http://hdl.handle.net/1721.1/7719 http://hdl.handle.net/1721.1/46661 Combinatorial optimization problems with concave costs Stratila, Dan In the first part, we study the problem of minimizing a separable concave function over a polyhedron. We assume the concave functions are nonnegative nondecreasing on R+, and the polyhedron is in RI' (these assumptions can be relaxed further under suitable technical conditions). We show how to approximate this problem to 1+ E precision in optimal value by a piecewise linear minimization problem so that the number of resulting pieces is polynomial in the input size of the original problem and linear in 1/c. For several concave cost problems, the resulting piecewise linear problem can be reformulated as a classical combinatorial optimization problem. As a result of our bound, a variety of polynomial-time heuristics, approximation algorithms, and exact algorithms for classical combinatorial optimization problems immediately yield polynomial-time heuristics, approximation algorithms, and fully polynomial-time approximation schemes for the corresponding concave cost problems. For example, we obtain a new approximation algorithm for concave cost facility location, and a new heuristic for concave cost multi commodity flow. In the second part, we study several concave cost problems and the corresponding combinatorial optimization problems. We develop an algorithm design technique that yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the corresponding combinatorial optimization problem. (cont.) Our technique preserves constant-factor approximation ratios as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. For example, we obtain new approximation algorithms for concave cost facility location and concave cost joint replenishment, and a new exact algorithm for concave cost lot-sizing. In the third part, we study a real-time optimization problem arising in the operations of a leading internet retailer. The problem involves the assignment of orders that arrive via the retailer's website to the retailer's warehouses. We model it as a concave cost facility location problem, and employ existing primal-dual algorithms and approximations of concave cost functions to solve it. On past data, we obtain solutions on average within 1.5% of optimality, with running times of less than 100ms per problem. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2009. Includes bibliographical references (p. 83-89). http://hdl.handle.net/1721.1/46387 Mitigating airport congestion : market mechanisms and airline response models Harsha, Pavithra Efficient allocation of scarce resources in networks is an important problem worldwide. In this thesis, we focus on resource allocation problems in a network of congested airports. The increasing demand for access to the world's major commercial airports combined with the limited operational capacity at many of these airports have led to growing air traffic congestion resulting in several billion dollars of delay cost every year. In this thesis, we study two demand-management techniques -- strategic and operational approaches -- to mitigate airport congestion. As a strategic initiative, auctions have been proposed to allocate runway slot capacity. We focus on two elements in the design of such slot auctions -- airline valuations and activity rules. An aspect of airport slot market environments, which we argue must be considered in auction design, is the fact that the participating airlines are budget-constrained. -- The problem of finding the best bundle of slots on which to bid in an iterative combinatorial auction, also called the preference elicitation problem, is a particularly hard problem, even more in the case of airlines in a slot auction. We propose a valuation model, called the Aggregated Integrated Airline Scheduling and Fleet Assignment Model, to help airlines understand the true value of the different bundles of slots in the auction. This model is efficient and was found to be robust to data uncertainty in our experimental simulations. (cont.) -- Activity rules are checks made by the auctioneer at the end of every round to suppress strategic behavior by bidders and to promote consistent, continual preference elicitation. These rules find applications in several real world scenarios including slot auctions. We show that the commonly used activity rules are not applicable for slot auctions as they prevent straightforward behavior by budget-constrained bidders. We propose the notion of a strong activity rule which characterizes straightforward bidding strategies. We then show how a strong activity rule in the context of budget-constrained bidders (and quasilinear bidders) can be expressed as a linear feasibility problem. This work on activity rules also applies to more general iterative combinatorial auctions.We also study operational (real-time) demand-management initiatives that are used when there are sudden drops in capacity at airports due to various uncertainties, such as bad-weather. We propose a system design that integrates the capacity allocation, airline recovery and inter-airline slot exchange procedures, and suggest metrics to evaluate the different approaches to fair allocations. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2009. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (leaves 157-165). http://hdl.handle.net/1721.1/46263 Implementing reusable solvers : an object-oriented framework for operations research algorithms Ruark, John Douglas, 1971- Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 1998. Includes bibliographical references (p. 325-338) and indexes. http://hdl.handle.net/1721.1/45947 The minority achievement gap in a suburban school district Chandler, Lincoln J., 1977- For many decades, the American educational system has yielded significant differences in achievement among students in different racial groups, a phenomenon commonly known as the "Achievement Gap". Despite the volume of research devoted to studying achievement gaps, school administrators faced with the challenge of reducing these gaps have had limited success. There are a number of factors, regarding the individual, the school, and the setting, which can contribute to achievement gaps, but in a particular community, the prevalence of such factors, and their individual contribution to the gap, is unclear. In this dissertation, we employ a variety of statistical methods that provide a bridge between large-scale studies of achievement gaps and the analyses necessary to address the needs of a single community. First, we establish a collection of metrics designed to measure relative and absolute differences in achievement, for groups of arbitrary size and distribution. Using data from a middle-class, racially integrated school district, we employ these metrics to measure the magnitude of the achievement gap for individual students from grades three through eight. We also assess the potential role of previously-identified correlates of low achievement, such as poverty and student mobility. Last, we evaluate the potential impact of strategies for narrowing the gap. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2008. Includes bibliographical references (p. 189-192).