Juan José Salazar González

Universidad de La Laguna | ULL · Department of Statistics, Operations Research and Computing

This paper concerns a new optimization problem arising in the management of a multi-object spectrometer with a configurable slit unit. The field of view of the spectrograph is divided into contiguous and parallel spatial bands, each one associated with two opposite sliding metal bars that can be positioned to observe one astronomical object. Thus s...

We introduce a new optimization problem arising in the management of a multi-object spectrograph in a telescope. The field of view of the spectrograph is divided in 55 contiguous and parallel spatial bands. Each band is associated with two opposite sliding bars that can be positioned to observe an astronomical object. The observation of an object r...

This paper concerns a new optimization problem arising in the management of a multi-object spectrometer with a configurable slit unit. The field of view of the spectrograph is divided into contiguous and parallel spatial bands, each one associated with two opposite sliding metal bars that can be positioned to observe one astronomical object. Thus s...

This paper addresses the design of routes for a fleet of vehicles serving customer requests. It is a pickup and delivery problem where each customer location can be visited several times, and load may be transshipped from one vehicle to another at specific locations. The aim is to minimize the sum of travel costs and transshipment costs. We present...

This paper describes a branch-and-cut algorithm for a generalization of the Capacitated Vehicle Routing Problem where a customer can be visited several times. The algorithm is based on solving a Mixed Integer Programming model for a relaxed problem, and a cutting-plane procedure to eliminate invalid integer solutions. Computational results on bench...

The Capacitated Vehicle Routing Problem (CVRP) is a classic combinatorial optimization problem for which many heuristics, relaxations and exact algorithms have been proposed. Since the CVRP is NP-hard in the strong sense, a natural research topic is relaxations that can be solved in pseudo-polynomial time. We consider several old and new relaxation...

Flight retiming in airline scheduling consists in slightly modifying the scheduled departure time of some flights with the goal of providing a better service with a cheaper cost. In this research, the departure times must be selected from a small discrete set of options. The whole problem embeds flight retiming, fleet assignment, aircraft routing a...

Transportation problems are essential in commercial logistics and have been widely studied in the literature during the last decades. Many of them consist in designing routes for vehicles to move commodities between locations. This article approaches a pickup-and-delivery single-vehicle routing problem where there is susceptibility to uncertainty i...

This paper considers a vehicle routing problem where the customer demands are stochastic variables. Because of uncertainty along a route, the vehicle may be unable to load all planned customers’ demand. Thus, the vehicle must return to the depot, unload, and then resume its trip. To avoid unplanned return trips to the depot, one may decide to make...

This paper presents a heuristic approach for a routing problem with two depots and involving vehicles and drivers. Vehicles must leave from one depot and arrive to the other, while drivers should leave and return to the same depot and their routes can not exceed a given duration. With these conditions, drivers must change vehicles in order to go ba...

The Periodic Vehicle Routing Problem is a generalization of the classical capacitated vehicle routing problem in which routes are determined for a planning horizon of several days. Each customer has an associated set of allowable visit schedules, and the objective of the problem is to design a set of minimum cost routes that give service to all the...

This paper studies a variant of the unit-demand Capacitated Vehicle Routing Problem, namely the Balanced Vehicle Routing Problem, where each route is required to visit a maximum and a minimum number of customers. A polyhedral analysis for the problem is presented, including the dimension of the associated polyhedron, description of several families...

This paper concerns the problem of designing a route of minimum cost for a capacitated vehicle moving a single commodity between a set of customers. The route must allow two characteristics uncommon in the literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as inter...

This article addresses the problem of designing routes of minimum cost for a capacitated vehicle moving a commodity between a set of customers, allowing two characteristics uncommon in the pickup-and-delivery literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as in...

In the vehicle routing literature it is generally assumed that each vehicle is driven by a single driver from the beginning to the end of its route. We introduce a new vehicle routing problem without this assumption. We consider a problem with two depots in which vehicles must departure from one depot and arrive to the other, while drivers should l...

The Team Orienteering Arc Routing Problem is a variation of the so-called Team Orienteering Problem where the customers are associated with the arcs of a directed graph. A fleet of uncapacitated vehicles, located at a depot, must give service to a set of regular customers, while another set of optional customers is available to be potentially servi...

Many problems arising in the area of telecommunication ask for solutions with a tree-star topology. This paper proposes a general procedure for finding optimal solutions to a family of these problems. The family includes problems in the literature named as connected facility location, rent-or-buy and generalized Steiner tree-star. We propose a solu...

This article introduces a combinatorial optimization problem that consists of assigning tasks to machines and operators, and sequencing the tasks assigned to each one. Two configurations exist. Machines alternate configurations, while the operators must start and finish the process in the same configuration. Moreover, machines and operator have lim...

We analyze the polytope associated with a combinatorial problem that combines the Steiner tree problem and the uncapacitated facility location problem. The problem, called connected facility location problem, is motivated by a real-world application in the design of a telecommunication network, and concerns with deciding the facilities to open, the...

We address the problem of designing two-level networks protected against single edge failures. A set of nodes must be partitioned into terminals and hubs, hubs must be connected through a backbone network, and terminals must be assigned to hubs and connected to them through access networks, being the objective to minimize the total cost. We conside...

This article considers the problem of designing a two-level network where the upper level consists of a backbone ring network connecting the so-called hub nodes, and the lower level is formed by access ring networks that connect the non-hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated t...

We study an integrated airline scheduling problem for a regional carrier. It integrates three stages of the planning process (i.e., fleet assignment, aircraft routing, and crew pairing) that are typically solved in sequence. Aircraft maintenance is also taken into account. The objective function aims at minimizing a weighted sum of the number of ai...

The sequential ordering problem (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hern�andez & Salazar introduced a multi-commodity flow (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formula...

This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through...

The Capacitated Vehicle Routing Problem is a much-studied (and strongly NP-hard) combinatorial optimization problem, for which many integer programming formulations have been proposed. We present two new multi-commodity flow (MCF) formulations, and show that they dominate all of the existing ones, in the sense that their continuous relaxations yiel...

This paper considers the classical vehicle routing problem (VRP) where the vehicle capacity is not fixed. Indeed, at the moment of acquiring (or renting) the vehicle that will serve all customers, there is some freedom of choice. A larger vehicle capacity implies a lower total distance travelled but larger operating costs. The reverse is true for a...

We study the hub location and routing problem where we decideon the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programm...

Statistical agencies collect input data from individuals and deliver output information to the society based on these data. A fundamental feature of output information is the “protection” of sensitive information, since too many details could disseminate privacy information from individuals and therefore violate their rights. Another feature of out...

This paper presents a new combinatorial optimization problem that can be used to model the deployment of broadband telecommunications systems in which optical fiber cables are installed between a central office and a number of end-customers. In this capacitated network design problem the installation of optical fiber cables with sufficient capacity...

The design of container shipping networks is an important logistics problem, involving assets and operational costs measured in billions of dollars. To guide the optimal deployment of the ships, a single vessel round trip is considered by minimizing operational costs and flowing the best paying demand under commercially driven constraints. This pap...

This paper is concerned with the connected facility location problem, which has been intensively studied in the literature. The underlying polytopes, however, have not been investigated. This work is devoted to the polytope associated with the asymmetric version of the problem. We first lift known facets of the related Steiner arborescence and of t...

This paper presents the results of a research project funded by a regional carrier operating inter-island services within the Canary Islands (Spain) in addition to services to Morocco and Portugal. It operates between 100 and 150 flights a day using three airline operators. The main scope of the project was to solve fleet-assignment, aircraft-routi...

Statistical agencies collect data from individuals and businesses, and deliver information to the society based on these data. A fundamental feature to consider when releasing information is the “protection” of sensitive values, since too many details could disseminate private information from respondents and therefore violate their rights. Another...

Port infrastructure has characteristics that are classified by quasifixed inputs, meaning they cannot be immediately adjusted, contributing to the production of transport services over long periods of time. Another important characteristic of port infrastructure is that its current technology is a consequence of investment decisions made in the pas...

Abstract–The “multi‐commodity Pickup‐and‐Delivery Traveling Salesman Problem” (m‐PDTSP) is a generalization of the well‐known “Traveling Salesman Problem” in which cities correspond to customers providing or requiring known amounts of m different products, and the vehicle has a known capacity. Each customer must be visited exactly once by the vehic...

The Double Traveling Salesman Problem with Multiple Stacks is a pickup-and-delivery single-vehicle routing problem which performs all pickup operations before the deliveries. The vehicle has a loading space divided into stacks of a fixed height that follows a Last-In-First-Out policy. It has to collect products following a Hamiltonian tour in a pic...

This article analyzes inequalities derived by projecting out the flow variables of a single-commodity flow model for a vehicle routing problem. These inequalities are called reverse multistar (RMS) inequalities and are related to the MS inequalities analyzed and used in other articles. Although the MS RMS inequalities are irrelevant for some vehicl...

International Network Optimization Conference (INOC) is the biennial meeting of the EURO working group on Network Optimization (ENOG). The last edition of this conference (INOC 2013) was held in Costa Adeje (Tenerife, Spain), May 20–22, 2013. This volume contains the short papers presented at INOC 2013.

This paper deals with the fleet-assignment, aircraft-routing and crew-pairing problems of an airline flying between Canary Islands. There are two major airports (bases). The company is subdivided in three operators. There are no flight during the night. A crew route leaves from and returns to the same base. An aircraft route starts from one base an...

The Vehicle Routing Problem with a minimum number of customers per route concerns the Capacitated Vehicle Routing Problem with unit-demand customers and a lower bound on the number of customers visited by each vehicle. This paper answers two open questions in the article (Gouveia et al., in press) [5]: finding a compact formulation for the problem...

This paper addresses an extension of the Traveling Salesman Problem where a vehicle with a limited capacity must transport commodities. Each commodity has a weight, and exactly one origin and one destination. The objective is to find a minimum length Hamiltonian tour satisfying all the transportation requests without ever violating the capacity con...

Aphylogeny is an unrooted binary tree that represents the evolutionary relationships of a set of n species. Phylogenies find applications in several scientific areas ranging from medical research, to drug discovery, to epidemiology, to systematics, and to population dynamics. In such applications, the available information is usually restricted to...

The design of container shipping networks is an important real world problem, with assets and operational costs in billions of dollars. To guide the optimal deployment of the ships, a single vessel roundtrip is considered by minimizing operational costs and flowing the best paying cargo under commercial constraints. Inspiration for formulation and...

School bus routing problems, combining bus stop selection and bus route generation, look simultaneously for a set of bus stops to pick up students from among a group of potential locations, and for bus routes to visit the selected stops and carry the students to their school. These problems, classified as Location-Routing problems, are of interest...

This article considers the network design problem that searches for a minimum-cost way of installing capacities on the edges of a network to simultaneously route a flow from a given access point to a subset of nodes representing customers with positive demands. We first consider compact and exponential-sized Mixed Integer Programming (MIP) formulat...

The Multiple Vehicle Traveling Purchaser Problem describes a school bus routing problem that combines bus stop selection and bus route generation. This problem aims at selecting a set of bus stops from among a group of potential locations to pick up students, and for designing bus routes to visit the selected stops and to carry the students to thei...

Thus far, our focus has been on achieving confidentiality protection through SDL procedures, which as we know mask the data that are to be disseminated. This is the restricted data approach.1 As we noted in Chapters 1 and 2, a different but complementary approach is for the DSO to instead control the process of accessing and analyzing the data.2 Re...

Before disseminating a data product for public use, a DSO needs to assess the risk of a data snooper compromising confidentiality. In its original form as the source data, a data product typically has unacceptably high disclosure risk. The data product must therefore be transformed to lower the disclosure risk to an acceptable level. We present a v...

In recent years, there has been an increased literature on so-called Generalized Network Design Problems, such as the Generalized Minimum Spanning Tree Problem and the Generalized Traveling Salesman Problem. In such problems, the node set of a graph is partitioned into clusters, and the feasible solutions must contain one node from each cluster. Up...

Confirming statistical confidentiality as vital to the stewardship of personal data, the United Nations set out Principle 6 of its Fundamental Principles of Official Statistics: Individual data collected by statistical agencies for statistical compilation, whether they refer to natural or legal persons, are to be strictly confidential and used excl...

Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testifled by the surveys on the problem that contain tables in which...

Why statistical confidentiality?- Concepts of statistical disclosure limitation.- Assessment of disclosure risk.- Protecting tabular data.- Providing and protecting microdata.- Disclosure rRisk and data utility.- Restrictions on data access.- Thoughts on the future.

This paper presents the main findings when approaching an optimization problem proposed to us by a telecommunication company in Austria. It concerns deploying a broadband telecommunications system that lays optical fiber cable from a central office to a number of end-customers, i.e., fiber to the home technology. End-customers represent buildings w...

This paper addresses an extension of the TSP where a vehicle with a limited capacity must transport certain commodities from their origins to their destinations. Each commodity has a weight, and the objective is to find a minimum length Hamiltonian tour satisfying all the transportation requests without ever violating the capacity constraint. We pr...

A microdata file is a compilation of data records. Each record contains values of attributes about a single unit—say a person with the attributes of their height, attitude toward minimum wage laws, cell-phone usage, and diastolic blood pressure. Microdata are special. Expanding Access to Research Data: Reconciling Risks and Opportunities (National...

As we have repeatedly argued, DSOs fulfill their stewardship responsibilities by resolving the tension between ensuring confidentiality and providing access (Duncan et al., 1993; Kooiman et al., 1999; Marsh et al., 1991). Data stewardship, therefore, requires disseminating data products that both (1) protect confidentiality—so get disclosure risk R...

The SDL literature has its own terminology. Understanding this terminology and, more importantly, the concepts underlying the terminology is essential to learning how statistical confidentiality can be best employed. In this chapter we look at the structure of disclosure risk, its assessment, and its limitation. Complicating our task is that many t...

Familiar to all of us, a statistical table displays aggregate information that is classified according to categories. Even in this age of electronic dissemination, tables remain important data products. In the past, DSOs published these tables in paper form as large statistical abstracts. Today, many DSOs provide users with an online capability for...

The future will surely bring challenges to statistical confidentiality. Some challenges will be familiar, much like the ones described in Chapter 1. But as the lead quotation suggests, we must prepare for exponential change in our responsibilities, the technology we employ, and the problems we face. Specifically, we must prepare for dramatic change...

This paper discusses several techniques to apply Cell Suppression Methodology to protect private information when publishing tabular data. All techniques are exact algorithms to find optimal suppression patterns, but they can also be used as heuristic approaches to find good suppression patterns. One of the technique is the branch-and-cut algorithm...

We show and discuss a family of inequalities for solving a variant of the classical vehicle routing problem where also a lower bound is considered. The inequalities are related to the projected inequalities from a single commodity flow formulation. Other inequalities are based on rounding procedures. We also show computational experiments proving t...

Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which...

We describe in this article a new heuristic approach for the capacitated fixed-charge network design problem. This is a well known NP-hard problem that has been extensively studied. We propose to use local branching to tackle it. Local branching is a novel metaheuristic technique presented by Fischetti and Lodi [Local branching. Mathematical Progra...

Companies in the concrete industry are facing the following scheduling problem on a daily basis: concrete produced at several plants has to be delivered at customers’ construction sites using a heterogeneous fleet of vehicles in a timely, but cost-effective manner. The distribution of ready-mixed concrete (RMC) is a highly complex problem in logist...

Given a graph G=(V,E) on n vertices, the Minimum Linear Arrangement Problem (MinLA) calls for a one-to-one function ψ:V→{1,…,n} which minimizes ∑{i,j}∈E|ψ(i)−ψ(j)|. MinLA is strongly NP-hard and very difficult to solve to optimality in practice. One of the reasons for this difficulty is the lack of good lower bounds. In this paper, we take a polyhe...

In the Traveling Salesman Problem with Pickup and Delivery (TSPPD) a single vehicle must serve a set of customer requests, each defined by an origin location where a load must be picked up, and a destination location where the load must be delivered. The problem consists of determining a shortest Hamiltonian cycle through all locations while ensuri...

This paper concerns a generalization of the traveling salesman problem (TSP) called multi-commodity one-to-one pickup-and-delivery traveling salesman problem (m-PDTSP) in which cities correspond to customers providing or requiring known amounts of m different commodities, and the vehicle has a given upper-limit capacity. Each commodity has exactly...

This paper studies how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting of the initial load. The paper first considers feasibility issues. This includes finding the smallest veh...

We address in this paper the one-commodity pickup-and-delivery traveling salesman problem, which is characterized by a set of customers, each of them supplying (pickup customer) or demanding (delivery customer) a given amount of a single product. The objective is to design a minimum cost Hamiltonian route for a capacitated vehicle in order to trans...

A basic problem in molecular biology is to rebuild phylogenetic trees (PT) from a set of DNA or protein sequences. Among different criteria used for this purpose, the minimum evolution criterion is an optimality based criterion aiming to rebuild PT characterized by a minimal length. This problem is known to be 𝒩𝒫-hard. We introduce in thi...

The editing-and-imputation problem concerns the question of finding errors in a record which does not satisfy a set of consistency rules. Once some potential errors have been localizated, it is also necessary to impute new values to the associated fields. The output dataset should consist of valid records and preserve similar statistical properties...

Statistical agencies collect individually identifiable data, process them, and publish statistical summaries (tables). During this process, the agencies are required to protect individually identifiable data through a variety of policies. In all cases, the scope is to provide the data users with useful statistical information, and to assure that th...

Given a graph G = (V, E) on n vertices, the Minimum Linear Arrangement Problem (MinLA) calls for a one-to-one function ψ : V → {1, . . . , n} which minimizes {i,j}∈E |ψ(i) − ψ(j)|. MinLA is strongly N P-hard and very difficult to solve to optimality in practice. One of the reasons for this difficulty is the lack of good lower bounds. In this paper,...

In this paper we address a problem consisting of determining the routes and the hubs to be used in order to send, at minimum cost, a set of commodities from sources to destinations in a given capacitated network. The capacities and costs of the arcs and hubs are given, and the arcs connecting the hubs are not assumed to create a complete graph. We...

This article concerns the “One-commodity Pickup-and-Delivery Traveling Salesman Problem” (1-PDTSP), in which a single vehicle of fixed capacity must either pick up or deliver known amounts of a single commodity to a given list of customers. It is assumed that the product collected from the pickup customers can be supplied to the delivery customers,...

The Capacitated m-Ring-Star Problem (CmRSP) is the problem of design-ing a set of rings that pass through a central depot and through some transi-tion points and/or customers, and then assigning each non-visited customer to a visited point or customer. The number of customers visited and assigned to a ring is bounded by an upper limit: the capacity...

Let K be an arbitrary field and {d1, . . . , dn} a set of all-different positive integers. The aim of this work is to propose and evaluate an algo- rithm for checking whether or not the toric ideal of the affine monomial curve {(td 1 , . . . , td n ) | t 2 K} � AnK is a complete intersection. The algorithm is based on new results regarding the tori...

Data collected by statistical agencies may contain mistakes made during the acquisition, transcription and coding process. Thus, before using all this information to infer statistical properties, the statistical agencies must check the consistency of their information. To this end, each record has to be tested on a set of consistency rules. Therefo...

The Error Localization Problem concerns finding the minimum number of fields in a record such that by modifying the values in these fields the new record satisfies a given set of rules. This problem is of great interest to statistical agencies in as far as cleaning microdata is concerned. It has been shown to be NP-hard, and exact methods in litera...

We consider a special case of the symmetric capacitated vehicle routing problem, in which a fleet of K identical vehicles must serve n customers, each with a given demand consisting in a set of rectangular two-dimensional weighted items. The vehicles have a two-dimensional loading surface and a maximum weight capacity. The aim is to find a partitio...

Controlled Rounding is a technique to replace each cell value in a table with a multiple of a base number such that the new table satisfies the same equations as the original table. Statistical agencies prefer a solution where cell values already multiple of the base number remain unchanged, while the others are one of the two closest multiple of t...