Adjustable robust optimization with nonlinear recourses

Over the last century, mathematical optimization has become a prominent tool for decision making. Its systematic application in practical fields such as economics, logistics or defense led to the development of algorithmic methods with ever increasing efficiency. Indeed, for a variety of real-world problems, finding an optimal decision among a set of (implicitly or explicitly) predefined alternatives has become conceivable in reasonable time. In the last decades, however, the research community raised more and more attention to the role of uncertainty in the optimization process. In particular, one may question the notion of optimality, and even feasibility, when studying decision problems with unknown or imprecise input parameters. This concern is even more critical in a world becoming more and more complex —by which we intend, interconnected —where each individual variation inside a system inevitably causes other variations in the system itself. In this dissertation, we study a class of optimization problems which suffer from imprecise input data and feature a two-stage decision process, i.e., where decisions are made in a sequential order —called stages —and where unknown parameters are revealed throughout the stages. The applications of such problems are plethora in practical fields such as, e.g., facility location problems with uncertain demands, transportation problems with uncertain costs or scheduling under uncertain processing times. The uncertainty is dealt with a robust optimization (RO) viewpoint (also known as "worst-case perspective") and we present original contributions to the RO literature on both the theoretical and practical side.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Practice location of physicians: a discrete choice model approach

Economists and policymakers have long been concerned with increasing the supply of health professionals in rural and remote areas. This work seeks to understand which factors influence physicians’ choice of practice location right after completing residency. Differently from previous papers, we analyse the Brazilian missalocation and assess the particularities of developing countries. We use a discrete choice model approach with a multinomial logit specification. Two rich databases are employed containing the location and wage of formally employed physicians as well as details from their post-graduation. Our main findings are that amenities matter, physicians have a strong tendency to remain in the region they completed residency and salaries are significant in the choice of urban, but not rural, communities. We conjecture this is due to attachments built during training and infrastructure concerns.

A reliability centered maintenance decision system for a discrete part manufacturing facility

This thesis develops and validates the framework of a specialized maintenance decision support system for a discrete part manufacturing facility. Its construction utilizes a modular approach based on the fundamental philosophy of Reliability Centered Maintenance (RCM). The proposed architecture uniquely integrates System Decomposition, System Evaluation, Failure Analysis, Logic Tree Analysis, and Maintenance Planning modules. It presents an ideal solution to the unique maintenance inadequacies of modern discrete part manufacturing systems. Well established techniques are incorporated as building blocks of the system's modules. These include Failure Mode Effect and Criticality Analysis (FMECA), Logic Tree Analysis (LTA), Theory of Constraints (TOC), and an Expert System (ES). A Maintenance Information System (MIS) performs the system's support functions. Validation was performed by field testing of the system at a Miami based manufacturing facility. Such a maintenance support system potentially reduces downtime losses and contributes to higher product quality output. Ultimately improved profitability is the final outcome. ^

Business micro-location: factors, preferences and indicators to assess the influence factors

The paper presents a study on business micro-location behaviour as well as corresponding factors of influence, conducted in two metropolitan areas, Bucharest-Ilfov (Romania) and Greater Porto (Portugal). By business micro-location we refer to a specific site such as a building or facility, accommodating a business within a small, compact geographical area (e.g. metropolitan area). At this geographical scale, the macroeconomic layer factors were excluded, applicable when discern between regions or countries. The factors derived from location theory and previous empirical studies were surveyed, completing a cross-sectional analysis in order to find out the specific weights of the location factors and preferences, by region and by industry. Based on already established firms’ feedback on location, the specific weights were granted by each industry to the main location factors, types of areas, and types of accommodation facilities. The authors also suggested a model to integrate these results into a Geographical Information System (GIS).

Resistance to experimental autoimmune encephalomyelitis development in Lewis rats from a conventional animal facility

Experimental autoimmune encephalomyelitis (EAE) is an inflammatory disease of the brain and spinal cord that is mediated by CD4+ T lymphocytes specific to myelin components. In this study we compared development of EAE in Lewis rats from two colonies, one kept in pathogen-free conditions (CEMIB colony) and the other (Botucatu colony) kept in a conventional animal facility. Female Lewis rats were immunized with 100 µl of an emulsion containing 50 µg of myelin, associated with incomplete Freund's adjuvant plus Mycobacterium butyricum. Animals were daily evaluated for clinical score and weight. CEMIB colony presented high EAE incidence with clinical scores that varied from three to four along with significant weight losses. A variable disease incidence was observed in the Botucatu colony with clinical scores not higher than one and no weight loss. Immunological and histopathological characteristics were also compared after 20 days of immunization. Significant amounts of IFN-gamma, TNF-alpha and IL-10 were induced by myelin in cultures from CEMIB animals but not from the Botucatu colony. Significantly higher levels of anti-myelin IgG1 were detected in the CEMIB colony. Clear histopathological differences were also found. Cervical spinal cord sections from CEMIB animals showed typical perivascular inflammatory foci whereas samples from the Botucatu colony showed a scanty inflammatory infiltration. Helminths were found in animals from Botucatu colony but not, as expected, in the CEMIB pathogen-free animals. As the animals maintained in a conventional animal facility developed a very discrete clinical, and histopathological EAE in comparison to the rats kept in pathogen-free conditions, we believe that environmental factors such as intestinal parasites could underlie this resistance to EAE development, supporting the applicability of the hygiene hypothesis to EAE.

Needs Assessment Study of the Iowa DOT Maintenance Facility Construction Needs, 1989

The purpose of this study is to provide recommendations relative to the location and construction needs for highway maintenance facilities within the state of Iowa. These recommendations were to be developed with consideration being given to the public's expectations and priorities for highway maintenance services. As a part of the study effort, a review was made of the methods used by other states to deliver highway maintenance services. To accomplish the study, Wilbur Smith Associates undertook a series of tasks. These efforts included gathering of data and information to characterize the various maintenance programs and the delivery of maintenance and operations services by the Department. We researched the delivery of highway maintenance services in other states. Interviews with Iowa DOT maintenance personnel were accomplished. A schedule of public hearings was developed and ten hearings were held. All the information was integrated and various analyses were made. From these analyses we drew conclusions and developed recommendations.

Involuntary Discharge from a Long-Term Facility

An involuntary discharge from a long-term care (LTC) facility occurs when the facility provides a 30-day written notice to a resident informing him/her of the need to move out of the facility. The notice must set out the reasons for the transfer or discharge as well as state the effective date, location of transfer or discharge, statement of appeal rights and the contact information (name, address and telephone number) for the Office of the State Long-Term Care Ombudsman.

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.

Discrete Time Inventory Models with/without Positive Service Time

In everyday life different flows of customers to avail some service facility or other at some service station are experienced. In some of these situations, congestion of items arriving for service, because an item cannot be serviced Immediately on arrival, is unavoidable. A queuing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served. Examples Include shoppers waiting in front of checkout stands in a supermarket, Programs waiting to be processed by a digital computer, ships in the harbor Waiting to be unloaded, persons waiting at railway booking office etc. A queuing system is specified completely by the following characteristics: input or arrival pattern, service pattern, number of service channels, System capacity, queue discipline and number of service stages. The ultimate objective of solving queuing models is to determine the characteristics that measure the performance of the system

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies; the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances. (C) 2004 Elsevier Ltd. All rights reserved.

Resistance to experimental autoimmune encephalomyelitis development in Lewis rats from a conventional animal facility

Experimental autoimmune encephalomyelitis (EAE) is an inflammatory disease of the brain and spinal cord that is mediated by CD4+ T lymphocytes specific to myelin components. In this study we compared development of EAE in Lewis rats from two colonies, one kept in pathogen-free conditions (CEMIB colony) and the other (Botucatu colony) kept in a conventional animal facility. Female Lewis rats were immunized with 100 µl of an emulsion containing 50 µg of myelin, associated with incomplete Freund's adjuvant plus Mycobacterium butyricum. Animals were daily evaluated for clinical score and weight. CEMIB colony presented high EAE incidence with clinical scores that varied from three to four along with significant weight losses. A variable disease incidence was observed in the Botucatu colony with clinical scores not higher than one and no weight loss. Immunological and histopathological characteristics were also compared after 20 days of immunization. Significant amounts of IFN-gamma, TNF-alpha and IL-10 were induced by myelin in cultures from CEMIB animals but not from the Botucatu colony. Significantly higher levels of anti-myelin IgG1 were detected in the CEMIB colony. Clear histopathological differences were also found. Cervical spinal cord sections from CEMIB animals showed typical perivascular inflammatory foci whereas samples from the Botucatu colony showed a scanty inflammatory infiltration. Helminths were found in animals from Botucatu colony but not, as expected, in the CEMIB pathogen-free animals. As the animals maintained in a conventional animal facility developed a very discrete clinical, and histopathological EAE in comparison to the rats kept in pathogen-free conditions, we believe that environmental factors such as intestinal parasites could underlie this resistance to EAE development, supporting the applicability of the hygiene hypothesis to EAE.