23 research outputs found
Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks
We study distributionally robust chance constrained programs (DRCCPs) with
individual chance constraints and random right-hand sides. The DRCCPs treat the
risk tolerances associated with the distributionally robust chance constraints
(DRCCs) as decision variables to trade off between the system cost and risk of
violations by penalizing the risk tolerances in the objective function. We
consider two types of Wasserstein ambiguity sets: one with finite support and
one with a continuum of realizations. By exploring the hidden discrete
structures, we develop mixed integer programming reformulations under the two
types of ambiguity sets to determine the optimal risk tolerance for the chance
constraint. Valid inequalities are derived to strengthen the formulations. We
test instances with transportation problems of diverse sizes and a demand
response management problem
Fleet type assignment and robust airline scheduling with chance constraints under environmental emission considerations
Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 85-87.Fleet Type Assignment and Robust Airline Scheduling is to assign optimally
aircraft to paths and develop a flight schedule resilient to disruptions. In this
study, a Mixed Integer Nonlinear Programming formulation was developed using
controllable cruise time and idle time insertion to ensure passengers’ connection
service level with the objective of minimizing the costs of fuel consumption, CO2
emissions, idle time and spilled passengers. The crucial contribution of the model
is to take fuel efficiency of aircraft into considerations to compensate for the idle
time insertion as well as the cost of spilled passengers due to the insufficient
seat capacity. The nonlinearity in the fuel consumption function associated with
controllable cruise time was handled by second order conic reformulations. In
addition, the uncertainty coming from a random variable of non-cruise time arises
in chance constraints to guarantee passengers’ connection service level, which
was also tackled by transforming them into conic inequalities. We compared the
performance of the schedule generated by the proposed model to the published
schedule for a major U.S. airline. On the average, there exists a 20% total cost
saving compared to the published schedule. To solve the large scale problems in a
reasonable time, we also developed a two-stage algorithm, which decomposes the
problem into planning stages such as fleet type assignment and robust schedule
generation, and then solves them sequentially.Şafak, ÖzgeM.S
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
Multi-Objective Probabilistically Constrained Programming with Variable Risk: New Models and Applications
We consider a class of multi-objective probabilistically constrained problems MOPCP with a joint chance constraint, a multi-row random technology matrix, and a risk parameter (i.e., the reliability level) defined as a decision variable. We propose a Boolean modeling framework and derive a series of new equivalent mixed-integer programming formulations. We demonstrate the computational efficiency of the formulations that contain a small number of binary variables. We provide modeling insights pertaining to the most suitable reformulation, to the trade-off between the conflicting cost/revenue and reliability objectives, and to the scalarization parameter determining the relative importance of the objectives. Finally, we propose several MOPCP variants of multi-portfolio financial optimization models that implement a downside risk measure and can be used in a centralized or decentralized investment context. We study the impact of the model parameters on the portfolios, show, via a cross-validation study, the robustness of the proposed models, and perform a comparative analysis of the optimal investment decisions
Mixed-Integer Programming for a Class of Robust Submodular Maximization Problems
We consider robust submodular maximization problems (RSMs), where given a set
of monotone submodular objective functions, the robustness is with respect
to the worst-case (scaled) objective function. The model we consider
generalizes two variants of robust submodular maximization problems in the
literature, depending on the choice of the scaling vector. On one hand, by
using unit scaling, we obtain a usual robust submodular maximization problem.
On the other hand, by letting the scaling vector be the optimal objective
function of each individual (NP-hard) submodular maximization problem, we
obtain a second variant. While the robust version of the objective is no longer
submodular, we reformulate the problem by exploiting the submodularity of each
function. We conduct a polyhedral study of the resulting formulation and
provide conditions under which the submodular inequalities are facet-defining
for a key mixed-integer set. We investigate several strategies for
incorporating these inequalities within a delayed cut generation framework to
solve the problem exactly. For the second variant, we provide an algorithm to
obtain a feasible solution along with its optimality gap. We apply the proposed
methods to a sensor placement optimization problem in water distribution
networks using real-world datasets to demonstrate the effectiveness of the
methods
Chance-constrained stochastic programming under variable reliability levels with an application to humanitarian relief network design
We focus on optimization models involving individual chance constraints, in which only the right-hand side vector is random with a finite distribution. A recently introduced class of such models treats the reliability levels / risk tolerances associated with the chance constraints as decision variables and trades off the actual cost / return against the cost of the selected reliability levels in the objective function. Leveraging recent methodological advances for modeling and solving chance-constrained linear programs with fixed reliability levels, we develop strong mixed-integer programming formulations for this new variant with variable reliability levels. In addition, we introduce an alternate cost function type associated with the risk tolerances which requires capturing the value-at-risk (VaR) associated with a variable reliability level. We accomplish this task via a new integer linear programming representation of VaR. Our computational study illustrates the effectiveness of our mathematical programming formulations. We also apply the proposed modeling approach to a new stochastic last mile relief network design problem and provide numerical results for a case study based on the real-world data from the 2011 Van earthquake in Turkey
Airline schedule planning and operations : optimization-based approaches for delay mitigation
Thesis (Ph. D. in Transportation Studies)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-162).We study strategic and operational measures of improving airline system performance and reducing delays for aircraft, crew and passengers. As a strategic approach, we study robust optimization models, which capture possible future operational uncertainties at the planning stage, in order to generate solutions that when implemented, are less likely to be disrupted, or incur lower costs of recovery when disrupted. We complement strategic measures with operational measures of managing delays and disruptions by integrating two areas of airline operations thus far separate - disruption management and flight planning. We study different classes of models to generate robust airline scheduling solutions. In particular, we study, two general classes of robust models: (i) extreme-value robust-optimization based and (ii) chance-constrained probability-based; and one tailored model, which uses domain knowledge to guide the solution process. We focus on the aircraft routing problem, a step of the airline scheduling process. We first show how the general models can be applied to the aircraft routing problem by incorporating domain knowledge. To overcome limitations of solution tractability and solution performance, we present budget-based extensions to the general model classes, called the Delta model and the Extended Chance-Constrained programming model. Our models enhance tractability by reducing the need to iterate and re-solve the models, and generate solutions that are consistently robust (compared to the basic models) according to our performance metrics. In addition, tailored approaches to robustness can be expressed as special cases of these generalizable models. The extended models, and insights gleaned, apply not only to the aircraft routing model but also to the broad class of large-scale, network-based, resource allocation. We show how our results generalize to resource allocation problems in other domains, by applying these models to pharmaceutical supply chain and corporate portfolio applications in collaboration with IBM's Zurich Research Laboratory. Through empirical studies, we show that the effectiveness of a robust approach for an application is dependent on the interaction between (i) the robust approach, (ii) the data instance and (iii) the decision-maker's and stakeholders' metrics. We characterize the effectiveness of the extreme-value models and probabilistic models based on the underlying data distributions and performance metrics. We also show how knowledge of the underlying data distributions can indicate ways of tailoring model parameters to generate more robust solutions according to the specified performance metrics. As an operational approach towards managing airline delays, we integrate flight planning with disruption management. We focus on two aspects of flight planning: (i) flight speed changes; and (ii) intentional flight departure holds, or delays, with the goal of optimizing the trade-off between fuel costs and passenger delay costs. We provide an overview of the state of the practice via dialogue with multiple airlines and show how greater flexibility in disruption management is possible through integration. We present models for aircraft and passenger recovery combined with flight planning, and models for approximate aircraft and passenger recovery combined with flight planning. Our computational experiments on data provided by a European airline show that decrease in passenger disruptions on the order of 47.2%-53.3% can be obtained using our approaches. We also discuss the relative benefits of the two mechanisms studied - that of flight speed changes, and that of intentionally holding flight departures, and show significant synergies in applying these mechanisms. We also show that as more information about delays and disruptions in the system is captured in our models, further cost savings and reductions in passenger delays are obtained.by Lavanya Marla.Ph.D.in Transportation Studie
AIRO 2016. 46th Annual Conference of the Italian Operational Research Society. Emerging Advances in Logistics Systems Trieste, September 6-9, 2016 - Abstracts Book
The AIRO 2016 book of abstract collects the contributions from the conference participants.
The AIRO 2016 Conference is a special occasion for the Italian Operations Research community, as AIRO annual conferences turn 46th edition in 2016. To reflect this special occasion, the Programme and Organizing Committee, chaired by Walter Ukovich, prepared a high quality Scientific Programme including the first initiative of AIRO Young, the new AIRO poster section that aims to promote the work of students, PhD students, and Postdocs with an interest in Operations Research.
The Scientific Programme of the Conference offers a broad spectrum of contributions covering the variety of OR topics and research areas with an emphasis on “Emerging Advances in Logistics Systems”.
The event aims at stimulating integration of existing methods and systems, fostering communication amongst different research groups, and laying the foundations for OR integrated research projects in the next decade.
Distinct thematic sections follow the AIRO 2016 days starting by initial presentation of the objectives and features of the Conference. In addition three invited internationally known speakers will present Plenary Lectures, by Gianni Di Pillo, Frédéric Semet e Stefan Nickel, gathering AIRO 2016 participants together to offer key presentations on the latest advances and developments in OR’s research
Contributions to robust and bilevel optimization models for decision-making
Los problemas de optimización combinatorios han sido ampliamente estudiados en la
literatura especializada desde mediados del siglo pasado. No obstante, en las últimas
décadas ha habido un cambio de paradigma en el tratamiento de problemas cada vez
más realistas, en los que se incluyen fuentes de aleatoriedad e incertidumbre en los
datos, múltiples criterios de optimización y múltiples niveles de decisión. Esta tesis
se desarrolla en este contexto. El objetivo principal de la misma es el de construir
modelos de optimización que incorporen aspectos inciertos en los parámetros que
de nen el problema así como el desarrollo de modelos que incluyan múltiples niveles
de decisión. Para dar respuesta a problemas con incertidumbre usaremos los modelos
Minmax Regret de Optimización Robusta, mientras que las situaciones con múltiples
decisiones secuenciales serán analizadas usando Optimización Binivel.
En los Capítulos 2, 3 y 4 se estudian diferentes problemas de decisión bajo incertidumbre
a los que se dará una solución robusta que proteja al decisor minimizando
el máximo regret en el que puede incurrir. El criterio minmax regret analiza el comportamiento
del modelo bajo distintos escenarios posibles, comparando su e ciencia
con la e ciencia óptima bajo cada escenario factible. El resultado es una solución con
una eviciencia lo más próxima posible a la óptima en el conjunto de las posibles realizaciones
de los parámetros desconocidos. En el Capítulo 2 se estudia un problema de
diseño de redes en el que los costes, los pares proveedor-cliente y las demandas pueden
ser inciertos, y además se utilizan poliedros para modelar la incertidumbre, permitiendo
de este modo relaciones de dependencia entre los parámetros. En el Capítulo
3 se proponen, en el contexto de la secuenciación de tareas o la computación grid,
versiones del problema del camino más corto y del problema del viajante de comercio
en el que el coste de recorrer un arco depende de la posición que este ocupa en el
camino, y además algunos de los parámetros que de nen esta función de costes son
inciertos. La combinación de la dependencia en los costes y la incertidumbre en los
parámetros da lugar a dependencias entre los parámetros desconocidos, que obliga a
modelar los posibles escenarios usando conjuntos más generales que los hipercubos,
habitualmente utilizados en este contexto. En este capítulo, usaremos poliedros generales
para este cometido. Para analizar este primer bloque de aplicaciones, en el Capítulo 4, se analiza un modelo de optimización en el que el conjunto de posibles
escenarios puede ser alterado mediante la realización de inversiones en el sistema.
En los problemas estudiados en este primer bloque, cada decisión factible es evaluada
en base a la reacción más desfavorable que pueda darse en el sistema. En los
Capítulos 5 y 6 seguiremos usando esta idea pero ahora se supondrá que esa reacción
a la decisión factible inicial está en manos de un adversario o follower. Estos dos
capítulos se centran en el estudio de diferentes modelos binivel. La Optimización
Binivel aborda problemas en los que existen dos niveles de decisión, con diferentes
decisores en cada uno ellos y la decisión se toma de manera jerárquica. En concreto,
en el Capítulo 5 se estudian distintos modelos de jación de precios en el contexto
de selección de carteras de valores, en los que el intermediario nanciero, que se
convierte en decisor, debe jar los costes de invertir en determinados activos y el
inversor debe seleccionar su cartera de acuerdo a distintos criterios. Finalmente, en
el Capítulo 6 se estudia un problema de localización en el que hay distintos decisores,
con intereses contrapuestos, que deben determinar secuencialmente la ubicación de
distintas localizaciones. Este modelo de localización binivel se puede aplicar en contextos
como la localización de servicios no deseados o peligrosos (plantas de reciclaje,
centrales térmicas, etcétera) o en problemas de ataque-defensa.
Todos estos modelos se abordan mediante el uso de técnicas de Programación
Matemática. De cada uno de ellos se analizan algunas de sus propiedades y se desarrollan
formulaciones y algoritmos, que son examinados también desde el punto de
vista computacional. Además, se justica la validez de los modelos desde un enfoque
de las aplicaciones prácticas. Los modelos presentados en esta tesis comparten la
peculiaridad de requerir resolver distintos problemas de optimización encajados.Combinatorial optimization problems have been extensively studied in the specialized
literature since the mid-twentieth century. However, in recent decades, there
has been a paradigm shift to the treatment of ever more realistic problems, which
include sources of randomness and uncertainty in the data, multiple optimization
criteria and multiple levels of decision. This thesis concerns the development of such
concepts. Our objective is to study optimization models that incorporate uncertainty
elements in the parameters de ning the model, as well as the development of
optimization models integrating multiple decision levels. In order to consider problems
under uncertainty, we use Minmax Regret models from Robust Optimization;
whereas the multiplicity and hierarchy in the decision levels is addressed using Bilevel
Optimization.
In Chapters 2, 3 and 4, we study di erent decision problems under uncertainty
to which we give a robust solution that protects the decision-maker minimizing the
maximum regret that may occur. This robust criterion analyzes the performance
of the system under multiple possible scenarios, comparing its e ciency with the
optimum one under each feasible scenario. We obtain, as a result, a solution whose
e ciency is as close as possible to the optimal one in the set of feasible realizations
of the uncertain parameters. In Chapter 2, we study a network design problem in
which the costs, the pairs supplier-customer, and the demands can take uncertain
values. Furthermore, the uncertainty in the parameters is modeled via polyhedral
sets, thereby allowing relationships among the uncertain parameters. In Chapter
3, we propose time-dependent versions of the shortest path and traveling salesman
problems in which the costs of traversing an arc depends on the relative position
that the arc occupies in the path. Moreover, we assume that some of the parameters
de ning these costs can be uncertain. These models can be applied in the context of
task sequencing or grid computing. The incorporation of time-dependencies together
with uncertainties in the parameters gives rise to dependencies among the uncertain
parameters, which require modeling the possible scenarios using more general sets
than hypercubes, normally used in this context. In this chapter, we use general
polyhedral sets with this purpose. To nalize this rst block of applications, in Chapter 4, we analyze an optimization model in which the set of possible scenarios
can be modi ed by making some investments in the system.
In the problems studied in this rst block, each feasible decision is evaluated
based on the most unfavorable possible reaction of the system. In Chapters 5 and
6, we will still follow this idea, but assuming that the reaction to the initial feasible
decision will be held by a follower or an adversary, instead of assuming the most
unfavorable one. These two chapters are focused on the study of some bilevel models.
Bilevel Optimization addresses optimization problems with multiple decision
levels, di erent decision-makers in each level and a hierarchical decision order. In
particular, in Chapter 5, we study some price setting problems in the context of
portfolio selection. In these problems, the nancial intermediary becomes a decisionmaker
and sets the transaction costs for investing in some securities, and the investor
chooses her portfolio according to di erent criteria. Finally, in Chapter 6, we study
a location problem with several decision-makers and opposite interests, that must
set, sequentially, some location points. This bilevel location model can be applied
in practical applications such as the location of semi-obnoxious facilities (power or
electricity plants, waste dumps, etc.) or interdiction problems.
All these models are stated from a Mathematical Programming perspective, analyzing
their properties and developing formulations and algorithms, that are tested
from a computational point of view. Furthermore, we pay special attention to justifying
the validity of the models from the practical applications point of view. The
models presented in this thesis share the characteristic of involving the resolution of
nested optimization problems.Premio Extraordinario de Doctorado U