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Over the last decade, much attention has been focused on the development of automated letter mail processing systems for postal sorting. Optical character readers and bar-code sorters have begun to augment mechanized processing that has been in use since the mid-1960s. Continuing automated mail processing programs are aimed at minimizing growth in labor costs, which at $30. 5 billion accounted for 83 percent of the total United States Postal Service (USPS) operating costs in fiscal year 1988. Simulation and mixed integer linear programming (MILP) models are developed in this thesis with the objective of assisting postal managers is designing automated systems for the general mail facilities. GMFs) of the USPS. The simulation model utilizes a probabilistic structure to channel processed mail between stations. Processing equipment and associated personnel are modelled as resources. The arrival process can accurately model daily input mail profiles and variability, as well as seasonal loads and secular trends such as changes in mail address quality. Such a detailed probabilistic model provides a realistic test of proposed equipment selections and resources schedules for strategic planning and operations management. A simulation model of a specific medium-sized GMF is constructed using the SLAMII simulation language.

Postoptimality analysis and parametric optimization techniques are fully developed aspects of linear programming. In the context of integer linear programming, however, these aspects have barely begun to be developed. The purpose of this paper is to take stock of what is known about this topic and to lay the foundation for future progress. Our conceptual starting point is the notion that, in practical applications, typically one is faced not with a single numerical integer linear program to solve but rather with an entire family of numerical problems of interest. The members of the family may all have the same structure but differ as to the values of one or more coefficients, or they may even have different (but related) structures. The scope of this paper is limited to be first mentioned case.

This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacement/modemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving (or approximately solving) infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions. (KAR) P. 2

This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacement/modemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving (or approximately solving) infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions. (KAR) P. 2

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.

Fundamental Disjunctive Conic Cut (DCC) methodology for Mixed-Integer Conic Linear Optimization (MICO) was developed. To describe the convex hull of the intersection of a convex set E and a linear disjunction is the fundamental problem, and that served as the core of solution techniques for MICO. It was proved that if there exists a cone K that has the same intersection with the boundary of the disjunction as the convex set E, then the convex hull of the disjunction is the intersection of E with K. While uniqueness of a DCC is proved for general MICO, the existence of such a cone is difficult to prove for the general case. Thorough analysis of a parametric family of quadrics allows to prove the existence and uniqueness of a second order cone, when E is the intersection of an affine space and a second order cone. An efficiently computable method was developed for finding that cone, which provided novel and powerful DCCs for Mixed Integer Second Order Cone Optimization (MISOCO), which can be used in branch-and-cut algorithms when solving MISOCO problems. All special and degenerate cases are carefully analyzed and easy to compute criteria are developed to compute a DCC for all cases. Limited, but rigorous computational experiments gave strong indication of the power of the DCCs.

We describe an approach for accomplishing the high-level mission planning required for a heterogeneous team of autonomous vehicles performing mine countermeasure (MCM) survey missions in multiple areas. The high-level mission scheduling and waterspace management requires sequencing the order and location of lower-level MCM tasks to be completed by each vehicle in the heterogeneous team: unmanned surface vessels (USVs) and unmanned underwater vehicles (UUVs). We propose solving this complex sequencing operation by leveraging unique information processing, communication, refueling, and planning windows that form constraints within the system within a formal scheduling optimization framework known as mixed-integer linear programming. We pose the problem using a mixed-integer linear programming optimization framework, compare several complexity reduction heuristics to the full optimization, and include methods to account for relative uncertainty in the duration of planned tasks in such a manner to balance the risk of schedule slips or conservative and sub-optimal schedule.

Motivated by Bland's linear-programming generalization of the renowned Edmonds-Karp efficient refinement of the Ford-Fulkerson maximum-flow algorithm, we discuss three closely-related natural augmentation rules for linear and integer-linear optimization. In several nice situations, we show that polynomially-many augmentation steps suffice to reach an optimum. In particular, when using "discrete steepest-descent augmentations" (i.e., directions with the best ratio of cost improvement per unit 1-norm length), we show that the number of augmentation steps is bounded by the number of elements in the Graver basis of the problem matrix, giving the first ever strongly polynomial-time algorithm for $N$-fold integer-linear optimization. Our results also improve on what is known for such algorithms in the context of linear optimization (e.g., generalizing the bounds of Kitahara and Mizuno for the number of steps in the simplex method) and are closely related to research on the diameters of polytopes and the search for a strongly polynomial-time simplex or augmentation algorithm.

This document is chiefly a bibliography listing titles such as: An Efficient Interactive Solution Framework for Bicriteria Integer Programming, An Improved Interactive Multicriteria Integer Programming Algorithm, An Interactive Multicriteria Linear Programming Method Using Constraints and Convex Cones.

This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacement/modemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving (or approximately solving) infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions.

The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean distances. In this paper we introduce a first attempt at using this lemma in the context of feasibility problems in linear and integer programming, which cannot be expressed only in function of Euclidean distances.

The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean distances. In this paper we introduce a first attempt at using this lemma in the context of feasibility problems in linear and integer programming, which cannot be expressed only in function of Euclidean distances.

The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean distances. In this paper we introduce a first attempt at using this lemma in the context of feasibility problems in linear and integer programming, which cannot be expressed only in function of Euclidean distances.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

A theorem is given that provides new strategies for solving integer programming problems, based on finding certain types of basic solutions to linear programs. The theorem is motivated by and extends ideas of Cabot and Hurter. An integer programming method based on the theorem is outlined.

The Persistent-Phylogeny Model is an extension of the widely studied Perfect-Phylogeny Model, encompassing a broader range of evolutionary phenomena. Biological and algorithmic questions concerning persistent phylogeny have been intensely investigated in recent years. In this paper, we explore two alternative approaches to the persistent-phylogeny problem that grow out of our previous work on perfect phylogeny, and on galled trees. We develop an integer programming solution to the Persistent-Phylogeny Problem; empirically explore its efficiency; and empirically explore the utility of using fast algorithms that recognize galled trees, to recognize persistent phylogeny. The empirical results identify parameter ranges where persistent phylogeny are galled trees with high frequency, and show that the integer programming approach can efficiently identify persistent phylogeny of much larger size than has been previously reported.

The paper discusses duality for linear and nonlinear programs in which some of the variables are arbitrarily constrained. The most important class of such problems is that of mixed-integer (linear and nonlinear) programs. The paper introduces the duality constructions and discusses algorithms based on them.

This report gives documentation for the computer code BDSCAN for solving integer linear programming problems using the bound-and-scan algorithm. A listing of the program with sample input and output is included. (Author)

This report gives documentation for the computer code BDSCAN for solving integer linear programming problems using the bound-and-scan algorithm. A listing of the program with sample input and output is included. (Author)

This report gives documentation for the computer code BDSCAN for solving integer linear programming problems using the bound-and-scan algorithm. A listing of the program with sample input and output is included. (Author)