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This paper proposes a new approach, based on an SBI, shared-input NDEA model, to assess the sport and value creation performance of football clubs that are playing in national and international competitions. The novel features of the proposed approach include the relationship between the different sub-processes that make the team transform their salaries into sporting results and these into market value; the computation of inefficiency scores for the participation in the national and international competitions as well as the inefficiency of the value creation stage; and the computation of target intervals for the sports results of the clubs. The proposed approach has been applied to 22 teams, from six major European football leagues that played the UEFA Champions league in the 2021/2022 season.

Top European football teams have large budgets mainly due to the high wage bills they pay to the players. Therefore, it would be interesting to determine if these football teams are paying inflated salaries considering the sports results that they obtain each season in both national and international competitions. This study focuses on the top five European football leagues (Italian, Spanish, English, French and German). We propose a novel non-convex, non-parametric metafrontier analysis approach to determine whether the football clubs are overpaying their players considering their sporting performance. Goals against in both national and international competitions are modelled as undesirable outputs. Each football team is benchmarked first within its own league and then against all five leagues. From this, apart from estimating the payroll efficiency of each team, the average efficiency of each of these five leagues can also be computed. An exhaustive analysis and discussion of the results is presented using data from three seasons (2020–2023). Some ‘important’ football clubs pay salaries that are not justified by their performance when compared with other, more modest, clubs that pay salaries more in line with the sports results obtained. Ligue 1 is the league that, on average, makes the most efficient use of their payroll, followed by the Bundesliga and, somewhat behind, La Liga and Serie A. The Premier League occupies the last position in terms of average payroll efficiency.

We analyze several time dependency issues for the selective traveling salesman problem with time-dependent profits. Specifically, we consider the case in which the profit collected at a vertex depends on the service time, understood as the time spent at this vertex, and when the service time at each vertex depends on the arrival time at the vertex. For each of these two cases, we formulate two continuous-time problems: (i) a vertex can be visited at most once, and (ii) vertices may be visited more than once. In each case, we consider general profit functions at the vertices, i.e., the profit functions are not limited to monotonic functions of time. We also formulate the problems as discrete-time problems using appropriate variants of an auxiliary time-extended graph, and we solve them with Gurobi. We apply our methodology to two sets of instances. First, we use a set of artificial instances to illustrate the main differences amongst the different versions of the problem. We then solve several instances adapted from TSPLIB to evaluate the computational capabilities of the methodology.

In this paper, we formulate and solve the urban line planning problem considering a multilayer representation of a bimodal transportation network. Classical formulations are usually constructed over a planar network, which implies the need to introduce several strong non-linearities in terms of frequencies when modeling transfer times. In the proposed network representation, each candidate line is stored in a specific layer and the passengers’ movements for each origin– destination pair are modelled considering a strategy subgraph, contributing to a sparse model formulation that guarantees feasibility and simplifies the assignment process. The methodology is first tested using the Mandl network, obtaining results that are comparable in terms of quality with the best metaheuristic approaches proposed in the scientific literature. With the aim of testing its applicability to large scenarios, the proposed approach is then used to design the main urban transit network of Seville, a large scenario with 141 nodes and 454 links, considering artificial unfavorable demand data. The reasonable computation time required to exactly solve the problem to optimality confirms the possibility of using the multilayer approach to deal with multimodal network design strategic problems.

In this paper a complex network analysis of global fertiliser trade during the period 2014–2018 has been carried out. The goal is to study its structure both at the global and local level, identifying communities and main players, motifs, structural holes and brokerage roles. The persistency and variability of trade links have also been analysed. The Global Fertiliser Trade Network is characterised as a small-world network with scale-free prop erties, revealing a high level of reciprocity and centralisation. The network has a core-periphery structure consisting of five core countries (namely EU, USA, China, Brazil, and the Russian Federation) which trade among themselves and with most periphery countries, which have sparse connections between them. The interregional and community analyses indicate a moderate level of heterophily and a geographical component in the trade communities. The network also exhibits an overall tendency toward intransitivity which implies a strategic advantage for countries that act as brokers. This study provides a clear picture of the situation prior to the COVID pandemic and the Ukraine military conflict. Those events have affected global fertiliser trade in a way that has yet to be fully ascertained. The purpose of this paper is to firmly establish a reference against which to gauge the direction and magnitude of those changes.

This paper presents a DEA approach for a company to assess the efficiency of its shipments and of the haulers that handle them. It is based on the concept of metafrontier, which benchmarks a given shipment, first against all the shipments of the same hauler and then against all the shipments of all the haulers. Thus, the efficiency of each shipment as well as that of the corresponding hauler can be determined. The scale efficiency of the shipments, related to the cost premium paid for shipments whose weight, volume or distance is not large enough, is determined. In addition, the model estimates the functional dependence of the shipment cost on the load weight, volume and distance. An experimental design to validate the proposed efficiency assessment approach and test the factors that influence its accuracy has been carried out. The application of the proposed approach to a large Spanish food company is presented and used to illustrate its usefulness. The proposed approach is able to determine the minimum cost of a shipment as a function of its weight, volume and distance. This tool proved to be useful to assess the price quotes received by the company and bargain better prices.

In this work, we address the Truck-multi-Drone Team Logistics Problem (TmDTL), devoted to visit a set of points with a truck helped by a team of unmanned aerial vehicles (UAVs) or drones in the minimum time, starting at a certain location and ending at a different one. It is an enhanced version of the multiple Flying Sidekicks Traveling Salesman Problem (mFSTSP) presented in Murray and Raj (2020) wherein drones are allowed to visit several customers per trip. In order to cope with large instances of the complex TmDTL, we have developed a novel agent-based method where agents represent the points that are going to be visited by vehicles. Agents evolve by means of movement inside a grid (locations vs. vehicles) according to a set of rules in the seek of better objective function values. Each agent needs to explore only a fraction of the complete problem, sharing its progress with the rest of the agents which are coordinated by one central agent which helps to maintain an asynchronous memory of solutions – e.g. on the control of the mechanism to escape from local minima. Our agent-based approach is firstly tested using the largest instances of the single TDTL problem reported in the literature, which additionally serves as upper bounds to the TmDTL problem. Secondly, we have solved instances up to 500 locations with up to 6 drones in the fleet. Thirdly, we have tested the behavior of our approach in 500 locations problems with up to 8 drones in order to test the fleet size sensitivity. Our experiments demonstrate the ability of the proposed agent-based system to obtain good quality solutions for complex optimization problems that arise. Further, the abstraction in solutions coding applied makes the agent-based approach scalable and flexible enough to be applied to a wide range of other optimization problems.

We consider a generalization of the selective traveling salesman problem (STSP) in which the benefit of visiting a location changes over time. This new problem, called the selective travelling salesman problem with time-dependent profits (STSP-TDP), is defined on a graph with time-dependent profits associated with the vertices, and consists of determining a circuit of maximal total profit. In the STSP-TDP the tour length must not exceed a maximum value, and its starting and ending times must both lie within a prespecified planning horizon. This problem arises in planning tourist itineraries, mailbox collection, military surveillance, and water sampling, where the traveler accumulates different profits upon visiting the locations throughout the day. We focus on analyzing several variants of the problem depending on the shape of the time-dependent profit function. If this function is not monotonic, it may be worth visiting a site more than once. We propose formulations for the single-visit case and for when multiple visits are allowed, in which case the problem reduces to an STSP, which is adapted to be solved as a longest path problem. These formulations are then solved for piecewise-linear profit functions using a general-purpose solver, and tested on several artificially created instances and on four TSPLib instances involving up to 535 vertices. A detailed analysis of the problem and the solution is performed.

There exist two types of Data Envelopment Analysis (DEA) approaches to the Olympic Games: conventional and fixed-sum outputs (FSO). The approach proposed in this paper belongs to the latter category as it takes into account the total number de medals of each type awarded. Imposing these constraints requires a centralized DEA perspective that projects all the countries simultaneously. In this paper, a multiobjective FSO approach is proposed, and the Weighted Tchebychef solution method is employed. This approach aims to set all output targets as close as possible to their ideal values. In order to choose between the alternative optima, a secondary goal has been considered that minimizes the sum of absolute changes in the number of medals, which also renders the computed targets to be as close to the observed values as possible. These targets represent the output levels that could be expected if all countries performed at their best level. For certain countries, the targets are higher than the actual number of medals won while, for other countries, these targets may be lower. The proposed approach has been applied to the results of the Tokyo 2020 Olympic Games and compared with both FSO and non-FSO DEA methods

The analysis of tandem truck–drone delivery systems has recently attracted the attention of the research community, mainly focused on extending classical operational research problems such as the multiple traveling salesperson or the vehicle-routing problem. In this paper, we explore the design of an urban massive combined delivery system using a continuum approximation (CA) method for a circular city characterized by a certain density of customers. Starting from a set of parameters defining the main characteristics of trucks and drones, a sectorization of the delivery area is first determined. Then, for a given truck capacity, the optimal number of trucks is obtained considering different scenarios using three integer programming models. We propose several performance indicators to compare the tandem approach with the alternative solely truck delivery system.

This paper deals with Data Envelopment Analysis (DEA) in centralised settings in which the operating units belong to the same organisation. In such a scenario, a global system-wide perspective may be adopted as regards resource allocation and target setting. In this paper, a new Lexicographic Goal Programming (lexGP) approach is proposed using three priority levels: the aggregated input consumption and output production goals; the input and output goals of the individual operating units; and the technical efficiency of the computed targets. It is assumed that the goals for the overall organisation are established by the Central Decision-Maker (CDM) and that they are consistent with those of the individual operating units. The proposed approach has been applied to the Spanish public university system, comprising 47 institutions. Given the CDM preferences in terms of input and output aggregate goals and relative importance weights, specific technical efficient targets have been computed for each university. The results show that the proposed approach is more suitable than the non-centralised DEA approach and produces targets that are more effective than other centralised resource allocation approaches in the sense that they are much closer to both the aggregate goals of the CDM and the specific goals of each university.

In this paper, we analyze both the deterministic and stochastic versions of a team orienteering problem (TOP) in which rewards from customers are dynamic. The typical goal of the TOP is to select a set of customers to visit in order to maximize the total reward gathered by a fixed fleet of vehicles. To better reflect some real-life scenarios, we consider a version in which rewards associated with each customer might depend upon the order in which the customer is visited within a route, bonusing the first clients and penalizing the last ones. In addition, travel times are modeled as random variables. Two mixed-integer programming models are proposed for the deterministic version, which is then solved using a well-known commercial solver. Furthermore, a biased-randomized iterated local search algorithm is employed to solve this deterministic version. Overall, the proposed metaheuristic algorithm shows an outstanding performance when compared with the optimal or near-optimal solutions provided by the commercial solver, both in terms of solution quality as well as in computational times. Then, the metaheuristic algorithm is extended into a full simheuristic in order to solve the stochastic version of the problem. A series of numerical experiments allows us to show that the solutions provided by the simheuristic outperform the near-optimal solutions obtained for the deterministic version of the problem when the latter are used in a scenario under conditions of uncertainty. In addition, the solutions provided by our simheuristic algorithm for the stochastic version of the problem offer a higher reliability level than the ones obtained with the commercial solver.

In Spain, the average remuneration of large electric distribution companies is much lower than that of smaller ones, which leads us to wonder if the smaller ones are managed efficiently. A meta-frontier DEA model is calculated in order to benchmark, in terms of remuneration and quality, different clusters of distributors that present different technologies. The sample is composed of 236 distributors (including the five largest units). The savings for the system would be approximately 174 million Euros per year. Moreover, compensation regulation should aim to guide distributors towards their respective intra-cluster frontiers

This paper extends two fuzzy ranking data envelopment analysis (DEA) approaches to the case of general networks of processes. The first approach provides an efficiency score for each possibility level which requires solving one linear program for each possibility level. The second approach is even simpler and provides an overall efficiency score solving just one linear program. The proposed approaches are tested on two datasets from the literature and compared with other fuzzy network DEA approaches. The results show that the two methods provide very highly correlated efficiency estimates which are also consistent with those of other fuzzy network DEA approaches.

This paper presents a solution methodology to solve the heterogeneous vehicle routing problem with time windows (HVRPTW). This problem appears when a limited fleet of vehicles, characterized by different capacities, fixed costs and variable costs, is available for serving a set of customers which have to be visited within a predefined time window. The objective is to perform the route design minimizing the total fixed vehicle costs and distribution costs and satisfying all problem constraints. The problem is solved using an Ant Colony System (ACS) algorithm which has been successfully applied to combinatorial optimization problems. Moreover, to improve the performance of the ACS on the HVRPTW, a hybridized ACS with local search, called memetic ACS algorithm is proposed where the local search is performed by a variable neighborhood Tabu Search algorithm. Experiments are conducted on sets of benchmark instances from the scientific literature to evaluate the performance of the proposed algorithm. The results show that the algorithm has a good performance on the HVRPTW. In particular, out of the 80 instances, it obtained 65 new best solutions and matched 6 within reasonable computational times.

This paper introduces the heterogeneous vehicle routing problem with time windows and a limited number of resources (HVRPTW-LR), a practical extension of the classical vehicle routing problem in which routes to be designed share common scarce resources. The HVRPTW-LR arises when a limited number of resources, such as vehicles, drivers, instruments, and so on, are available but are insufficient to serve all customers in a route planning. Therefore, the route design involves the selection of customers to be visited at each route and resources to be used. Applications to this problem are found in real services companies with high seasonal demand which attend to different types of works and have to decide on how to effectively manage their resources. For designing optimal routes, a hierarchical objective function is considered, maximizing the total number of served customers as the primary objective, and minimizing the travel costs as secondary. A mathematical model of linear programming is introduced to describe and understand all constraints clearly. The problem is first heuristically solved by a semi-parallel insertion heuristic. Then, solutions are improved by a hybrid variable neighborhood descent metaheuristic based on a Tabu Search algorithm for the exploration of the neighborhood and a holding list. Experiments are conducted on numerous sets of benchmark instances from the literature to evaluate the performance of the proposed algorithm. Results show that the algorithm proposed in this paper has a good performance and can be easily applied for solving numerous vehicle routing problem variants from the literature. A new set of benchmark cases for the HVRPTW-LR are also presented and solved.

Many systems can operate in different modes of functioning. Conventional data envelopment analysis (DEA) would ignore that fact and consider instead that the system is a black box, paying attention just to the overall input consumption and output production. In this paper a more fine-grained approach is proposed consisting of explicitly modelling the different modes of functioning as specific processes and using the observed data on the input consumption and output production in each of the modes of functioning to infer the corresponding mode-specific technology. The system technology results from composing these mode-specific technologies according to the corresponding time allocations. The proposed approach allows computing efficient operating points for every mode of functioning, looking for improvements in the overall system performance. Two efficiency assessment DEA models are presented depending on whether the observed time allocation is maintained or the model is free to modify it. An application of the proposed approach to assessing the efficiency of NFL teams, operating in defence and offence modes in a given game, is presented.

This paper focuses on designing waste collection routes with a single landfill using eco-efficiency as a performance indicator. In this problem, there are a limited number of heterogeneous vehicles based at a single depot. Empty vehicles leave the depot, collect waste from a set of locations and drop off the collected waste at a specific landfill. Then, vehicles leave the landfill and may collect more waste from other locations or return empty to the depot. Traditional performance indicators in vehicle routing problems are mainly focused on economic objectives, not explicitly considering environmental issues. In this paper, a mathematical model is presented with an eco-efficient objective function that takes into account external costs (climate change and air pollution). The COPERT model is used for estimating fuel consumption, carbon dioxide and pollutant emissions. The problem is first heuristically solved using a semi-parallel construction algorithm. Then, solutions are improved by a variable neighborhood tabu search algorithm developed for this problem. The algorithm is validated for a real problem in the municipality of Alcalá de Guadaíra, within the metropolitan area of Seville (Spain). Results obtained on a set of case studies improve the solution that is currently implemented in the municipality, in terms of total distance traveled, carbon dioxide emissions and pollutant emissions.

This paper considers a multiproduct supply network, in which losses (e.g., spoilage of perishable products) can occur at either the nodes or the arcs. Using observed data, a Network Data Envelopment Analysis (NDEA) approach is proposed to assess the efficiency of the product flows in varying periods. Losses occur in each process as the observed output flows are lower than the observed input flows. The proposed NDEA model computes, within the NDEA technology, input and output targets for each process. The target operating points correspond to the minimum losses attainable using the best observed practice. The efficiency scores are computed comparing the observed losses with the minimum feasible losses. In addition to computing relative efficiency scores, an overall loss factor for each product and each node and link can be determined, both for the observed data and for the computed targets. A detailed illustration and an experimental design are used to study and validate the proposed approach. The results indicate that the proposed approach can identify and remove the inefficiencies in the observed data and that the potential spoilage reduction increases with the variability in the losses observed in the different periods.

This paper is the first to tackle the problem of designing routes in service companies that are responsible for the metrological control of measuring equipments at customer sites. This real-world problem belongs to the well-known Rich Vehicle Routing Problems which combine multiple attributes that distinguish them from traditional vehicle routing problems. The attributes include fixed heterogeneous fleet of vehicles, time windows for customers and depot, resource synchronization between tours, driver-customer and vehicle-customer constraints, customer priorities and unserved customers. This routing and scheduling problem is modeled with linear programming techniques and solved by a variable neighborhood descent metaheuristic based on a tabu search algorithm with a holding list. A real-life case study faced by a company in the region of Andalusia (Spain) is also presented in this work. The performance of the metaheuristic is compared with the literature for the standard fixed heterogeneous vehicle routing problem. Results obtained on a real case instance improve the solutions implemented by the company.

En el presente trabajo se propone una metodología basada en DEA que proporcione la eficiencia de redes de metro. A partir de las dos salidas que se han identificado como las que mejor representan el buen funcionamiento de las redes de metro (pasajeros y pasajeros por Km.), se establece una regresión multivariante que determine, de entre todos los recursos utilizados por la red, los que mejor explican las salidas consideradas. Este resultado se analiza mediante un análisis DEA, para posteriormente diseñar un perceptrón multinivel capaz de prever los targets de una red no analizada.

El objetivo principal en este trabajo es la programación de horarios de viajes en tren de acuerdo a los deseos de movilidad de los pasajeros, en el caso de frecuencias medias. Por tanto, se analiza el diseño de horarios en recorridos de media y larga distancia. Este problema, resulta de interés para satisfacer las necesidades de los usuarios, adicionalmente es significativo porque existen actualmente pocas aproximaciones sobre este tema. Otros aspectos que resultan inseparables del problema de scheduling, como la medición de la capacidad del servicio o la propia calidad del servicio, se estudian de manera conjunta.

En este trabajo se presenta una revisión del estado del arte de la Logística Urbana de Mercancías (LUM) en España. Para hacerlo, se informa sobre las fuentes de información y opinión a las que se puede recurrir sin necesidad de recurrir a estudios directos. Se realiza también una descripción de la situación actual de los tres grupos principales de actores-proveedores, receptores y Administración Pública, y se esbozan algunas iniciativas que empiezan a aparecer a nivel local en muchas ciudades de España. Las dos últimas secciones tienen un mayor contenido de opinión, reflejando la visión de los autores sobre el estado actual de la Logística Urbana de Mercancías en España.