Diego Klabjan - US grants

This project develops a decision support tool for robust airline crew scheduling. A model that solves the airline crew-scheduling problem and captures two objectives the crew cost and the number of crews that can be swapped in operations will be devleoped. The former cost forms the traditional objective function and the latter cost is a measure of robustness since schedules with many swappable crews are likely to be robust. Two methodologies to solve the model are proposed. A Lagrangian decomposition approach relaxes the 'robustness' constraints and iteratively solves the crew-scheduling problem with different objective coefficients. A parallel branch-and-cut algorithm for solving these crew-scheduling problems will be developed. The second approach uses subgradient optimization and the new concept of computing a 'dual' of an integer program. An algorithm for computing such a dual vector will be developed and implemented.

The proposed methodology will yield crew schedules that can potentially reduce operational crew cost. The operational crew cost increases up to seven times due to various disruptions in the flight schedule. Using robust crew schedules obtained by this research can significantly reduce this factor and hence it can provide substantial benefit to airlines. The proposed methodologies use the concept of 'dual' vectors for integer programs. In this case they are used as a subgradient but it can also be used for sensitivity analysis, pricing, and producing alternative optimal solution to integer programs.

The strength of linear programming duality is well known and it is one of the most acclaimed results in theory and practice. On the other hand, it is usually taken for granted that duality is not doable for integer programs. The objective of this proposal is to break the perception barrier by showing that indeed it is possible to compute an analog to the linear programming dual vector for an integer program. A new family of dual functions for integer programs is proposed. Several properties and many results with linear programming counterparts are given. More importantly, an algorithm is proposed that computes such a function for an integer program and it is shown that in a reasonable amount of time an optimal dual function can be computed. The proposed dual functions apply only to pure integer programs and their extension to mixed integer programs is required. In addition, the framework for an algorithm that computes a dual function from the branch-and-cut tree is given. One of the applications of dual functions is in decomposition algorithms. We design a novel decomposition approach to integrated airline planning.
Many decision support systems require sensitivity analysis of the underlying optimization models. For example, decision makers like to get estimates on the change of profitability if a unit of a resource is changed or price of a product is modified by a small amount. Existing tools use ad-hoc techniques to perform sensitivity analysis. In this proposal we explore the area of more scientific and practical approaches to sensitivity analysis. The proposed theory and algorithms also yield new methodology for solving large-scale models deemed so far intractable.

In this proposal we plan to study solution methodologies for general multi-echelon systems with possible stochastic lead-times, economies of scale, production and transportation capacities, and demand occurring at each stage or node of the system. The main objective is in developing novel state of the art solution methodologies for these complex systems.
General multi-echelon systems are modeled as stochastic dynamic programs, which are solved by approximate dynamic programming techniques.

One of the main contributions of this proposal is the notion of multivariate piecewise linear functions, which are called the ridge functions. These functions are easy to encode and several properties of these functions are easily stated. The key component of the dynamic programming algorithm is a suitable value function approximation. We first embed ridge functions in the approximate dynamic programming algorithm and then we plan to study properties typical for inventory systems. An important feature of the algorithm is its robustness and generality. For example, the algorithm can easily handle stochastic lead-times, capacity constraints, economies of scale, and correlated demand, in addition to general materials flows. We also modify the algorithm for a different type of problems like the vendor managed inventory problem, where the time between two consecutive decisions is non stationary.

The main impact is in showing the applicability of ridge functions in operations research and management. They are particularly appealing in approximating complex functions in an underlying mathematical programming model. Per se, they do not introduce nonlinearities. Perhaps even a bigger impact is in solving complex multi-echelon inventory and production systems, where among other features the materials flows are arbitrarily. We firmly believe that such a global view of the proposed algorithm can have a significant impact on the current practice.

1010147- Klabjan

Abstract

An Operations model will be developed for supporting science projects at Summit Station, in the context of NSF's other activities in Greenland. Input options for logistics, research activities, cost attributes and energy and emission options will be processed in the model. Solutions will be expressed in costs per year, carbon footprints, and operations and logistics strategies. The project will be assisted by a graduate student for two years and upon graduation the knowledge acquired will transfer to the industrial, governmental, and public world. Attempts to recruit a student from a minority or underrepresented group will be undertaken.

The main objective of this project is to develop a stochastic portfolio optimization model to address the problem of renewable
portfolio selection for a business entity with large real estate properties, and to develop algorithmic approaches for solving the underlying models. In addition to considering various renewable options, the model also includes battery storage since power storage can significantly increase the benefits of intermittent renewable sources. If the decisions of renewables are fixed, the remaining problem
is a dynamic program with decisions of power distribution and how much power to store or extract from batteries in each hour. A further complicating factor resulting from a long time horizon is the requirement of battery replacement after reaching their lifespan. The overarching optimization problem minimizes the cost of installing renewable sources where the objective function is the value function
of the aforementioned dynamic program, which depends on the installed renewable sources. Several algorithms will be designed for
solving this unique optimization problem by exploiting the inherent structure.

Due to technological advancements and fierce manufacturing competition, it is anticipated that many firms will find a positive return
on investment on renewable on-site sources. Such on-site installations will directly benefit from the proposed models and algorithms. First, the models will assist decision makers in selecting the best options at a single site or across several sites. Second, uncertainties inherent in the business - grid prices, renewable energy credits, technological advancements, to name only a few of them
will be directly incorporated in the models, which will provide robust solutions. General Motors will provide test cases of their existing renewable generation projects and those under consideration. The modeling framework and methodologies do not include anything specific to the automotive industry and thus can easily adopt by any entity owing large properties.

This National Science Foundation Research Traineeship (NRT) award prepares master's and doctoral students at Northwestern University with the data-analysis skills to advance the research frontiers in astronomy, physics, and Earth science. While providing students with training in data-enabled science and engineering, the program promotes collaborations with research and education that will lead to the development of new data tools with broad applicability. Through internships, evidence-based curricular approaches, and capstone citizen science projects, trainees will develop the core competencies in demand by a wide range of employers. Trainees will learn how to effectively engage the public in discoveries on the solar system, stellar explosions, star clusters and galaxies, gravitational waves, and seismic waves. The citizen science projects will be used for innovative recruiting, strengthening the participation of the public and students from underrepresented groups. By diversifying the graduate student population and improving instruction and mentoring, the research will be contributing to a diverse, inclusive scientific workforce in academia and industry.

This program will bridge computer science, electrical engineering, applied math, and statistics to physics, astronomy, and Earth sciences in order to develop students with the skills required to analyze datasets of unprecedented size and complexity. Trainees will be prepared for the technical challenges of extensive data generated at major research equipment and facilities, including Large Syntopic Survey Telescope, Advanced Laser Interferometer Gravitational-wave Observatory, and EarthScope. Trainees will learn data analytics and management, statistical methods, and image processing skills to ask new questions and choose the appropriate tools from the method disciplines and adapt them to solve problems in physics, astronomy, and Earth sciences. The program will also prepare students to work in a collaborative scientific community, advancing their leadership, communication, mentoring, and management skills. Internships at major research facilities, national laboratories, and the private sector will help students gain transferrable professional skills to pursue a range of career paths.

? DESCRIPTION (provided by applicant): The Biomedical Data Driven Discovery (BD3) Training Program at Northwestern University (NU) is a collaborative proposal that brings together Big Data educators and researchers from the Feinberg School of Medicine (FSM), the McCormick School of Engineering and Applied Science (MEAS), the Weinberg College of Arts and Sciences (WCAS) and the School of Communication. The goal of BD3 is to train Big Data scientists for both academic and industry research positions, who will develop the next generation of methodologies and tools. BD3 will to create a truly multidisciplinary data science training environment. In doing so, BD3 will encompass multiple departments and degree-programs, leveraging three existing data-intensive doctoral programs-- the well-established and nationally recognized program in Data Analytics in MEAS, led by Diego Klabjan, PhD, and two innovative and growing programs led by Justin Starren, MD, PhD: the Informatics track of the Driskill Graduate Program, focusing on Bioinformatics, and the Informatics track of the Health Sciences Integrated Program, focusing on clinical and population informatics. Together, Drs. Klabjan and Starren have expertise that spans three critical areas: computer science/informatics, statistics/mathematics, and biomedical domain knowledge. BD3 brings together the biomedical Big Data and domain expertise across multiple departments of FSM with methodological expertise in computation, informatics, statistics, and mathematics. The program will recruit three candidates per year and support each trainee for two years. Success in data science requires mastery of three distinct skill sets: 1) an understanding of the target domain, 2) an understanding of the nature and structure of the data within that domain, and 3) a mastery of the computational and statistical techniques for manipulating and analyzing the data. This translates into a number of more specific competencies, including: deep Domain Knowledge in the target domain, Statistical Methods, Computer Programming, Ontologies, Databases, Text Analytics, Predictive Analytics, Data Mining, Analytics for Big Data, and Responsible Conduct of Research. BD3 will utilize a co-mentoring model, with each student having a domain mentor and a methodological mentor. Each student's program will be based on an Individual Development Plan (IDP). Students will have many opportunities for both laboratory and industrial rotations leveraging well-established programs at MEAS. Additional educational activities include: an annual retreat, monthly trainee meetings, departmental seminars and speakers, journal clubs, teaching training and experience, and writing and presentation training. Trainees benefit from extensive institutional support for this program, such as: tuition supplements, stipend supplements, administrative support, the Writing Workshop for Graduate Students, the Searle Center for Advancing Learning and Teaching, the Management for Scientists and Engineers, nationally recognized mentor and mentee training programs, and formal training in Team Science.