Federico Perea

Universidad de Sevilla | US · Applied Mathematics II

This paper addresses an unrelated parallel machines scheduling problem with the need of additional resources during the processing of the jobs, as well as during the setups that machines need between the processing of any two jobs. This problem is highly complex, and therefore in this paper we propose several constructive heuristics to solve it. To...

The aim of this paper is to introduce the Flexible Periodic Vehicle Routing Problem with Heterogeneous Fleet, a variant of the Periodic Vehicle Routing Problem. Flexibility is introduced in service schedules and delivered quantities, heterogeneity comes from different vehicles capacities and speeds. Three Mixed-Integer Linear Programming formulatio...

In this paper, we present a network-based model for human migration in which a utility function is maximized. The resulting nonlinear optimization problem is characterized by a variational inequality formulation. Due to the high complexity of this problem, in order to efficiently solve realistic instances a heuristic method is proposed. The present...

We present a bi-objective parallel machine scheduling problem with machine and job sequence dependent setup times, with the additional consideration of resources needed during setups. The availability of such resources is limited. This models many practical situations where setup times imply, for example, cleaning and/or the reconfiguration of prod...

In this paper we analyze the computational complexity of transportation infrastructure network design problems, in the presence of a competing transportation mode. Some of these problems have previously been introduced in the literature. All problems studied have a common objective: the maximization of the number of travelers using the new network...

This paper provides practitioners with new approaches for solving realistic scheduling problems that consider additional resources, which can be implemented on expert and intelligent systems and help decision making in realistic settings. More specifically, we study the unrelated parallel machine scheduling problem with setup times and additional l...

This paper introduces a row and column generation algorithm for finding the nucleolus, based on a linear programming model proposed in an earlier research. Since this approach cannot return an allocation for large games, we also propose a heuristic approach, which is based on sampling the coalitions space. Experiments over medium sized games show t...

Parallel machine scheduling problems have many practical and industrial applications. In this paper we study a generalization which is the unrelated parallel machine scheduling problem with machine and job sequence setup times (UPMS) with makespan minimization criterion. We propose new mixed integer linear programs and a mathematical programming ba...

The problem studied in this paper takes as input data a set of lines forming a railway network, and an origin–destination (OD) matrix. The OD pairs may use either the railway network or an alternative transportation mode. The objective is to determine the frequency/headway of each line as well as its number of carriages, so that the net profit of t...

In this paper we analyze a parallel machine scheduling problem in which the processing of jobs on the machines requires a number of units of a scarce resource. This number depends both on the job and on the machine. The availability of resources is limited and fixed throughout the production horizon. The objective considered is the minimization of...

In this paper, we characterize minimax and Pareto-optimal security payoff vectors for general multicriteria zero-sum matrix games, using properties similar to the ones that have been used in the single criterion case. Our results show that these two solution concepts are rather similar, since they can be characterized with nearly the same sets of p...

The goal in this paper is to analyze a particular problem within municipal waste collection. This problem consists of finding an assignment of collection sites to service days, so that sites collected on the same day are close to each other. We consider two different types of waste that are collected simultaneously by specialized trucks, which adds...

This paper deals with the swath acquisition planning problem for multisatellite Earth observation missions. Given a set of satellites and a mission time frame, the problem we solve consists of selecting a set of acquisitions from the satellites in order to cover a given region of interest during the requested time frame, optimizing a certain object...

Given the set of lines representing a railway network, and other parameters such as costs, speed, origin/destination matrix, etc., the goal of this paper is to fix the frequency of each line and the capacity of each train so that the net profit of the network is maximized. To introduce the net profit, a rigorous analysis for the calibration of diff...

In this paper we study the problem of locating a new station on an existing rail corridor and a new junction on an existing road network, and connecting them with a new road segment under a budget constraint. We consider three objective functions and the corresponding optimization problems, which are modeled by means of mixed integer non-linear pro...

The railway planning problem consists of several consecutive phases: network design, line planning, timetabling, personnel assignment and rolling stocks planning. In this paper we will focus on the line planning process. Traditionally, the line planning problem consists of determining a set of lines and their frequencies optimizing a certain object...

Every day, ground stations need to manage numerous requests for allocation of antenna time slots by customers operating satellites. For multi-antenna, multi-site ground networks serving numerous satellite operators, oftentimes these requests yield conflicts, which arise when two or more satellites request overlapping time slots on the same antenna....

In this paper we compare two solution concepts for general multicriteria zero-sum matrix games: minimax and Pareto-optimal security payoff vectors. We characterize the two criteria based on properties similar to the ones that have been used in the corresponding counterparts in the single criterion case, although they need to be complemented with tw...

In this paper we compare two solution concepts for general multicriteria zero-sum matrix games: minimax and Pareto-optimal security payoff vectors. We characterize the two criteria based on properties similar to the ones that have been used in the corresponding counterparts in the single criterion case, although they need to be complemented with tw...

In this paper we show a new method for calculating the nucleolus by solving a unique minimization linear program with O(4n)O(4n) constraints whose coefficients belong to {−1,0,1}{−1,0,1}. We discuss the need of having all these constraints and empirically prove that they can be reduced to O(kmax2n)O(kmax2n), where kmax is a positive integer compara...

This paper discusses and extends some competitive aspects of the games proposed in an earlier work, where a robust railway network design problem was proposed as a non-cooperative zero-sum game in normal form between a designer/operator and an attacker. Due to the importance of the order of play and the information available to the players at the m...

This paper analyzes the solvability of a railway network design problem and its robust version. These problems are modeled as integer linear programming problems with binary variables, and their solutions provide topological railway networks maximizing the trip coverage in the presence of a competing mode, both assuming that the network works fine...

In this paper we will show how hypergraphs and some measures related to them can help in extracting information about Collective Transportation Line Networks. We will also prove that these measures satisfy certain properties that validate their use to compare the connectivity of different networks.

This paper deals with cooperation situations in linear production problems in which a set of goods are to be produced from a set of resources so that a certain benefit function is maximized, assuming that resources not used in the production plan have no value by themselves. The Owen set is a well-known solution rule for the class of linear product...

In this paper we introduce and analyze new classes of cooperative games related to facility location models. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service diameter of the coalition.We study the e...

In this paper the following facility location problem in a mixed planar-network space is considered: We assume that traveling along a given network is faster than traveling within the plane according to the Euclidean distance. A pair of points (A i ,A j ) is called covered if the time to access the network from A i plus the time for traveling along...

The purpose of this paper is to provide passenger robustness measures for a rail transit network. A network is robust when it reacts well to disruptions on links or stations. In order to measure robustness, indexes relative to the overall travel time of a network when links fail are introduced for two different cases: without-bridging interruptions...

This paper studies a municipal waste collection problem, whose ultimate goal is to find an assignment of containers to service days and posterior routing so that the total distance covered by the waste collection trucks is minimized. Due to the complexity of this problem, we divide it into several subproblems. The focus of this paper is on the firs...

In this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is the service radius...

Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally, operations research methods have not played a major role at the planning level but several tools developed in recent years can assis...

The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension d ∈ N is to match groups of d objects in such a way that each measurement is associated with at most one track and each track is associated with at...

The aim of this paper is to propose a model for the design of a robust rapid transit network. In this paper, a network is said to be robust when the effect of disruption on total trip coverage is minimized. The proposed model is constrained by three different kinds of flow conditions. These constraints will yield a network that provides several alt...

This paper reviews the multi dimensional assignment problem (MAP) and some of its applications. The MAP is a higher dimensional version of the classic two-sided assignment problem, and has applications in areas such as target tracking and robot vision. These applications are reviewed as well as the game arising from the MAP, called the m-sided assi...

In this paper a new concept of robustness is introduced and the corresponding optimization problem is stated. This new concept is applied to transportation network designs in which the set of scenarios arising from the uncertainty of the parameters follows a probability distribution. The p-robustness concept is aimed to problems where the feasibili...

The Owen set is a well-know solution concept for the class of Linear Production games, which is included in the core. Despite their stability, Owen allocations might give null payoff to players which are absolutely necessary for any possible benefit to arise. We introduce a new solution set that overcomes such drawbacks. Some of its properties are...

In this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces. The players are the customers (demand points) in the location problem and the characteristic value of a coalition is the cost of serving its members. Specifically, the cost in our games is either the service...

This paper proposes a game theoretic framework for the problem of designing an uncapacitated railway transit network in the presence of link failures and a competing mode. It is assumed that when a link fails, another path or another transportation mode is provided to transport passengers between the endpoints of the affected link. The goal is to b...

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically releva...

Traditionally, when designing robust transportation systems, one wants to increase the functionality of the system in presence of failures, even though they might not work optimally when no failures occur, which is the usual case. In this paper we make an attempt to integrate robust network design and line planning without decreasing the efficiency...

This paper uses dynamic programming to investigate when contestants should use lifelines or when they should just stop answering in the TV quiz show ‘Who wants to be a millionaire?’. It obtains the optimal strategies to maximize the expected reward and to maximize the probability of winning a given amount of money.

In this paper a new concept of robustness is introduced and the corresponding optimization problem is stated. This new concept is applied to transportation network designs in which the set of scenar- ios arising from the uncertainty of the parameters follows a probability distribution. The p-robustness concept is aimed to problems where the feasibi...

The multidimensional assignment problem (MAP) is a combinatorial optimization problem arising in many applications, for instance in multi-target multi-sensor tracking problems. It is well-known that the MAP is NP-hard. The objective of a MAP is to match d-tuples of objects in such a way that the solution with the optimum total cost is found. In thi...

En este trabajo estudiamos un juego de cartas llamado "Siete y Media". Empezaremos describiendo el juego. En el siguiente capítulo hablamos de reglas para tomar decisiones: qué son reglas de decisión y cuál vamos a utilizar. El siguiente paso es mostrar un argumento teórico para resolver el juego. Después de eso simulamos que estamos jugando a este...

Beyond the topics, the Mathematics folklore says that pupils think that this field is a boring, non-practical mental exercise, far apart from daily life. This thought is influencing the entire education system and even society, motivating important lack of mathematical skills among students. This work presents experiences, developed within the MaMa...

In this paper a new concept of robustness is introduced and the corresponding optimization problem is stated. This new concept is applied to transportation network designs in which the set of scenarios arising from the uncertainty of the parameters follows a probability distribution. The $p$-robustness concept is aimed to problems where the feasibi...