A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions

Quality Representation in Multiobjective Programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along the way, several interesting results about obtuse, simplicial cones are also proved. Both the BCS and CCS methods are tested and show promise on a variety of problems: linear, convex, nonconvex (CCS only), two-dimensional, and three-dimensional. Sample Matlab code for two of these examples can be found in the appendices as well as tables containing the generated solution points. The manuscript closes with conclusions and ideas for further research in this field

Integrated management of chemical processes in a competitive environment

El objetivo general de esta Tesis es mejorar el proceso de la toma de decisiones en la gestión de cadenas de suministro, tomando en cuenta principalmente dos diferencias: ser competitivo considerando las decisiones propias de la cadena de suministro, y ser competitivo dentro de un entorno global. La estructura de ésta tesis se divide en 4 partes principales: La Parte I consiste en una introducción general de los temas cubiertos en esta Tesis (Capítulo 1). Una revisión de la literatura, que nos permite identificar las problemáticas asociadas al proceso de toma de decisiones (Capítulo 2). El Capítulo 3 presenta una introducción de las técnicas y métodos de optimización utilizados para resolver los problemas propuestos en esta Tesis. La Parte II se enfoca en la integración de los niveles de decisión, buscando mejorar la toma de decisiones de la propia cadena de suministro. El Capítulo 4 presenta una formulación matemática que integra las decisiones de síntesis de procesos y las decisiones operacionales. Además, este capítulo presenta un modelo integrado para la toma de decisiones operacionales incluyendo las características del control de procesos. El Capítulo 5 muestra la integración de las decisiones del nivel táctico y el operacional, dicha propuesta está basada en el conocimiento adquirido capturando la información relacionada al nivel operacional. Una vez obtenida esta información se incluye en la toma de decisiones a nivel táctico. Finalmente en el capítulo 6 se desarrolla un modelo simplificado para integrar múltiples cadenas de suministro. El modelo propuesto incluye la información detallada de las entidades presentes en una cadena de suministro (suministradores, plantas de producción, distribuidores y mercados) introduciéndola en un modelo matemático para su coordinación. La Parte III propone la integración explicita de múltiples cadenas de suministro que tienen que enfrentar numerosas situaciones propias de un mercado global. Asimismo, esta parte presenta una nueva herramienta de optimización basada en el uso integrado de métodos de programación matemática y conceptos relacionados a la Teoría de Juegos. En el Capítulo 7 analiza múltiples cadenas de suministro que cooperan o compiten por la demanda global del mercado. El Capítulo 8 incluye una comparación entre el problema resuelto en el Capítulo anterior y un modelo estocástico, los resultados obtenidos nos permiten situar el comportamiento de los competidores como fuente exógena de la incertidumbre típicamente asociada la demanda del mercado. Además, los resultados de ambos Capítulos muestran una mejora sustancial en el coste total de las cadenas de suministro asociada al hecho de cooperar para atender de forma conjunta la demanda disponible. Es por esto, que el Capítulo 9 presenta una nueva herramienta de negociación, basada en la resolución del mismo problema (Capítulo 7) bajo un análisis multiobjetivo. Finalmente, la parte IV presenta las conclusiones finales y una descripción general del trabajo futuro.This Thesis aims to enhance the decision making process in the SCM, remarking the difference between optimizing the SC to be competitive by its own, and to be competitive in a global market in cooperative and competitive environments. The structure of this work has been divided in four main parts: Part I: consists in a general introduction of the main topics covered in this manuscript (Chapter I); a review of the State of the Art that allows us to identify new open issues in the PSE (Chapter 2). Finally, Chapter 3 introduces the main optimization techniques and methods used in this contribution. Part II focuses on the integration of decision making levels in order to improve the decision making of a single SC: Chapter 4 presents a novel formulation to integrate synthesis and scheduling decision making models, additionally, this chapter also shows an integrated operational and control decision making model for distributed generations systems (EGS). Chapter 5 shows the integration of tactical and operational decision making levels. In this chapter a knowledge based approach has been developed capturing the information related to the operational decision making level. Then, this information has been included in the tactical decision making model. In Chapter 6 a simplified approach for integrated SCs is developed, the detailed information of the typical production‐distribution SC echelons has been introduced in a coordinated SC model. Part III proposes the explicit integration of several SC’s decision making in order to face several real market situations. As well, a novel formulation is developed using an MILP model and Game Theory (GT) as a decision making tool. Chapter 7 includes the tactical and operational analysis of several SC’s cooperating or competing for the global market demand. Moreover, Chapter 8 includes a comparison, based on the previous results (MILP‐GT optimization tool) and a two stage stochastic optimization model. Results from both Chapters show how cooperating for the global demand represent an improvement of the overall total cost. Consequently, Chapter 9 presents a bargaining tool obtained by the Multiobjective (MO) resolution of the model presented in Chapter 7. Finally, final conclusions and further work have been provided in Part IV.Postprint (published version

Evaluation of process systems operating envelopes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 229-238).This thesis addresses the problem of worst-case steady-state design of process systems under uncertainty, also known as robust design. Designing for the worst case is of great importance when considering systems for deployment in extreme and hostile environments, where operational failures cannot be risked due to extraordinarily high economic and/or environmental expense. For this unique scenario, the cost of "over-designing" the process far outweighs the cost associated with operational failure. Hence, it must be guaranteed that the process is sufficiently robust in order to avoid operational failures. Many engineering, economic, and operations research applications are concerned with worst-case scenarios. Classically, these problems give rise to a type of leader-follower game, or Stackelberg game, commonly known as the "minimax" problem, or more precisely as a max-min or min-max optimization problem. However, since the application here is to steady-state design, the problem formulation results in a more general nonconvex equality-constrained min-max program, for which no previously available algorithm can solve effectively. Under certain assumptions, the equality constraints, which correspond to the steady-state model, can be eliminated from the problem by solving them for the state variables as implicit functions of the control variables and uncertainty parameters. This approach eliminates explicit functional dependence on the state variables, and in turn reduces the dimensionality of the original problem. However, this embeds implicit functions in the program, which have no explicit algebraic form and can only be approximated using numerical methods. By doing this, the max-min program can be reformulated as a more computationally tractable semi-infinite program, with the caveat that there are embedded implicit functions. Semi-infinite programming with embedded implicit functions is a new approach to modeling worst-case design problems. Furthermore, modeling process systems--especially those associated with chemical engineering--often results in highly nonconvex functions. The primary contribution of this thesis is a mathematical tool for solving implicit semi-infinite programs and assessing robust feasibility of process systems using a rigorous model-based approach. This tool has the ability to determine, with mathematical certainty, whether or not a physical process system based on the proposed design will fail in the worst case by taking into account uncertainty in the model parameters and uncertainty in the environment.by Matthew David Stuber.Ph.D