Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input \u2013 output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input – output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Healthcare staff scheduling in a fuzzy environment : a fuzzy genetic algorithm approach

In the presence of imprecise management targets, staff preferences, and patients’ expectations, the healthcare staff scheduling problem becomes complicated. The goals, preferences, and client expectations, being humanistic, are often imprecise and always evolving over time. We present a Jarosite precipitate (FGA) approach for addressing healthcare staff scheduling problems in fuzzy environments. The proposed FGA-based approach can handle multiple conflicting objectives and constraints. To improve the algorithm, fuzzy set theory is used for fitness evaluations of alternative candidate schedules by modeling the fitness of each alternative solution using fuzzy membership functions. Furthermore, the algorithm is designed to incorporate the decision maker’s choices and preferences, in addition to staff preferences. Rather than prescribing a sing solution to the decision maker, the approach provides a population of alternative solutions from which the decision maker can choose the most satisfactory solution. The FGA-based approach is potential platform upon which useful decision support tools can be developing for solving healthcare staff scheduling problems in a fuzzy environment characterized with multiple conflicting objectives and preference constraints

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

Revisiting the Evolution and Application of Assignment Problem: A Brief Overview

The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on   a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc

Best matching processes in distributed systems

The growing complexity and dynamic behavior of modern manufacturing and service industries along with competitive and globalized markets have gradually transformed traditional centralized systems into distributed networks of e- (electronic) Systems. Emerging examples include e-Factories, virtual enterprises, smart farms, automated warehouses, and intelligent transportation systems. These (and similar) distributed systems, regardless of context and application, have a property in common: They all involve certain types of interactions (collaborative, competitive, or both) among their distributed individuals—from clusters of passive sensors and machines to complex networks of computers, intelligent robots, humans, and enterprises. Having this common property, such systems may encounter common challenges in terms of suboptimal interactions and thus poor performance, caused by potential mismatch between individuals. For example, mismatched subassembly parts, vehicles—routes, suppliers—retailers, employees—departments, and products—automated guided vehicles—storage locations may lead to low-quality products, congested roads, unstable supply networks, conflicts, and low service level, respectively. This research refers to this problem as best matching, and investigates it as a major design principle of CCT, the Collaborative Control Theory. The original contribution of this research is to elaborate on the fundamentals of best matching in distributed and collaborative systems, by providing general frameworks for (1) Systematic analysis, inclusive taxonomy, analogical and structural comparison between different matching processes; (2) Specification and formulation of problems, and development of algorithms and protocols for best matching; (3) Validation of the models, algorithms, and protocols through extensive numerical experiments and case studies. The first goal is addressed by investigating matching problems in distributed production, manufacturing, supply, and service systems based on a recently developed reference model, the PRISM Taxonomy of Best Matching. Following the second goal, the identified problems are then formulated as mixed-integer programs. Due to the computational complexity of matching problems, various optimization algorithms are developed for solving different problem instances, including modified genetic algorithms, tabu search, and neighbourhood search heuristics. The dynamic and collaborative/competitive behaviors of matching processes in distributed settings are also formulated and examined through various collaboration, best matching, and task administration protocols. In line with the third goal, four case studies are conducted on various manufacturing, supply, and service systems to highlight the impact of best matching on their operational performance, including service level, utilization, stability, and cost-effectiveness, and validate the computational merits of the developed solution methodologies

Multi-objective combinatorial optimization problems in transportation and defense systems

Multi-objective Optimization problems arise in many applications; hence, solving them efficiently is important for decision makers. A common procedure to solve such problems is to generate the exact set of Pareto efficient solutions. However, if the problem is combinatorial, generating the exact set of Pareto efficient solutions can be challenging. This dissertation is dedicated to Multi-objective Combinatorial Optimization problems and their applications in system of systems architecting and railroad track inspection scheduling. In particular, multi-objective system of systems architecting problems with system flexibility and performance improvement funds have been investigated. Efficient solution methods are proposed and evaluated for not only the system of systems architecting problems, but also a generic multi-objective set covering problem. Additionally, a bi-objective track inspection scheduling problem is introduced for an automated ultrasonic inspection vehicle. Exact and approximation methods are discussed for this bi-objective track inspection scheduling problem --Abstract, page iii

FLIGHT RISK MANAGEMENT AND CREW RESERVE OPTIMIZATION

There are two key concerns in the development process of aviation. One is safety, and the other is cost. An airline running with high safety and low cost must be the most competitive one in the market. This work investigates two research efforts respectively relevant to these two concerns. When building support of a real time Flight Risk Assessment and Mitigation System (FRAMS), a sequential multi-stage approach is developed. The whole risk management process is considered in order to improve the safety of each flight by integrating AHP and FTA technique to describe the framework of all levels of risks through risk score. Unlike traditional fault tree analysis, severity level, time level and synergy effect are taken into account when calculating the risk score for each flight. A risk tree is designed for risk data with flat shape structure and a time sensitive optimization model is developed to support decision making of how to mitigate risk with as little cost as possible. A case study is solved in reasonable time to approve that the model is practical for the real time system. On the other hand, an intense competitive environment makes cost controlling more and more important for airlines. An integrated approach is developed for improving the efficiency of reserve crew scheduling which can contribute to decrease cost. Unlike the other technique, this approach integrates the demand forecasting, reserve pattern generation and optimization. A reserve forecasting tool is developed based on a large data base. The expected value of each type of dropped trip is the output of this tool based on the predicted dropping rate and the total scheduled trips. The rounding step in current applied methods is avoided to keep as much information as possible. The forecasting stage is extended to the optimization stage through the input of these expected values. A novel optimization model with column generation algorithm is developed to generate patterns to cover these expected level reserve demands with minimization to the total cost. The many-to-many covering mode makes the model avoid the influence of forecasting errors caused by high uncertainty as much as possible