edge of the graph can be reduced in the first instance by upgrading
one of its extremes (with an associated cost), and it can be reduced even
more by upgrading both extremes. In this way, every time a cost is paid to
upgrade a node, all edges inciding in this node benefit from this upgrad-
ing.
We introduce here the THLP with upgrading (THLPU), a mixture of
these two problems. In addition to locate the hubs, to determine the tree
connecting hubs and to allocate non-hub nodes to hubs, a decision has to
be taken about which of the hubs will be upgraded, taking into account
that there is a budget to be invested in the upgrading. Then we formulate
the problem as a Mixed Integer Linear Programming Problem, trying to get
∗Research supported by Ministerio de Economía y Competitividad, project MTM2015-65915-
R, Fundación Séneca, project 19320/PI/14, and Fundación BBVA, project “Cost-sensitive clas-
sification. A mathematical optimization approach” (COSECLA)
46
a tight formulation, and we generate several families of valid inequalities.
A preliminary computational study is also presented.
References
[1] Álvarez-Miranda, E., and M. Sinnl (2017). “Lagrangian and branch-and-cut ap-
proaches for upgrading spanning tree problems,” Computers and Operations
Research 83, 13-27.
[2] Contreras, I., E. Fernández and A. Marín (2010). “The Tree of Hubs Location
Problem,” European Journal of Operational Research 202, 390-400.
VIII Workshop on Locational Analysis and Related Problems 2017 47
A stochastic multi-period covering model
Alfredo Marín,1Luisa I. Martínez-Merino,2Antonio M. Rodríguez-
Chía,3Francisco Saldanha-da-Gama,4
1Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Uni-
versidad de Murcia, Murcia, Spain, amarin@um.es
2Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Cádiz,
Spain, luisa.martinez@uca.es
3Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Cádiz,
Spain, antonio.rodriguezchia@uca.es
4Departamento de Estatística e Investigação Operacional/ Aplicações Fundamentais e In-
vestigação Operacional, Faculdade de Ciências da Universidade de Lisboa, Portugal, fa-
conceicao@fc.ul.pt
This work focuses on a general covering location problem, denoted as
GSMC, which includes stochastic and multi-period features. It general-
izes most of the covering models in the literature. In the GSMC, a plan-
ning horizon divided in several time periods is considered and uncertainty
about the demand for coverage is also taken into account. Concretely, given
a set of potential locations for facilities and a set of demand points, the
purpose is to decide which facilities must be operating in each time period
to minimize the total expected cost satisfying some coverage constraints.
A formulation for this model is proposed and analyzed. In addition, a La-
grangian relaxation based heuristic is used not only to obtain lower bounds
on the solutions, but also to find good feasible solutions for the model.
1. Introduction to the problem
Two main classic covering models can be found in literature: the set cover-
ing location problem (SCP) proposed in [4], and the maximal covering lo-
cation problem (MCLP) introduced in [1]. The objective of the former prob-
lem is to minimize the cost of installed facilities restricting that all demand
48
points must be covered. The latter consists of maximizing the covered de-
mand limiting the number of operating facilities. These two main models
and some others related with covering are generalized in [2]. This general
model is extended in the present work adding stochastic and multi-period
features.
In the GSMC a finite planning horizon divided in a set of time periods
(T) is considered. Besides, a set of potential locations for facilities (I) and
a set of demand points (J) is given. In each potential location i∈I, a
maximum of eifacilities can be operating and only a total of ptfacilities
can be active in each time period t∈T. When a facility is installed or
closed in a certain time period a cost must be paid. Similarly, an operating
cost for the activity of a facility in a time period is considered.
The GSMC model also assumes that it exists uncertainty associated with
the minimum threshold for coverage of each demand point and with the
coverage capability of each facility. Moreover, a profit related with the num-
ber of facilities covering a demand point above its minimum threshold,
and a penalty associated with the coverage shortage are modeled. These
profits/penalties are also uncertain. It is considered that the uncertainty
can be explained by a finite set of scenarios with some previously known
probabilities.
Given the previous framework, GSMC model aims to decide which fa-
cilities must be installed or closed in each time period to minimize the total
expected cost satisfying some coverage constraints. As a result, GSMC gen-
eralizes not only the models appearing in [2], but also some other covering
models that include some time-dependent parameters, see [3].
In addition to the model analysis, a Lagrangian relaxation based heuris-
tic which provides lower bounds and good feasible solutions is developed.
Some preliminary computational results were performed to see the impor-
tance of this Lagrangian heuristic.
References
[1] Church, R., ReVelle, C. (1974). “The maximal covering location problem”, Pa-
pers of the Regional Science Association, 32, 1, 101-118.
[2] García, S., Marín, A. (2015). “Covering location problems”, in G. Laporte, S.
Nickel, and F. Saldanha da Gama, editors, Location Science, chapter 5, 93-113.
Springer.
[3] Gunawardane,G. (1982). “Dynamic versions of set covering type public facility
location problems”, European Journal of Operational Research, 10, 2, 190-195.
[4] Toregas, C., Swain, A., ReVelle, C., Bergman, L. (1971). “The location of emer-
gency service facilities”, Oper. Res., 19, 1363-1373.
VIII Workshop on Locational Analysis and Related Problems 2017 49
Supply chain complexity and the network
design : Location does matter!
Mozart B.C. Menezes, 2,3Diego Ruiz-Hernández 1,3
1University College for Financial Studies, Department of Quantitative Methods, Leonardo
Prieto Castro 2, 28040, Madrid, Spain d.ruiz@cunef.edu
2Kedge Business School, Operations Management and Information Systems Department,
KEDGE Business School Bordeaux, 680 Cours de la Libération, 33405, Cedex, France
3Supply Chain and Complexity Lab, KEDGE Business School
Facility location problems are well known problems in the field of com-
binatorial optimization, where -broadly speaking- the objective is typically
to locate a collection of facilities aimig at minimising the cost incurred in
serving the customer base. There are several papers dealing with facility
location algorithm complexity starting by showing that most belong to the
class of NP-hard problems (e.g., see [2]). Additionally, some very sophisti-
cated results take advantage of structural properties of some location prob-
lems and present a bound on the performance of a greedy algorithm [1]. In
this paper we focus on another type of complexity. Our study brings to the
community of facility location the concept of operations complexity, where
the objective is to measure the amount of information those managing a
supply network have to deal with. THis new concept opens up a new re-
search line within the field. When determining the location of a facility one
should aim not only at reducing operational costs but also at keeping (op-
erational) complexity in what we call a complexity comfort range, in which
tactical and operational decisions are at their bests. Preliminary (empirical)
results suggest that ignoring complexity issues may hurt that same bottom
line that the locational problem is trying to improve.
50
References
[1] Nemhauser, G., Wolsey, L., Fisher, M. (1978). An analysis of approximations for
maximizing submodular set functions - I. Math. Programming, 14, 265–294.
[2] Nemhauser, G. L., L. A. Wolsey. 1988. Integer Programming and Combinatorial
Optimization. John Wiley & Sons, New York.
VIII Workshop on Locational Analysis and Related Problems 2017 51
Heuristics for the stochastic uncapacitated
r-allocation p-hub median problem
Juanjo Peiró1, Ángel Corberán1, Rafael Martí1and
Francisco Sandanha-da-Gama2
1Departament d’Estadística i Investigació Operativa. Universitat de València, Spain.
juanjo.peiro@uv.es, angel.corberan@uv.es, rafael.marti@uv.es
2Departamento de Estatística e Investigação Operacional.
Centro de Matemática Aplicações Fundamentais e Investigação Operacional,
Faculdade de Ciências, Universidade de Lisboa, Portugal
fsgama@ciencias.ulisboa.pt
In this work we study a class of hub median problems that has been re-
ferred to in the literature as the r-allocation p-hub median problem. We
consider an existing modeling framework and extend it by including sev-
eral features that include fixed allocation costs, non-stop services between
terminals and stochasticity in the traffic and transportation costs. For the
situation in which the support of the underlying random vector is finite we
propose a heuristic algorithm for finding high-quality feasible solutions.
1. Introduction
The starting point for your study is the so-called uncapacitated r-allocation
p-hub median problem (UrApHMP) introduced by Yaman [1] and studied
by other authors such as Peiró et al. [2] and Martí et al. [3]. In this problem,
a set of nodes Vis given such that some traffic tij must be routed between
many pairs of nodes (i, j)∈V×V. The goal is to select a set H⊆Vwith
|H|=pfor installing hubs. In this model, the hub network is assumed to
be complete and all the traffic must be routed via at least one hub (direct
shipments are not possible). Each node can be allocated to at most rhubs,
where ris exogenously defined. The goal is to minimize the total trans-
52
portation cost. The unitary transportation costs are assumed to satisfy the
triangle inequality.
2. Extensions to the uncapacitated rApHMP
We extend the above mentioned model in several directions namely, by
considering: (i) fixed allocation costs, (ii) the possibility of having direct
transportation between terminals, and (iii) uncertainty in transportation
costs and traffics. We call the extended problem, the stochastic uncapaci-
tated r-allocation p-hub median problem with non-stop services—Stochastic
UrApHMP-NSS.
This new setting is much general since it captures several particular
cases/problems of interest such as the stochastic single allocation p-hub
median problem, the stochastic multiple allocation p-hub median problem,
and each of those problems combined with the possibility of including
allocation costs and/or non-stop services. Hence, we are not studying a
particular problem of interest but a broader setting that captures several
particular problems that may be of interest.
We assume that uncertainty can be described probabilistically using a
joint distribution function know in advance (e.g., instance estimated using
historical data). This makes intuitive the use of a stochastic programming
modeling framework: in the first stage we consider the network design
decisions (location and allocation decisions); in the second stage (after un-
certainty is disclosed) we consider the transportation decisions.
Assuming that the support of the underlying random vector is finite,
we can go further in terms of mathematical modeling and derive a com-
pact formulation for the deterministic equivalent of the stochastic problem
developed. Unfortunately, even for very small instances of the problem,
the model becomes too large, which prevents the use of a general-purpose
solver for tackling it. This motivates the development of an approximate
procedure for finding feasible solutions to the problem.
References
[1] Yaman, H. (2011) Allocation strategies in hub networks. European Journal of Op-
erational Research 211 (3), 422–451.
[2] Peiró, J., Corberán, Á., Martí, R. (2014) GRASP for the uncapacitated r-allocation
p-hub median problem. Computers & Operations Research 43 (1), 50–60.
[3] Martí, R., Corberán, Á., Peiró, J. (2015) Scatter search for an uncapacitated p-hub
median problem. Computers & Operations Research 58, 53–66.
VIII Workshop on Locational Analysis and Related Problems 2017 53
Profiling the inherent complexity of
different facility location strategies
Jesús María Pinar-Pérez,1, Diego Ruiz-Hernández, 1,3Mozart Menezes,2,3
1University College for Financial Studies, Department of Quantitative Methods, Leonardo
Prieto Castro 2, 28040, Madrid, Spain jesusmaria.pinar@cunef.edu
2Kedge Business School, Operations Management and Information Systems Department,
KEDGE Business School Bordeaux, 680 Cours de la Lib’eration, 33405, Cedex, France
3Supply Chain and Complexity Lab, KEDGE Business School
Facility location problems are well known combinatorial problems where
the objective is to minimize the cost incurred to serve customers from a set
of facilities. Our aim is to bring to the field of facility location the concept of
operations complexity, opening up a new research line. The main objective
is to create awareness about the need of considering complexity issues and
its impact on profitability, rather than only a cost/profit perspective, when
deciding the location and size of a distribution network.
In our preliminary numerical assessment, we consider both randomly
generated and real life networks, taking into consideration their tempo-
ral evolution, using proxies for organic growth, mergers and acquisitions
and optimised design. We also evaluate the effect of different opimisation
strategies and provide insights for further development and discussion.
54
VIII Workshop on Locational Analysis and Related Problems 2017 55
Approval voting problem
under the k-centrum criterion
Diego Ponce,1Justo Puerto,2Federica Ricca,3and Andrea Scozzari4
1Universidad de Sevilla, Dep. de Estadística e Investigación Operativa, IMUS, dponce@us.es
2Universidad de Sevilla, Dep. de Estadística e Investigación Operativa, IMUS, puerto@us.es
3Sapienza Universitá di Roma, Dip. MEMOTEF federica.ricca@uniroma1.it
4Universitá degli Studi Niccoló Cusano, Facoltá di Economia andrea.scozzari@unicusano.it
In this work we model the approval voting problem as a mixed integer
linear program. Different formulations for the Minisum, Minimax and k-
centrum objective functions have been developed. The usefulness of these
new approach to solve this problem is evaluated with a computational
study.
1. Introduction
Consider a set of nvoters and a set of mcandidates. Let Pbe a n×m
matrix representing the set of nvoters profiles, that is, Pi,i= 1, . . . , n, is
a boolean vector of length mthat specifies each voter’s preference on each
candidate. For instance, pij = 1 means that voter iapproves candidate j;
pij = 0 otherwise. The problem consists of selecting a committee, that is, a
(sub)set of candidates in order to minimize a given objective function.
Given a committee x(a boolean vector xof length m,xj= 1 if candidate
jbelongs to the committee; xj= 0 otherwise), the Hamming distance is
used to evaluate the distance between a committee and each profile Pi,
i= 1, . . . , n. Let xbe a committee, the Hamming distance di(x)between
the profile Piof voter ito xis di(x) =
m
P
j=1
|pij −xj|.
The two criteria commonly used for electing a committee are:
56
1. Minisum criterion: Elect a committee minimizing the sum of Ham-
ming distances to the profiles.
2. Minimax criterion [2]: Elect a committee minimizing the maximum
of Hamming distances to the profiles.
From a computational point of view, the Minisum problem is polynomially
solvable [1]. The aim of this work is to consider criteria that are between
the Minisum and the Minimax ones. This consists of a family of functions,
parameterized by a vector Wof length n, mapping a vector of scores Hto
an aggregated score.
2. The k-centrum voting problem
The family of Approval Voting rules parameterized by a vector Wthat we
will consider here is
W(k) = (1,...,1
| {z }
k
,0,...,0)
where kis the number of ones. For example, if k=nwe have the Minisum
criterion, if k= 1 we have the Minimax criterion. We want to study the
general case when 1< k < n.
More specifically, given 1< k < n, the problem turns out to be: elect a
committee that minimizes the sum of the k-largest weights (k-centrum).
Let σ(x)be an ordering function such that dσ1(x)≥dσ2(x)≥. . . ≥dσn(x).
The problem can be formulated as follows:
min
x
k
X
h=1
dσh(x) : x∈ {0,1}m.(1)
In this work, we propose several formulations and methodologies which
are experimentally compared in a data base from the literature.
References
[1] Brams, Steven J., and Kilgour, D. Marc, and Sanver, M. Remzi. (2007). “A min-
imax procedure for electing committees” Public Choice 132(3): 401–420.
[2] Kilgour, D. Marc, and Brams, Steven J., and Sanver, M. Remzi. (2006). “How to
Elect a Representative Committee Using Approval Balloting” Mathematics and
Democracy 83–95.
VIII Workshop on Locational Analysis and Related Problems 2017 57
The ordered median tree of hubs location
problem
Miguel A. Pozo,1Justo Puerto,2and Antonio M. Rodríguez-Chía,3
1Universidad de Cádiz, Spain., miguelpozo@us.es
2Universidad de Sevilla, Spain., puerto@us.es
3Universidad de Cádiz, Spain., antonio.rodriguezchia@uca.es
Hub-and-spoke models have a great importance in transportation and tele-
communication systems in which several origin-destination points exchange
flows. In such models the key feature is to connect each pair via specific
subsets of links to consolidate, and distribute the flows in order to reduce
costs based on the economy of scale of intermediate connections. There-
fore, Hub Location Problems integrate two level of decisions: location of
facilities (hubs) to consolidate deliveries and network design to determine
the routes that different origin-destination pairs follow to improve perfor-
mance.
The standard model of hub-and-spoke networks assume that inter-hub
connections between an origin-destination pair can be routed through one
or at most two hubs. However, it has been observed by several authors
that in many applications the backbone network is not fully interconnected
[1,2] or it can even be not necessarily connected.It is of special interest the
case where the underlying interconnection network is connected by means
of a tree. Such problem is called the Tree of Hubs Location Problem and
was introduced by Contreras et al ( [3,4]).
Recently, another feature, namely weighted averaging objective func-
tions, has also been incorporated to the analysis of Hub Locations Prob-
lems [5, 6]. It has been recognized as a powerful tool from a modeling
point of view because its use allows to distinguish the roles played by the
different entities participating in a hub-and-spoke network inducing new
type of distribution patterns. Each one of the components of any origin-
destination delivery path gives rise to a cost that is weighted by different
58
compensation factors depending on the role of the entity that supports the
cost. This adds a “sorting”-problem to the underlying hub location prob-
lem. The objective is to minimize the total transportation cost of the flows
between each origin-destination pair after applying rank dependent com-
pensation factors on the transportation costs.
In this paper, we propose the Ordered Median Tree of Hub Location
Problem (OMTHLP). The OMTHLP is a single allocation hub location prob-
lem where phubs must be placed on a network and connected by a non-
directed tree. Each non-hub node is assigned to a single hub and all the
flow between origin-destination pairs must circulate using the links con-
necting the hubs. The objective is to minimize the sum of the ordered
weighted averaged assignment costs plus the sum of the circulating flow
costs. We will present different MILP mathematical formulations for the
OMTHLP based on the properties of the Minimum Spanning Tree Prob-
lem and the Ordered Median optimization. We establish a theoretical and
empirical comparison between these new formulations and we also pro-
vide reinforcements that together with a proper formulation are able to
solve medium size instances on general graphs.
References
[1] J.F. Campbell, A. Ernst, and M. Krishnamoorthy. Hub arc location problems.
II: Formulations and optimal algorithms. Manage. Sci. 51(10):1556-1571, 2005.
[2] A.M. Campbell, T.J. Lowe and L. Zhang. The p-hub center allocation problem.
European Journal of Operational Research, 176(2):819-835, 2007.
[3] I. Contreras, E. Fernández, and A. Marín. The tree of hubs location problem.
European Journal of Operational Research, 202(2):390-400, 2010.
[4] I. Contreras, E. Fernández, and A. Marín. Tight bounds from a path based for-
mulation for the tree of hub location problem. Computers & Operations Research,
36(12):3117-3127, 2009.
[5] J. Puerto, A.B. Ramos and A.M. Rodríguez-Chía. Single-Allocation Ordered
Median Hub Location Problems. Computers and Operations Research, 38:559-570,
2011.
[6] Justo Puerto, A. B. Ramos and A. M. Rodríguez-Chía, A specialized branch
& bound & cut for Single-Allocation Ordered Median Hub Location problems.
Discrete Applied Mathematics, 161:16-17, 2624-2646, 2013.
VIII Workshop on Locational Analysis and Related Problems 2017 59
Location theory and some physical
principles in a nutshell
Justo Puerto,1
1IMUS. Universidad de Sevilla, Spain., puerto@us.es
Location Theory is an appealing field of Operations Research that shares
many links with optimization. The most important problems in this area
can be formulated as mathematical programming problems in different
framework spaces: continuous, networks or discrete [9]. Lots of insights
are gained on the original problems analyzing their mathematical pro-
grams counterparts and reciprocally, many results can be inherited from
the structure of the original problems; what helps in solving the models.
This presentation would like to focus on a different aspect that is not so
well-known: the relationship between classical principles in Physics and
some models and solution methods applied in standard location problems.
We will revisit some well-known laws as the equilibrium of forces, sym-
metry, maximum entropy, law of Snell, law of gravity or the optimal mass
transport theory [6]. The goal will be to link them to some problems in the
field of Location analysis [9].
In this talk, we show how the equilibrium of forces can be used to derive
algorithms to solve continuous (single and multiple) facility location [1,2,
4], symmetry is the basis of the ordered median problem [10], maximum
entropy can explain obnoxious facility location models, the law of Gravity
can be used to determine market shared areas or to define territorial units
[5,7], the Snell’s law is applicable to modeling different transport modes in
location or transportation problems [3] or how the optimal mass transport
theory can be used to compute optimal territory design [8]. We will explain
the connections, interpret the results in the jargon of location analysis and
show some applications.
60
References
[1] Blanco V., El-Haj Ben-Ali S. and Puerto J. (2013). Minimizing ordered weighted
averaging of rational functions with applications to continuous location, Computers
& Operations Research 40, 1448–1460.
[2] Blanco V., Puerto J. and El-Haj Ben-Ali S. (2014). Revisiting several problems and
algorithms in continuous location with `pnorms. Computational Optimization and
Applications 58(3), 563–595.
[3] V. Blanco, J. Puerto, D. Ponce. (2016). “Continuous location under the effect of
refraction”, Mathematical Programming, 161(1) 33-72.
[4] V. Blanco, J. Puerto, S. El-Haj Ben-Ali, “Continuous multifacility ordered me-
dian location problems”, European Journal of Operational Research 250(1): 56–
64, 2016.
[5] Kalcsics, J.: Districting problems, in Location Science, G. Laporte, S. Nickel and
F. Saldanha da Gama (Eds.), Springer (2015)
[6] Kantorovich, L.V.: On the transfer of masses. Dokl. Akad. Nauk. 37, 227-229
(1942).
[7] Huff DL (1964). Defining and estimating a trading area. Journal of Marketing
28, 34–38.
[8] L. Mallozi, J. Puerto. “The geometry of optimal partitions in location prob-
lems”. Optimization Letters, 2017.
[9] S. Nickel and J. Puerto. Location Theory — A Unified Approach. Springer, 2005.
[10] J. Puerto and F.R. Fernández. Geometrical properties of the symmetrical single
facility location problem. Journal of Nonlinear and Convex Analysis, 1(3):321–342,
2000.
VIII Workshop on Locational Analysis and Related Problems 2017 61
The periodic vehicle routing problem with
driver consistency∗
Inmaculada Rodríguez-Martín,1Juan-José Salazar-González,1and
Hande Yaman2
1DMEIO, Facultad de Ciencias, Universidad de La Laguna, Tenerife, Spain irguez@ull.es,
jjsalaza@ull.es
2Dpt. of Industrial Engineering, Bilkent University, Ankara, Turkey hyaman@bilkent.edu.tr
The Periodic Vehicle Routing Problem is a generalization of the classi-
cal VRP in which routes are determined for a planning horizon of several
days. Each customer has an associated set of allowable visit schedules, and
the objective of the problem is to design a set of minimum cost routes that
give service to all the customers respecting their visit requirements. In this
paper we study a variant of this problem in which we impose that each
customer should be served by the same vehicle/driver at all visits. We call
this problem the Periodic Vehicle Routing Problem with Driver Consis-
tency (PVRP-DC). We present different integer linear programming formu-
lations for the problem and derive several families of valid inequalities. We
solve it using an exact branch-and-cut algorithm, and show computational
results on a wide range of randomly generated instances.
∗This work has been partially supported by the Spanish research project MTM2015-63680-R
(MINECO/FEDER)
62
VIII Workshop on Locational Analysis and Related Problems 2017 63
The effect of products’ short lifecycle on
network design
Diego Ruiz-Hernández,1,3Mozart B.C. Menezes,2,3and Oihab Allal-
Cheriff2
1University College for Financial Studies, Department of Quantitative Methods, Leonardo
Prieto Castro 2, 28040, Madrid, Spain d.ruiz@cunef.edu
2Kedge Business School, Operations Management and Information Systems Department,
KEDGE Business School Bordeaux, 680 Cours de la Lib’eration, 33405, Cedex, France
3Supply Chain and Complexity Lab, KEDGE
In this work we address the problem of designing a distribution net-
work for new/seasonal products. The complexity of this problem becomes
magnified because the location/capacity decisions are made long before
the product is released to the market and, thus, knowledge about its de-
mand is limited. Moreover, in general new (or seasonal) products show
very short life-cycles, making location and capacity one-shot decisions. An
example of that could be the production of a completely new model of car,
where the assembly facilities are designed with a fixed number of lines and
changes to the initial decision are both costly and not very simple, if pos-
sible at all. Another example, could be the case of temporary facilities for
humanitarian aid, where adapting existing buildings for housing a sup-
ply center requires some important investment (including security of the
premises) and it is a one go decision. In this case, the need for the facility
is short lived while the real demand is highly uncertain. The relevance of
location and capacity decisions is better appreciated by considering that
about 80% of the supply chain costs are locked-in once the facilities’ loca-
tion and capacity are fixed [6].
Assuming that production can either be fully manufactured in-house or
partially outsourced, we imply that, when outsourcing, the firm has cer-
tain flexibility with respect to the quantities ordered. The resulting trade-
off between over- and under-capacity is hereby exploited for defining the
capacity of each facility which, consequently, has an impact on its location.
64
The model that has traditionally been called-for when dealing with capac-
ity issues is the Newsvendor model. Regarding location, the deterministic
variant of the capacitated facility location problems has been thoroughly
addressed in literature, see for example [1,3]. However, stochasticity has
only recently been included in capacitated frameworks. See, for example,
[4], [2], or [5].
To our knowledge, this is the first time that the problem of simultane-
ously locating facilities and determining their capacities is addressed with
full consideration of demand’s stochasticity. We show that for the single
facility case, the expected profit of the strategic problem is non-decreasing
and concave in the facility capacity, resulting in a uniquely determined op-
timal capacity. We further show that when the facility’s location is fixed,
the problem of choosing the capacity becomes a variation of the classi-
cal Newsvendor model. A critical-ratio based heuristic is proposed for the
multi-facility case. We finally provide an illustrative example.
References
[1] Melo, M. T., Nickel, S., Saldanha-Da-Gama, F. (2009). Facility location and sup-
ply chain management - A review. European Journal of Operational Research,
196(2), 401-412.
[2] Zhou, J., Liu, B. (2003). New stochastic models for capacitated location-
allocation problem. Computers & Industrial Engineering, 45(1), 111-125.
[3] Amiri, A. (2006). Designing a distribution network in a supply chain system:
Formulation and efficient solution procedure. European Journal of Operational
Research. 171(2), 567-576.
[4] Berman, O., Krass, D., and Wang, J. (2011) Early Work on the Introduction of
Stochastic Analysis in Location Research; H.A. Eiselt and V. Marianov, eds.,
Invited Chapter for Foundations of Location Analysis International Series Op-
erations Research and Management, Springer; Issue: 155; 2011; Pages: 241-272.
[5] Snyder, L.V., Z Atan, P Peng, Y Rong, AJ Schmitt, and B Sinsoysal (2016).
OR/MS models for supply chain disruptions: A review. IIE Transactions 48 (2),
89-109.
[6] Watson, M. (2013). Supply chain network design: applying optimization and analyt-
ics to the global supply chain. Pearson Education, 2013.
VIII Workshop on Locational Analysis and Related Problems 2017 65
Facilities delocation in the retail sector
María Sierra-Paradinas,1Antonio Alonso-Ayuso,2and J. Francisco
Rodríguez-Calo 3
1Escuela Técnica Superior de Ingeniería Informática, Universidad Rey Juan Carlos, Madrid,
Spain, maria.sierrap@urjc.es
2Escuela Técnica Superior de Ingeniería Informática, Universidad Rey Juan Carlos, Madrid,
Spain, antonio.alonso@urjc.es
3Repsol S.A., Madrid, Spain, jfrodriguezc@repsol.com
A facilities delocation problem in the retail sector is addressed by propos-
ing a mixed integer programming model. The aim of the problem is to
decide the cease of existing facilities in order to optimize the income of the
whole retail network.
1. Introduction
Facilities location models have been broadly studied in the literature. Nev-
ertheless, the concept of delocation has been introduced recently. In [1] de-
location is defined as the operation ceased of existing facilities.
As shown in [2] several delocation models have been presented in both
the private and the public sector. In particular, [2] presents two models to
reduce the number of facilities in a given area with firm competition and
without it. In the first case their aim is to reduce the quantity of facilities to
a fixed number, minimizing the impact on demand loss to competitors. In
the second case, a measure of the decline of the service is minimized.
Along the same line, in [1] a model to downsize a firm’s existing distri-
bution network with known supplier locations is presented. The firm seeks
the closure of a fixed number of the supplier nodes. The model proposed
contemplates that all demand nodes must be served from their respective
supplier except if the existing supplier is eliminated.
More recently in [3] a model for resizing a bank network is presented.
Seeking to maintain a constant service level, the objective is to decide which
66
branches should stay opened within a colletion of possibly redundant ones.
2. Definition of the problem
Delocation models have been addressed in the literature due to several
reasons. In our case a franchise chain wants to optimize the operation of
his network of stores. The decision to make is whether the existing stores
should cease operations or change the operating mode.
The stores can be operated by the franchise chain itself or by an external
dealer. Each operating mode has a different repercusion in the final income
of the stores due to the client’s behaviour, when this behaviour is given
by their tendency to abandon. In case of the closure of a store the clients
with tendency to abandon will leave the entire franchise chain and will
not report any benefits. If the store’s operating mode is changed, the final
prices and final income change as well, but no repercusion in the clients is
noticed.
Capacity constraints are imposed in the number of stores that should
stay opened and cease operations cost, client behavoiur and final prices
depending on the operating mode are known.
Due to business demands refering to the behaviour of the clients, a non-
linear constraint appears in the definition of the model. Fortet’s innequal-
ities are used in order to linearize the constraint and therefore obtain an
integer linear programming model.
Because of the size of the network, border constraints have been im-
posed in order to get results in a reasonable computational time and model
optimization is done by introducing smart index sets in order to reduce
the number of constraints and variables. The model has been written into
AMPL and solved using CPLEX version 12.7.
References
[1] P.K. Bhaumik. Optimal shrinking of the distribution chain: the facilities delo-
cation decision. International Journal of Systems Science, 41(3):271–280, 2010.
[2] C. ReVelle, A. T. Murray, and D. Serra. Location models for ceding market
share and shrinking services. The International Journal of Management Science,
Omega 35: 533-540, 2007.
[3] D. Ruiz-Hernández, D. Delgado-Gómez, and J. López-Pascual. Restructur-
ing bank networks after mergers and acquisitions: A capacitated delocation
model for closing and resizing branches. Computers & Operations Research, 62:
316-324, 2015.
Author Index
A
Allal-Cherif, Oihab
KEDGE Business School, France, oihab@kedgebs.com .................63
Alonso-Ayuso, Antonio
Universidad Rey Juan Carlos, Spain, antonio.alonso@urjc.es ...........65
Arcos-Vargas, Ángel
Universidad de Sevilla, Spain, aarcos@us.es .........................27
B
Barrena, Eva
Universidad de Granada, Spain, ebarrena@ugr.es ....................15
Benavent, Enrique
Universitat de València, Spain, enrique.benavent@uv.es ................17
Bender, Matthias
Research Center for Information Technology (FZI), Germany,
mbender@fzi.de ......................................................19
Blanco, Víctor
Universidad de Granada, Spain, vblanco@ugr.es .....................21
Bonami, Pierre
Aix Marseille Université/ IBM, France, pierre.bonami@es.ibm.com ......9
Bruno, Giuseppe
University of Naples Federico II, Italy, giuseppe.bruno@unina.it ........23
C
Calvete, Herminia I. 67
Universidad de Zaragoza, Spain, herminia@unizar.es .................25
Camacho-Vallejo, José Fernando
Universidad Autónoma de Nuevo León, Mexico,
jose.camachovl@uanl.edu.mx ...........................................25
Campbell, James F.
University of Missouri, USA, campbell@umsl.edu .....................11
Canca, David
Universidad de Sevilla, Spain, dco@us.es .................15,27,29,31
Casas-Ramírez, Martha-Selene
Universidad Autónoma de Nuevo León, Mexico,
martha.casasrm@uanl.edu.mx ..........................................25
Cavola, Manuel
University of Naples Federico II, Italy, manuelcavola@live.com .........23
Corberán, Ángel
Universitat de València, Spain, angel.corberan@uv.es ..............17,51
D
De-Los-Santos, Alicia
Universidad de Córdoba, Spain, aliciasantos@uco.es ..................31
Dias, Joana
University of Coimbra, Portugal, joana@fe.uc.pt .....................33
Diglio, Antonio
University of Naples Federico II, Italy, manuelcavola@live.com .........23
E
Elizalde Blasco, Javier
Universidad de Navarra, Spain, jelizalde@unav.es ....................35
Erro Garcés, Amaya
Universidad Pública de Navarra, Spain, amaya.erro@unavarra.es ......35
Esteban Pérez, Adrián
Universidad de Valladolid, Spain, adrianesteban@live.com .............37
G
Gómez-Muñoz, Carlos Q.
Universidad de Castilla-La Mancha, Spain, carlosquiterio.gomez@uclm.es
43
Galé, Carmen
Universidad de Zaragoza, Spain, cgale@unizar.es ....................25
Gutierrez-Alcoba, Alejandro
Universidad de Málaga, Spain, agutierrez@ac.uma.es .................39
H
Halvorsen-Weare, Elin E.
AUTHOR INDEX 69
MARINTEK,Norway, elin.halvorsen-weare@marintek.sintef.no ............39
Haugland, Dag
Bergen University, Norway, dag.haugland@uib.no .....................39
Hendrix, Eligius M.T.
Universidad de Málaga, Spain, eligius@uma.es .......................39
K
Kalcsics, Jörg
University of Edinburgh, Scotland, joerg.kalcsics@ed.ac.uk ............19
L
López-de-los-Mozos, M. Cruz
Universidad de Sevilla, Spain, mclopez@us.es .......................43
Laganà, Demetrio
Università della Calabria, Italy, demetrio.lagana@unical.it ...............17
Landete, Mercedes
Universidad Miguel Hernández, Spain, landete@umh.es .............41
Laporte, Gilbert
HEC Montreal, Canada, gilbert.laporte@cirrelt.ca .......................31
M
Marín, Alfredo
Universidad de Murcia, Spain, amarin@um.es ....................45,47
Martínez-Merino, Luisa I.
Universidad de Cádiz, Spain, luisa.martinez@uca.es ...................47
Martí, Rafael
Universitat de València, Spain, rafael.marti@uv.es .....................51
Menezes, Mozart B.C.
KEDGE Business School, France, Mozart.Menezes@kedgebs.com . 49, 53, 63
Mesa, Juan A.
Universidad de Sevilla, Spain, jmesa@us.es ......................31,43
Meyer, Anne
Research Center for Information Technology (FZI), Germany,
meyer@fzi.de .........................................................19
N
Nickel, Stefan
Karlsruhe Institute of Technology (KIT), Germany,
stefan.nickel@kit.edu ..................................................19
Nuñez, Fernando
Universidad de Sevilla, Spain, fnunuezh@us.es .......................27
70 AUTHOR INDEX
O
Ortega, Francisco A.
Universidad de Sevilla, Spain, riejos@us.es ..........................15
Ortega, Gloria
Universidad de Almería, Spain, gloriaortega@ual.es .................. 39
P
Peiró, Juanjo
Universitat de València, Spain, juanjo.peiro@uv.es .....................51
Piccolo, Carmela
University of Naples Federico II, Italy, carmela.piccolo@unina.it ........23
Pinar-Pérez, Jesús María
University College for Financial Studies, Spain,
jesusmaria.pinar@cunef.edu ............................................53
Ponce, Diego
Universidad de Sevilla, Spain, dponce@us.es ........................55
Pouls, Martin
Research Center for Information Technology (FZI), Germany,
pouls@fzi.de .........................................................19
Pozo, Miguel A.
Universidad de Cádiz, Spain, miguelpozo@us.es ......................57
Puerto, Justo
Universidad de Sevilla, Spain, puerto@us.es ...............21,55,57,59
R
Ricca, Federica
Sapienza Universitá di Roma, Italy, federica.ricca@uniroma1.it ..........55
Rodríguez-Chía, Antonio M.
Universidad de Cádiz, Spain, antonio.rodriguezchia@uca.es . . . . . . 21, 47, 57
Rodríguez-Martín, Inmaculada
Universidad de La Laguna, Spain, irguez@ull.es .....................61
Rodríguez-Calo, J. Francisco
Repsol S.A., Spain, jfrodriguezc@repsol.com ............................65
Ruiz-Hernández, Diego
University College for Financial Studies, Spain,
d.ruiz@cunef.edu .......................................35,43,49,53,63
S
Sáez-Aguado, Jesús
Universidad de Valladolid, Spain, jsaez@eio.uva.es ..................37
Salazar-González, Juan-José
Universidad de La Laguna, Spain, jjsalaza@ull.es ....................61
INDEX 71
Saldanha-da-Gama, Francisco
Universidade de Lisboa, Portugal, fsgama@ciencias.ulisboa.pt . . . . . . 47, 51
Scozzari, Andrea
Universitá degli Studi Niccoló Cusano, Italy,
andrea.scozzari@unicusano.it ...........................................55
Sierra-Paradinas, María
Universidad Rey Juan Carlos, Spain, maria.sierrap@urjc.es ............65
V
Vocaturo, Francesca
Università della Calabria, Italy, francesca.vocaturo@unical.it ............17
Y
Yaman, Hande
Bilkent University, Turkey, hyaman@bilkent.edu.tr .....................61
Z
Zarzo, Alejandro
Universidad Politécnica de Madrid, Spain, alejandro.zarzo@upm.es . . . . 29
.
