New Complexity Results and Algorithms for the Minimum Tollbooth Problem

The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of edges are tolled may be preferable over others due to its ease of implementation in real networks. In this paper we consider the minimum tollbooth (MINTB) problem, which seeks social optimum inducing tolls with minimum support. We prove for single commodity networks with linear latencies that the problem is NP-hard to approximate within a factor of $1.1377$ through a reduction from the minimum vertex cover problem. Insights from network design motivate us to formulate a new variation of the problem where, in addition to placing tolls, it is allowed to remove unused edges by the social optimum. We prove that this new problem remains NP-hard even for single commodity networks with linear latencies, using a reduction from the partition problem. On the positive side, we give the first exact polynomial solution to the MINTB problem in an important class of graphs---series-parallel graphs. Our algorithm solves MINTB by first tabulating the candidate solutions for subgraphs of the series-parallel network and then combining them optimally

Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds

The allocation of buffer space in flow lines with stochastic processing times is an important decision, as buffer capacities influence the performance of these lines. The objective of this problem is to minimize the overall number of buffer spaces achieving at least one given goal production rate. We optimally solve this problem with a mixed-integer programming approach by sampling the effective processing times. To obtain robust results, large sample sizes are required. These incur large models and long computation times using standard solvers. This paper presents a Benders Decomposition approach in combination with initial bounds and different feasibilitycutsfortheBufferAllocationProblem,whichprovidesexactsolutionswhile reducing the computation times substantially. Numerical experiments are carried out to demonstrate the performance and the flexibility of the proposed approaches. The numerical study reveals that the algorithm is capable to solve long lines with reliable and unreliable machines, including arbitrary distributions as well as correlations of processing times

Resource-constrained scheduling for maritime traffic management

National Research Foundation (NRF) Singapore under Corp Lab @ Universit

Decomposition methods for large-scale network expansion problems

Network expansion problems are a special class of multi-period network design problems in which arcs can be opened gradually in different time periods but can never be closed. Motivated by practical applications, we focus on cases where demand between origin-destination pairs expands over a discrete time horizon. Arc opening decisions are taken in every period, and once an arc is opened it can be used throughout the remaining horizon to route several commodities. Our model captures a key timing trade-off: the earlier an arc is opened, the more periods it can be used for, but its fixed cost is higher, since it accounts not only for construction but also for maintenance over the remaining horizon. An overview of practical applications indicates that this trade-off is relevant in various settings. For the capacitated variant, we develop an arc-based Lagrange relaxation, combined with local improvement heuristics. For uncapacitated problems, we develop four Benders decompositi

Planificación de la logística en redes de salud: análisis y resolución

Healthcare networks bring together a wide range of public and private entities (hospitals, specific service units, healthcare professionals, …) at local or regional level that seek for management effectiveness, decisional efficacy and coordination. This thesis analyzes the problem statement: "How can those organizations integrate their internal logistic network?" Theories, concepts and integration guidelines from supply chain management theory have been applied to investigate this problem. On healthcare networks already in place, the application of centralized planning procedures is the more appropriate management strategy to rationalize and pilot the change processes. Hence, a general tactical level model is stated as a mixed integer linear programming (MILP) model supporting decisions on the global view of network layout and the coordinating policy among facilities in such networks. Apart from the adoption of optimization tools to provide a framework for costefficient operations, we have identified that information sharing and service level agreements are the key aspects in the effective accomplishment of logistics integration. We have conducted a case study at the Andalusian Regional Network of Clinical Laboratories (ANCL), a large healthcare network with geographically dispersed hospitals, clinics, and testing laboratories, that initiated an organizational strategy to enhance accessibility to services, quality of care and cost savings. Different solution strategies have been addressed in the MILP model that arises, in order to embed this model into a graphical, interactive and responsive Decision Support System (DSS) tool to support ANCL planners’ analysis of What-If scenarios. Drawing on the ANCL case study, it appears that the integration of the Information Tecnologies (IT) Systems at the different facilities and locations within the network and the centralization of the logistic planning procedure can be of invaluable help for aligning operational models and organizational behavior around demand, capacity and network configuration. This suggests that although such integration projects are difficult, costly and complex, they seem worth undertaking.Las Redes de Salud se basan en el trabajo en común de una variedad de entidades públicas y privadas (hospitales, unidades de servicios específicos, profesionales sanitarios,...) a nivel local o regional, en busca de una gestión efectiva, con toma de decisiones y coordinación eficientes. Esta tesis analiza la siguiente pregunta de investigación: "¿Cómo pueden las organizaciones integrar su red logística interna" Las teorías, conceptos y directrices de integración de la Cadena de Suministro se han aplicado para investigar este problema. En redes de salud ya funcionando, la aplicación de procedimientos de planificación centralizada se identifica como la estrategia de gestión más adecuada para racionalizar y pilotar los procesos de cambio. Por ello, planteamos abordar el objeto de la tesis mediante un modelo de programación lineal entera mixta (MILP) de nivel táctico, del que emanarán las decisiones sobre la visión global del diseño de la red y la política de coordinación entre los miembros de la red. Además de la adopción de herramientas de optimización para proporcionar un marco para operaciones eficientes en costes, hemos identificado como aspectos clave en la consecución efectiva de la integración logística en este tipo de redes el intercambio de información y el cumplimiento de acuerdos de nivel de servicio. Como caso práctico, hemos realizado esta integración en la Red Andaluza Regional de Laboratorios Clínicos (ANCL), una red sanitaria extensa con hospitales, clínicas y laboratorios clínicos dispersos geográficamente, que inició una estrategia de cambio organizacional para mejorar la accesibilidad al servicio de pruebas clínicas, la calidad del servicio y propiciar ahorro de costes. Sobre el MILP que resulta al abordar este caso de estudio, hemos aplicado diferentes estrategias de solución. Puesto que este modelo de optimización ha de usarse como el corazón de un Sistema de Soporte a la Decisión (DSS) a disposición de los planificadores ANCL para realizar análisis de escenarios, la agilidad en la generación de soluciones es un requisito primordial. Basándonos en nuestra experiencia con la ANCL, parece que tanto la integración de los sistemas de Tecnologías de Información de los diferentes miembros en la red como la centralización del procedimiento de planificación logística (a través del cual se fijan las directrices de coordinación anual) son de inestimable ayuda para la alineación del modelo operativo y el comportamiento organizacional en torno a demanda, capacidad y configuración de red. Esto sugiere que aunque tales proyectos de integración sean difíciles, costosos y complejos, el esfuerzo parece valer la pena