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Elche, Spain
January 31-February 1, 2022
XI International Workshop on
Locational Analysis and Related Problems
Partners and sponsors
Red de Localización y problemas afines
Gobierno de España
Centro de Investigación Operativa (UMH)
Prometeo 2021 (Consellería de Innovación,
Universidades, Ciencia y Sociedad Digital)
Universitat Politècnica de Catalunya
Universidad de las Palmas de Gran Canaria
Matías Henríquez
Monday Jan 31st Tuesday Feb 1st
9:00 Registration
9:30 Opening Session
9:45 Session 1:
Facility Location I
Session 4:
Routing
11:05 Coffee break Coffee break
11:35 Invited Speaker:
Hande Yaman
Invited Speaker:
Juan A. Mesa
12:35 Social Event:
+
Session 5:
Applications II
13:45 Lunch Lunch
15:30 Session 2:
Applications I
Session 6:
Network design
16:30 Coffee break Coffee break
17:00 Session 3:
Multiperiod Problems
Session 7:
Covering Problems
18:00 Network Meeting Social event
21:00 Conference dinner
PROCEEDINGS OF
THE XI INTERNATIONAL WORKSHOP
ON LOCATIONAL ANALYSIS AND
RELATED PROBLEMS (2021)
Edited by
Maria Albareda-Sambola
Marta Baldomero-Naranjo
Juan Manuel Muñoz Ocaña
Jessica Rodríguez Pereira
ISBN: 978-84-123480-6-4
Fotografía de cubierta: Matías Henríquez
Elche, 2022
Preface
The International Workshop on Locational Analysis and Related Problems
will take place during January 31–February 1, 2022 in Elche (Spain). It is
organized by the Spanish Location Network and the Location Group GE-
LOCA from the Spanish Society of Statistics and Operations Research(SEIO).
The Spanish Location Network is a group of more than 140 researchers
from several Spanish universities organized into 7 thematic groups. The
Network has been funded by the Spanish Government since 2003. This
edition of the conference is organized in collaboration with project PROM-
ETEO/2021/063 funded by the Valencian government.
One of the main activities of the Network is a yearly meeting aimed at
promoting the communication among its members and between them and
other researchers, and to contribute to the development of the location field
and related problems. The last meetings have taken place in Sevilla (Jan-
uary 23–24, 2020), Cádiz (January 20–February 1, 2019), Segovia (Septem-
ber 27–29, 2017), 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. This in-
cludes location models, networks, transportation, logistics, exact and heuris-
tic solution methods, and computational geometry, among others.
The organizing committee.
vi Preface
Scientific committee:
Maria Albareda Sambola (Universitat Politécnica de Cataluña, Spain)
Giuseppe Bruno (Università degli Studi di Napoli Federico II, Italy)
Sergio García (University of Edinburgh, United Kingdom)
Jörg Kalcsics (University of Edinburgh, United Kingdom)
Alfredo Marín (Universidad de Murcia, Spain)
Blas Pelegrín (Universidad de Murcia, Spain)
Justo Puerto (Universidad de Sevilla, Spain)
Antonio M. Rodríguez-Chía (Universidad de Cádiz, Spain)
Francisco Saldanha da Gama (Universidade de Lisboa, Portugal)
Organizing committee:
Maria Albareda Sambola (Universitat Politècnica de Catalunya)
Javier Alcaraz Soria (Universidad Miguel Hernández)
Laura Antón Sánchez (Universidad Miguel Hernández)
Marta Baldomero Naranjo (Universidad de Cádiz)
Mercedes Landete Ruiz (Universidad Miguel Hernández)
Marina Leal Palazón (Universidad Miguel Hernández)
Juan Francisco Monge Ivars (Universidad Miguel Hernández)
Alejandro Moya Martínez (Universidad Miguel Hernández)
Juan Manuel Muñoz Ocaña (Universidad de Cádiz)
Jessica Rodríguez Pereira (Universitat Pompeu Fabra)
Dolores Rosa Santos Peñate (Universidad de Las Palmas de Gran Ca-
naria)
José Luis Sainz-Pardo Auñón (Universidad Miguel Hernández)
Contents
Preface v
Program 1
Invited Speakers 7
Robust Alternative Fuel Refueling Station Location Problem with
Routing under Decision-Dependent Flow Uncertainty 9
Ö. Mahmutogullari, H. Yaman
Pair-demand Covering Facility Location and Network Design Prob-
lems 11
J.A. Mesa
Abstracts 15
Upgrading Strategies in the p-Center Location Problem 17
L. Anton-Sanchez, M. Landete, F. Saldanha-da-Gama
On the complexity of the upgrading version of the Maximal Cov-
ering Location Problem 19
M. Baldomero-Naranjo, J. Kalcsics, A. M. Rodríguez-Chía
Fairness in Maximal Covering Facility Location Problems 21
V. Blanco, R. Gázquez
Location, Regions and Preferences 23
V. Blanco, R. Gázquez, M. Leal
Hybridizing discrete and continuous maximal covering location
problems 25
vii
viii CONTENTS
V. Blanco, R. Gázquez, F. Saldanha-da-Gama
A locational analysis perspective of deregulation policies in the
pharmaceutical sector 27
G. Bruno, M. Cavola, A. Diglio, J. Elizalde, C. Piccolo
The dicrete ordered median problem for clustering STEM-image
intensities 29
J.J Calvino, M. López-Haro, J.M. Muñoz-Ocaña, A.M. Rodríguez-Chía
An Iterated Greedy Matheuristic for Solving the Stochastic Rail-
way Network Construction Scheduling Problem 31
D. Canca, G. Laporte
Profit-maximizing hub network design under hub congestion and
time-sensitive demands 33
C.A. Domínguez, E. Fernández, A. Lüer-Villagra
A new heuristic for the Driver and Vehicle Routing Problem 35
B. Domínguez-Martín, I. Rodríguez-Martín, J.J. Salazar-González
Multistage multiscale facility location and expansion under un-
certainty 37
L.F. Escudero, J.F. Monge
A column-and-row generation algorithm for allocating airport
slots 39
P. Fermín Cueto, S. García, M. F. Anjos
How to invest to expand a firm: a new model and resolution
methods 41
J. Fernández, B.G.-Tóth, L. Anton-Sanchez
An exact method for the two-stage multi-period vehicle routing
problem with depot location 43
I. Gjeroska, S. García
Formulations for the Capacitated Dispersion Problem 45
M. Landete, J. Peiró, H. Yaman
Capacitated Close Enough Facility Location 47
A. Moya-Martínez, M. Landete, J.F. Monge, S. García
CONTENTS ix
Emergency Vehicles Location: the importance of including the
dispatching problem 49
J. Nelas, J. Dias
Selective collection routes of urban solid waste by means of multi-
compartment vehicles 51
R. Piedra-de-la-Cuadra, J.A. Mesa, F. A. Ortega, G. Marseglia
Multi-Depot VRP with Vehicle Interchanges: Heuristic solution 53
V. Rebillas-Loredo, M. Albareda-Sambola, J.A. Díaz, D.E. Luna-Reyes
Optimizing COVID-19 Test and Vaccine distributions 55
J.L. Sainz-Pardo, J. Valero
Locating a rectangle in the sky to get the best observation 59
J.J. Salazar-González
Multiple Allocation P-Hub Location Problem explicitly consid-
ering Users’ preferences 61
N. Zerega, A. Lüer-Villagra
PROGRAM
Monday January 31st
09:00-09:30 Registration
09:30-09:45 Opening Session
09:45-11:05 Session 1: Facility Location
Upgrading Strategies in the p-Center Location Problem
L. Anton-Sanchez, M. Landete, F. Saldanha-da-Gama
Capacitated Close Enough Facility Location
A. Moya-Martínez, M. Landete, J.F. Monge, S. García
Location, Regions and Preferences
V. Blanco, R. Gázquez, M. Leal
Formulations for the Capacitated Dispersion Problem
M. Landete, J. Peiró, H. Yaman
11:05-11:35 Coffee break
11:35-12:35 Invited Speaker: Hande Yaman
Robust Alternative Fuel Refueling Station Location Problem with Rout-
ing under Decision-Dependent Flow Uncertainty
12:35-15:30 Social Event and Lunch
15:30-16:30 Session 2: Applications I
Emergency Vehicles Location: the importance of including the dis-
patching problem.
J. Nelas, J. Dias
Optimizing COVID-19 Test and Vaccine distributions
J.L. Sainz-Pardo, J. Valero
Locating a rectangle in the sky to get the best observation
J.J. Salazar-González
4
16:30-17:00 Coffee break
17:00-18:00 Session 3: Multiperiod Problems
An exact method for the two-stage multiperiod vehicle routing prob-
lem with depot location
I. Gjeroska, S. García
Multistage multiscale facility location and expansion under uncer-
tainty
L.F. Escudero, J.F. Monge
How to invest to expand a firm: a new model and resolution methods
J. Fernández, B.G.-Tóth, L. Anton-Sanchez
18:00 Network meeting
5
Tuesday February 1st
09:45-11:05 Session 4: Routing
Selective collection routes of urban solid waste by means of multi-
compartment vehicles
R. Piedra-de-la-Cuadra, J.A. Mesa, F. A. Ortega, G. Marseglia
Multi-Depot VRP with Vehicle Interchanges: Heuristic solution
V. Rebillas-Loredo, M. Albareda Sambola, J.A. Díaz, D.E. luna
A new heuristic for the Driver and Vehicle Routing Problem
B. Domínguez-Martín, I. Rodríguez-Martín, J.J. Salazar-González
11:05-11:35 Coffee break
11:35-12:35 Invited Speaker: Juan A. Mesa
Pair-demand Covering Facility Location and Network Design Prob-
lems
12:35-13:35 Session 5: Applications II
A column-and-row generation algorithm for allocating airport slots
P. Fermín Cueto, S. García, M. F. Anjos
A locational analysis perspective of deregulation policies in the phar-
maceutical sector
G. Bruno, M. Cavola, A. Diglio, J. Elizalde, C. Piccolo
The discrete ordered median problem for clustering STEM-image in-
tensities
J.J Calvino, M. López-Haro, J.M. Muñoz-Ocaña, A.M. Rodríguez-Chía
13:45-15:30 Lunch
15:30-16:30 Session 6: Netwok Design
An Iterated Greedy Matheuristic for Solving the Stochastic Railway
Network Construction Scheduling Problem
D. Canca, G. Laporte
6
Multiple Allocation P-Hub Location Problem explicitly considering
Users’ preferences
N. Zerega, A. Lüer-Villagra
Profit-maximizing hub network design under hub congestion and
time-sensitive demands
C.A. Domínguez, E. Fernández, A. Lüer-Villagra
16:30-17:00 Coffee break
17:00-18:00 Session 7: Covering Problems
On the complexity of the upgrading version of the Maximal Covering
Location Problem
M. Baldomero-Naranjo, J. Kalcsics, A. M. Rodríguez-Chía
Fairness in Maximal Covering Facility Location Problems
V. Blanco, R. Gázquez
Hybridizing discrete and continuous maximal covering location prob-
lems
V. Blanco, R. Gázquez, F. Saldanha-da-Gama
18:00 Social Event
21:00 Conference dinner
INVITED SPEAKERS
XI Workshop on Locational Analysis and Related Problems 2022 9
Robust Alternative Fuel Refueling Station
Location Problem with Routing under
Decision-Dependent Flow Uncertainty∗
Özlem Mahmuto˘gulları1and Hande Yaman2
1ORSTAT, FEB, KU Leuven, 3000 Leuven, Belgium ozlem.mahmutoullar@kuleuven.be
2ORSTAT, FEB, KU Leuven, 3000 Leuven, Belgium hande.yaman@kuleuven.be
1. Introduction
Transportation is heavily dependent on fossil fuels, especially petroleum-
based products. Using alternative fuel vehicles is a solution to break the
transportation sector’s reliance on consuming fossil fuels. The lack of al-
ternative fuel station (AFS) infrastructure and the rather limited range of
alternative fuel vehicles (AFVs) are two significant obstacles that are slow-
ing down the introduction of AFVs. In this regard, the refueling station
location problem (RSLP) has recently started to be studied in the litera-
ture. In the RSLP, the AFSs are located on the drivers’ predetermined paths.
Since the drivers may sometimes tolerate deviating from their paths to re-
fuel their vehicles, the RSLP with routing (RSLP-R) extends the RSLP and
determines the locations of stations and routes of drivers simultaneously.
It is likely to observe uncertainties in the flows because the rollout of
AFVs and the development of the AFS network are still at their initial
stages. Moreover, the statistical data shows that the number of AFSs has a
significant impact on the number of AFVs. It is thus important to consider
that the availability of AFSs in the neighborhood affects the proliferation
of AFVs during the development of infrastructure. Hence, we incorporate
robustness and decision-dependency into the RSLP-R.
∗Research supported the KU Leuven grant 3H180528
10
2. Problem and Solution Methods
The RSLP-R is defined on a road network and aims to maximize the to-
tal amount of AFV flows that can be refueled by locating a predetermined
number of AFSs on the network by considering the willingness of drivers
to deviate from their shortest paths to refuel their vehicles as well as the
limited range of the vehicles. We use the deterministic problem introduced
by [1] and introduce our flow uncertainty set using the hybrid model (
[2]). The hybrid model comprises a hose model and an interval model. We
define the hybrid uncertainty set of the vehicle flows under the impact of
station location decisions. We suppose that, when a new station is opened,
vehicle flows in the neighborhood increase. We derive two mathematical
programming formulations. As the problem size grows, we encounter dif-
ficulties in solving these models, and thus we propose a Benders reformu-
lation. We solve this formulation using a branch-and-cut algorithm. The
separation, which is exact and polynomial, is done by inspection.
3. Computational Results
We use four different sized data sets to perform our computational experi-
ments. The first one is a commonly used data set in the RSLP literature. We
generated the other data sets based on the road network of Belgium. We
perform the following computational experiments: We first compare the
performances of the proposed solution methods. We observe that the Ben-
ders reformulation outperforms the other formulations. Then, we investi-
gate the changes in station locations and total covered flows when the opti-
mal solutions of the deterministic, robust (without decision-dependency),
and decision-dependent robust problems are employed. We also analyze
the changes under different parameter settings. We observe that recogniz-
ing the uncertainty in flows and the decision-dependency of uncertain flow
realizations may lead to significant gains in the total AFV flows covered.
References
[1] Arslan, O., Kara¸san, O. E., Mahjoub, A. R., & Yaman, H. (2019). A branch-and-
cut algorithm for the alternative fuel refueling station location problem with
routing. Transportation Science, 53 (4), 1107–1125.
[2] Meraklı, M., & Yaman, H. (2016). Robust intermodal hub location under poly-
hedral demand uncertainty. Transportation Research Part B: Methodological, 86,
66–85.
XI Workshop on Locational Analysis and Related Problems 2022 11
Pair-demand Covering Facility Location
and Network Design Problems∗
Juan A. Mesa 1
1Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain
jmesa@us.es
Covering along with median and center are three classical branches of Fa-
cility Location Problems. Covering problems have been extended to ex-
tensive facility location, where facilities are too large to be represented as
isolated points, as well as to network design where a (sub)network is to
be selected from an (physical or not) underlying network with the aim of
being used by traffic of goods or people.
Covering problems in graphs have attracted the attention of researchers
since the middle of last century. As far as the author is aware the first pa-
pers on the vertex-covering problem were due to Berge (1957 [1], and Nor-
man and Rabin (1959) [2]. The problem dealt with in these papers was to
find a subset of vertices in a graph with minimum caridinality such that
each edge is incident to at least one vertex.This problem is related with
the set-covering problem is which a family of sets is given and the mini-
mal subfamility which union contains all the element is sought. The deci-
sion versions of both problems were proved to be NP-complete (Karp, 1972
[3]). The vertex-covering problem was formulated as a integer linear pro-
gramming model and solved by using Boolen functions by Hakimi (1965,
[4]). This problem was applied to the location of emergency services by
Toregas et al. (1971, [5]). They assume a vertex is covered by other if it is
within a given coverage distance from the other. When the number of fa-
cilities to be located is fixed then the maximal covering location problem
arise (Church and ReVelle, 1974, [6]) in which problem each vertex has an
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project RED2018-102363-T, Ministerio de Investigación (Spain)/FEDER under grant PID2019-
533 106205GB-I00, and Operational Programme FEDER-Andalucía under grant US-1381656.
12
associated population and the objective is to cover the maximum popula-
tion within a given distance threshold. Since then many variants and ex-
tensions of the vertex-covering and maximal covering problems have been
researched (see Schilling el at., 1993 [7], Farahani et al. 2012 [8], Church and
Murray, 2018 [9] and García and Marín, 2019 [10] for a review on models,
theoretical results and solving procedures regarding point covering prob-
lems.)
An extensive facility location problem on networks consists of locating
a subbgraph such that optimizes some objective function with some con-
straints regarding demand points (Puerto et al. 2018, [11], Mesa 2018, [12]).
The extensive vertex-covering and maximal covering problems are exten-
sions of the point vertex-covering and maximal covering problems where
the number of vertices of the coverage is substituted by the length or other
characteristic of the covering subgraph.
All the previously reviewed research considers origin-facility or facility-
destination systems, where the demand is satisfied by accessing the point
or the extensive facilities. However, in many cases to reach or be closed the
facility is not enough for completing the service. In many telecommuni-
cation, transportation, public services and other systems the demand uses
the facility as an intermediate instead of a final destination. In these cases
the demand is given by pairs instead of single points, and usually each pair
has an associated weight indicating the traffic between the origin and the
destination. This is for example the case of public transportation networks,
where a customer have to spend a time to reach the stop/station from its
origin, then wait for the next service, spend an in-vehicle time, and finally
reach its destination. When planning a new network, often there exists a
network already functioning and offering its service to the same origin-
destination pairs. For example, in order to improve the mobility of a big
city or metropolitan area, a new rapid transit system is planned. The cur-
rect transit system could be more dense than the rapid transit planned but
is slower since uses the same right-of-way than the private traffic. Thus, in
some way both systems compete between then and both compete with the
private mode of transportation. In a recent paper [13] Benders decomposi-
tion is applied to the Maximal Covering Network Design and the Partial
Covering Network Design problems.
A review of origin-facility-destination demand Network Design prob-
lems is included in the paper by Contreras and Fernández, 2015 [14], in
which mathematical programming models for Location-Network Design
problems are formulated. Within this framework, Hub Location and Net-
work Design problems have been intensively researched. Integer program-
ming formulations for the Hub Set Covering Location and the Hub Max-
Pair-demand Covering and Network Design 13
imal Covering problems were provided in the paper by Campbell, 1995
[15]. For more details on Hub Location problems we refer the reader to the
chapter (2019), [16].
Most of the research on origin-facility-destination covering problems
adopts a discrete formulations. However, some applications have a con-
tinuous nature, either because the facilities can be located on edges of a
given network or because the space for locating the networks is a continu-
ous one. In these cases a continuous formulation better fits to the problem.
Nevertheless, the research on continuous pair covering Location and Net-
work Design is scarce. An example of these problems can be found in the
papers by López-de-los-Mozos et al. 2017 [17], and López-de-los-Mozos
and Mesa [18], in which new transfer points in a network are located for
satisfying the pair demand. A review on the location of dimensional facili-
ties in continuous spaces can be found in Schoebel, 2019 [19].
Therefore, when the demand is given by pairs of points instead of sin-
gle points, new covering Location and Network Design problem arise. In
this tallk, we will revise some problems that have been already researched
and their solving approaches, propose a classification and a framework for
these problems, and suggest some lacks in the state-of-the-art.
References
[1] Berge, C., (1957). Two theorems in Graph Theory. Proc. Natl. Acad. Sci. U.S.A,
43(9), 842–844.
[2] Norman, Z., & Rabin, M.O., (1959). An algorithm for a minimum cover of a
graph. Proc. Amer. Math. Soc. 10, 315–319.
[3] Karp, R.M., (1971). Reducibility among combinatorial problems. Complexity of
Computer Computations (Miller, R.e., Tatcher, J.W., Bohlinger, J.D., eds.) 85–103,
Plenum, New York.
[4] Hakimi, L., (1965). Optimum distribution of switching centers in a communica-
tion network and some related graph theoretic problems. Operations Research,
13, 462–475.
[5] Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emer-
gency service facilities. Operations Research, 19, 1363–1373.
[6] Church, R., & ReVelle, C. (1974). The maximal covering location problem. Pa-
pers of the Regional Sciene Association, 32, 101–118.
[7] Schilling, D.A., Jayamaran, V., & Barhi, R., (1993). A review of covering prob-
lems in facility location. Location Science, 1, 25–55.
[8] Farahani, R.Z., Asgari, N., Heidari, N., Hosseininia, M., & Goh, M. (2012). Cov-
ering problem in facility location: a review. Computers and Industrial Engineer-
ing, 62, 368–407.
14
[9] Church, R., & Murray, A., (2018). Location Covering Models, Springer.
[10] García, S., & Marín, A. (2019). Covering location problems. Chapter 5, in Loca-
tion Science (Nickel, S. Laporte, G., Saldanha da Gama, eds.), Springer.
[11] Puerto, J., Ricca, F., & Scozzari, A., (2018). Extensive facility location problems
on networks: an updated review. TOP, 26, 187–226.
[12] Mesa, J.A., (2018). Comments on Extensive facility location problems on net-
works. an updated review. TOP, 26, 227–228.
[13] Bucarey, V., Fortz, B., González-Blanco, N., Labbé, M., & Mesa J.A. (2022). Ben-
ders decomposition for network design covering problems. Computers and Op-
erations Research, 137, article 105417.
[14] Contreras, I., & Fernández, E., (2012). General network design :a unified view
of combined location and network design problems. European Journal of Opera-
tional Research, 219, 680–697.
[15] Campbell, J.F., (1994). Integer formulations of discrete hub location problems.
European Journal of Operational Research, 72, 387–405.
[16] Contreras, I., & O’kelly, M., (2019). Hub location problems. Chapter 12, in Lo-
cation Science (Nickel, S. Laporte, G., Saldanha da Gama, eds.), Springer.
[17] López-de-los-Mozos, M.C., Mesa, J.A., & Schoebel, A., (2017). A general ap-
proach for the location of transfer points on a network with a trip-covering
criterion and mixed distances. European Journal of Operational Research, 260, 108–
121.
[18] López-de-los-Mozos, M.C., & Mesa, J.A. (2022). To stop or not to stop: a time-
constrained trip covering location problem on a tree network. Annals of Opera-
tions Research, https://doi.org/10.1007/s10479-021-03981-w.
[19] Schoebel, A. (2019). Locating dimensional facilities in a continuous space.
Chapter 7, in Location Science (Nickel, S. Laporte, G., Saldanha da Gama, eds.),
Springer.
ABSTRACTS
XI Workshop on Locational Analysis and Related Problems 2022 17
Upgrading Strategies in the
p-Center Location Problem ∗
Laura Anton-Sanchez,1Mercedes Landete,1and Francisco Saldanha-
da-Gama2
1Departamento de Estadística, Matemáticas e Informática, Centro de Investigación Opera-
tiva, Universidad Miguel Hernández, Spain, l.anton@umh.es landete@umh.es
2Departamento de Estatística e Investigação Operacional, Centro de Matemática, Apli-
cações Fundamentais e Investigação Operacional, Faculdade de Ciências, Universidade de
Lisboa, Portugal, fsgama@ciencias.ulisboa.pt
1. Introduction
Given a set of nodes in a metric space, the p-center problem consists of
determining at most ppoints in such a way that the maximum distance
between the given nodes and the closest centers is minimized [2].
The p-center problem and its variants have many applications among
which we can point out those in Telecommunications, Logistics, Emer-
gency facility location, etc. To the best of the authors’ knowledge, the lit-
erature on the p-center problems assumes that the costs (distances, travel
times, etc) are known beforehand and do not change. Nevertheless, in prac-
tice, one may ask whether a better solution can be achieved by somehow
compressing/reducing the allocation costs thus obtaining the so-called up-
graded solutions. In this work we investigate different upgrading strate-
gies in the context of the p-center problem.
∗This work was partially supported by the grants PID2019-105952GB-I00/ AEI /10.13039/
501100011033 and PGC2018-099428-B-100 by the Spanish Ministry of Science and Innova-
tion, PROMETEO/2021/063 by the governments of Spain and the Valencian Community, and
UIDB/04561/2020 by National Funding from FCT — Fundação para a Ciência e Tecnologia,
Portugal.
18
2. Upgrading connections and facilities
We focus on the so-called unweighted vertex-restricted p-center problem. We
consider the possibility of upgrading a set of connections to different facil-
ities, as well as the possibility of upgrading entire facilities, i.e., upgrading
all connections to an open facility. Further, we consider two perspectives
when it comes to upgrading decisions (connections or facilities): (i) a limit
is imposed on the number of connections or facilities that can be upgraded;
(ii) a budget exists that limits the upgrades that can be made. For other up-
grading versions of location problems, see e.g. [1,5].
We introduce different MILP models for the different upgrading strate-
gies. Our models are based on those previously proposed by [3] and [4].
Furthermore, we derive lower and upper bounds for the new models. We
show that a significant decrease in the optimal covering cost can be at-
tained by upgrading connections or facilities. Therefore, the information
provided by the new models can be extremely useful to a decision-maker
because together with the location decision, the models directly seek to
find structures underlying the problem that can be ”upgraded” in such a
way that a better after-upgrading solution is obtained. Moreover, the re-
search done in this work indicate different directions for future work in
the topic.
References
[1] Blanco, V., & Marín, A. (2019). Upgrading nodes in tree-shaped hub location.
Computers & Operations Research, 102:75–90.
[2] Calik, H., Labbé, M., & Yaman, H. (2019). p-Center Problems. In Gilbert La-
porte, Stefan Nickel, and Francisco Saldanha da Gama, editors, Location Science,
pages 51–65. Springer, International Publishing, second edition.
[3] Calik, H., & Tansel, B.C. (2013). Double bound method for solving the p-center
location problem. Computers & Operations Research, 40:2991–2999.
[4] Daskin, M.S. (2013). Network and Discrete Location: Models, Algorithms, and Ap-
plications. John Wiley & Sons, Ltd, second edition.
[5] Sepasian, A.R. (2018). Upgrading the 1-center problem with edge length vari-
ables on a tree. Discrete Optimization, 29:1–17.
XI Workshop on Locational Analysis and Related Problems 2022 19
On the complexity of the upgrading version
of the Maximal Covering Location Problem∗
Marta Baldomero-Naranjo,1Jörg Kalcsics,2and Antonio M. Rodríguez-
Chía1
1Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Spain,
marta.baldomero@uca.es antonio.rodriguezchia@uca.es
2School of Mathematics, University of Edinburgh, UK, joerg.kalcsics@ed.ac.uk
We study the upgrading version of the maximal covering location prob-
lem with edge length modifications on networks (Up-MCLP). The Up-
MCLP aims at locating pfacilities to maximize the coverage taking into
account that the length of the edges can be reduced subject to a budget
constraint. Therefore, we look for both solutions: the optimal location of p
facilities and the optimal upgraded network. Note that for each edge, we
are given its current length, an upper bound on the maximal reduction of
its length, and a cost per unit of reduction (which can be different for each
edge). Furthermore, a total budget for reductions is given.
In this talk, we focus on the complexity of this problem. Since it is a par-
ticular case of the Maximal Covering Location Problem, the Up-MCLP is
NP-hard on general graphs. We analyze different types of graphs (paths,
trees, stars, etc.) and study the complexity of the single-facility and the
multi-facility version of the problem under different assumptions on the
model parameters. We prove that this problem can be solved in polyno-
mial time and pseudo-polynomial time in some particular cases. We derive
algorithms for solving them. Moreover, we show several particular cases
in which the problem is NP-hard.
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project RED2018-102363-T
XI Workshop on Locational Analysis and Related Problems 2022 21
Fairness in Maximal Covering Facility
Location Problems
Víctor Blanco,1and Ricardo Gázquez1
1Institute of Mathematics (IMAG), Universidad de Granada, Granada, Spain, vblanco@ugr.es
rgazquez@ugr.es
According to the Cambridge Dictionary the term fairness is defined as
“the quality of treating people equally or in a way that is right or rea-
sonable”. It is an abstract but widely studied concept in Decision Sciences
in which some type of indivisible resources are to be shared among dif-
ferent agents. Fair solutions should imply impartiality, justice and equity
allocation patterns, which are usually quantified by means of inequality
measures that are usually minimized. The importance of fairness issues in
resource allocation problems has been recognized and well studied in a
variety of settings with tons of applications in different fields.
The covering location problem is a core problem in Location Science
(see [3]). Here, we focus in Maximal Covering Location Problem (MCLP) in
which it is assumed the existence of a budget for opening facilities and the
goal is to accommodate it to satisfy as much demand of the users as possi-
ble. This problem has attracted the attention of many researchers since its
introduction by Church and ReVelle [2], both because its practical interest
in different disciplines (see [4]) and the mathematical challenges it poses.
The efficiency measure used in the MCLP is the overall covered demand,
that is, as much covered demand the better. However, when one looks at
the individual utilities of each of the constructed facilities, one may ob-
tain solutions with highly saturated facilities in contrast to others that only
cover a small amount of demand, which results in an unfair system from
the facilities’ perspective.
In this paper we provide a general mathematical programming based
framework to incorporate fairness measures from the facilities’ perspective
to Discrete and Continuous MCLPs. In a fairly ideal solution, one would
desire to “independently” maximize the covered demand of each of the
services, not affecting negatively to the coverage of the others. However,
22
since the demands are usually indivisible, in most cases, an advantageous
solution for one service harms others. As already happens in other decision
problems, one may prefer to slightly sacrifice the overall covered demand
in order to equalize the different covered demands among the open ser-
vices. This might be the case of the location of public schools, in which it is
preferable to find an homogeneous distribution of kids among the schools,
or the location of routers with high capacities, where a “good” location for
them would be the one in which the performance of all the routers can
be better used instead of saturating some and leaving others more free.
We incorporate fairness criteria into covering location models by means
of two powerful tools: (1) the Ordered Weighted Averaging (OWA) aggre-
gation operators of the covered demands of each service (introduced by
Yager [5]), and (2) the α-fairness scheme that, depending on the value of
the parameter α, may represent classic measures of fairness (introduced by
Atkinson [1]).
References
[1] Atkinson, A.B. (1970). On the measurement of inequality. Journal of Economic
Theory, 2(3), 244–263.
[2] Church, R., & ReVelle, C. (1974). The maximal covering location problem. Pa-
pers of the regional science association, 32(1), 101–118.
[3] García-Quiles, S., & Marín, A. (2020). Covering location problems. In Location
Science (pp. 99–119). Springer.
[4] Wei, R., & Murray, A.T. (2015). Continuous space maximal coverage: Insights,
advances and challenges. Computers & Operations Research, 62, 325–336.
[5] Yager, R.R. (1988). On ordered weighted averaging aggregation operators in
multicriteria decisionmaking. IEEE Transactions on systems, Man, and Cybernet-
ics, 18(1), 183– 190.
XI Workshop on Locational Analysis and Related Problems 2022 23
Location, Regions and Preferences ∗
Víctor Blanco,1Ricardo Gázquez,1and Marina Leal2
1Institute of Mathematics, Universidad de Granada
2Operational Research Center (CIO), Universidad Miguel Hernández
Customer preferences when purchasing goods and services have been
widely analyzed by Utility Theory in Economics. This theory makes the
decisions about the best ways of satisfying customer’s demands easier for
the companies [1, 6]. In this work, we analyze the incorporation of pref-
erence measures to the continuous facility location problem with regional
demands.
In continuous location problems with regional demands, it has been an-
alyzed the minimization of the expected distance from the new facility to
the demand region [2], the expected demand [7] or the maximum distance
between the new facility and the region [4, 5] among others. To the best
of our knowledge, there has not been attempt to incorporate user’s prefer-
ences in these type of location problems.
We propose a framework to deal with the incorporation of customer’s
preferences in continuous location problems with demand regions. We as-
sume that each user is served in a spatial region and that a preference func-
tion is given over each region. The service points of the demand regions
are served from a new central facility. The goal is to determine the locations
of the service points in each demand region and the location of the new
central facility at minimum transportation cost and reaching certain pref-
erence level of the customers. We consider different preference functions
(see Figure 1 for an example with linear preferences functions). An appli-
cation of the proposed model can be found, for instance, in the location
design of central storehouses and containers of e-commerce companies.
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project PID2020-114594GB-C21, also by project Junta de Andalucía P18-FR-1422 and Project
I+D+i FEDER Andalucía US-1256951
24
Figure 1. Illustration of a Continuous Location Problem with Demand Regions
and Linear Preference Funtions (the star represents the central facility and the tri-
angles the service points in each demand region).
References
[1] Berliant, M., & Ten Raa, T. (1988). A foundation of location theory: Consumer
preferences and demand. Journal of Economic Theory, 44(2), 336–353.
[2] Carrizosa, E., Muñoz-Márquez, M., & Puerto, J. (1998). The Weber problem
with regional demand. European Journal of Operational Research, 104(2), 358-365.
[3] Cobb, C.W., & Douglas, P.H. (1928). A Theory of Production" (PDF). American
Economic Review. 18 (Supplement): 139–165.
[4] Dinler, D., Tural, M. K., & Iyigun, C. (2015). Heuristics for a continuous multi-
facility location problem with demand regions. Computers & Operations Re-
search, 62, 237-256.
[5] Jiang, J., & Yuan, X. (2012). A Barzilai-Borwein-based heuristic algorithm for
locating multiple facilities with regional demand. Computational Optimization
and Applications, 51(3), 1275-1295.
[6] Robinson, J. (1932). Economics is a serious subject: the apologia of an economist
to the mathematician, the scientist and the plain man. Cambridge: Heffer and
Son.
[7] Yao, J., & Murray, A. T. (2014). Serving regional demand in facility location.
Papers in Regional Science, 93(3), 643-662.
XI Workshop on Locational Analysis and Related Problems 2022 25
Hybridizing discrete and continuous
maximal covering location problems∗
Víctor Blanco,1Ricardo Gázquez,1and Francisco Saldanha-da-Gama2
1Institute of Mathematics (IMAG), Universidad de Granada, Spain. {vblanco, rgazquez}@ugr.es
2Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Universi-
dade de Lisboa, Portugal. faconceicao@fc.ul.pt
1. Introduction
Among the most popular problems in Location Analysis are those in which
a user can receive a service in case it is located close enough to an open fa-
cility providing it. These problems are usually called Covering Location prob-
lems. In case it is assumed the existence of a budget for opening facilities
and the goal is to accommodate it to satisfy as much demand of the users
as possible, the problems belong to the family of Maximal Covering Loca-
tion Problems (MCLP) that have attracted the attention of many researchers
since its introduction in [2], both because its practical interest in different
disciplines and the mathematical challenges it poses. The interested read-
ers are referred to the surveys in [1] and [3] for further details on covering
location problems.
A feature shared by most of the existing literature focusing the MCLP
concerns the existence of a single type of facility. However, in practice, this
may not be the case. If not by other reasons, the progressive technology
development often calls for older equipment that is still operational to be
used together with more recent one. Another possibility emerges when two
technologies can be looked at as complementing each other. For instance,
when locating equipment for early fire detection in forests, surveillance fa-
cilities requiring human resources operating them may be complemented
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project RED2018-102363-T
26
with equipment such as remotely controlled cameras to ensure a better
coverage of the area of interest. When facilities can be installed in different
phases (e.g. multi-period facility location) the facilities to be located in each
phase can also be looked at as belonging to a different group (that we still
call type) of facilities.
We investigate here the MCLP with multiple facility types. We assume
that the number of facilities of each type to be located is known beforehand
and that each type of facilities is characterized by the shape of their cover-
age areas and the metric space from which they are selected. By consider-
ing a hybrid setting it becomes possible to take advantage from choosing
some services in finite sets of pre-specified preferred locations and then
deciding flexible positions of the servers in the whole space. This setting
can be useful, for instance, in telecommunications networks with a certain
number of the servers being located inside adequately prepared infrastruc-
tures and additional servers being located at any place in the given space.
The goal is of course to capture as much demand as possible no matter the
equipment doing it. The continuous facilities can be looked at as a set of
servers to be located in the future and that must complement the equip-
ment located in a discrete setting.
First, we present a general mathematical programming formulation for
the problem. Afterwards, motivated by some practical settings we inves-
tigate the hybridization of discrete and continuous facility location. We
consider that several types of facilities are to be selected in finite sets of
possibilities (one for each type) whereas the other types of facilities can
be located continuously in the whole space. Finally, we report the results
of an extensive battery of computational experiments performed to assess
the methodological contribution of this work. The data consists of up to
920 demand nodes using real geographical and demographic data.
References
[1] Church, R., & Murray, A. (2018). Location Covering Models. Springer.
[2] Church, R., & ReVelle, C. (1974). The maximal covering location problem. Pa-
pers of the Regional Science Association, 32, 101–118.
[3] Garcia-Quiles, S., & Marín, A. (2019). Covering location problems, in: Laporte,
G., Nickel, S., Saldanha-da-Gama, F. (Eds.), Location Science. Springer Interna-
tional Publishing, 2nd edition. chapter 5, pp. 93–113.
[4] Hakimi, S. (1965). Optimum distribution of switching centers in a communica-
tion network and some related graph theoretic problems. Operations research,
13, 462–475.
XI Workshop on Locational Analysis and Related Problems 2022 27
A locational analysis perspective of
deregulation policies in the pharmaceutical
sector
Giuseppe Bruno,1Manuel Cavola,1, Antonio Diglio1, Javier Elizalde2
and Carmela Piccolo1
1Università degli Studi di Napoli Federico II, Department of Industrial Engineering (DII),
Piazzale Tecchio, 80 - 80125 Naples, Italy, {giuseppe.bruno, manuel.cavola, antonio.diglio,
carmela.piccolo}@unina.it
2Facultad de Ciencias Económicas y Empresariales, Universidad de Navarra, Campus Uni-
versitario, 31080 Pamplona, Spain, jelizalde@unav.es
The retail pharmaceutical sector has been characterized in the last decades
by profound deregulation policies, aiming at fostering the entry process of
new competitors in the market to improve users’ access and quality of ser-
vices. Extending a previous study by the authors ([1]), the present work ex-
plores the effects of such reforms in the Navarre Region (Spain), where the
existing entry restrictions were relaxed in 2000. Using a GIS-based method-
ology and very disaggregated real data, we show that the massive entry of
new pharmacies improved users’ access in urban and rural areas but led to
intense agglomeration of competitors within limited distances, thus failing
to result in a more fair spatial competition.
We then propose solving a mathematical programming model that can
support policy-makers for an ex-ante assessment of the (spatial) effects de-
termined by changing regulatory frameworks. We cast the model as the
facility location problem with threshold requirements introduced by [2],
which is further enhanced in this work with explicit dispersion criteria
among facilities.
Specifically, given the presence of an existing set of already located drug-
stores J, we assume that a decision-maker is interested in regulating the
entry process of new drugstores across a set of potential locations Jn. The
model takes into account different aspects of practical relevance in pharma-
ceutical market regulation. In particular, we assume that at most Fphar-
28
macies can coexist in the market (demographic criterion) and that new en-
trants should locate at least at a distance ¯cfrom another (old or new) com-
petitor (dispersion criteria). The objective is to minimize the distance users
must travel to reach the closest active drugstore, i.e. the average accessibil-
ity distance. Such an objective fosters the location of the highest possible
number of pharmacies, which may be suggested to locate in peripheral
areas with scarce customers. In order to provide an entry incentive, we im-
pose that a minimum number of users is assigned to each new entrant.
In other words, we are granting a minimum market share (MS) to newly
located pharmacies. This way, the model pursues the best users’ accessi-
bility conditions while: (i) protecting - through spatial dispersion criteria -
extant competitors from the threat posed by new entrants; (ii) stimulating
new entries with minimum (guaranteed) quotas of customers.
Results from our computational experiments on the entire Navarre Re-
gion demonstrate that, if adequately oriented at guaranteeing predefined
minimum profitability to new entrants, spatial deregulation policies may
result in win-win scenarios for both users and pharmacies. Indeed, the ob-
tained solutions (almost) perfectly replicate the current accessibility condi-
tions while ensuring more equitable market shares’ distribution.
The present work intends to contribute to the ongoing debate on the
effects of policy reforms in the pharmaceutical sector and, through an in-
depth spatial analysis and a computational experience on a real case study,
it aims at showing the benefit of these analytical tools to inform and im-
prove the practice of decision-making in public services ([3]) or, as per the
case at hand, in regulated markets and sectors of general economic interest.
References
[1] Barbarisi, I., Bruno, G., Diglio, A., Elizalde, J., & Piccolo, C. (2019). A spatial
analysis to evaluate the impact of deregulation policies in the pharmacy sector:
Evidence from the case of Navarre. AHealth Policy, 123 (11), 1108–11156.
[2] Carreras, M., & Serra, D. (1999). On optimal location with threshold require-
ments. On optimal location with threshold requirements, 33 (2), 91-103.
[3] Bruno, G., Cavola, M., Diglio, A., Piccolo, C., & Pipicelli, E. (2021). Strategies to
reduce postal network access points: from demographic to spatial distribution
criteria. Utilities Policy, 69, 101189.
XI Workshop on Locational Analysis and Related Problems 2022 29
The dicrete ordered median problem for
clustering STEM-image intensities ∗
José J. Calvino3, Miguel López-Haro3, Juan M. Muñoz-Ocaña1, Justo
Puerto2and Aantonio M. Rodríguez-Chía 1
1Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Cádiz,
Spain, juanmanuel.munoz@uca.es, antonio.rodriguezchia@uca.es
2IMUS, Universidad de Sevilla, Sevilla, Spain, puerto@us.es
3Departamento de Ciencia de los Materiales e Ingeniería Metalúrgica y Química Inorgánica,
Universidad de Cádiz, Cádiz, Spain miguel.lopezharo@uca.es, jose.calvino@uca.es
Electron tomography is a technique for imaging three-dimensional struc-
tures of materials at nanometer scale. This technique consists on recon-
structing nano-objects thanks to projections provided by a electron micro-
scope from different tilt angles. The Scanning-Transmission Electron Mi-
croscope images obtained are used for identifying the elements that con-
stitute the nano-objects under study. This recognition procedure is known
as segmentation which consists of classifying the image intensities into dif-
ferent clusters.
Classical segmentation models stand out for their ability to provide one
segmentation of the original image very quickly and with low computa-
tional burden [1]. However, they do not usually achieve high quality seg-
mentations with a small number of clusters to classify the different ele-
ments which compose the structures represented in the image.
The main idea behind this work is to apply the ordered median prob-
lem to locate pintensities as the representatives of pdifferent clusters and
allocate every intensity to one cluster representative [2]. The advantage of
using this function is its good adaptability to the different types of particles
to be studied due to the wide range of vector weights that can be cast [3].
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project RED2018-102363-T
30
Moreover, to reduce the computational time needed to solve these prob-
lems, some improvements are introduced for the formulations by taking
advantage of the vector weight structure. These alternative improvements
are based on the idea developed in [4]. Finally, we propose different ways
of analysing the quality of the segmentations provided by our approach
using different choices of the vector weights in some real instances.
References
[1] Gontar, L.C., Ozkaya, D., & Dunin-Borkowski, R.E. (2011). A simple algorithm
for measuring particle size distributions on an uneven background from TEM
images. Ultramicroscopy, 111 (2), 101-106.
[2] Boland, N., Domínguez-Marín, P., Nickel, S., & Puerto, J. (2006). Exact proce-
dures for solving the discrete ordered median problem. Computers & Operations
Research, 33 (11), 3270-3300.
[3] Marín, A., Ponce, D., & Puerto, J. (2020). A fresh view on the Discrete Ordered
Median Problem based on partial monotonicity. European Journal of Operational
Research, 286 (3), 839-848.
[4] Ogryczak, W., & Tamir, A. (2003). Minimizing the sum of the k largest functions
in linear time. Information Processing Letters, 85 (3), 117-122.
XI Workshop on Locational Analysis and Related Problems 2022 31
An Iterated Greedy Matheuristic for Solving
the Stochastic Railway Network Construction
Scheduling Problem
David Canca 1and Gilbert Laporte 2
1Department of Industrial Engineering and Management Sciecnce, School of Engineering,
Av. de los Descubrimientos s/n, 41092, Seville, Spain, dco@us.es
2HEC Montréal, CIRRELT 3000 Chemin de la Côte-Sainte-Catherine, Montréal, QC H3T
2A7, Montréal Canada, gilbert.lapor te@cirrelt.net
We propose an iterated greedy matheuristic for efficiently solving stochas-
tic railway rapid transit transportation network construction scheduling
problems, where both the construction duration of the segments and the
passenger demand rate of increase are considered stochastic. The problem
consists of sequencing the construction of lines of a urban transportation
network with the aim of maximizing the discounted long-term profit . This
problem can be viewed as a resource-constrained project scheduling prob-
lem, where both the budget and the available construction equipment act
as resources. We consider that partial lines can be put into operation, thus
benefiting users with a partial and quick usage of the network infrastruc-
ture. In this situation, both the costs and the revenues dependent on the
schedule. After analyzing some characteristics of the best solutions, we
propose an iterated greedy matheuristic for solving the real-size network
construction scheduling problems. To illustrate our methodology we ap-
ply the algorithm to the construction of the full metro network of the city
of Seville.
References
[1] Canca, D., & Laporte, G. (2022). Solving real-size stochastic railway rapid
transit network construction scheduling problems. Computers & Operations Re-
search, 138, 105600.
XI Workshop on Locational Analysis and Related Problems 2022 33
Profit-maximizing hub network design
under hub congestion and time-sensitive
demands∗
Carmen-Ana Domínguez,1Elena Fernández,1and Armin Lüer-Villagra2
1Department of Statistics and Operational Research, Universidad de Cádiz, Puerto Real,
Spain, carmenana.dominguez@uca.es, elena.fernandez@uca.es
2Department of Engineering Sciences, Universidad Andres Bello, Antonio Varas 880, San-
tiago, Chile, armin.luer@unab.cl
Hub location models are used to design transportation networks for air-
lines, parcel delivery, LTL truck companies, etc. There are previous works
considering congestion, time-sensitive demands, and profit maximization,
but not necessarily at the same time. We formulate and solve a profit-
maximizing hub network design problem considering simultaneously hub
congestion and time-sensitive demands through stepwise functions. The
resulting formulation is very challenging to solve up to optimality, result-
ing in large optimality gaps. We develop variable fixing procedures as well
as some families of valid inequalities. Preliminary results are encouraging.
Introduction
Hub location is an active research area, as shown by the frequent literature
reviews [2,4]. Current topics of interest include extensions of earlier mod-
els like, for instance, incorporating capacity selection and/or congestion
[3, 5, 6], explicitly considering sensitive demands [7], or moving from cost
minimization to profit maximization [1,8].
To the best of our knowledge, no previous studies jointly consider the
above three modeling aspects. Our contribution is to formulate and solve a
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project MINECO MTM2019-105824GB-I00 and RED2018-102363-T, and by the Chilean
FONDECYT through grant 1200706.
34
profit-maximizing hub network design problem that incorporates simulta-
neously hub congestion, time-sensitive demands through step-wise func-
tions, where service paths with one or two stops are allowed.
A stepwise function on transportation times is used to model demand.
Hub congestion is expressed in terms of processing times at the hubs, which
are also modeled as a stepwise function. A profit is obtained from captured
demand, while costs include fixed setup cost for enabling hubs and inter-
hub edges, as well as the usual transportation costs.
We develop a set of conditions to either fix variables or add additional
constraints to the formulation. Families of valid inequalities are also pre-
sented together with their separation procedures. These allow us to im-
prove the LP bound of our formulation, decreasing the computational time
required.
References
[1] Alibeyg, A., Contreras, I., & Fernández, E. (2018). Exact solution of hub net-
work design problems with profits. European Journal of Operational Research, 266,
57–71.
[2] Alumur, S.A., Campbell, J.F., Contreras, I., Kara, B.Y., Marianov, V., & O’Kelly,
M.E. (2021). Perspectives on modeling hub location problems. European Journal
of Operational Research, 291, 1–17.
[3] Alumur, S.A., Nickel, S., Rohrbeck, B., & Saldanha-da-Gama, F. (2018). Model-
ing congestion and service time in hub location problems. Applied Mathematical
Modelling, 55, 13–32.
[4] Contreras, I., & O’Kelly, M.E. (2019). Hub Location Problems. Chapter 12, 311–
344, in Location Science, 2nd. Ed. G. Laporte, S. Nickel, and F. Saldanha da
Gama (Eds.). Springer.
[5] Elhedhli, S., & Wu, H. (2010). A Lagrangean heuristic for hub-and-spoke sys-
tem design with capacity selection and congestion. INFORMS Journal on Com-
puting, 22, 282–296.
[6] Marianov, V., & Serra, D. (2003). Location models for airline hubs behaving as
M/D/c queues. Computers & Operations Research, 30, 7, 983–1003.
[7] O’Kelly, M.E., Luna, H.P.L., de Camargo, R.S., & de Miranda, G. (2015). Hub Lo-
cation Problems with Price Sensitive Demands. Networks and Spatial Economics,
15, 917–945.
[8] Taherkhani, G., & Alumur, S.A. (2019). Profit maximizing hub location prob-
lems. Omega, 86, 1–15.
XI Workshop on Locational Analysis and Related Problems 2022 35
A new heuristic for the Driver and Vehicle
Routing Problem∗
Bencomo Domínguez-Martín,1Inmaculada Rodríguez-Martín,1and
Juan-José Salazar-González1
1Department of Mathematics, Statistics, and Operations Research, University of La La-
guna, Tenerife, Spain, bdomingu@ull.edu.es, jjsalaza@ull.edu.es, irguez@ull.edu.es
The Driver and Vehicle Routing Problem (DVRP) addressed here was in-
troduced by Domínguez-Martín et al. [1] ant it is defined as follows. We
are given two depots, where a given number of vehicles and drivers are
based, and a set of customers. Each customer must be served by a vehi-
cle and a driver. Vehicles start their routes at their base depot and end at
the other depot, while drivers must start and end their routes at their base
depot. The vehicles have to be always led by a driver, and drivers need a
vehicle to move from one location to another, either driving themselves or
traveling as passengers. When there are more than one driver in a vehicle,
any of them can lead the vehicle. The duration of a driver route is the time
between the departure from and the arrival to the depot, and it includes
the time driving and traveling as passenger. Moreover, drivers’ routes can-
not exceed a given time duration. Drivers can switch vehicles only at some
given points known as exchange locations, which are the only customer
locations that can be visited by more than one vehicle. The objective is to
design the routes of the vehicles and the drivers in order to minimize the
total drivers’ routes cost.
We present a new heuristic method for the DVRP that provides high
quality solutions for the instances considered. The first phase of the al-
gorithm creates driver’s routes using a constructive method, and the sec-
ond phase improves those routes through local search. The two phases are
embedded in a multistart loop. Vehicles’ routes can be derived from the
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project PID2019-104928RB-I00
36
drivers’routes to end up with a feasible DVRP solution. This heuristic pro-
vides good solutions for the benchmark instances in the literature, and is
able to cope with instances with up to 1000 nodes.
References
[1] Domínguez-Martín, B., Rodríguez-Martín, I., & Salazar-González, J-J. (2018).
The driver and vehicle routing problem. Computers and Operations Research, 92,
56–64.
XI Workshop on Locational Analysis and Related Problems 2022 37
Multistage multiscale facility location and
expansion under uncertainty ∗
Laureano F. Escudero,1and Juan F. Monge2
1Area of Statistics and Operations Research, Universidad Rey Juan Carlos, URJC, c/Tulipán,
28933 Móstoles (Madrid), Spain, laureano.escudero@urjc.es
2Center of Operations Research, Universidad Miguel Hernández, UMH, Av. de la Univer-
sidad, 03202 Elche (Alicante), Spain, monge@umh.es
This work focuses on the development of a stochastic mixed integer lin-
ear optimization (traditionally, named MILP) modeling framework and a
matheuristic approach for solving the multistage multiscale multiproduct
facility location network expansion planning problem under uncertainty.
Two types of time scaling are considered, namely, a long one and the other
scale whose timing is much shorter. Then, two types of decisions are to
be considered, viz., the strategic and the operational ones. The strategic
decisions are the selection of facility locations in a network as well as the
related initial capacity dimensioning and expansion along a time horizon.
The operational decisions are the raw material supplying, the flow traf-
fic through the available facility network, product manufacturing in some
facilities and its distribution for demand satisfaction in some other avail-
able facilities at the minimum cost. Two types of uncertain parameters are
also considered, namely, strategic and operational ones. It is assumed that
the strategic uncertainty is stagewise-dependent, being captured by a finite
set of scenarios that are represented in Hamiltonian paths from the first
stage to the last one along the nodes in a multistage scenario tree. The op-
erational uncertainty is stage-dependent, being captured by another type
of a finite set of scenarios; the modeling scheme considers a set of two-
stage trees, each one rooted at a node in the strategic multistage scenario
tree. The goal is to minimize the expected total cost in the scenarios. Some
∗Research partially supported by the Spanish Ministry of Science and Innovation through
projects PID2019-105952GB-I00 and RTI2018-094269-B-I00
38
strategic variables are binary and others are integer; they are the state vari-
ables linking a node with its successor ones. In any case, those variables
are modelled by considering the step variable modeling object approach.
It is tighter than its impulse counterpart one and, on the other hand, it
implies that a node is only linked with its immediate successor ones, a
feature that some decomposition algorithms for problem solving can take
benefit from. By using the special structure of the location problems among
others, the time-consistent risk averse measure Expected Conditional sec-
ond order Stochastic Dominance is considered. Given the intrinsic prob-
lem’s difficulty and the huge instances’ dimensions (due to the network
size of realistic instances as well as the cardinality of the strategic scenario
tree and operational ones), it is unrealistic to seek an optimal solution. The
matheuristic algorithm SFR3 is considered, it stands for Scenario variables
Fixing and constraints and variables’ integrality iteratively Randomizing
Relaxation Reduction. It obtains a (hopefully, good) feasible solution in rea-
sonable time and a lower bound of the optimal solution value to assess the
solution quality. The performance of the overall approach is computation-
ally assessed.
XI Workshop on Locational Analysis and Related Problems 2022 39
A column-and-row generation
algorithm for allocating airport slots
Paula Fermín Cueto,1Sergio García,1and Miguel F. Anjos1
1School of Mathematics, The University of Edinburgh, The King’s Buildings, Edinburgh,
United Kingdom, paula.fermin@ed.ac.uk
Air transport demand often exceeds capacity at congested airports. For this
reason, airlines need to be granted permission to use airport infrastructure.
They must submit a list of regular flights that they wish to operate over a
five to seven-month period and a designated coordinator is responsible for
allocating the available airport slots, which represent the permission to op-
erate a flight at a specific date and time. From an optimisation perspective,
this problem is a special class of Resource Constrained Project Scheduling
Problem (RCPSP) [1] where the objective is to minimise the difference be-
tween the allocated and requested flight times subject to airport capacity
constraints and other operational restrictions.
Most studies on this topic focus on developing fast heuristics and com-
plex models that capture the needs and particularities of various stake-
holders [1, 3, 4]. It has been claimed that exact methods cannot cope with
the size and complexity of real-world problems [5].
In this work we show that it is possible to find optimal solutions for
large instances quickly and with modest memory requirements. We de-
velop a column-and-row generation algorithm that uses the same principle
as the Zebra algorithm for the p-median problem of García et al. [2]. Our al-
gorithm capitalises on two interesting properties of airport slot allocation
problems:
1. We have a good intuition about the optimal solutions, as it is known
that, in real-world instances, the great majority of flights can be allo-
cated to their requested time.
2. Most flights are regular services and airport capacity limits are typi-
cally constant throughout the season. This introduces an element of
40
periodicity in the problem that results in a great number of identical
or dominated capacity constraints.
We show the effectiveness of this algorithm using real-world data pro-
vided by Airport Coordination Limited (ACL) from the most congested
airports in the United Kingdom.
References
[1] Androutsopoulos, K.N., & Madas, M.A. (2019). Being fair or efficient? A
fairness-driven modeling extension to the strategic airport slot scheduling
problem. Transportation Research Part E: Logistics and Transportation Review, 130,
37–60.
[2] García, S., Labbé, M., & Marín, A. (2011). Solving Large p-Median Problems
with a Radius Formulation. INFORMS Journal on Computing, 23, 4, 546–556.
[3] Pellegrini, P., Castelli, L., & Pesenti, R. (2011). Metaheuristic Algorithms for
the Simultaneous Slot Allocation Problem. Intelligent Transport Systems, IET, 6,
546–556.
[4] Ribeiro, N.A., Jacquillat, A., & Antunes, A.P. (2019). A Large-Scale Neighbor-
hood Search Approach to Airport Slot Allocation. Transportation Science, 53, 6,
1772–1797.
[5] Zografos, K.G., Madas, M.A., & Androutsopoulos, K.N., (2016). Increasing air-
port capacity utilisation through optimum slot scheduling: review of current
developments and identification of future needs. Journal of Scheduling, 20, 1,
3–24.
XI Workshop on Locational Analysis and Related Problems 2022 41
How to invest to expand a firm: a new
model and resolution methods∗
José Fernández,1Boglárka G.-Tóth,2and Laura Anton-Sanchez3
1Dpt. Statistics and Operations Research, University of Murcia, Spain, josefdez@um.es
2Dpt. Computational Optimization, University of Szeged, Hungary, boglarka@inf.szte.hu
3Dpt. Statistics, Mathematics and Computer Science, Miguel Hernández University, Spain,
l.anton@umh.es
When locating a new facility in a competitive environment, both the
location and the quality of the facility need to be determined jointly and
carefully in order to maximize the profit obtained by the locating chain.
This fact has been highlighted in [1–3] among other papers.
However, when a chain has to decide how to invest in a given geograph-
ical region, it may also invest part of its budget in modifying the quality
of other existing chain-owned centers (in case they exist) up or down, or
even in closing some of those centers in order to allocate the budget de-
voted to those facilities to other chain-owned facilities or to the new one
(in case the chain finally decides to open it). In this paper, we extend the
single facility location and design problem introduced in [1] to accommo-
date these possibilities as well. The possibility of changing the quality of
the existing chain-owned facilities makes the problem closer to the reality,
but also harder to solve.
A mixed integer nonlinear programming formulation is proposed to
model this new problem. Both an exact interval branch-and-bound method
and an ad-hoc heuristic are proposed to solve the model. Some computa-
tional results are reported which show that both methods are able to solve
this MINLP problem within a reasonable time and with good accuracy. Ac-
cording to the results, small variations in the available budget may produce
very different results.
∗Research supported by Fundación Séneca through project 20817/PI/18
42
References
[1] Fernández, J., Pelegrín, B., Plastria, F., & Tóth. B. (2007). Solving a Huff-like
competitive location and design model for profit maximization in the plane.
European Journal of Operational Research, 179, 3, 1274–1287.
[2] Redondo, J.L., Fernández, J., García, I., & Ortigosa, P.M. (2009). A robust and ef-
ficient global optimization algorithm for planar competitive location problems.
Annals of Operations Research, 167, 1, 87–106.
[3] Tóth, B., Plastria, F., Fernández, J., & B. Pelegrín. (2009). On the impact of
spatial pattern, aggregation, and model parameters in planar Huff-like com-
petitive location and design problems. OR Spectrum, 31, 1, 601–627.
XI Workshop on Locational Analysis and Related Problems 2022 43
An exact method for the two-stage multi-
period vehicle routing problem with depot
location
Ivona Gjeroska,1and Sergio García 2
1School of Mathematics, University of Edinburgh, i.gjeroska@sms.ed.ac.uk
2School of Mathematics, University of Edinburgh, sergio.garcia-quiles@ed.ac.uk
1. Problem description
We introduce a vehicle routing problem (VRP) variation motivated by a
company with a large distribution network in a city in Ecuador. The com-
pany sells a product of negligible size, works with roughly 1600 small re-
tailers (customers), and has two types of “vehicles": sellers and trucks. Each
customer is visited exactly once per week by a seller who takes the order.
On the following working day, the same customer is visited by a truck that
delivers their order. At the start of each day, the sellers meet at a meeting
point that can vary. At the end of their working day they return to the de-
pot. The trucks start and finish their routes at the depot. The goal is to find
the optimal starting point for each working day for the sellers and create
routes for the trucks and sellers that minimise the total travelling cost, such
that the workload is balanced.
2. Contribution
We introduced a multi-period VRP with depot location that consists of two
stages that need to be solved simultaneously and a planning horizon with
multiple periods with the addition of depot location. We provide two dif-
ferent mathematical models that fully describe the problem - one being
a compact formulation with an adjustment to the degree constraints to
44
serve the variation of the starting point, and one that is an adaptation of
the standard capacitated VRP (CVRP). The latter comes in handy when
applying existing algorithms for the CVRP. We introduce a tailor-made
generalisation of the well known 2-matching and comb inequalities that
are valid for this problem. These inequalities were first introduced and
proven to be very efficient for the travelling salesman problem (TSP) [1],
and later adapted for the CVRP [2]. Finally, we separate these inequalities
using an adequate procedure that exploits the graph structure and uses
cut-nodes and blocks as main tools. The idea comes from [3] who first
used block structures to identify handles of violated 2-matching inequali-
ties. We present results generated using a branch-and-cut algorithm, with
and without the addition of the generalised comb inequalities. The test
instances are subsets of the original set of customers provided by the com-
pany, created accounting for the geographical location and distribution of
the original data set, preserving its main properties. For many of the in-
stances the addition of the new valid inequalities proves to be beneficial:
after two hours, it either results in a better solution or in a significantly
lower number of nodes in the branch and bound tree. The latter is useful
for larger instances, as the problem is less likely to run out of memory thus
improving the chances to find a feasible solution.
References
[1] Grötschel, M., & Padberg, M.W. (1979). On the symmetric travelling salesman
problem I: Inequalities. Mathematical Programming, 16, 265–280.
[2] Lysgaard, J., Letchford, A.N., & Eglese, R. (2004). A new branch-and-cut algo-
rithm for the capacitated vehicle routing problem. Mathematical Programming,
(A-100), 423–445.
[3] Padberg, M., & Hong, S. (1980). On the symmetric travelling salesman problem:
a computational study. Mathematical Programming, 12, 78–107.
XI Workshop on Locational Analysis and Related Problems 2022 45
Formulations for the Capacitated Dispersion
Problem∗
Mercedes Landete,1Juanjo Peiró,2and Hande Yaman3
1Universidad Miguel Hernández, Elche, Spain, landete@umh.es
2Universitat de València, Burjassot (València), Spain, juanjo.peiro@uv.es
3KU Leuven, Leuven, Belgium, hande.yaman@kuleuven.be
We study the capacitated dispersion problem (see [1]) in which, given a
set Vof nnodes (facilities), a positive capacity cifor each node i, a nonneg-
ative distance dij between any pair of distinct nodes iand j, and a positive
demand Bto cover, we would like to find a subset V0of nodes such that
the sum of capacities of nodes in this subset is large enough to cover the
demand, i.e., Pi∈V0ci≥Band the nodes in V0are as distant as possible
from one another, i.e., mini,j∈V0:i6=jdij , is maximum.
This problem arises, for instance, when we would like to locate facilities
to cover the demand for a service, and we would like the facilities to be as
distant as possible to decrease the risk of damage from accidents at other
facilities.
In this talk we focus on several mathematical formulations for the prob-
lem in different spaces using variables associated with nodes, edges and
costs. These formulations are then strengthened with families of valid in-
equalities and variable fixing procedures.
Several sets of computational experiments are conducted to illustrate
the usefulness of the findings, as well as the aptness of the formulations
for different types of instances.
∗Research partially supported by the Spanish Ministry of Science and Innovation through
projects PGC2018-099428-B-100 and RED2018-102363-T.
46
References
[1] Rosenkrantz, D., Tayi, G.K., & Ravi, S.S. (2000). Facility dispersion problems
under capacity and cost constraints. Journal of Combinatorial Optimization, 4, 7–
33.
XI Workshop on Locational Analysis and Related Problems 2022 47
Capacitated Close Enough Facility
Location ∗
Alejandro Moya-Martínez,1Mercedes Landete,1Juan Franciso Monge1
and Sergio García 2
1Centro de Investigación Operativa, Universidad Miguel Hernández, Elche, a.moya@umh.es,
landete@umh.es,monge@.umh.es
2School of Mathematics, University of Edinburgh, sergio.garcia-quiles@ed.ac.uk
Nowadays, companies face a continuously inreasing need of deliver-
ing goods. Mathematical programming models, and, in particular, location
models can be used to improve these logistic activities. We find in the liter-
ature, various types of problems, to start with p-median problem to prob-
lems with cooperation between customers. In this paper, we present the
Capacity - Close Enough Facility Location Problem (C-CEFLP). C-CEFLP
is the problem of deciding where to locate pfacilities among the finite set
of candidates, and where to locate tpickup points close enough to cus-
tomers. These pick up points have a limited capacity. Furthermore, it will
be presented how this problem restricted to a graph behaves and a new col-
umn generation algorithm will be presented to solve it. We show that, the
problem when the movements are restricted to a graph is computationally
easier than the case without restrictions on the movements of the clients. A
broad computational experiment is reported, and the performance of the
heuristic approach is computationally assessed.
References
∗This research was funded by the Spanish Ministry of Science and Innovation and the State
Research Agency under grant PID2019-105952GB-I00/AEI/10.13039/ 50110 0 011033, by the
Spanish Ministry of Science and Innovation and the European Regional Development Fund
under grant PGC2018-099428-B-100 and by the Spanish Ministry of Science and Innovation
under the project RED2018-102363-T
48
[1] Moya-Martínez, A., Landete, M., & Monge, J.F. (2021). Close-Enough Facility
Location. Mathematics, 9, 6, 670.
[2] Hernández-Pérez, H., Landete, M., & Rodríguez-Martín, I. (2021). The single-
vehicle two-echelon one-commodity pickup and delivery problem. Computers
&Operations Research, 127, 2, 105152.
[3] Bertsimas, D., & Sim, M. (2003). Robust discrete optimization and network
flows. Mathematical Programming, 96, 1, 49-71.
[4] Calvete, H.L., Domínguez, C., Galé, C., Labbé, M., & Marín, A. (2019). The
rank pricing problem: Models and branch-and-cut algorithms. Computers &
Operations Research, 105, 3, 12-31.
[5] Marín, A., Cánovas, L., & Landete, M. (2006). New formulations for the unca-
pacitated multiple allocation hub location problem. European Journal of Opera-
tional Research, 172, 1, 274-292.
[6] Corberán, A., Landete, M., Peiró, J., & Saldanha-da-Gama, F. (2020). The fa-
cility location problem with capacity transfers. Transportation Research Part E:
Logistics and Transportation Review, 138, 101943.
XI Workshop on Locational Analysis and Related Problems 2022 49
Emergency Vehicles Location:
the importance of including the dispatching
problem∗
José Nelas1,3and Joana Dias1,2
1University of Coimbra, Faculty of Economics, Av. Dias da Silva, 165, 3004-512 Coimbra,
Portugal
2INESC Coimbra, University of Coimbra, Rua Sílvio Lima, Pólo II,3030-290 Coimbra Por-
tugal, joana@fe.uc.pt
3Centro Hospitalar e Universitário de Coimbra - Hospital Pediátrico, R. Dr. Afonso Romão,
3000-602 Coimbra Portugal, eunelas@gmail.com
Proper location of emergency vehicles is crucial to assure that assistance
arrives on time where it is needed. The location of emergency vehicles is a
strategic decision that highly influences the performance of the dispatch-
ing decisions: the choice of the vehicle that should be sent to an emer-
gency episode. Although the dispatching decisions are operational deci-
sions, they should be taken into account when deciding where to locate the
vehicles, since dispatching decisions clearly influence the availability of re-
sources. In this presentation, an emergency vehicle location model that ex-
plicitly considers resource availability by including dispatching decisions
will be presented. Some results considering a real case study will also be
shown.
1. Introduction
The location of emergency vehicles represents an active research area, and
many mathematical models and algorithmic approaches have been devel-
∗This study has been funded by national funds, through FCT, the PortugueseScience Founda-
tion, under project UIDB/00308/2020 and with the collaboration of Coimbra Pediatric Hos-
pital – Coimbra Hospital and University Centre, and INEM.
50
oped, that consider different situations and that rely on different assump-
tions. The model to be presented has some distinguishing features that
close the gap between model representation and the real situation of ve-
hicle emergency management. This model explicitly considers, simultane-
ously, the existence of different vehicle types, capable of assuring different
levels of care, and the possibility of one vehicle being substituted by an-
other vehicle or set of vehicles that are equivalent in terms of the level of
care they can provide. It is assumed that there is a set of potential and pre-
determined locations where the emergency vehicles can be located. The
emergency episodes can occur anywhere within a predefined geographi-
cal area. Moreover, it is also possible to explicitly consider the evolution of
the emergency episode, by assuming that one episode can have different
stages and establishing different resource needs for these different stages
depending on the evolution of the victims’ health conditions. The model
also represents the assumption that it is better to have some assistance ar-
riving, even if it is not the most suitable one, than not having any assistance
at all.
2. Real Case Study
The case study considers the emergency episodes that occurred in 2017, in
the district of Coimbra, Portugal. All the data was totally anonymized and
provided by INEM. In this civil year, a total of 50732 emergency episodes
occurred, requiring 60343 vehicles’ dispatches. It is possible to conclude
that including the dispatching decisions significantly influences the loca-
tion decisions. The solution calculated is able to achieve a better coverage
of the geographic area considered than the current solution.
References
[1] Nelas J., & Dias J. (2021) Locating Emergency Vehicles: modelling the substi-
tutability of resources and the impact of delays in the arrival of assistance, Op-
erations Research Perspectives (accepted for publication).
[2] Nelas J., & Dias J. (2020) Locating Emergency Vehicles: Robust Optimization
Approaches. In: Gervasi O. et al. (eds) Computational Science and Its Applica-
tions – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science, vol 12251.
Springer, Cham.
[3] Nelas, J., & Dias J. (2020) Optimal Emergency Vehicles Location: An approach
considering the hierarchy and substitutability of resources, European Journal of
Operational Research, Volume 287 (2), pp 583-599.
XI Workshop on Locational Analysis and Related Problems 2022 51
Selective collection routes of urban solid
waste by means of multi-compartment
vehicles∗
Ramón Piedra-de-la-Cuadra,1Juan A. Mesa,2Francisco A. Ortega3
and Guido Marseglia 4
1Departamento Matemática Aplicada I, Universidad de Sevilla Spain, rpiedra@us.es
2Departamento Matemática Aplicada II, Universidad de Sevilla, Spain, jmesa@us.es
3Departamento Matemática Aplicada I, Universidad de Sevilla, Spain riejos@us.es
4Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain, marseglia@us.es
The rapid and constant increase in urban population has led to a drastic
rise in urban solid waste production with worrying consequences for the
environment and society. In many cities, an efficient waste management
combined with a suitable design of vehicle routes (VR) can lead to benefits
in the environmental, economic, and social impacts.
In recent years, the growth in urban population density has implied a ma-
jor rise in the production of various kinds of Municipal Solid Waste (MSW),
whose management includes several functional phases, such as waste gen-
eration, storage, collection, transportation, processing, recycling, and dis-
posal in a suitable landfill. As a consequence, administrations, such as mu-
nicipalities, have defined suitable waste collection areas to obtain efficiency
and low environmental impact.
In Spain, the so-called eco-points are large waste containers with water-
tight sections to separate the collection of a wide variety of items. The
management of eco-points gives rise to several problems that can be for-
mulated analytically. The location and number of eco-point containers, the
determination of the fleet size for picking up the collected waste, and the
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project RED2018-102363-T, Ministerio de Investigación (Spain)/FEDER under grant PID2019-
533 106205GB-I00, and Operational Programme FEDER-Andalucía under grant US-1381656.
52
design of itineraries are all intertwined, but present computationally diffi-
cult problems, and therefore must be solved in a sequential way.
The mathematical optimization model formulated for this purpose has been
identified as a combined version of BP problem and the VR problem, whose
computational complexity motivates the use of heuristics to face large real-
life scenarios. Following that recommendation, a greedy algorithm has been
developed to solve the proposed mathematical programming model. Two
strategies have been identified for designing the configurations of the mo-
bile multi-block containers that will visit the demand nodes. The results
obtained from the numerical simulations show the validation of the pro-
posed methodology carried out for the Sioux Falls network benchmark and
the specific real case study.
XI Workshop on Locational Analysis and Related Problems 2022 53
Multi-Depot VRP with Vehicle Interchanges:
Heuristic solution ∗
Victoria Rebillas-Loredo1, Maria Albareda-Sambola1, Juan A. Díaz2,
and Dolores E. Luna-Reyes2
1Departament d’Estadística i Investigació Operativa, Universitat Politècnica de Catalunya,
Spain, {victoria.rebillas, maria.albareda}@upc.edu
2Department of Actuary, Physics and Mathematics, Universidad de las Américas Puebla
(UDLAP), Mexico {juana.diaz, dolorese.luna}@udlap.mx
1. Introduction
The classical variants of the Vehicle Routing Problem (VRP) aim at defining
vehicle routes that, starting and ending at a given depot are able to provide
service to a set of geographically scattered customers in the fastest/cheapest
possible way. A natural extension of these problems consider settings where
more than one depot is available. In those cases, each route is usually
forced to finish at the same route where it started.
Among the most typical constraints considered in this type of problems
we find the vehicle capacities, that limit the amount of customer demands
that can be collected by each vehicle, and the limits on the total driving dis-
tance/time that can be assigned to each driver. Depending on the locations
of the customers and on the distribution pattern of their demands, these
constraints can cause optimal routes to underuse some of the resources; i.e.
we can find short routes where the vehicle capacity constraints are bind-
ing, together with long routes where vehicle capacities are far from being
completely used.
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project RED2018-102363-T
54
The Multi-Depot Vehicle Routing Problem with Driver Interchanges (MD-
VRPDI) explores the following strategy to overcome this undesired behav-
ior:
Vehicle routes are decoupled from driver routes in a way that only driver
routes are forced to start and finish at the same depot, while a vehicle can
finish its route at a depot different from its starting point. To do so, sev-
eral interchange points are set beforehand where two drivers can meet and
interchange their vehicles. The reader is referred to [1] for furhter details.
This introduces additional flexibility to the model, allowing for a better
usage of the available resources. However, by allowing these interchanges
the complexity of the problem is heavily increased, since the interchanges
require route synchronization.
2. Proposed heuristic
Even if, in the studied problem, the vehicle and driver routes are decou-
pled, for any feasible solution, the vehicle routes completely determine the
driver routes. Therefore, solutions can be built by just focusing on the ve-
hicle routes, and imposing feasibility of the resulting driver routes.
With this in mind, we observe that any feasible vehicle route can be
obtained by combining two open vehicle routes. This combination must be
made through an interchange point if the two open routes do not share the
same depot, and without an interchange point if they both use the same
depot. Moreover, if an interchange point is used, it must be used by an
even number of combinations, yielding feasible driver routes.
The proposed heuristic applies different strategies to build promising
open routes. Then, the above ideas are used to build a mathematical pro-
gram that is used to iteratively combine open routes to build feasible solu-
tions.
The performance of the heuristic is tested on a set of computational ex-
periments.
References
[1] V. Rebillas-Loredo. The MDVRP with Vehicle Interchanges. PhD Thesis. Uni-
versitat Politècnica de Catalunya, 2018. url: http://hdl.handle.net/10803/664634
XI Workshop on Locational Analysis and Related Problems 2022 55
Optimizing COVID-19 Test
and Vaccine distributions ∗
José Luis Sainz-Pardo,1José Valero2
1Centro de Investigación Operativa (Universidad Miguel Hernández de Elche), Spain,
jose.sainz-pardo@umh.es
2Centro de Investigación Operativa (Universidad Miguel Hernández de Elche), Spain,
jvalero@umh.es
The experience of Singapore and South Korea makes it clear that under
certain circumstances massive testing is an effective way for containing
the advance of the COVID-19. We propose a modified SEIR model which
takes into account tracing and massive testing. After that, we introduce a
heuristic approach in order to minimize the COVID-19 spreading by plan-
ning effective test distributions among the populations of a region over a
period of time.
In a similar way, we propose a modified SEIR model which takes into
account the effect of vaccination. The criteria to assess public health poli-
cies are fundamental to distribute vaccines in an effective way in order to
avoid as many infections and deaths as possible. Usually these policies are
focused on determining socio-demographic groups of people and estab-
lishing a vaccination order among these groups. This work also focuses on
optimizing, from the proposed SEIR model, the way of distributing vac-
cines among the different populations of a region for a period of time once
established the priority socio-demographic groups.
∗Research partially supported by Generalitat Valenciana (Spain), project 2020/NAC/00022;
Spanish Ministry of Science, Innovation and Universities, projects PGC2018-099428-B-I00 and
PGC2018-096540-B-I00
56
1. Test and vaccination models
On the one hand, we develop two SEIR models to forecast the evolution of
the pandemic. SEIR models are compartmental models based on differen-
tial equations. Acronym SEIR is due to the fact that these models represent
the evolution of Susceptible, Exposed, Infected and Recovered cases. The
first introduced model, which is employed to optimize the test distribution,
takes into account the impact of COVID testing and isolated cases. The sec-
ond model, which is employed to optimize the vaccine distribution, takes
into account the impact of vaccinated people.
2. Parameters estimation and planning
distribution
We use Differential Evolution technique for estimating the parameters. Re-
garding the optimal planning distribution, this is obtained from gain ma-
trices computed from the SEIR models.
3. Simulations and computational
experience
For the computational test distribution experience, it has been simulated
the pandemic spreading in New York counties from the first of April to the
first of July of 2020. Table 1 shows the infections, the savings and the ad-
vantages in terms of infections to distribute several COVID test quantities
both by homogeneous distribution and by the proposed approach.
Regarding the vaccine distribution we have reproduced the pandemic
spread in the Spanish region called Valencian Community during the pe-
riod from 1st of Juny to 31th of December of 2020. Figure 1 shows the in-
fections by random vaccine distribution versus the proposed approach.
References
[1] Iorio, A.W., & Li, X. Incorporating directional information within a differential
evolution algorithm for multi-objective optimization. Proceeding of the Genetic
and Evolutionary Computation Conference, 81–116, 2006.
[2] Falco, I. D., Cioppa, A. D., Scafuri, U., & Tarantino, E. Coronavirus Covid–19
spreading in Italy: optimizing an epidemiological model with dynamic social.
Optimizing COVID-19 Test and Vaccine distributions 57
#Tests F. H.Inf. Ap.Inf. H.Saving Ap.Saving Adv.
10,000 1 3,365,783 3,365,709 34 108 74
10,000 3 3,365,716 3,365,494 101 323 222
10,000 9 3,365,514 3,364,851 303 966 663
50,000 1 3,365,666 3,365,280 151 537 386
50,000 3 3,365,365 3,364,209 452 1,608 1,156
50,000 9 3,364,462 3,361,026 1,355 4,791 3,436
100,000 1 3,365,519 3,364,744 298 1,073 775
100,000 3 3,364,924 3,362,612 893 3,205 2,312
100,000 9 3,363,144 3,357,124 2,673 8,693 6,020
500,000 1 3,364,346 3,360,256 1,471 5,561 4,090
500,000 3 3,361,416 3,354,512 4,401 11,305 6,904
500,000 9 3,352,700 3,341,480 13,117 24,337 1,1220
1,000,000 1 3,362,884 3,355,417 2,933 10,400 7,467
1,000,000 3 3,357,058 3,344,645 8,759 21,172 12,413
1,000,000 9 3,339,880 3,316,234 25,937 49,583 23,646
Table 1. Number of infected cases and saved infections with 10% tests per day
limitation
Figure 1. Infected cases by vaccine distribution methods
arxiv, 2004.00553, 2020.
[3] He, S., Peng, Y., & Sun, K. SEIR modeling of the COVID-19 and its dynamics.
Nonlinear Dynamics, 101:1667–1680, 2020.
XI Workshop on Locational Analysis and Related Problems 2022 59
Locating a rectangle in the sky to get the
best observation∗
Juan-José Salazar-González1
1Departamento de Matemáticas, Universidad de La Laguna, Spain, jjsalaza@ull.edu.es
This paper concerns a new optimization problem arising in the manage-
ment of a multi-object spectrometer with a configurable slit unit. The field
of view of the spectrograph is divided into contiguous and parallel spatial
bands, each one associated with two opposite sliding metal bars that can be
positioned to observe one astronomical object. Thus several objects can be
analyzed simultaneously within a configuration of the bars called a mask.
Due to the high demand from astronomers, pointing the spectrograph’s
field of view to the sky, rotating it, and selecting the objects to conform a
mask is a crucial optimization problem for the efficient use of the spectrom-
eter. The paper describes this problem, presents a Mixed Integer Linear
Programming formulation for the case where the rotation angle is fixed,
presents a non-convex formulation for the case where the rotation angle is
unfixed, describes a heuristic approach for the general problem, and dis-
cusses computational results on real-world and randomly-generated in-
stances.
The combinatorial problem is related to locating a rectangle on a plane.
It is an interesting problem in the Computational Geometry community,
where there are many articles dealing with enclosing subsets of points with
all kinds of geometric elements. Given a finite planar point set, the enclos-
ing problem is to find the smallest geometrical element of a given type and
arbitrary orientation that encloses all the n points. A kind of dual variant
of the enclosing problem is finding the translation and orientation for a
geometrical element of a given size to maximize the number of enclosed
points.
∗Research partially supported by the Spanish Ministry of Science and Innovation through
project PID2019-104928RB-I00 (MINECO/FEDER, UE)
60
The full paper was recently accepted for publication in the journal Omega:
https://doi.org/10.1016/j.omega.2021.102392 . At IWOLOCA we will sum-
marize the main findings and will mention open questions.
XI Workshop on Locational Analysis and Related Problems 2022 61
Multiple Allocation P-Hub Location
Problem explicitly considering Users’
preferences ∗
Nicolás A. Zerega,1Armin Lüer-Villagra,2
1Department of Statistics and Operations Research, Universidad de Cádiz, Facultad de
Ciencias, 11510 Puerto Real, Cádiz, Spain, nicolas.zerega@uca.es
2Department of Engineering Sciences, Universidad Andres Bello, Antonio Varas 880, Piso
6, Santiago, Chile, armin.luer@unab.cl
Hub location problems (HLPs) are a well-known family of problems within
General Network Design, which combine location and design decisions [1].
Hubs are facilities in which flow gets collected, bunched and then dis-
tributed to different nodes inside the network at reduced unitary costs
thanks to the presence of economies of scale.
This type of problems have been widely studied in the last 30-40 years
[2,3].
In general, the entities that interact with the network are considered to
be passive, i.e., their actions are based on the design decisions taken by
the Network Manager. When the entities that interact with the network
are humans, their preferences will not necessarily match with those of the
Network Manager. For this reason, it is interesting to study how these in-
dividual decisions influence the performance of an existing network and,
also, how they will influence the design of a new one.
This research develops the above idea by modelling users’ decisions
through deterministic utility functions [4]. Users try to maximize their util-
ity when travelling from their Origin to their Destination nodes, mean-
while the Network Manager tries to maximize his/her profits.
We propose an extension of the Hub network design problem with prof-
its (HNDPP) presented in Alibeyg et. al. 2016 [5] in which the users pref-
∗Research supported by the Chilean National Fund for Scientific and Technological Develop-
ment (FONDECYT) through project 1200706
62
erences are incorporated to the decision making process through the inclu-
sion of Maximum Utility Constraints (MUC) [6]. This type of constraints
implicitly model the users preferences and have been studied and applied
in previous research [7,8].
Current results show that the inclusion of the users’ preferences has no-
table effects in the network design and performance, so considering them
when making changes or designing a new network will provide a more
realistic behavior.
References
[1] Contreras, I., & Fernández, E. (2012). General network design: A unified view
of combined location and network design problems. European Journal of Oper-
ational Research, 219(3), 680–697
[2] O’Kelly, M. E. (1987). A quadratic integer program for the location of interact-
ing hub facilities. European Journal of Operational Research, 32(3), 393–404.
[3] Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state of
the art. European Journal of Operational Research, 190(1), 1–21.
[4] Eiselt, H. A., Marianov, V., & Drezner, T. (2015). Competitive Location Models.
In G. Laporte, S. Nickel, & F. Saldanha da Gama (Eds.), Location Science (pp.
365–398).
[5] Alibeyg, A., Contreras, I., & Fernández, E. (2016). Hub network design prob-
lems with profits. Transportation Research Part E: Logistics and Transportation Re-
view, 96,40–59.
[6] Espejo, I., Marín, A., & Rodríguez-Chía, A. M. (2012). Closest assignment con-
straints in discrete location problems. European Journal of Operational Research,
219(1), 49–58.
[7] Marianov, V., Eiselt, H. A., & Lüer-Villagra, A. (2018). Effects of multipurpose
shopping trips on retail store location in a duopoly. European Journal of Opera-
tional Research, 269(2), 782–792.
[8] Marianov, V., Eiselt, H. A., & Lüer-Villagra, A. (2019). The Follower Compet-
itive Location Problem with Comparison-Shopping. Networks and Spatial Eco-
nomics, 20(2), 367-393.
Author Index
A
Albareda-Sambola, Maria
Statistics and Operations Research Department, Universitat
Politècnica de Catalunya, Spain, maria.albareda@upc.edu ..................53
Anjos, Miguel F.
School of Mathematics, The University of Edinburgh, Edinburgh, UK,
Miguel.F.Anjos@ed.ac.uk ...................................................39
Anton-Sanchez, Laura
Universidad Miguel Hernández, Spain, l.anton@umh.es ..............17
B
Baldomero-Naranjo, Marta.
Universidad de Cádiz, Spain, marta.baldomero@uca.es ................19
Blanco, Víctor
Universidad de Granada, Spain, vblanco@ugr.es ..............21,23,25
Bruno, Giuseppe
Department of Industrial Engineering (DII), Università degli Studi di
Napoli Federico II, Italy, giuseppe.bruno@unina.it ..........................27
C
Calvino, José J.
Universidad de Cádiz, Spain, jose.calvino@uca.es ....................29
Canca, David
School of Engineering, Seville, Spain, dco@us.es ....................31
Cavola, Manuel 63
Department of Industrial Engineering (DII), Università degli Studi di
Napoli Federico II, Italy, manuel.cavola@unina.it ...........................27
D
Díaz, Juan A.
Department of Actuary, Physics and Mathematics, Universidad de las
Américas Puebla (UDLAP), Mexico, juana.diaz@udlap.edu ................53
Dias, Joana
University of Coimbra, Portugal, joana@fe.uc.pt .....................49
Diglio, Antonio
Department of Industrial Engineering (DII), Università degli Studi di
Napoli Federico II, Italy, antonio.diglio@unina.it ............................27
Domínguez, Carmen-Ana
Universidad de Cádiz, Spain, carmenana.dominguez@uca.es ...........33
Domínguez-Martín, Bencomo
Universidad de La Laguna, Spain, bdomingu@ull.edu.es ...............35
E
Elizalde, Javier
Facultad de Ciencias Económicas y Empresariales, Universidad de
Navarra, Spain, jelizalde@unav.es ........................................27
Escudero, Laureano F.
Universidad Rey Juan Carlos, Spain, laureano.escudero@urjc.es ........37
F
Fermín Cueto, Paula
School of Mathematics, The University of Edinburgh, Edinburgh, UK,
paula.fermin@ed.ac.uk ....................................................39
Fernández, Elena
Universidad de Cádiz, Spain, elena.fernandez @uca.es ................33
Fernández, José
Dpt. Statistics and Operations Research, University of Murcia, Spain,
josefdez@um.es .........................................................41
G
G.-Tóth, Boglárka
Dpt. Computational Optimization, University of Szeged, Hungary,
boglarka@inf.szte.hu ......................................................41
Gázquez, Ricardo
Universidad de Granada, Spain, rgazquez@ugr.es .............21,23,25
García, Sergio
School of Mathematics, University of Edinburgh, UK,
sergio.garcia-quiles@ed.ac.uk ........................................39,43,47
AUTHOR INDEX 65
Gjeroska, Ivona
School of Mathematics, University of Edinburgh, UK,
i.gjeroska@sms.ed.ac.uk ...................................................43
K
Kalcsics, Jörg
University of Edinburgh, Spain, joerg.kalcsics@ed.ac.uk ...............19
L
Lüer-Villagra, Armin
Universidad Andres Bello, Chile, armin.luer@unab.cl ..................33
Lüer-Villagra, Armin
Universidad Andres Bello, Chile, armin.luer@unab.cl ..................61
López-Haro, Miguel
Universidad de Cádiz, Spain, miguel.lopezharo@uca.es ................29
Landete, Mercedes
Centro de Investigación Operativa, Universidad Miguel Hernández,
Elche, landete@umh.es ............................................17,45,47
Laporte, Gilbert
HEC Montrèal, CIRRELT, gilber t.laporte@cirrelt.net .....................31
Leal, Marina
Universidad Miguel Hernández, Spain, m.leal@umh.es ..............23
Luna, Dolores E.
Department of Actuary, Physics and Mathematics, Universidad de las
Américas Puebla (UDLAP), Mexico, dolorese.luna@udlap.edu ..............53
M
Mahmuto˘gulları, Özlem
ORSTAT, Faculty of Economics and Business, KU Leuven, Belgium,
ozlem.mahmutoullar@kuleuven.be ............................................9
Marseglia, Guido
Universidad de Sevilla, Spain, marseglia@us.es ......................51
Mesa, Juan A.
Universidad de Sevilla, Spain, jmesa@us.es ......................11,51
Monge, Juan Francisco
Centro de Investigación Operativa, Universidad Miguel Hernández,
Elche, monge@umh.es ................................................37,47
Moya-Martínez, Alejandro
Centro de Investigación Operativa, Universidad Miguel Hernández,
Elche, a.moya@umh.es ...................................................47
Muñoz-Ocaña, Juan M.
Universidad de Cádiz, Spain, juanmanuel.munoz@uca.es ...............29
66 AUTHOR INDEX
N
Nelas, José
University of Coimbra, Portugal, eunelas@gmail.com .................49
O
Ortega, Francisco A.
Universidad de Sevilla, Spain, riejos@us.es ..........................51
P
Peiró, Juanjo
Universitat de València, Burjassot (València) Spain, juanjo.peiro@uv.es 45
Piccolo, Carmela
Department of Industrial Engineering (DII), Università degli Studi di
Napoli Federico II, Italy, carmela.piccolo@unina.it ..........................27
Piedra-de-la-Cuadra, Ramón
Universidad de Sevilla, Spain, rpiedra@us.es .........................51
Puerto, Justo
Universidad de Sevilla, Spain, puerto@us.es .........................29
R
Rebillas-Loredo, Victoria
Statistics and Operations Research Department, Universitat
Politècnica de Catalunya, Spain, victoria.rebillas@upc.edu ..................53
Rodríguez-Martín, Inmaculada
Universidad de La Laguna, Spain, irguez@ull.edu.es ..................35
Rodríguez-Chía, Antonio M.
Universidad de Cádiz, Spain, antonio.rodriguezchia@uca.es .........19,29
S
Sainz-Pardo, José Luis
Centro de Investigación Operativa (Universidad Miguel Hernández
de Elche), Spain, jose.sainz-pardo@umh.es .................................55
Salazar-González, Juan J.
Universidad de La Laguna, Spain, jjsalaza@ull.edu.es .............35,59
Saldanha-da-Gama, Francisco
Universidade de Lisboa, Portugal, fsgama@ciencias.ulisboa.pt . . . . . . 17, 25
V
Valero, José
Centro de Investigación Operativa (Universidad Miguel Hernández
de Elche), Spain, jvalero@umh.es .........................................55
INDEX 67
Y
Yaman, Hande
KU Leuven, Leuven, Belgium hande.yaman@kuleuven.be ............9,45
Z
Zerega, Nicolás A.
Universidad de Cádiz, Spain, nicolas.zerega@uca.es ..................61
