Proceedings of the VI International Workshop on Locational Analysis and Related Problems
Maria Albareda-Sambola, Luisa I. Martínez-Merino, Antonio M. Rodríguez-Chía
VI International W orkshop onLocational Analysisand Related Problem s
Barcelona, Spain -Novem ber 25-27, 2015
Proceedings of P r o g r a m O v e r v i e w W e d n e s d a y N o v . t h T h u r s d a y N o v . t h F r i d a y N o v . t h S E SS I O N : S E SS I O N : : - : C O N T I N U O U S L O C A T I O N D I S C R E T EL O C A T I O N : - : C o ff ee b r e a k C o ff ee b r e a k I n v i t e d S p e a k e r : I n v i t e d S p e a k e r : : - : M a tt e o F i s c h e tt i M . G r az i a S p e r a n za S E SS I O N : S E SS I O N : : - : L O C A T I O N O NN E T W O R K S R O U T I N G P R O BLE M S : - : L o c a t . N e t w o r k M ee t i n g L U N C H : - : L U N C H S E SS I O N : : - : D I S C R E T EL O C A T I O N : - : R E G I S T R A T I O N C o ff ee b r e a k : - : O P E N I N G S E SS I O N S E SS I O N : L O C A T I O N O NN E T W O R K S : - : S E SS I O N : D I S C R E T EL O C A T I O N : - :
50 20 : W e l c o m e R e c e p t i o n D I NN E R ROCEEDINGS OFTHE VI INTERNATIONAL WORKSHOPON LOCATINAL ANALYSIS ANDRELATED PROBLEMS (2015)
Edited by
Maria Albareda-SambolaLuisa I. Martínez-MerinoAntonio M. Rodríguez-Chía
ISBN: 978-84-944229-8-0doi: http://dx.doi.org/10.3926/redloca15 reface
The International Workshop on Locational Analysis and Related Problemswill take place during November 25-27, 2015 in Barcelona (Spain). It is or-ganized by the Spanish Location Network and Location Group GELOCA(SEIO). GELOCA is a working group on location belonging to the Statisticsand Operations Research Spanish Society. The Spanish Location Networkis a group of more than 140 researchers distributed into 16 nodes corre-sponding to several Spanish universities. The Network has been fundedby the Spanish Government.Every year, the Network organizes a meeting to promote the communi-cation among its members and between them and other researchers, and tocontribute to the development of the location field and related problems.Previous meetings took place in Sevilla (October 1-3, 2014), Torremolinos(Málaga, June 19-21, 2013), Granada (May 10-12, 2012), Las Palmas de GranCanaria (February 2-5, 2011) and Sevilla (February 1-3, 2010).The topics of interest are location analysis and related problems. Thisincludes location, routing, networks, transportation and logistics models;exact and heuristic solution methods, and computational geometry, amongothers.The organizing committee. cientific committee:
Emilio Carrizosa (U. de Sevilla)Ángel Corberán (U. de Valencia)Elena Fernández Aréizaga (U. Politécnica de Cataluña)Alfredo Marín Pérez (U. de Murcia)Juan A. Mesa (U. de Sevilla)Blas Pelegrín (U. de Murcia)Justo Puerto Albandoz (U. de Sevilla)Antonio M. Rodríguez-Chía (U. de Cádiz)
Organizing committee:
Maria Albareda-Sambola (U. Politécnica de Cataluña)Luisa Martínez-Merino (U. de Cádiz)Francisco A. Ortega (U. de Sevilla)Dolores R. Santos Peñate (U. de Las Palmas de G.C) ontents
Preface v
Program 1Invited Speakers 7
Simplified Benders cuts for facility location 9
M. Fischetti, I. Ljubi´c and M. Sinnl
Kernel search for location problems 11
M. Grazia Speranza
Abstracts 13
Locating capacitated unreliable facilities 15
M. Albareda-Sambola, M. Landete, J.F. Monge, and J.L. Sainz-Pardo
The p -center problem with uncertainty in the demands 17 M. Albareda-Sambola, L.I. Martínez-Merino and A.M. Rodríguez-Chía
Conditions to LP relax the allocation variables of the reliabilityfixed-charge location problem 19
J. Alcaraz, M. Landete, J.F. Monge and J.L. Sainz-Pardo
A variable neighborhood search approach for the 3-maneuveraircraft conflict resolution problem 21
A. Alonso-Ayuso, L.F. Escudero, F.J. Martín-Campo, N. Mladenovi´c
The probabilistic pickup and delivery problem 23
E. Benavent, M. Landete, J.J. Salazar and G. Tirado vii ultisource linear regression 25
V. Blanco and J. Puerto
A dispersion model in ODEs 27
R. Blanquero, E. Carrizosa, M.A. Jiménez-Cordero and B. G. Tóth
Rapid transit network design: competition and transfers 29
L. Cadarso and A. Marín
The maximal covering location bi-level problem 31
J.F. Camacho-Vallejo, M.S. Casas-Ramírez, J.A. Díaz and D.E. Luna
A decomposition scheme for the railway rapid transit depot lo-cation and rolling stock circulation problem 33
D. Canca, A. de los Santos, E. Barrena and G. Laporte
Robust p -median problem with vector autoregressive demands 37 E. Carrizosa, A.V. Olivares-Nadal and P. Ramírez-Cobo
Using an interior-point method for huge capacitated multiperiodfacility location 39
J. Castro, S. Nasini and F. Saldanha-da-Gama
On the hierarchical rural postman problem on a mixed graph 41
M. Colombi, Á. Corberán, R. Mansini, I. Plana and J.M. Sanchis
Strategic oscillation for a hub location problem with modularlink capacities 43
A. Corberán, J. Peiró, F. Glover and R. Martín
Ordered Weighted Average Optimization in multiobjective span-ning tree problems 47
E. Fernández, M. A. Pozo, J. Puerto and A. Scozzari
Set-packing problems in discrete location 49
A. Marín and M. Pelegrín
Robust rapid transit railway rescheduling 51
Á. Marín and L. Cadarso
New products supply chains: the effect of short lifecycles on thesupply chain network design. 53
M.B.C. Menezes. K. Luo and O. Allal-Cherif ial-a-ride problems in presence of transshipments 55
J.A. Mesa, F. A. Ortega and M.A. Pozo
Optimal routes to a destination for airline expansion 57
B. Pelegrín Pelegrín, P. Fernández Hernández, and J.D. Pelegrín García
Locating new stations and road links on a road-rail network 61
F. Perea
Convex ordered median problem 63
D. Ponce and J. Puerto On k -centrum optimization with applications to the location ofextensive facilities on graphs and the like 65 J. Puerto and A.M. Rodríguez-Chía
Analyzing the impact of capacity volatility on the design of asupply chain network 67
D. Ruiz-Hernández, M.B.C. Menezes and S. Gueye
Location of emergency units in collective transportation line net-works 69
T. Tan and J.A. Mesa
ROGRAM ednesday November 25th
Locating capacitated unreliable facilitiesM. Albareda-Sambola, M. Landete, J.F. Monge, and J.L. Sainz-PardoConditions to LP relax the allocation variables of the reliability fixed-charge location problemJ. Alcaraz, M. Landete, J.F. Monge and J.L. Sainz-PardoThe maximal covering location bi-level problemJ.F. Camacho-Vallejo, M.S. Casas-Ramírez, J.A. Díaz and D.E. LunaUsing an interior-point method for huge capacitated multiperiod fa-cility locationJ. Castro, S. Nasini and F. Saldanha-da-Gama hursday November 26th
Multisource linear regressionV. Blanco and J. PuertoA dispersion model in ODEsR. Blanquero, E. Carrizosa, M.A. Jiménez-Cordero and B. G. TóthOrdered Weighted Average Optimization in multiobjective spanningtree problemsE. Fernández, M. A. Pozo, J. Puerto and A. ScozzariOptimal routes to a destination for airline expansionB. Pelegrín Pelegrín, P. Fernández Hernández, and J.D. Pelegrín Gar-cía
Simplified Benders cuts for facility locationM. Fischetti, I. Ljubi´c and M. Sinnl
Rapid transit network design: competition and transfersL. Cadarso and Á. MarínA decomposition scheme for the railway rapid transit depot locationand rolling stock circulation problemD. Canca, A. de los Santos, E. Barrena and G. LaporteLocation of emergency units in collective transportation line Net-worksT. Tan and J.A. Mesa
The p-center problem with uncertainty in the demandsM. Albareda-Sambola, L.I. Martínez-Merino and A.M. Rodríguez-ChíaSet-packing problems in discrete locationA. Marín and M. PelegrínConvex ordered median problemD. Ponce and J. PuertoA variable neighborhood search approach for the 3-maneuver air-craft conflict resolution problemA. Alonso-Ayuso, L.F. Escudero, F.J. Martín-Campo, N. Mladenovi´c
Robust rapid transit railway reschedulingÁ. Marín and L. CadarsoDial-a-ride problems in presence of transshipmentsJ.A. Mesa, F. A. Ortega and M.A. PozoLocating new stations and road links on a road-rail networkF. Perea riday November 28th On k -centrum optimization with applications to the location of ex-tensive facilities on graphs and the likeJ. Puerto and A.M. Rodríguez-ChíaRobust p -median problem with vector autoregressive demandsE. Carrizosa, A.V. Olivares-Nadal and P. Ramírez-CoboNew products supply chains: the effect of short lifecycles on the sup-ply chain network designM.B.C. Menezes. K. Luo and O. Allal-CherifAnalyzing the impact of capacity volatility on the design of a supplychain networkD. Ruiz-Hernández, M.B.C. Menezes and S. Gueye Kernel search for location problemsM. G. Speranza
The probabilistic pickup and delivery problemE. Benavent, M. Landete, J.J. Salazar and G. TiradoOn the hierarchical rural postman problem on a mixed graphM. Colombi, Á. Corberán, R. Mansini, I. Plana and J.M. SanchisStrategic oscillation for a hub location problem with modular linkcapacitiesÁ. Corberán, J. Peiró, F. Glover and R. Martín
NVITED SPEAKERS
I Workshop on Locational Analysis and Related Problems 2015 9
Simplified Benders cuts for facility location
Matteo Fischetti, Ivana Ljubi´c, and Markus Sinnl Dept. of Information Engineering, Univ. of Padua, Italy, matteo.fi[email protected] ESSEC Business School of Paris, France, [email protected] Dept. of Statistics and Op. Res., Univ. of Vienna, Austria, [email protected]
A simple reformulation of generalized Benders cuts is presented, that greatlysimplifies their practical implementation. Successful applications to Facil-ity Location Problems (FLPs) with convex (linear and quadratic) costs willbe discussed.Consider the convex Mixed-Integer (possibly Nonlinear) Problem min f f ( x; y ) : g ( x; y ) (cid:20) ; Ay (cid:20) b; y integer g (1)where x m , y n , and functions f : ℜ m + n
7! ℜ and g : ℜ m + n p are assumed to be differentiable and convex. In FLPs, y variables aretypically associated to facilities, and x variables to allocation decisions.To simplify our treatment, we assume that S := f y : Ay (cid:20) b g is anonempty polytope, while the convex sets X ( y ) := f x : g ( x; y ) (cid:20) g arenonempty, closed and bounded for all y S , as it happens for FLPs. Prob-lem (1) can trivially be restated as the master problem in the y space min f w : w (cid:21) (cid:8)( y ) ; Ay (cid:20) b; y integer g (2)where (cid:8)( y ) := min x X ( y ) f ( x; y ) is the convex (nonlinear) function expressing the optimal solution value ofthe problem (1) as a function of y S , and w is a continuous variable thatcaptures its value in the objective function.Master problem (2) can be solved by an LP-based branch-and-cut ap-proach where (cid:8)( y ) is under-approximated by linear cuts to be generatedon the fly and added to the current LP relaxation. A crucial point is thefficient generation of the approximation cuts. To this end, consider a (pos-sibly noninteger) solution y (cid:3) of the LP relaxation of the current master.Because of convexity, (cid:8)( y ) can be underestimated by a supporting hyper-plane at y (cid:3) , so we can write the following generalized Benders (linear) cut w (cid:21) (cid:8)( y ) (cid:21) (cid:8)( y (cid:3) ) + (cid:24) ( y (cid:3) ) T ( y (cid:0) y (cid:3) ) (3)Here (cid:24) ( y (cid:3) ) denotes a subgradient of (cid:8) in y (cid:3) that can be computed as (cid:24) ( y (cid:3) ) = ∇ y f ( x (cid:3) ; y (cid:3) ) + u (cid:3) ∇ y g ( x (cid:3) ; y (cid:3) ) (4)where x (cid:3) and u (cid:3) are optimal primal and (Lagrangian) dual solutions of theconvex problem obtained from (1) by replacing y with the given y (cid:3) [1, 2].The above formula involves the computation of partial derivatives of f and g with respect to the y j ’s, so it is problem specific and sometimescumbersome to apply. We next introduce a very simple reformulation thatmakes its implementation straightforward. For a given y S , (cid:8)( y ) can becomputed by solving the convex slave problem (cid:8)( y ) = min f f ( x; q ) : g ( x; q ) (cid:20) ; y (cid:0) q = 0 g (5)The variable-fixing equation in (5) is meant to be imposed as y (cid:20) q (cid:20) y byjust modifying the lower and upper bounds on the q variables, so it can behandled very efficiently by the solver in a preprocessing phase when y isgiven.By construction, y only appears in the variable-fixing equation in (5),hence the subgradient (4) is just (cid:24) ( y (cid:3) ) = r (cid:3) , where r (cid:3) is the vector of op-timal reduced costs returned by a convex solver applied to (5) for y = y (cid:3) .This leads to completely general and easily computable generalized Ben-ders cut w (cid:21) (cid:8)( y (cid:3) ) + n ∑ j =1 r (cid:3) j ( y j (cid:0) y (cid:3) j ) (6)Extensive computational results for various FLPs confirm the practicaleffectiveness of the above family of cuts. References [1] J. Benders. “Partitioning procedures for solving mixed-variables programmingproblems,” Numerische Mathematik, 4, 238–252, 1962-63.[2] A. Geoffrion. “Generalized Benders Decomposition,” Journal of OptimizationTheory and Applications, 10, 237–260, 1972.I Workshop on Locational Analysis and Related Problems 2015 11
Kernel search for location problems
M. Grazia Speranza Department of Economics and Business, University of Brescia, Italy, [email protected]
In this talk a general heuristic approach, known as Kernel Search, willbe presented that has been successfully applied to several MILP problems,and in particular to location problems. The Kernel Search is a general andsimple heuristic framework that has been introduced in [1] and [2] for thesolution of MILP problems with binary variables, in particular of a port-folio optimization problem and the Multidimensional Knapsack Problem.The original idea was to consider all the problem variables through thesolution of a sequence of MILP problems, each restricted to a subset ofvariables. This restriction is equivalent to setting to 0 a subset of variables.In the sequence of restricted MILP problems the size of the solved prob-lems was increasing because at each iteration new variables may be addedto the subset and none was removed. Some enhancements of the KernelSearch were proposed in Guastaroba and Speranza [3], where the removalof variables was allowed. A new variant was also proposed that refinesthe solution found through the first sequence of restricted problems. Theidea of the variant is to perform variable fixing (binary variables set to 1)in the original MILP problem on the basis of the solutions found in the firstsequence, and to solve to optimality the MILP problem restricted to theremaining variables.The Kernel Search has been later extended and applied to two well stud-ied location problems, namely the Capacitated Facility Location Problem(CFLP) and the Single Source Capacitated Facility Location Problem (SS-CFLP). In [4] the Kernel Search has been extended to solve problems wherea large number of continuous variables are associated with each binaryvariable, in particular to the CFLP, while in [5] it has been extended to solveany problem with binary variables, in particular the SSCFLP. The compu-tational results prove that the Kernel Search can solve instances of largeize of the CFLP and of the SSCFLP with negligible errors with respect tothe optimum, and outperforms previous heuristics.
References [1] Angelelli, E., Mansini, R. and Speranza, M.G., “Kernel search: A general heuris-tic for the multi-dimensional knapsack problem”,
Computers and Operations Re-search , 37, 2017-2026, 2010.[2] Angelelli, E., Mansini, R. and Speranza, M.G., “Kernel search: A new heuristicframework for portfolio selection”,
Computational Optimization and Applications ,51, 345361, 2012.[3] Guastaroba, G. and Speranza, M.G., “Kernel Search: An application to the in-dex tracking problem”,
European Journal of Operational Research , 217, 54-68, 2012.[4] Guastaroba, G. and Speranza, M.G., “Kernel Search for the Capacitated FacilityLocation Problem”,
Journal of Heuristics
18, 877-917, 2012.[5] Guastaroba, G. and Speranza, M.G., “A Heuristic for BILP Problems: The Sin-gle Source Capacitated Facility Location Problem”,
European Journal of Opera-tional Research
BSTRACTS
I Workshop on Locational Analysis and Related Problems 2015 15
Locating capacitated unreliable facilities (cid:3)
M. Albareda-Sambola, M. Landete, J.F. Monge, and J.L. Sainz-Pardo Univ. Politècnica de Catalunya, Barcelona Tech., Terrassa, Spain [email protected] Universidad Miguel Hernández, Elche, Spain [email protected], [email protected],[email protected]
This work is focused on a fixed charge facility location problem wherefacilities are considered to be capacitated and unreliable. We explore dif-ferent strategies for considering facility capacities in a reasonably flexibleway: facility capacities refer to the maximum acceptable workload in regu-lar conditions, but extra load can be occasionally dealt with in emergencysituations where some failures have affected the system. However, theseeventual overloads must be kept reasonably small and unlikely to occur.We propose several models, and analyze their capability to generate solu-tions with these characteristics in a series of computational experiments.
1. Problem definition
The problems we consider are defined on a discrete setting. A set of poten-tial facility locations is given, each with an associated fixed opening costand a capacity. This set of facilities is partitioned into two subsets. The fail-ing and the non-failing facilities. A failure probability, common to all thefailing facilities, is also known. Moreover, it is assumed that facility fail-ures take place independently of each other. On the other hand, a set ofcustomers with different associated demands is considered together withtheir service costs (proportional to distances) from each of the potential fa-cility locations. Additionally, we consider a cost associated with loosing oroutsourcing a customer. In order to introduce this possibility in our mod-els, we just add to the set of potential facilities a dummy non-failing facility (cid:3)
Research funded by the Spanish Ministry of Economy and Competitiveness and ERDF fundsthrough Project MTM2012-36163-C06 ith zero fixed opening cost and infinite capacity whose distance to all thecustomers equals this outsourcing cost.The goal is to decide on the set of facilities to open and design a distri-bution pattern such that capacity constraints are nearly always satisfied , at aminimum total cost. In this work we consider this total cost to be a convexcombination of the sum of fixed and service costs in the scenario where nofailures occur, and the expected service cost over all scenarios.
2. Modeling assumptions
When considering location problems with unreliable facilities, the systembehavior upon failure has to be clearly defined. Do customers have com-plete information on facility failures? Can customers be always served bytheir closest available facility? To what extent can the a priori assignmentsbe modified to adapt to scenarios with failures?Since facilities are capacitated and have fixed opening costs, it wouldbe quite expensive to design systems capable to satisfy the capacity con-straints even if customers are always served by their closest available facil-ity, as it is assumed in [3]. Although this may be a reasonable assumptionto make in the location of essential services, it can be rather unrealistic inmore general ones. So, we assume customers can be served by any avail-able facility. However, to keep the effect of failures as local as possible, weconsider that customers cannot be all freely relocated at each scenario, asit is assumed in [2], but assignments at different levels are defined a priori ,like in uncapacitated models such as [1], and each customer is served fromthe available facility it has been assigned to at the lowest level.Three model types are proposed: limiting the expected loads, limitingestimates of the expected overloads, or using auxiliary staggered capaci-ties, being the two last strategies the ones yielding the best solutions.
References [1] J. Alcaraz, M. Landete, J.F. Monge, and J.L. Sainz-Pardo. Strenghening the re-liability fixed-charge location model using clique constraints.
Computers andOperations Research , 60:14–26, 2015.[2] N. Aydin and A. Murat. A swarm intelligence based sample average approxi-mation algorithm for the capacitated reliable facility location problem.
Interna-tional Journal of Production Economics , 145:173–183, 2013.[3] I. Espejo, A. Marín, and A. M. Rodríguez-Chía. Capacitated p-center problemwith failre foresight.
European Journal of Operational Research , 247:229–244, 2015.I Workshop on Locational Analysis and Related Problems 2015 17
The p -center problem with uncertainty inthe demands (cid:3) Maria Albareda-Sambola, Luisa I. Martínez-Merino, and AntonioM. Rodríguez-Chía, Departamento de Estadística e Investigación Operativa, Univ. Politècnica de Catalunya.BarcelonaTech, Barcelona, Spain, [email protected] Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Spain, [email protected] Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Spain, [email protected]
Keywords: p -center problem, probabilistic This work deals with the p-center problem, where the aim is to minimizethe maximum distance between any user and his center taking into ac-count that the demand occurs in any site with a specific probability. Theproblem is of interest when locating emergency centers . We consider dif-ferent formulations for the problem and extensive computational tests arereported, showing the potentials and limits of each formulation on severaltypes of instances. Finally, different techniques to obtain accurate boundson the optimal solution of the problem are explained.
1. Introduction to the problem
The p -center problem (pCP) is a well-known discrete optimization locationproblem which consists of locating p centers out of n sites and assigning(allocating) the remaining n (cid:0) p sites to the centers so as to minimize themaximum distance (cost) between a site and the corresponding center, see[1, 2]. It was shown in [2] that pCP is NP-hard. (cid:3) Thanks to Spanish Research projects: MTM2012-36163-C06-05 and MTM2013-46962-C2-2-P straight application of the pCP is the location of emergency serviceslike ambulances, hospitals or fire stations, since the whole population shouldbe inside a small radius around some emergency center. pCP has been ex-tensively studied, and both exact and heuristic algorithms have been pro-posed.The uncertainties can be generally classified into three different cate-gories: provider-side uncertainty, receiver-side uncertainty, and in-betweenuncertainty. The provider-side uncertainty may capture the randomness infacility capacity and the reliability of facilities, etc.; the receiver-side uncer-tainty can be the randomness in demands; and the in-between uncertaintymay be represented by the random travel time, transportation cost, etc.In this paper we focus on the receiver-side uncertainty and in the stochas-tic programming approach. The SP approach has been widely applied toemergency logistics for short-notice disasters (e.g., hurricanes, flooding,and wild fires) by assuming that possible impacts of these disasters canbe estimated based on historical and meteorological data. The commongoal of these stochastic location models is to optimize the expected valueof a given objective function. A classical example of applying SP to disas-ter relief is the scenario-based, two-stage stochastic model proposed by [3],for medical supply pre-positioning and distribution in emergency manage-ment.Different formulations of this problem are proposed and we show theirstrengths and limits. Besides we adapt Variable Neighborhood Search (VNS)which is a heuristic to solve combinatorial problems originally proposedfor the p -median problem. Computational tests show that VNS provideshigh quality solutions. References [1] M. Albareda-Sambola, J. Díaz, and E. Fernández. Lagrangean duals and exactsolution to the capacitated p -center problem. European Journal Operational Re-search, 201:71–81, 2010.[2] O. Kariv and S. Hakimi. An algorithmic approach to network location prob-lems I: The p -centers. SIAM Journal on Applied Mathematics, 37 (3):513–538,1979.[3] H. O. Mete and Z. B. Zabinsky. Stochastic optimization of medical supply loca-tion and distribution in disaster management. International Journal of ProductionEconomics , 126:76-84, 2010.I Workshop on Locational Analysis and Related Problems 2015 19
Conditions to LP relaxthe allocation variables of thereliability fixed-charge location problem
Javier Alcaraz, Mercedes Landete, Juan F. Mongeand José L. Sainz-Pardo Departamento de Estadística, Matemáticas e Informática,Centro de Investigación Operativa,Universidad Miguel Hernández de Elche, Spain,[email protected], [email protected], [email protected], [email protected]
The Reliability Fixed-Charge Location Problem is an extension of the Sim-ple Plant Location Problem which considers that some facilities have aprobability of failure. Snyder and Daskin (2005) proposed a binary formu-lation for the Reliability FixedCharge Location Problem. They defined thetwo classical families of binary variables on location problems, the locationvariables and the allocation variables and assumed that the LP relaxationof the allocation variables was straightforward. In this work we show thatalthough for the instances tested in Snyder and Daskin (2005) the assump-tion was true, the allocation variables can be LP relaxed only if certain con-ditions hold.
1. On LP relaxing the allocation variables
We prove that we can LP relax all the allocation variables associated tonon-failable facilities or all the allocation variables associated to failablefacilities but not both simultaneously. We also prove that all the allocationvariables could be LP relaxed by adding a family of valid equalities to theset of constraints. Finally, we show and demonstrate in which cases we canto LP relax all the allocation variables simultaneously. . Computational experience
The figure 1 shows the magnitude of the objective value errors in order toillustrate how wrong it is to LP relax all the allocation variables.
Figure 1.
Objective value errors
References [1] L. Cánovas, M. Landete, A. Marín, On the facets of the simple plant locationpolytope. Discrete Applied Mathematics 124 (2002) 27-53.[2] I. Espejo, A. Marín, A.M. Rodriguez-Chia, Closest assignment constraints indiscrete location problems. European Journal of Operational Research (2012)219 4958.[3] J. Alcaraz, M. Landete, J.F. Monge, J.L. Sainz-Pardo, Strengthening the reliabil-ity fixed-charge location model using clique constraints. Computers & Opera-tions Research (2015) 60 1426[4] L.V. Snyder, M.S. Daskin, Reliability models for facility location: the expectedfailure cost case. Transportation Science (2005) 39 400–416.I Workshop on Locational Analysis and Related Problems 2015 21
A variable neighborhood search approachfor the 3-maneuver aircraft conflictresolution problem (cid:3)
A. Alonso-Ayuso, L.F. Escudero, F.J. Martín-Campo, N. Mladenovi´c Universidad Rey Juan Carlos, Madrid, Spain, [email protected],[email protected] Universidad Complutense de Madrid, Madrid, Spain, [email protected] Université de Valenciennes et du Hainaut-Cambrésis, France
1. Problem description and resolution
The aircraft conflict resolution problem takes an important role within theAir Traffic Management problem. The aim of the problem consists of pro-viding a new aircraft configuration, almost in real-time, in such a way thatevery conflict situation during the cruise phase is avoided. A conflict is de-fined as that event in which two or more aircraft violate the safety distancesthat must be kept in flight. The distances are 5 nautical miles as horizontaland 2000 feet as vertical. This means that every aircraft is in the center of asafety zone which is a cylinder with 2.5 nautical miles of radius and 2000feet of height. In order to avoid conflict situations, three maneuvers may beperformed: Velocity and heading angle changes as horizontal maneuversand altitude level changes as vertical ones.The most critical point in the study of this problem is the resolutiontime, being necessary to have a solution in almost real-time. It is worthpointing out that the problem to be solved assumes only the aircraft of acertain region of the airspace so-named air sector which may contain up (cid:3)
This research is partially supported by the projects OPTIMOS3 MTM2012-36163-C06-06 andPCDASO MTM2012-31514, both funded by the Spanish Ministry of Economic Affairs andCompetitiveness. o 20-25 aircraft at most. Our previous studies on the problem are basedon a mixed integer nonlinear and nonconvex optimization. The three ma-neuvers are considered at once. However, the resolution time grows as thenumber of aircraft under consideration does (increasing the model dimen-sions), due to the high number of nonlinearities in the constraint system. Ametaheuristic approach based on sequentially solving mixed integer linearoptimization problems has been also studied but the resolution time is notgood when more than 20 aircraft are considered at once. Those models arestudied in a multicriteria framework where different criteria are taken intoaccount (lexicographical, compromise, etc.).We present a Variable Neighborhood Search (VNS) metaheuristic ap-proach able to provide good solutions by using a small computing timeconsidering the three maneuvers and in a multicriteria environment. Aprevious work, only considering heading angle changes, reported goodresults in terms of computing time and solutions quality.The VNS metaheuristic consists of two important steps: the local searchand the shaking phase. The link between them is the penalty cost functioncomposed by two terms in our case: the objective function and the infeasi-bility condition which is highly penalized. In our case, using a geometricconstruction presented in a previous work in the literature, the infeasibilitycondition for horizontal conflict situations is well defined.For the local search, we have experimented two options: first improve-ment and best improvement. The previous study with only heading anglechanges showed that no important differences on solutions quality appear,so, as the first improvement method needs less computing time, we choosethat option. The criterion to go from one solution to another consists ofchanging the angle for each aircraft until no improvement is found. In thethree-maneuvers case, a similar procedure will be implemented, but con-sidering the different maneuvers.The shaking phase is important to jump from one possible local optimalsolution to another zone in which the best solution found can be improved.A subset of aircraft under consideration is selected to change the headingangle. For the three-maneuvers case, the selected aircraft will be allowedto change at least one of the three maneuvers. The new approach combineslocal search and shaking procedure until the time limit is reached.A broad computational experience is reported for the case where onlyheading angle changes are considered, comparing the VNS approach withthe state-of-the-art Mixed Integer Nonlinear Optimization engine solverMinotaur and the metaheuristic based on sequentially solving mixed inte-ger linear optimization models. Preliminary results are also presented onthe three-maneuvers case by using VNS.
I Workshop on Locational Analysis and Related Problems 2015 23
The probabilisticpickup and delivery problem
E. Benavent , M. Landete , J.J. Salazar , G. Tirado Departament d’Estadistica i Investigacio Operativa, Universitat de Valencia, Spain Universidad Miguel Hernandez de Elche, Alicante, Spain Universidad de La Laguna, Spain Universidad Complutense de Madrid, Spain
In this paper we introduce the Probabilistic Pickup-and-Delivery Travel-ling Salesman Problem (PPDTSP). It is a variant of the PTSP where onelocation (called depot) is the starting and ending location of the route, andthe others locations are grouped in pairs. Each pair of locations representsa potential request to transport a product from one location (pickup) to theother (delivery). Each potential request may be formalized or not accord-ing to a Bernoulli probability distribution. If a potential request is formal-ized, its pickup location must precede its delivery location along the route.Otherwise, the vehicle must skip visiting the pair of locations associated tothat request. A feasible solution for the PPDTSP (also called a-priori route)is a Hamiltonian route to allow serving all requests.Once an a-priori routehas being decided, the realization of the random variables is known andthe vehicle visits the locations of the formalized requests as they appear inthe a-priory route. We present two different formulations and we comparethem.
I Workshop on Locational Analysis and Related Problems 2015 25
Multisource linear regression
Víctor Blanco y and Justo Puerto zy Dpt. Quant. Methods for Economics & Business, Universidad de Granada [email protected] z Dpt. Statistics & OR, Universidad de Sevilla [email protected]
We present here a mathematical programming approach to linear re-gression when structural changes occur in the data. We extend the familyof methods introduced in [1] where different distance-based residuals andgeneralized ordered weighted averaging operators to aggregate the resid-uals were considered. This natural extension is analogous to the one fromsingle-facility location to the multifacility case. General formulations areprovided and exhaustive analysis of some especial cases of residuals arereported.
1. Introduction
Regression analysis studies the functional relationship between a set of vari-ables X ; : : : ; X d . Such a dependence is expressed through an equation ofthe form f ( X ; : : : ; X d ) = 0 , and a sample of data is used to estimate f .It is usual to fix the parametric family of functions where f belongs andthe parameters are estimated from the sample. In linear regression, f is as-sumed to be a linear functional and estimating it consists of determiningits coefficients.Given set of data f x ; : : : ; x n g (cid:26) R d , to obtain an estimation of the coef-ficients of the linear model, one tries to find the coefficients of f , ^ (cid:12) R d +1 ,that minimize some measure of the deviation of the data with respect to thefitting body H (^ (cid:12) ) = f z R d : ^ (cid:12) + ∑ dk =1 ^ (cid:12) k z k = 0 g . For a certain obser-vation x R d in the sample, such a deviation is known as the residual . Weconsider that the residual of a model is a mapping " x : R d +1 ! R + , thatmaps any set of coefficients (cid:12) , into a measure that represents how muchdeviates the fitting of the model, with those parameters, from the observa-tion x . The larger this measure, the worse the fitting for such a single ob-ervation x . The final goal of a regression model is to find the coefficientsminimizing a globalizing function, (cid:8) : R n ! R , of the residuals of all thepoints. Different choices for the residuals and the globalizing criteria willgive, in general, different estimations for the parameters and thus differ-ent properties for the resulting models. This statistical problem is closelyrelated with continuous location problem, whenever one wants to com-pute a point (coefficients of the models) provided that it minimizes certainfunction of the “distances” from the point to a given set of points (sample).In this paper linear regression models where possible structural changesoccur in the data are analyzed. These models are particularly useful whenthe variables are time-indexed and certain past situations (breakpoints)provoked that the linear relationship of the variables before and after thosemoments changes. These linear regression models are known in the lit-erature as piecewise regression [5], segmented regression [4] or partitionregression.Whenever the breakpoints are known one may apply linear re-gression methods to all the partitions obtained from the points, reducing toseveral independent linear regression models, but in practical applications,those points are unknown and need to be determined.We propose a new family of methods to estimate the coefficients of thisstructural change problems in linear regression. These methods allows notonly to estimate the models but also the breakpoints where the behaviourof the data changes. We point out the analogy between linear regression( breakpoints problem) and this problem, which is the same that the onebetween single facility and multi-facility location problems [2, 3]. References [1] Blanco, V., Puerto J. and Salmerón, R. (2015),
A general framework for multiplelinear regression.
Submitted. http://arxiv.org/abs/1505.03451 .[2] Brimberg, J., Hansen, P., Mladonovic, N. and Salhi, S. (2008)
A survey of solutionmethods for the continuous location allocation problem . International J. of Opera-tions Research, 5 (1), 1–12.[3] Drezner Z., Hamacher H.W. (2002).
Facility location: applications and theory .Springer.[4] Lerman, P.M. (1980).
Fitting segmented regression models by grid search . AppliedStatistics, 29, 77–84.[5] McGee, V.E. and Carleton, W.T. (1970).
Piecewise Regression . Journal of theAmerican Statistical Association 65 (331), 1109-1124.I Workshop on Locational Analysis and Related Problems 2015 27
A dispersion model in ODEs
Rafael Blanquero , Emilio Carrizosa , M. Asunción Jiménez-Cordero ,and Boglárka G.-Tóth University of Seville, Spain, [email protected], [email protected], [email protected] Budapest University of Technology and Economics , Hungary, [email protected]
We consider initial value problems in Ordinary Differential Equations (ODE)in which the initial conditions are decision variables.Locating the initial conditions yielding n trajectories as disperse as pos-sible (in a sense to be formalised) is a continuous location problem whichcan be numerically addressed using a geometrical branch and bound. Keywords: dispersion models, ordinary differential equations, location ofinitial values.
I Workshop on Locational Analysis and Related Problems 2015 29
Rapid transit network design: competitionand transfers
Luis Cadarso, and Ángel Marín Rey Juan Carlos University, Departamental III Building, Camino del Molino s/n, Fuen-labrada 28943, Spain, [email protected] Universidad Politécnica de Madrid, E.T.S.I. Aeronáuticos, Pza. Cardenal Cisneros, 3,Madrid 28040, Spain, [email protected]
The problem of increasing traffic congestion is raising the concerns aboutenergy constraints and greenhouse emissions. Considerable attention hasbeen given to the utilization of freight and passengers railway systems asa relative efficient and eco-friendly traffic mode. Increasing mobility andlonger journeys caused by the growth of cities have also stimulated theconstruction and expansion of rail transit systems such as metro, urbanrail, and light rail systems. Due to their high cost of construction, it is im-portant to pay close attention to the effectiveness in solving the networkdesign problem. The location decisions and the maximum coverage of thedemand for the new network is the main goal, taking a list of potentialrapid transit corridors and stations, and considering budget availability.Transportation demand models are used to develop forecasts of passen-ger demand for each origin-destination pair as a function of attributes suchas average fares, service frequencies, and travel times. Given these totaldemand estimates, passenger choice models are used to estimate for eachcompetitor and each origin-destination pair, the proportion of demand (orthe share) it captures in that origin-destination pair.Travel time is one of the most important attributes on which the dif-ferent operators may compete in rapid transit networks. A network canattract more passengers in a origin-destination pair by decreasing traveltime. For a given unconstrained total demand, the market share of eachoperator depends, among other factors, on its own travel time and on thetravel time of its competitors. Another convenient attribute for attractingpassengers is to offer direct trips without transfers. Transfers are usuallyxtremely discouraging. Both, travel time and transfers strongly dependon the network design. Therefore, it is extremely important to account forthem in order to make an efficient design.In this paper, we present a mixed integer, non-linear programming modelfor the rapid transit network design problem that includes a passengerchoice model to capture multi-modal competition between the new net-work to be constructed and the current network.Our major contributions include:1. Development of a new formulation for the rapid transit network de-sign problem which embeds a logit model for modeling passengerbehavior.2. Introduction of transfers in the modeling approach; a decisive at-tribute for attracting passengers to the new network is to offer directtrips without transfers. We embed the transfer cost in the passengertrip generalized cost.3. We solve this model using realistic problem instances obtained fromthe network of Seville in Spain. Because current commercial soft-ware fails to solve medium and large scale problems, we use the La-grangian Relaxation to obtain the optimal solution of the problem.
I Workshop on Locational Analysis and Related Problems 2015 31
The maximal covering locationbi-level problem (cid:3)
José-Fernando Camacho-Vallejo, Martha-Selene Casas-Ramírez, JuanA. Díaz and Dolores E. Luna Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, NuevoLeón, México, {jose.camachovl}, {martha.casasrm}@uanl.edu.mx Universidad de las Américas Puebla, Puebla, México, {juana.diaz}, {dolorese.luna}@udlap.mx
In this presentation the maximal covering location bi-level problem is pro-posed. The aim of the problem is to maximize the customer’s demand cov-ered by a predefined number of opened facilities. The main assumptionconsidered through this research is that customers are allowed to freelychoose their allocation to the facilities within a coverage set. The problemis modelled as a bi-level mathematical programming problem where twodecision makers are considered: the leader and the follower. The leader ison charge of locate the facilities seeking to maximize the covered demand.On the other hand, the follower will allocate customers to the opened fa-cilities based on their preferences towards the facilities. By doing this, thefollower will maximize a utility function that relates those preferences. Theproblem is optimally solved by two single-level reformulations of the bi-level problem and some equivalency results between the models are dis-cussed. The complexity resulting from preliminary computational exper-imentation after solving large instances of the problem led us to developheuristic methods for obtaining good quality solutions. In order to achievethe latter, we implemented a tabu search method and a genetic algorithm.The performance of both heuristics over a large set of instances is shown.Also, the main differences and advantages arising from the numerical ex-perimentation are discussed. (cid:3)
Thanks to the Mexican National Council for Science and Technology (CONACYT) throughgrant SEP-CONACYT CB-2014-01-240814. . Problem statement
In this section the problem’s description of the maximal covering locationbi-level problem (MCLBP) is described. Consider the situation when a setof customers has a demand associated to each of them. These customersare covered -or not- by a existing firm in the market. Then, a competingfirm intends to enter to the market by opening some facilities. Therefore,the already covered customers will decide if they stay with they currentfacility or will change to a new one. Also, the non-covered customers willchoose a new facility for being allocated.The problem is conformed by a leader -the entering competing firm-and a follower -the set of customers-. On the one hand, the leader will de-cide the location of a limited number of facilities aiming to maximize thedemand covered. On the other hand, the follower will allocate the cus-tomers to their most preferred opened facilities seeking to maximize thecustomer’s preferences towards the facilities.Some considerations need to be made by the follower. First, the cus-tomers may be allocated to old or new opened facilities; also, some ofthem may be uncovered. Second, the allocation of the customers can beonly made to a facility within a coverage set. That is, if a customer prefersa facility that exceeds the maximum coverage distance, then, the customercannot be allocated to that facility; instead of, it will be allocated to it mostpreferred opened facility in the set of facilities that cover that specific cus-tomer. Third, the preferences of the customers are assumed to be integerpositive consecutive numbers from 1 to the total number of facilities in themarket, including the already existing and the potential ones. A greatervalue implies better preference from that customer to the facility.Also, it is important to mention that the already existing facilities in themarket cannot be closed. It is evident that the leader does not has controlover that decision; but, he will try to capture the maximum customer’s de-mand belonging to the existing firm.
I Workshop on Locational Analysis and Related Problems 2015 33
A decomposition scheme for the railwayrapid transit depot location and rolling stockcirculation problem
David Canca, Alicia de los Santos, Eva Barrena, and Gilbert Laporte School of Engineering, Department of Industrial Engineering and Management Science,Av. de los Descubrimientos sn, 41092, Seville, Spain, [email protected] School of Engineering,Department of Applied Mathematics II, Av. de los Descubrimientossn, 41092, Seville, Spain, [email protected] School of Computing,University of Leeds, Leeds, LS2 9JT, United Kingdom, [email protected] CIRRELT and HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, CanadaH3T 2A7, [email protected]
Network design and line planning are the two first stages in the railwayplanning process. However, the network configuration does not includethe location of depots where trains have to rest every day. In Rapid TransitNetworks, the depot location drastically influences the number and lengthof empty rolling stock runs, devising in long term high operating costs.Rolling stock is one of the most important operational issues for railwaytransportation companies. Rolling stock and infrastructure maintenancesuppose about 75% of total annual cost for a typical railway transporta-tion. Basically, rolling stock circulation consists of determining individualtrain paths over the network with the objective of minimizing costs whileaccomplishing a pre-defined schedule. In this work we formulate the inte-grated depot location and rolling stock circulation problem and propose adecomposition mechanism in order to solve medium and large instancesin reasonable computation times with commercial state-of-the art solvers. . Introduction
Rolling stock management supposes huge capital investment decisions forservice operators that cannot be changed frequently, which means thatrolling stock becomes a strategic decision with a future impact of severaldecades. In general, rolling stock circulation plan includes a set of interre-lated sub-problems such as train composition determination (locomotivesand carriages coupling and decoupling), vehicle and carriage rest loca-tion (avoiding empty movements), vehicle circulation problem and main-tenance policies. In the context of RRT systems, services are usually per-formed by train units with various composition types (e.g. with two, threeor four carriages), what means that coupling and decoupling decisions canbe avoided. Then, the problem can be viewed as a special multi-commoditycapacitated minimum cost flow problem where a set of different commodi-ties (trains with different characteristics) must be routed every day througha network from certain stations (rest places) in order to ensure a set ofservices and to guarantee minimum operation cost. The problem becomesmore complex when train maintenance decisions are also incorporated.Several models have been proposed for railway rolling stock problems.[11] minimizes the number of train units needed to satisfy a given de-mand. Related with this paper, [3] study the problem of routing singlecarriages through a network, considering empty carriage movements. [4]present a Benders decomposition approach for determining a set of mini-mum cost equipment cycles such that every trip is covered using appropri-ate equipment. [5] extend their model incorporating maintenance issues.[8] describe a model and a solution approach for a car assignment problemthat arises when individual car routings must be determined consideringmaintenance constraints and minimum connection depending on the posi-tions of cars. [1] present an integer programming model with the objectiveof minimizing seat shortage during morning rush hours.[2] propose an integer programming model in order to obtain the circu-lation of rolling stock considering order in train compositions. The modelis devoted to a single line and for only one day of operation. [10] use atransition graph (see [2]) to represent the possible changes in trains com-position at each station.Maintenance issues have also been incorporated in some contributions.[12] set up a large scale integer programming model for locomotive assign-ment considering that locomotives requiring inspection must be sent toappropriate shops within a given time limit. [5] propose a multicommod-ity network flow-based model for assigning locomotives and cars to trains.The work of [8] supports operational aspects concerning locomotive-hauledailway cars. They consider maintenance constraints inside a model withthe objective of maximizing the expected profit. [9] propose a multicom-modity flow type model for routing units that require maintenance in theforthcoming one to three days.We propose a sequence of optimization models taking advantage of theproblem structure in order to first determine the minimum number of ve-hicles needed to perform the actual train schedule. In a second phase, weobtain the cyclic weekly train circulation which is used to define the mostconvenient maintenance policy, developed in a third stage.
References [1] Abbink, E. J. W., Berg, B. W. V. van den, Kroon, L. G. & Salomon, M. (2004).Allocation of railway rolling stock for passenger trains. Transportation Science,38(1), 3342.[2] Alfieri, A., Groot, R., Kroon, L. Schrijver, A. (2006). Eficient Circulation of Rail-way Rolling Stock. Transportation Science, 40(3), 378391.[3] Brucker, P., Hurink, J. L. Rolfes, T. (2003). Routing of railway carriages. Journalof Global Optimization, 27(2-3), 313332.[4] Cordeau, J. F., Soumis, F. Desrosiers, J. (2000). A benders decomposition ap-proach for the locomotive and car assignment problem. Transportation Science,34(2), 133149.[5] Cordeau, J. F., Soumis, F. Desrosiers, J. (2001). Simultaneous assignment of lo-comotives and cars to passenger trains. Operations Research, 49, 49(4), 531548.[6] Fioole, P.-J., Kroon, L., Maróti, G. Schrijver, A. (2006). A rolling stock circulationmodel for combining and splitting of passenger trains. European Journal ofOperational Research, 174(2), 12811297.[7] Holmberg, K. Yuan, D. (2003). A multicommodity network flow problem withside constraints on paths solved by column generation. Informs Journal onComputing, 15(1), 4257.[8] Lingaya, N., Cordeau, J. F., Desaulniers, G., Desrosiers, J. Soumis, F. (2002).Operational car assignment at VIA rail Canada. Transportation Research PartB: Methodological, 36(9), 755778.[9] Maroti, G. Kroon, L. (2005). Maintenance Routing for Train Units: The Transi-tion Model. Transportation Science, 39(4), 518525.[10] Peeters, M. Kroon, L. (2008). Circulation of railway rolling stock: a branch-and-price approach. Computers & Operations Research, 35(2), 538556.[11] Schrijver, A. (1993). Minimum circulation of railway stock. CWI Quarterly, 6,205217.[12] Ziarati, K., Soumis, F., Desrosiers, J., Gélinas, S. Saintonge, A. (1997). Locomo-tive assignment with heterogeneous consists at CN North America. EuropeanJournal of Operations Research, 98, 281292.I Workshop on Locational Analysis and Related Problems 2015 37
Robust p -median problem withvector autoregressive demands Emilio Carrizosa, Alba V. Olivares-Nadal, and Pepa Ramírez-Cobo Universidad de Sevilla Universidad de Cádiz
Most robust location problems are based in either distributional assump-tions over the clients’ demands, or in scenario analysis. However, lately anew approach is raising: nominal values for the future demands are as-sumed to be given and uncertainty structures are built taking into accountthose values. Although authors like to think no statistical procedures areinvolved in these approaches, the truth is that those nominal values forthe demand must have been obtained somehow relying in prediction orestimation methods, and the user has no control over it. Moreover, theseuncertainty sets allow demand realizations for time t that do not dependon the realization of the demand for time t (cid:0) ; i.e., these uncertainty setsmight contain paths that do not preserve the inner behaviour of the de-mands.In this work we assume the demands of the clients follow a Vector Au-toregressive Process (VAR), whose parameters are given. Instead of usingthe nominal values to model the uncertainty sets, we make use of parame-ters of the VAR. In particular, we aim to solve a robust p -median problemwhere the demand is uncertain but required to follow the VAR process,whose errors are bounded ∥∥ p (cid:20) (cid:14) . I Workshop on Locational Analysis and Related Problems 2015 39
Using an interior-point method for hugecapacitated multiperiod facility location (cid:3)
Jordi Castro, Stefano Nasini, and Francisco Saldanha-da-Gama Dept. of Statistics and Operations Research, Universitat Politècnica de Catalunya, JordiGirona 1–3, 08034 Barcelona, Catalonia, Spain. [email protected] Dept. of Production, Technology and Operations Management, IESE Business School,University of Navarra, Av. Pearson 21, 08034 Barcelona, Catalonia, Spain. [email protected] Dept. of Statistics and Operations Research/Operations Research Center, Faculdade deCiências, Universidade de Lisboa, Campo Grande 1749-016 Lisboa, Portugal. [email protected]
The capacitated facility location problem is a well known MILP, whichhas been efficiently solved, among others, by cutting-plane procedures. Inthis work we focus on a multiperiod variant of this problem. We refer thereader to [4] for a recent survey on facility location.The solution of the multiperiod capacitated facility location by cuttingplanes requires the solution of a master problem involving a convex non-differentiable function Q ( y ) , y being the binary variables. This function Q ( y ) is lower approximated by cutting planes, which are obtained by com-puting Q (^ y ) and a subdifferential s @Q (^ y ) for some particular ^ y : thismeans the solution of a linear optimization subproblem in the continuousvariables. In essence, this is Benders decomposition.Our focus is on world-wide facility locations problems that may be faced,for instance, by internet-based retailer multinational companies. Such prob-lems may involve a few hundreds of world locations for warehousing ac-tivities, and millions of customers, associated to cities over some thresh-old population. In those situations the dimension of the subproblems ofthe cutting-plane procedure can be of order of hundreds of millions or bil-lions of variables. These subproblems, one for time period, exhibit a block- (cid:3) Work supported by grant MTM2012-31440 of the Spanish Ministry of Economy and Com-petitiveness ngular structure that can be exploited by the solver BlockIP [1], which im-plements a specialized interior-point method for block-angular structures(see, for instance, [2] for details).Extensive computational testing showed the efficiency of this combina-tion of cutting planes with interior-point methods for huge problems: thelargest instances involved up to 3 time periods, 200 locations and 1 mil-lion customers, resulting in MILPs of 600 binary and 600 million continu-ous variables. Those MILP instances were optimally solved by the cutting-plane-interior-point approach in less than one hour of CPU, while state-of-the-art solvers (i.e., CPLEX) were unable to solve them (either using itsinternal branch-and-cut MILP solver, or their continuous solvers within thecutting-plane approach). Indeed, the state-of-the-art solver was not able toperform any single iteration since it exhausted the 144 Gigabytes of mem-ory of the server used for these experiments.
References [1] J. Castro (2015). Interior-point solver for convex separable block-angular problems, Optimization Methods & Software, (2015) in press,doi:10.1080/10556788.2015.[2] J. Castro and J. Cuesta (2011). Quadratic regularizations in an interior-pointmethod for primal block-angular problems, Mathematical Programming, 130,414-445.[3] J. Castro, S. Nasini and F. Saldanha-da-Gama (2015). A cutting-plane approachfor large-scale capacitated multi-period facility location using a specializedinterior-point method, Research Report DR 2015/01, Dept. of Statistics and Op-erations Research, Universitat Politeècnica de Catalunya.[4] M.T. Melo, S. Nickel and F. Saldanha-da-Gama (2009). Facility location andsupply chain management - A review, European Journal of Operational Re-search, 196, 401–412.I Workshop on Locational Analysis and Related Problems 2015 41
On the hierarchical rural postmanproblem on a mixed graph
Marco Colombi, Ángel Corberán, Renata Mansini, Isaac Plana, and José M. Sanchis Universita degli Studi di Brescia, Italy, marco.colombi, [email protected] Universidad de Valencia, Spain, angel.corberan, [email protected] Universidad Politécnica de Valencia, Spain, [email protected]
In this talk we present a special case of the Rural Postman Problem on amixed graph where arcs and edges that require a service are divided intosubsets that have to be serviced in a hierarchical order. In this paper wepropose a new mathematical formulation, provide a polyhedral analysisof the problem and propose a branch-and-cut algorithm for its solutionbased on the introduced classes of valid inequalities.
1. The HMRPP
In many practical applications (garbage collection, snow plowing), con-straints may be imposed on the order in which clusters of streets (edges orarcs) have to be visited. For example, in snow plowing, main streets have tobe cleared before secondary streets and, in turn, secondary streets shouldbe cleaned before residential ones. Up to now the problem has been ana-lyzed mainly on undirected graphs in which all the edges require a service(the Hierarchical Chinese Postman Problem – HCPP).In this paper, we extend the HCPP in two ways by first consideringmixed instead of undirected graphs and then by requiring a service only ona subset of arcs and edges. The resulting problem, the Hierarchical MixedRural Postman Problem (HMRPP), is defined as follows. Let G = ( V; E; A ) be a strongly connected mixed graph, where V is the set of nodes, E is theset of edges, and A is the set of arcs. Node is the depot. From now on,we will use the term link to refer both to an edge or an arc, indistinctly.inks requiring a service are divided into classes (hierarchies) indicating apredefined priority on the service.Let E R = E R [ E R [ ::: [ E pR be the set of required edges and A R = A R [ A R [ ::: [ A pR the set of required arcs, where p is the number of hierarchies.Following the specified hierarchical order, all the links in E kR [ A kR must beserviced before those in E mR [ A mR if k < m .As in [1], we consider three different costs associated with each requiredlink ( i; j ) E R [ A R : ^ c ij : the cost of traversing a link ( i; j ) that has not been serviced yet, (cid:22) c ij : the cost of traversing and servicing link ( i; j ) , ~ c ij : the cost of traversing a link ( i; j ) that has already been serviced.A crossing cost c ij is associated with each non-required link ( i; j ) . The costof traversing an edge is the same in both directions. Usually it is assumed(see [1]) that (cid:22) c ij > ^ c ij > ~ c ij . Consider, for example, snow removal opera-tions, where removing snow on a street is the most time-consuming oper-ation, followed by traversing an uncleaned street and, finally, crossing analready cleaned one. Nevertheless, other sorting of costs may find a prac-tical justification as well. For instance, it is not difficult to assume that insnow removal ^ c ij > (cid:22) c ij holds for some links, that is, the cost of traversinga non serviced link is definitely more expensive than that of servicing itsince a non-cleaned street can be hardly traversed.The HMRPP consists of finding a minimum cost tour starting and end-ing at the depot while servicing all the required links in the specified hi-erarchical order. Note that the subgraph induced by the required links E R [ A R and the subgraphs induced by the sets E kR [ A kR , for all k , donot need to be connected. Moreover, since the required links must be ser-viced in a hierarchical order, a tour for the HMRPP can be interpreted as asequence of consecutive connected paths, each one servicing the requiredlinks in each hierarchical level, plus a final path back to the depot.In this paper we propose a new mathematical formulation, provide apolyhedral analysis of the problem and propose a branch-and-cut algo-rithm for its solution based on the introduced classes of valid inequalities. References [1] Cabral, E.A., Gendreau, M., Ghiani, G., Laporte, G. “Solving the hierarchicalchinese postman problem as a rural postman problem”.
European Journal of Op-erational Research
Strategic oscillation for a hub locationproblem with modular link capacities
Ángel Corberán , Juanjo Peiró , Fred Glover , and Rafael Martí Departament d’Estadística i Investigació Operativa, Universitat de València, Spain. [email protected]; [email protected]; [email protected] OptTek Systems, Boulder (CO), USA. [email protected]
Hub location problems related to the design of transportation networksare one of the most extensively studied problems in combinatorial opti-mization due to their variety and importance. In a hub location problem,one is given a network G = ( V; E ) with a set of demand nodes V , and aset of edges E . For each pair of nodes i and j V , there is a traffic t ij (ofgoods, people, etc.) to be transported through a set of facility locations se-lected from a given set of potential locations V . It is assumed that directtransportation between terminals is not possible and, therefore, the traffic t ij travels along a path i ! h i ! h j ! j , where i and j are assigned tohubs h i and h j , respectively. The goal is to identify an optimal subset of fa-cilities in order to minimize a transportation cost function while satisfyinga set of constraints.Among the family of hub location problems, we focus on a specificvariant known as the capacitated single assignment hub location problem withmodular link capacities (CSHLPMLC). This problem was formulated as aquadratic mixed integer programming problem by Yaman and Carello [1],with the following characteristics: Opening a hub at node i has a fixed in-stallation cost C ii . Each hub i has a capacity Q h limiting the total amountof traffic transiting through i . There are two types of edges between nodes:edges of the first type are used to connect terminals with hubs, and we callthem access edges . Let m i be the number of access edges needed to routethe incoming and outgoing traffic at node i , and let Q a be the maximumcapacity an access edge allows to transfer through it in each direction. So, i = max {⌈ ∑ j V t ij Q a ⌉ ; ⌈ ∑ j V t ji Q a ⌉} : The cost of installing m i edgesbetween terminal i and hub k is denoted by C ik . Edges of the second typeare used to transfer traffics between hubs, and we call them backbone edges .Each backbone edge has a maximum traffic capacity of Q b (in each direc-tion). We define A as the set of (directed) arcs associated with the (undi-rected) edges in E , A = f ( k; l ) : k; l V; k ̸ = l g .If nodes k and l are hubs, the amount of traffic on arc ( k; l ) , denotedas z kl , is the traffic that has to be transported from nodes assigned to k tonodes assigned to l . The capacity Q b of a given edge f k; l g cannot be lessthan the maximum traffic on its corresponding arcs ( k; l ) and ( l; k ) , and thecost of installing the edge is denoted by R kl .Three different costs have to be considered in this problem: The openingcosts of the hubs ( C kk ), the assignment costs of terminals to hubs ( C ik ),and the traffic costs between hubs. While cost C ik corresponds to that oftransporting all the traffic involving i through hub k , R kl represents thecost of using only one backbone edge f k; l g .The following variables are defined in [1] in order to provide the math-ematical programming model shown below:The assignment variable x ik is equal to 1 if terminal i is assigned tohub k , and 0 otherwise. If node i receives a hub, then x ii takes value1. z kl is the traffic on an arc ( k; l ) A and w kl is the number of copiesof the edge f k; l g 2 E .Then, the capacitated single assignment hub location problem with mod-ular link capacities can be formulated as follows ([1]): min ∑ i V ∑ k V C ik x ik + ∑ f k;l g2 E R kl w kl (1) ∑ k V x ik = 1 i V (2) x ik (cid:20) x kk i V; k V n f i g (3) ∑ i V ∑ j V ( t ij + t ji ) x ik (cid:0) ∑ i V ∑ j V t ij x ik x jk (cid:20) Q h x kk k V (4) z kl (cid:21) ∑ i V ∑ j V t ij x ik x jl ( k; l ) A (5) Q b w kl (cid:21) z kl k; l g 2 E (6) b w kl (cid:21) z lk k; l g 2 E (7) x ik ; g 8 i; k V (8) w kl Z + k; l g 2 E (9) z kl (cid:21) ( k; l ) A: (10)Many heuristics and metaheuristics have been proposed to solve differ-ent variants of hub location problems, including GRASP, VNS, tabu search,and several complex hybrid techniques. In this research we present a sim-ple, easily adaptable and powerful algorithm, based on the iterated greedy– strategic oscillation (SO) methodology. Our purpose is to investigate theSO proposal, which alternates between constructive and destructive phasesas a basis for creating a competitive method for this hub location problem.We will also present a comparison between methods and optimal results.Computational outcomes on a large set of instances show that, while onlysmall instances can be optimally solved with exact methods, our meta-heuristic is able to find high-quality solutions on larger instances in shortcomputing times, and outperforms the previous tabu search implementa-tion. References [1]
Yaman, H., and Carello, G.
Solving the hub location problem with mod-ular link capacities.
Computers & Operations Research 32 , 12 (2005), 3227–3245.I Workshop on Locational Analysis and Related Problems 2015 47
Ordered Weighted Average Optimizationin multiobjective spanning tree problems
Elena Fernández, Miguel A. Pozo, Justo Puerto andAndrea Scozzari Universitat Politècnica de Catalunya – Barcelona Tech (Spain) [email protected] University of Seville (Spain) [email protected], [email protected] University Niccolò Cusano. Roma (Italy) [email protected]
Multiobjective Spanning Tree Problems are analyzed in this paper. The or-dered median objective function is used as an averaging operator to aggre-gate the vector of objective values of feasible solutions. This leads to thestudy of the Ordered Weighted Average Spanning Tree Problem, a nonlin-ear combinatorial optimization problem. Different formulations as a mixedinteger linear problem are proposed, based on the most relevant Minimumcost Spanning Tree models in the literature. These formulations are ana-lyzed and several enhancements proposed. Their empirical performanceis tested over a set of randomly generated benchmark instances. The re-sults of the computational experiments show that the choice of an appro-priate formulation allows to solve larger instances with more objectivesthan those previously solved in the literature.
References [1] Fernández, E., Pozo, M.A. and Puerto, J. (2014) “Ordered weighted averagecombinatorial optimization: Formulations and their properties”.
Discrete Ap-plied Mathematics , vol. 169: 97–118.[2] Galand, L. and Spanjaard, O. (2012) “Exact algorithms for OWA-optimizationin multiobjective spanning tree problems”.
Computers & Operations Research ,vol. 39: 1540–1554.[3] Magnanti, T.L. and Wolsey, L.A. (1995) “Optimal trees”. In
Network Models,Chapter 9 , vol. 7 of
Handbooks in Operations Research and Management Science ,pp. 503 – 615. Elsevier.I Workshop on Locational Analysis and Related Problems 2015 49
Set-packing problems in discrete location
Alfredo Marín and Mercedes Pelegrín Murcia University, Murcia, Spain [email protected] Murcia University, Murcia, Spain [email protected]
Set-packing problems are a typical matter of discrete optimization in gen-eral. Given a collection of subsets of f ; : : : ; n g together with their weights,set-packing problems consist of optimize a linear objective function satis-fying that every pair of subsets in the group has not any point in common.Many practical location issues can be formulated as set-packing problems,for instance the uncapacitated facility location problem, two-stage locationproblems, hub location problems and so on. Some other times only a partof the formulation can be described as a set-packing problem. This workreviews different approaches that have been used to solve discrete locationproblems from the scope of the set-packing problem. I Workshop on Locational Analysis and Related Problems 2015 51
Robust rapid transit railwayrescheduling (cid:3)
Ángel Marín, and Luís Cadarso Technical University of Madrid, Aeronautic and Space ETSI, Pl. Cardenal Cisneros, 3,28040 Madrid, Spain, [email protected] Rey Juan Carlos University, Departamental III Building, Office 012, 28943, Fuenlabrada,Madrid, Spain, [email protected]
A new integrated approach to the Rail Scheduling problem for the rollingstock (RS) assignment, train maintenance routing and crew scheduling prob-lems in rapid transit networks (RTN) is proposed all while considering thepassengers use optimization. RS circulation with train routing and inte-grated short-term maintenance is a large problem, so it is basic considerthat maintenance required covering a given set of services and considermaintenance covering a given set of tasks and works with a minimumamount of rolling stock units, avoiding the empty services and coveringa given passenger demand.Well-known examples of these RT planning models are strategic, tacticaland operative problems addressed during the planning process. Due to thetremendous size of the planning process, it is usually divided into severalsteps such as:1. Network design: the infrastructure location decisions and the maxi-mum coverage of the demand for the new network are the main goalhere. ([5]).2. Line planning: designing a line system (i.e., determining origin anddestination stations, stops and frequencies) aims at satisfying the traveldemand while maximizing the service towards the passengers orminimizing the operating costs. ([4]).3. Timetabling: The general aim of the railway timetabling problem isto construct a train schedule that matches the frequencies determinedin the line planning problem.([2]). (cid:3)
This research was supported by Project Grants TRA2011-27791-C03-01 and TRA2014-52530-C3-1-P by the Ministerio de Economía y Competitividad, Spain. . Given a fleet of train units and finding the optimal train unit assign-ment to each train to satisfy both the timetable and the demand ina dense RTN is known as the RT RS assignment problem. The rout-ing problem is the process of determining a sequence for each trainunit in the network once the RS assignment is known. These routingmust verify the maintenance constraints, the goal is to obtain rollingsequences that minimize some cost such as the propagated delay inorder to achieve a robust solution.([1]).5. The overall crew management problem is usually approached in twophases, namely crew scheduling and crew rostering. Here, we con-sider the short-term schedule of the crews. A duty represents a se-quence of operations to be covered by a single crew within a giventime period (e.g., a work day). The long-term schedule of the crewsis out of the scope of this paper. ([3]).The simultaneous consideration of the crew assignment joint with theabove considerations drive to large models, will require total trainservice and demand coverage. We solve the integrated model us-ing different decomposition and heuristic methods evaluating theirperformances. Preliminary computational experiments for real casestudies drawn from RENFE (the main Spanish train operator) showthat the efficient of the integrated models and methods.
References [1] Cadarso, L. & Á. Marín, Robust rolling stock in rapid transit networks, Com-puters & Operations Research, 32, 1131-1142 (2011).[2] Cadarso, L. & Á. Marín, Integration of timetable planning and rolling stock inrapid transit networks, Annals of Operations Research, 199(1), 113-135 (2012).[3] Huisman, D., L.G. Kroon, R.M. Lentink, M.J.C.M. Vromans, Operations re-search in passenger railway transportation, Statistica Neerlandica, 59(4), 467-497 (2005).[4] López, F., E. Codina , Á. Marín, Integrating network design and line frequencysetting in rapid transit systems, Public Transport, under review (2014).[5] Marín, Á., J.A. Mesa , F. Perea, Integrating robust railway network design andline planning under failures, in Ahuja, R.K., et al. (Eds.), Robust and onlinelarge-scale optimization, Lecture Notes in Computer Science, 5868, 273-292(2009).I Workshop on Locational Analysis and Related Problems 2015 53
New products supply chains:the effect of short lifecycles on the supplychain network design.
Mozart B.C. Menezes, Kai Luo, and Oihab Allal-Cherif Operations Management and Information Systems DepartmentResearch Cluster in Supply Chain ManagementKedge Business School, France
We attempt to shed light on the effect of stochastic demand on the locationand capacity of production facilities. We consider the very early stages of anew product development; i.e., locational decisions about warehouse andproduction facilities are being made as well as their capacities, outsourcingdecisions are also being made through capacity reservation, markets aretested for getting knowledge about potential demand. At that time, thereis the stochastic total demand D where each demand point i in set N willget a fraction (cid:21) i of the total demand D . Thus, we consider that there is fullcorrelation on the realization of demand seen by each demand point. Thisis the case when the major source of demand variability is the state of theworld in terms of economic situation.The framework is that of a traditional Newsvendor problem where de-cisions will generate expected under- and over-capacity costs, which arefunction of both unitary cost of acquiring capacity and transportation cost(function of facility location). What makes this work different from severalother inventory-location problems is that in this work the ’critical fractile’is not uniform across facilities. We focus on the situation where decisionmakers may attempt to provide higher service level for a group of de-mand points and lower service levels to another. The objective of the deci-sion maker is that of profit maximization after computing the revenue, thetransportation costs, capacity costs and the cost of not being able to servedemand from the capacity in place. The major constraint for the decisionmaker is that the return-on-assets is above a pre-stipulated threshold.his paper fits the stream of research aimed at jointly considering facilitylocation and inventory management. On the facility location side,It is asthe generalization of the classical Capacitated Facility Location Problem(CFLP) which seeks to find optimal location for a certain number of newfacilities so as to maximize the amount of demand captured. It can also beviewed as a generalization of the maximization with fixed costs version ofthe p -median model, Hakimi [2].Effects of inventory and location decisions originate with Erlebacherand Meller [1] who introduced a highly non-linear integer model that com-bines location and inventory decisions. Shen [3] and Shen, Coullard andDaskin [5] develop several efficient algorithms for the joint inventory loca-tion problem that considers costs of facilities, shipments and safety stocks.The algorithms include Branch and Price and Lagrangian relaxation meth-ods. For more on inventory location models, readers can refer to the recentsurvey paper of Shen [4].We depart from the previous work by considering that there is no uni-form service level (as most work above assumes) which makes the prob-lem more difficult. We also do not consider that each facility has a fixedpartition of the network to serve. On the other hand, by assuming perfectcorrelation of node-demand, we simplify the problem and make it moretractable. Note that this last assumption is perfectly aligned with the frame-work of the problem and, hence, does not constitute a strong assumption.Finally, we shift the focus of our work to structural properties and the in-sights they can bring as opposed to numerical approaches where previouswork have focused on. References [1] Erlebacher, S.J. and Meller, R.D. (2000) The interaction of location and inven-tory in designing distribution systems.
IIE Transactions , , 155-166.[2] Hakimi, S. L. (1964) Optimum Locations of switching centers and the absolutecenters and medians of a graph. Operations Research , , 450-459.[3] Shen, Z.-J. (2000) Efficient algortihtms for various supply chain problems.Ph.D. dissertation, Northwestern University, Evanston, Illinois.[4] Shen, Z.J. (2007) Integrated supply chain design models: a survey and futureresearch directions. Journal of Industrial and Management Operations , 3(1), 1-20,2007.[5] Shen, Z.-J.M., Coullard, C.R. and Daskin, M.S. (2003) A joint location-inventorymodel.
Transportation Science , , 40-55.I Workshop on Locational Analysis and Related Problems 2015 55 Dial-a-ride problemsin presence of transshipments
Juan A. Mesa, Francisco A. Ortega and Miguel A. Pozo Dep. of Applied Mathematics II. Higher Tech. School of Engineering, University of Seville,Camino de los Descubrimientos s/n, Seville 41092, Spain, [email protected] Dep. of Applied Mathematics I. Higher Tech. School of Architecture, University of Seville,Av. Reina Mercedes 2, Seville 41012, Spain, [email protected] Dep. of Statistics and Operative Research. Faculty of Mathematics, University of Seville,C/ Tarfia s/n, Seville 41012, Spain, [email protected]
The Dial-A-Ride Problem (DARP) consists of determining a number ofroutes of minimum cost in order to satisfy to a set of transportation re-quests. Each request implies transporting a group of users from their re-spective origins, called pickup points to their corresponding destina-tions,called delivery points. Users who belong to different requests can share thesame vehicle while its capacity is not exceeded.For each request, there exists a maximum ride time associated with themaximum duration of the trip between the pickup point and the deliv-erypoint. This work addresses the generalization of the DARP when the userscan be transferred from one vehicle to another at specific in-termediatepoints, called transfer points.
I Workshop on Locational Analysis and Related Problems 2015 57
Optimal routes to a destinationfor airline expansion
B. Pelegrín Pelegrín, P. Fernández Hernández, and J.D. Pelegrín García Department of Statistics and Operational Research, University of Murcia, {pelegrin,pfdez}@um.es Department of Engineering Science, University of Oxford, [email protected]
Abstract
A topic of interest for airline managers is whether the company couldincrease its revenue by increasing the number of flights to a specific des-tination. When a sufficient number of travelers in a certain region withmultiple airports is expected to travel to the destination, the airline has achance to maximize its revenue by gaining a higher portion of the market.For this reason managers might be interested in knowing how to maximizemarket share by making decisions on flight frequency from each airport inthe region to the destination. The market share captured by the airline willnot only depend on the airline decision, but also on the airline´s competitorsand their ability to perform efficiently in the market. Therefore, managersneed to know about the airports and the airline choice criteria used by theair travelers in the region in order to estimate the airline market share.To date, a number of studies have modeled passenger choices of airportand airline by taking into account several factors such as the distance fromdeparture point to airport, ticket price, frequency of flights, timetable, andlevel of the service. The passenger demand of the airline could vary withrespect to the current demand if any of such factors changes (see for in-stance [1],[2],[5]). Most studies use discrete choice models to predict therobability that a traveler will choose one alternative among a finite set,based on the attributes of the different alternatives which are integratedin a variety of utility functions. The most common models used in airlinecompetition are the multinomial logit (MNL) model ( see [3],[4],[6],[10])and the nested logit (NL) model ( see [8],[11],[12],[13]). These studies ana-lyze the significant factors affecting passenger choice behaviour by usingregression analysis tools for parameter estimation based on survey datacollected via mail, telephone and face to face interviews. By using suchprobabilities, the market share can be expressed in different ways depend-ing on the variables considered. To our knowledge, the effect of increasingflight frequency on market share has not been addressed in the existing lit-erature. This may be due to the fact that the functions obtained for marketshare estimation by using the MNL and NL models are not of any stan-dard type and then standard optimizers can not be employed to solve thecorresponding maximization problem.In a region with multiple airports many travelers are willing to spend 3or 4 hours to drive to larger metropolitan airports where they have morechoices of airlines and departure times with lower airfares. This behaviourseems to suggest that distance is a key factor in our problem of marketshare estimation. In this paper, we use a Huff-like (see [7, 9]) spatial inter-action model for airline market share estimation together with an utilityfunction which depend on distance to the airport, airport characteristics,ticket price and flight frequency. Then we develop a formulation of the air-line market share maximization problem when the decision variables areflight frequencies which can be solved by standard optimizers. An illus-trative example with data from Spanish airports is presented which showsthat real size problems can be solved by using the proposed formulation.
References [1] Babic D.,Kuljanin J., Kalic M. 2014. Market share modelling in airline industry:an emerging market economic application.
Transportation Research Procedia
Omega
29 , 405-415.[3] Chang L-Y, Sun P-Y 2012. Stated-choice analysis of willingness to pay for lowcost carrier services.
Journal of Air Transport Management
20 , 15-17.[4] Coldren G.M., Koppelman F.S. 2005. Modeling the competition among air-travel itinerary shares: GEV model development.
Transportation Research PartA
39, 345-365.5] Hess, S., Adler, T., Polak, J.W., 2007. Modeling airport and airline choice behav-ior with the use of stated preference survey data.
Transportation Research Part E
43 , 221-233.[6] Jung S-Y, Yoo K-E 2014. Passenger airline choice behaviour for domestic short-haul travel in South Korea.
Journal of Air Transport Management
38, 43-47.[7] Nakanishi, M., Cooper, L.G., 1974. Parameter estimate for multiplicative inter-active choice model: Least square approach.
Journal of Marketing Research
Transportation Research Part E
45, 335-344.[9] Serra D. and Colomé R. (2001), Consumer choice and optimal locations model:Formulations and heuristics.
Papers in Regional Science
80, 439-464.[10] Suzuki, Y., Tyworth, J. E. Novack, R., A., 2001. Airline market share and cus-tomer service quality: a reference-dependent model.
Transportation ResearchPart A
35, 773-788.[11] Wen C-H, Lai S-C 2010. Latent class models of international air carrier choice.
Transportation Research Part E
46, 211-221.[12] Wen C-H, Chen T-N, Fu C. 2014. A factor-analytic generalized nested logitmodel for determining market position of airlines.
Transportation Research PartA
62, 71-80.[13] Yang C-W, Lu J-L, Hsu C-Y 2014. Modelling joint airport and route choicebehaviour for international and metropolitan airports.
Journal of Air TransportManagement
39, 89-95I Workshop on Locational Analysis and Related Problems 2015 61
Locating new stations and road linkson a road-rail network
Federico Perea Instituto Tecnológico de Informática.Universitat Politècnica de València (Spain), [email protected]
In this paper we study the problem of locating new stations on an existingrail corridor and new junctions on an existing road network, and connect-ing them with a new road segment under a budget constraint, with theobjective of attracting as many passengers as possible.
1. Introduction
The advantages of railway systems with respect to other transportationmodes in short-medium distances are commonly agreed: non-dependenceon petrol, reduction of polluting emissions, higher safety, comfort, etc. Forthis reason, many new railway systems are being constructed from scratchor extended. The latter problem is what we are dealing with in this work.Following previous references, this problem is here called the railroad net-work extension problem . In such problem two different transportation net-works, namely a road network and a railway network, are both competingand collaborating. They compete in the sense that each network wants toattract as many travelers as possible. They collaborate in the sense thatmulti-modal trips, in which both transportation systems are used to reachyour destination, are allowed.
2. The problem
The problem here presented considers a road-rail connected network, whichconsists of road links and rail links, as well as cities, train stations and junc-tions. Using graph terminology, we consider an undirected road-rail net-ork G = ( R [ T; E R [ E T ) . As usual, R [ T is the node set and E R [ E T is the edge set. The node subset R consists of a set of cities and junctionswithout a train station, and the node subset T consists of cities and junc-tions with a train station. As for the edges, the elements in E R are roadlinks directly joining two nodes of R , or one node of R with one node of T . Finally, the edges in E T directly link two railway stations, that is, twonodes of T .As an example, consider Figure 1. The existing stations in set T are rep-resented by filled squares. The cities and junctions without a train stationin set R are represented by filled circles. The road links E R are representedby dotted lines, and the railway links E T are represented by filled lines.The aim is to build new stations on the rail network (in the figure rep-resented by empty squares) and new junctions on the road network (in thefigure represented by empty circles), and to build road links between thenew stations and the new junctions (in the figure represented by dashedlines), optimizing a certain objective. The most commonly used objectiveis the maximization of the ridership: the number of potential travelersthat would prefer the railway network over other existing transportationmodes. Figure 1.
An extended rail-road network.
This research extends [1], where only one station and one junction werelocated. The models and algorithms there introduced will serve as a start-ing point to solve this railroad network extension problem.
References [1] Perea, F., Juan A. Mesa, and Gilbert Laporte. (2014). “Adding a new stationand a road link to a road-rail network in the presence of modal competition”.Transportation Research B 68, 1–16.I Workshop on Locational Analysis and Related Problems 2015 63
Convex ordered median problem
Diego Ponce and Justo Puerto Universidad de Sevilla [email protected], [email protected]
The Ordered Median Problem is a modeling tool that provides flexible rep-resentations of a large variety of problems, which include most of the clas-sical location problems considered in the literature. It consists in minimiz-ing a globalizing function that assigns weights depending not of the costsinduced by the facilities themselves but to their position in the relativevector of ordered costs. In the discrete version the assignment costs are de-fined a priori or they are induced from the distances between nodes in anetwork. In this talk we present specific formulations for the ContinuousConvex Ordered Median Problem, which is the continuous version of theabove problem that occurs whenever the costs are induced from distancesbetween point in a continuous space and the vector of lambda weights ismonotone no decreasing. We exploit new findings to this particular prob-lem, such as the column generation algorithm or recently developed tech-niques for solving SOC programs .
References [1] N. Boland,P. Domínguez-Marín, S.Nickel, J.Puerto, Exact procedures for solv-ing the discrete ordered median problem, Computers & Operations Research33(2006) 3270-3300.[2] A. Marín, S. Nickel, J. Puerto, S. Velten, A flexible model and efficient solu-tion strategies for discrete location problems, Discrete Applied Mathematics157(2009) 1128-1145.[3] S. Nickel. Discrete ordered weber problems. In Operations Research Proceed-ings 2000, 71-76. Springer Verlag, 2001.[4] S. Nickel, J. Puerto. Location Theory: A Unified Approach. Springer Verlag,2005.5] J. Puerto, A new formulation of the capacitated discrete ordered median prob-lems with {0,1}-Assignment, Operations Research Proceedings 2007 165-170.[6] A. Rodríguez-Chía, S. Nickel, J. Puerto, F.R. Fernández, A flexible approach tolocation problems. Math Methods Oper Res 51(2000):6989I Workshop on Locational Analysis and Related Problems 2015 65 On k -centrum optimization with applicationsto the location of extensive facilities on graphsand the like Justo Puerto, Antonio M. Rodríiguez-Chía, IMUS, Universidad de Sevilla, Spain [email protected] Universidad de Cádiz, Spain [email protected]
Keywords:
Ordered Median Problems, Extensive Location
This talk addresses a class of combinatorial optimization models that in-clude among others, bottleneck and k-centrum and that extends furtherto general ordered median objective functions. These problems have beenanalyzed under different names for different authors in the last years ([1],[2], [3], [4], [5], [6, 7], [8] and [9]). We study the common framework thatunderlines those models, present different formulations and study somerelationships and reinforcements. This approach leads to polynomial timealgorithms for the location of extensive facilities on trees that were not pre-viously known as for instance the k -centrum subtree and k -centrum pathlocation on trees. References [1] Calvete H and Mateo PM (1998), Lexicographic optimization in generalizednetwork flow problems. J. Oper. Res. Soc., 49(2):519–529.[2] De la Croce et al.(1999), An improved general procedure for lexicographic bot-tleneck problems. OR Letters 24, 187-194.[3] Lee J (1992) On constrained bottleneck extrema. Oper Res 40:813-814[4] S.Nickel and J.Puerto.
Location Theory: A unified approach . Springer-Verlag, Hei-delberg, Germany, 2005.5] Puerto J., Tamir A (2005), Locating tree-shaped facilities using the ordered me-dian objective. Math. Programming, 2005.[6] Punnen AP, Aneja YP (1996) On k-sum optimization. OR letters 18, 233-236.[7] Punnen AP, Aneja YP (2004) Lexicographic balanced optimization problems.Oper Res Lett 32:27-30.[8] Turner L and Hamacher HW, (2011)
Universal Shortest Paths . Preprint Univer-sität Kaiserslautern.[9] Turner L, Punnen AP, Aneja YP and Hamacher HW (2011). On generalizedbalanced optimization problems. Math Meth Oper Res, 73:19-27.I Workshop on Locational Analysis and Related Problems 2015 67
Analyzing the impact of capacity volatilityon the design of a supply chain network
Ruiz-Hernández, Diego, Menezes, Mozart B.C., and Gueye, Serigne University College for Financial Studies - Leonardo Prieto Castro 2, 28040, Madrid,Spain, [email protected] KEDGE Business School - Bordeaux, France,
[email protected] Universitè d’Avignon et des Pays du Vaucluse - Avignon, France, [email protected]
Service facilities can and usually, at some point in time, do fail. Failuresoriginate from different sources, ranging from natural disasters and locallydisruptive events (e.g. tornados, strikes, and so on), to temporary shortagesof capacity due to human or natural factors (e.g. work accidents, electricityoutages, and so on). In order to mitigate the financial effect of these ca-pacity disruptions, managers must take decisions aimed at guaranteeingthe availability and reliability of their distribution network. Among the as-pects that must be taken into consideration we can highlight the capacityand resilience of the facilities (i.e. how resistent they are to exogenous dis-ruptions) and their location.While the classical location theory tended to ignore the reliability as-pects, there is a growing interest in better understanding the impact of im-perfect reliability on the optimal location patterns and the resulting costs.In this work we aim at shedding light on the problem of locating facili-ties in the knowledge that their respective capacities may be disrupted and,consequently, reduced from their theoretical (planned) value. We examinea class of problems where service facilities may fail, understanding a fail-ure as a deviation of the facility’s capacity from its theoretical value, givencertain probability distribution. Moreover, we allow for the possibility offailures to be correlated across different facilities.The problem is parameterized by introducing, for each facility, a coupleof values, C and (cid:12) , that represent the facility’s theoretical capacity and itsesilience to external shocks, respectively. Therefore, a manager concernedabout availability and reliability of its distribution network may be inter-ested on investing either in capacity (increasing C ), in resilience (increasingthe facility’s (cid:12) ) or in both of them simulataneously.Moreover, for a given combination of capacity and resilience, the finan-cial impact of a capacity shortcut may depend on both the location of thefacility and the location of other sister facilites that may be available forproviding backup services. Therefore, strategic location plays an impor-tant role for mitigating the economic impact of capacity fluctuations. Inorder to address this, we propose the Unreliable Capacitated Facility LocationProblem (UCFLP) that aims at maximizing profit by means of identifyingthe optimal location of a number of facilities. The problem is formulated asa stochastic programming problem, where a collection of scenarios is usedto model the occurrence and severity of exogenous disruptions.The proposed UCFLP extends the Median Problem with Unreliable Fa-cilitis proposed by Berman et al. [1] in three main directions: (i) it considerscorrelated failure events; (ii) it does not restrict failures to complete lossesof capacity, i.e. a disruption can affect a faciliy’s capacity only partially;and (iii) introduces fixed costs, empowering the endogenous election ofthe number of facilities.An extensive numerical investigation is conducted to asses the practicalimplications of our model. In particular, we pay special attention to the ef-fects of diferent configurations of parameters C and (cid:12) on the spacial distri-bution (concentration/dispersion) of the facilities. We also investigate thefinancial benefit, for a given location, of strategic increases in the facility’scapacity and/or resilience. References [1] Berman, O., Krass, D. & Menezes, M. B. C. (2007). Reliability issues, strate-gic co-location and centralization in m -median problems. Operations Research .55(2), 332-350.I Workshop on Locational Analysis and Related Problems 2015 69
Location of emergency units in collectivetransportation line networks (cid:3)
Tunzi Tan, and Juan A. Mesa, University of Chinese Academy of Sciences, Beijing, China, [email protected] University of Seville, Seville, Spain, [email protected]
Due to different causes, disruptions on transportation networks oftenhappen. For example, in railway networks, infrastructure failures (failingsignals, broken catenary, etc.), rolling stock failures (engine break-downs,power failures, problems with closing doors, etc.), human factors of thecrew (drivers out of conditions), accident with other traffic, suicides andvandalism (stones or coins on the tracks), disturb railway traffic and re-quire a quick response of the operator company. In most cases repairmenshould go to the place where those accidents happen and take actions.A railway system can be represented by a graph where each station isrepresented by a node and the links between adjacent stations are shownby edges. However, this representation does not capture all the character-istics of a railway network which is structured by lines. For this purposethe concept of hypergraph is useful. In the railway representation by hy-pergraph, stations are nodes and lines are hyperedges. The combinationof both concepts is called hyperstructure and captures both the binary re-lationship between adjacent stations and the multiple relationship of thestations belonging to the same line.In this paper, we tackle the problem of locating emergency units in arailway network. For this purpose, we use a minmax hypergraph partitionof the network with balanced constraints which allows us to apply in eachpart a center location problem to determine the stations where to establishthe emergency units.The minmax hypergraph partition problem, which only recently hasbeen defined [1], aims at partition a hypergragh in parts so that the max- (cid:3)
This research was partially supported by Ministerio de Economía y Competitividad(Spain)/FEDER under grant MTM2012-37048 mum number of hyperedges covering each part is minimized. Balancedconstraints are imposed in order to equilibrate the number of stations ineach part. Graph partition problem is NP-hard, so is the hypergraph parti-tioning problem. For this purpose, apart of designing exact algorithms it isalso required to design approximation and/or heuristic algorithms. Also amathematical programming formulation of this problem is provided. Thepaper finishes with some computational experience and the application toactual metro networks.
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[email protected] . . . . . . . 21Monge, Juan F.Universidad Miguel Hernández de Elche, Spain, [email protected] . . . . . 15, 19 N Nasini, StefanoIESE Business School, University of Navarra, Spain, [email protected] . . . . 39 O Olivares-Nadal, Alba V.University of Seville, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Ortega, Francisco A.niversity of Seville, Seville, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . 55 P Peiró, JuanjoUniversitat de València, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . 43Pelegrín García, Juan D.University of Oxford, [email protected] . . . . . . . . . . . . . . . . . . . . 57Pelegrín Pelegrín, BlasUniversity of Murcia, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Pelegrín, MercedesUniversity of Murcia, Murcia, Spain, [email protected] . . . . . . . 49Perea, FedericoUniversitat Politècnica de València , Spain, [email protected] . . . . . . . . . . . . . 61Plana, IsaacUniversitat de València, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . 41Ponce, DiegoUniversidad de Sevilla, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Pozo, Miguel A.University of Seville, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . 47, 55Puerto, JustoUniversidad de Sevilla, Spain, [email protected] . . . . . . . . . . . . . . . . . . . 25, 47, 63, 65 R Ramírez-Cobo, PepaUniversidad de Cádiz, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Rodríguez-Chía, Antonio M.Universidad de Cádiz, Spain, [email protected] . . . . . . . . . . . . . 17, 65Ruiz-Hernández, DiegoUniv. College for Financial Studies, Madrid , Spain, [email protected] . . . . . 67 S Sainz-Pardo, José L.Univ. Miguel Hernández de Elche, Spain, [email protected] . . . . 15, 19Salazar, Juan J.Universidad de La Laguna, Spain, [email protected] . . . . . . . . . . . . . . . . . . . . . . . . 23Saldanha-da-Gama, FranciscoUniversidade de Lisboa, Portugal, [email protected] . . . . . . . . . . . . . . . . . . . 39Sanchis, José M.Universidad Politécnica de Valencia, Spain , [email protected] . . . . . . . . 41Scozzari, AndreaUniversity Niccolò Cusano, Italy, [email protected] . . . . . . . . . . . . . 47Sinnl, Markusniversity of Vienna, Austria, [email protected] . . . . . . . . . . . . . . . . . . . . 9Speranza, M. GraziaUniversity of Brescia, Italy, [email protected] . . . . . . . . . . . . . . . . . . . . . . . 11 T Tan, TunziUniv. of Chinese Academy of Sciences, China, [email protected] . . . . . . . . . . . 69Tirado, GregorioUniversidad Complutense de Madrid, Spain, [email protected]@mat.ucm.es.