One-way and two-way cost allocation in hub network problems

We consider a cost allocation problem arising from a hub network problem design. Finding an optimal hub network is NP-hard, so we start with a hub network that could be optimal or not. Our main objective is to divide the cost of such network among the nodes. We consider two cases. In the one-way flow case, we assume that the cost paid by a set of nodes depends only on the flow they send to other nodes (including nodes outside the set), but not on the flow they receive from nodes outside. In the two-way flow case, we assume that the cost paid by a set of nodes depends on the flow they send to other nodes(including nodes outside the set) and also on the flow they receive from nodes outside. In both cases, we study the core and the Shapley value of the corresponding cost game

Un problema de diseño de redes multi-período con capacidad y congestión en los hubs

Tesis (Magíster en Ciencias de la Ingeniería, mención Logística y Gestión de Operaciones)El diseño de redes es un área amplia dentro de Investigación de Operaciones, que busca construir redes para satisfacer algún tipo de demanda. Un área activa corresponde al diseño de redes hub-and-spoke, que usan instalaciones especiales para consolidar flujos, comúnmente llamadas hubs. En la literatura se han estudiado problemas de diseño de redes con múltiples períodos de planificación, congestión en los nodos, o con múltiples objetivos, pero no con todas estas características simultáneamente. La contribución de este trabajo es la formulación y resolución exacta para instancias de tamaño pequeño de un problema de diseño de redes hub-and-spoke. Nuestro modelo busca simultáneamente maximizar la demanda captura y minimizar los costos totales de la red, para un horizonte temporal discreto y finito. Se usan funciones lineales por tramos en el flujo entrante a los hubs para modelar la congestión en ellos. Se estudia el impacto de la congestión, capacidad en los hubs y la longitud del horizonte temporal. Los experimentos computacionales demuestran que el modelo propuesto logra representar la congestión dentro de una red de múltiples períodos de tiempo, ya que, al aumentar la demanda, los hubs fueron mostrando una saturación creciente al ir aumentando la demanda y junto a esto, los tiempos de viaje promedio también fueron mostrando un aumento en cada período de tiempo, indicación clara de la saturación de la red. Como trabajo futuro se propone encontrar la ubicación óptima de los hubs dentro de la red mediante un modelo de localización, al igual que considerar costos fijos al momento de habilitarlos y la existencia de capacidad en los arcos de la red, todo esto con el fin de complementar el modelo propuesto

The design of capacitated intermodal hub networks with different vehicle types

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.trb.2016.01.011 © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this study, we allow using alternative transportation modes and different types of vehicles in the hub networks to be designed. The aim of the problem is to determine the locations and capacities of hubs, which transportation modes to serve at hubs, allocation of non-hub nodes to hubs, and the number of vehicles of each type to operate on the hub network to route the demand between origin-destination pairs with minimum total cost. Total cost includes fixed costs of establishing hubs with different capacities, purchasing and operational costs of vehicles, transportation costs, and material handling costs. A mixed-integer programming model is developed and a variable neighborhood search algorithm is proposed for the solution of this problem. The heuristic algorithm is tested on instances from the Turkish network and CAB data set. Extensive computational analyzes are conducted in order to observe the effects of changes in various problem parameters on the resulting hub networks. (C) 2016 Elsevier Ltd. All rights reserved.Scientific and Technological Research Council of Turkey (TUBITAK) [111M553

Modeling congestion and service time in hub location problems

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.apm.2017.10.033 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, we present a modeling framework for hub location problems with a service time limit considering congestion at hubs. Service time is modeled taking the traveling time on the hub network as well as the handling time and the delay caused by congestion at hubs into account. We develop mixed-integer linear programming formulations for the single and multiple allocation versions of this problem. We further extend the multiple allocation model with a possibility of direct shipments. We test our models on the well-known AP data set and analyze the effects of congestion and service time on costs and hub network design. We introduce a measure for the value of modeling congestion and show that not considering the effects of congestion may result in increased costs as well as in building infeasible hub networks

Profit Maximizing Hub Location Problems

The final publication is available at Elsevier via https://doi.org/10.1016/j.omega.2018.05.016 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, we study profit maximizing hub location problems. We formulate mathematical models determining the location of hubs, designing the hub networks, and routing the demand in order to maximize profit. The profit is calculated by summing the total revenue minus total cost. Total cost includes the total transportation cost, the installation cost of hubs, and the cost of operating hub links. We consider all possible allocation strategies: multiple allocation, single allocation, and r-allocation. As an extension, for each allocation strategy, we also model the cases in which direct connections between non-hub nodes are allowed. To test and evaluate the performances of the proposed models, we use two well-known data sets from the literature. We analyze the resulting hub networks under various different parameter settings.Natural Sciences and Engineering Research Council of Canada [RGPIN-2015-05548

Shipment Scheduling In Hub Location Problems

In this thesis, we incorporate shipment scheduling decisions into hub location problems. Our aim is to determine optimal locations of hubs, hub network structure, and the number of vehicles to operate on the hub network as well as the time period of dispatching each vehicle from a hub. We develop mathematical models for di erent versions of this problem. We initially propose a mixed-integer shipment scheduling hub network design model where the costs of holding freight are negligible. We then expand the model to keep track of the holding decisions where the holding costs are not negligible. We further analyze the shipment scheduling model with holding costs when di erent types of vehicles are available to operate on the inter-hub links. We investigate the impact of shipment scheduling decisions and holding costs on hub network con gurations, routing decisions, and total cost of the network. We solve the models on instances from a new USAF dataset with real data

Multi-period hub network design problems with modular capacities

In this paper, a modeling framework is proposed for multi-period hub location. The problems to be studied are extensions of classical hub location problems to the situation in which the hub network can be progressively built and its capacity gradually expanded over time. Both the single allocation and the multiple allocation cases are considered. For each case, a mixed-integer linear programming formulation is proposed and a set of valid inequalities is derived for enhancing the corresponding model. The results of a set of computational tests performed using the formulations proposed and their enhancements are reported. The value of the multi-period solution is discussed as a measure for evaluating the relevance of considering a multi-period model instead of a static counterpart

Hub Network Design and Discrete Location: Economies of Scale, Reliability and Service Level Considerations

In this thesis, we study three related decision problems in location theory. The first part of the dissertation presents solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p-hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a greedy randomized adaptive search algorithm that is used to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed solution algorithms. In the second part of this dissertation, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes. In the last part of this dissertation we study the dynamic facility location problem with service level constraints (DFLPSL). The DFLPSL seeks to locate a set of facilities with sufficient capacities over a planning horizon to serve customers at minimum cost while a service level requirement is met. This problem captures two important sources of stochasticity in facility location by considering known probability distribution functions associated with processing and routing times. We present a nonlinear mixed integer programming formulation and provide feasible solutions using two heuristic approaches. We present the results of computational experiments to analyze the impact and potential benefits of explicitly considering service level constraints when designing distribution systems

Modelos de optimización para el diseño estratégico-táctico de una red de transporte intermodal

[ES] En esta tesis doctoral se desarrollan modelos de programación matemática para el diseño estratégico-táctico de una red de transporte intermodal que combina dos tipos de problemas de decisiones: la localización de instalaciones y el diseño de la red de transporte. Esta combinación se reconoce en la literatura como problemas combinados LI-DR. El problema combinado se estudia para una situación real y se analizan el comportamiento de la solución óptima, a partir de distintos aspectos como: la disponibilidad del presupuesto de inversión, capacidad de las instalaciones intermodales, múltiples periodos de decisiones, interdependencia en la priorización de las decisiones, múltiples fuentes de financiación y criterios de optimización para las tres dimensiones de sostenibilidad. Para la situación real se referencian las condiciones de acceso y conectividad de la Zona de Desarrollo Económico y Social (ZODES) Magdalena Medio del departamento de Bolívar en Colombia, y el potencial de la industria agroalimentaria para esta subregión. Con el propósito de identificar factores clave que perfilen la formulación respecto a la composición y funcionamiento de los sistemas intermodales y en los problemas combinados LI-DR se analiza la literatura desde estas dos perspectivas. El análisis de la literatura ha permitido aportar dos clasificaciones novedosas e identificar retos para la investigación futura. Para la formulación de los modelos se lleva a cabo la sistemática de pasos definidos para la aplicación de las técnicas de programación matemática. Con estos pasos se logra transformar el problema del mundo real a un problema manejable con estas técnicas. La transformación favorece la interpretación matemática del problema combinado LI-DR intermodal, la modelación de los datos y la definición de una estructura de red de entrada para indexar las decisiones estratégicas y tácticas. Los modelos de programación matemática se construyen de manera gradual. En concreto, se proponen 2 versiones que se representan en 5 variantes. Se comienza formulando un modelo de programación lineal entero-mixto (MPLEM) mono-periodo para analizar, desde un enfoque económico, la sensibilidad de las capacidades del sistema intermodal, la capacidad financiera de los tomadores de decisiones y la variación de la demanda. A continuación, sobre la base de este modelo se propone un MPLEM multi-periodo y dos variantes para validar las condiciones de interdependencia en la toma de decisiones estratégica y la participación de múltiples actores en la financiación de los proyectos de inversión. Finalmente, se formula un MPLEM multi-objetivo para optimizar simultáneamente las tres dimensiones de sostenibilidad. Para resolver y validar los modelos se implementaron dos esquemas de resolución. En los esquemas se utilizan los lenguajes de programación R y Python con el software de optimización matemática Gurobi Optimizer. Se realizan experimentos numéricos para distintos escenarios y se analiza el comportamiento de las soluciones considerando distintos valores a los parámetros. Los resultados obtenidos permiten comprobar la utilidad de los modelos matemáticos e identificar las principales limitaciones y futuras líneas de trabajo.[CA] En aquesta tesi doctoral es desenvolupen models de programació matemàtica per al disseny estratègic-tàctic d'una xarxa de transport intermodal que combina dos tipus de problemes de decisions: la localització d'instal·lacions i el disseny de la xarxa de transport. Aquesta combinació es reconeix en la literatura com problemes combinats LI-DR. El problema combinat s'estudia per a una situació real i s'analitzen el comportament de la solució òptima, a partir de diferents aspectes com: la disponibilitat de l'pressupost d'inversió, capacitat de les instal·lacions intermodals, múltiples períodes de decisions, interdependència en la priorització de les decisions, múltiples fonts de finançament i criteris d'optimització per a les tres dimensions de sostenibilitat. Per a la situació real es referencien les condicions d'accés i connectivitat de la Zona de Desenvolupament Econòmic i Social (ZODES) Magdalena Medio de el departament de Bolívar a Colòmbia, i el potencial de la indústria agroalimentària per a aquesta subregió. Amb el propòsit d'identificar factors clau que perfilin la formulació respecte a la composició i funcionament dels sistemes intermodals i en els problemes combinats LI-DR s'analitza la literatura des d'aquestes dues perspectives. L'anàlisi de la literatura ha permès aportar dues classificacions noves i identificar reptes per a la investigació futura. Per a la formulació dels models es porta a terme la sistemàtica de passos definits per l'aplicació de les tècniques de programació matemàtica. Amb aquests passos s'aconsegueix transformar el problema de l'món real a un problema manejable amb aquestes tècniques. La transformació afavoreix la interpretació matemàtica de el problema combinat LI-DR intermodal, la modelació de les dades i la definició d'una estructura de xarxa d'entrada per indexar les decisions estratègiques i tàctiques. Els models de programació matemàtica es construeixen de manera gradual. En concret, es proposen 2 versions que es representen en 5 variants. Es comença formulant un model de programació lineal sencer-mixt (MPLEM) mono-període per analitzar, des d'un enfocament econòmic, la sensibilitat de les capacitats de sistema intermodal, la capacitat financera dels prenedors de decisions i la variació de la demanda. A continuació, sobre la base d'aquest model es proposa un MPLEM multi-període i dues variants per validar les condicions d'interdependència en la presa de decisions estratègica i la participació de múltiples actors en el finançament dels projectes d'inversió. Finalment, es formula un MPLEM multi-objectiu per optimitzar simultàniament les tres dimensions de sostenibilitat. Per resoldre i validar els models es van implementar dos esquemes de resolució. En els esquemes s'utilitzen els llenguatges de programació R i Python amb el programari d'optimització matemàtica Gurobi Optimizer. Es realitzen experiments numèrics per a diferents escenaris i s'analitza el comportament de les solucions considerant diferents valors als paràmetres. Els resultats obtinguts permeten comprovar la utilitat dels models matemàtics i identificar les principals limitacions i futures línies de treball.[EN] In this doctoral thesis, mathematical programming models are developed aiming at the strategic-tactical design of an intermodal transport network that combines two types of decision problems: the location of facilities and the transport network design. In the literature, this combination is recognized as combined LI-DR problems. The combined problem is studied for a real situation and the performance of the optimal solution is analyzed in relation to different aspects such as the investment budget availability, the intermodal facilities capacity, multiple decision periods, interdependence in the prioritization of the decisions, multiple sources of funding and optimization criteria for the three dimensions of sustainability. In what concern to the real situation, the access and connectivity conditions of the Magdalena Medio Economic and Social Development Zone (ZODES, for its acronym in Spanish) of the Bolívar department in Colombia, and the potential of the agri-food industry for this subregion, are considered. Aiming the identification of key factors that outlines the formulation regarding the composition and operation of intermodal systems and, in combined LI-DR problems, the literature is reviewed from these two perspectives. The literature analysis has made it possible to provide two novel classifications and to identify challenges for future research. The formulation of models follows the systematic steps already defined for the application of mathematical programming techniques. Following these steps, it is possible to transform the problem from a real-world problem to a manageable one. The transformation promotes the mathematical interpretation of the intermodal LI-DR combined problem, the data modeling, and the definition of an input network structure to index strategic and tactical decisions. Mathematical programming models are built gradually. Specifically, 2 versions are proposed, which are represented by 5 variants. Firstly, it is formulated a single-period mixed-integer linear programming model (MILPM) in order to analyze, from an economic perspective, the sensitivity of the intermodal system capacities, the financial capacity of the decision-makers, and the demand changes. Based on the aforementioned model, a multi-period MILPM and two variants are proposed aiming to validate the conditions of interdependence in strategic decision-making and the participation of multiple actors in the investment projects financing. Finally, a multi-objective MILPM is formulated to simultaneously optimize all three dimensions of sustainability. To solve and validate the models, two resolution schemes were implemented. The schematics use the R and Python programming languages with the mathematical optimization software Gurobi Optimizer. Numerical tests are carried out for different scenarios and the performance of the solutions is analyzed considering different values for the parameters. The results obtained allow us to verify the usefulness of the models proposed and identify the main limitations and future lines of work.Agamez Arias, ADM. (2021). Modelos de optimización para el diseño estratégico-táctico de una red de transporte intermodal [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/177015TESI