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The aim of this dissertation is to present an algorithm for mixed integer programs which when started with a good heuristic solution can find improved solutions and reduce the error estimate as quickly as possible. This is achieved by using two ideas: a fixed order branch-and-bound method with selective expansion of subproblems and the sieve strategy which uses stronger than optimal bounds. The fixed order branch-and-bound method with selective expansion of subproblems is effective in reducing the error estimate quickly whereas the sieve strategy is effective in reducing the error estimate as well as finding improved solutions quickly. Computational experience is reported.

Well-publicized lost opportunities for U.S. and coalition air forces to strike enemy leadership targets in Afghanistan and Iraq demonstrate the importance of Time Sensitive Targeting. How do we "pair" the weapon and weapons delivery platform with their target? The available platforms (aircraft, manned or unmanned) may be on the ground in an alert status, loitering airborne, or on their way to attack other targets. The problem is compounded by the facts that we actually wish to (a) create multiple strike packages simultaneously, (b) recompose existing strike packages that are disrupted by the new plans, (c) minimize such disruptions, (d) satisfy minimum kill probabilities, and (e) avoid the attrition of tasked assets. This thesis develops an automated, optimizing, heuristic decision aid, "RAPT-OR", that rapidly revises a current Air Taking Order (ATO) to meet the requirements above. Using a set-packing model, RAPT-OR, an ATO near optimally, on a desktop PC, in less than two seconds, for a typical scenario with 40 aircraft, four new targets and hundreds of potential strike packages. RAPT-OR allows decision makers the ability of adjusting risk acceptance in the formulation of possible courses of action by manipulating friendly attrition importance in formulating a solution.

In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the three-group classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the three-group classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a two-phase algorithm. The same algorithm can be used to improve the classificatory performance of any interval-based mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiple-group extension of a mathematical programming model for the two-group classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory non-inferiority of one model over another in the training sample.

by Kenneth Wing Chung Tang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 64-65). / LIST OF TABLES --- p.vi / LIST OF FIGURES --- p.vii / Chapter 1. --- INTRODUCTION --- p.1 / Chapter 1.1 --- Staff Scheduling Overview --- p.2 / Chapter 1.1.1 --- Days-off scheduling --- p.7 / Chapter 1.1.2 --- Shift Scheduling --- p.8 / Chapter 1.1.3 --- Tour Scheduling --- p.9 / Chapter 1.2 --- Outline of The Work of The Thesis --- p.11 / Chapter 2. --- NETWORK MODEL FOR STAFF SCHEDULING --- p.13 / Chapter 2.1 --- The Basic Network Model --- p.13 / Chapter 2.1.1 --- General Idea --- p.13 / Chapter 2.1.2 --- Modeling Precedent Relationship Constraints by Arcs --- p.15 / Chapter 2.1.3 --- Modeling Shift Stretch Constraints by Nodes --- p.16 / Chapter 2.1.4 --- Modeling to Handle Side Constraints --- p.17 / Chapter 2.1.5 --- Mathematical Model --- p.21 / Chapter 2.2 --- Solving The Network Model With Side Constraints --- p.23 / Chapter 2.2.1 --- Basis Partitioning Network Simplex method --- p.23 / Chapter 2.2.2 --- A Two-Phase Heuristic for Schedules Construction --- p.29 / Chapter 3. --- APPLICA TION IN AN AIR CARGO TERMINAL --- p.55 / Chapter 3.1 --- Background And Problem Statement --- p.35 / Chapter 3.2 --- Generation of Staff Requirement Patterns --- p.38 / Chapter 3.3 --- A Typical Setting of Parameters --- p.41 / Chapter 3.4 --- Case One: Staff Requirement for Each Shift Is Fixed --- p.43 / Chapter 3.4.1 --- Conversion of hourly requirements to shift requirements --- p.43 / Chapter 3.4.2 --- Network Modeling --- p.44 / Chapter 3.4.3 --- An Example --- p.47 / Chapter 3.4.4 --- Computational result on different staff requirements --- p.49 / Chapter 3.5 --- Case Two: Staff Requirement for Each Shift Is Changing --- p.50 / Chapter 3.5.1 --- Network modeling --- p.51 / Chapter 3.5.2 --- An Example --- p.52 / Chapter 3.5.2.1 --- Overlapping shifts with one kind of break times --- p.54 / Chapter 3.5.2.2 --- Overlapping shifts with two kinds of break times --- p.56 / Chapter 3.5.2.3 --- Overtime work --- p.57 / Chapter 3.5.3 --- Computational results on different staff requirement patterns --- p.60 / Chapter 4. --- CONCLUSION --- p.62 / Chapter 5. --- BIBLIOGRAPHY --- p.64 / Chapter 6. --- APPENDIX --- p.66 / Chapter 6.1 --- Applying the heuristic to complete the incomplete schedules --- p.66 / Chapter 6.2 --- List of Schedules --- p.68 / Chapter 6.2.1 --- Terminologies --- p.68 / Chapter 6.2.2 --- The Optimal Schedules for Case One --- p.69 / Chapter 6.2.3 --- The Optimal Schedules for Case Two --- p.70 / Chapter 6.2.4 --- The Optimal Schedules with One-hour Break in One Shift --- p.71 / Chapter 6.2.5 --- The Optimal Schedules with Breaks after 4 and 3 Hours of Work --- p.72 / Chapter 6.2.6 --- The Optimal Schedules with Overtime Shifts --- p.73

This dissertation is motivated by the problem of uncertainty and sensitivity in business- class models such as the carbon emission abatement policy model featured in this work. Uncertain model inputs are represented by numerical random variables and a computational methodology is developed to numerically compute business-class models as if sharp inputs were given. A new description for correlation of random variables is presented that arises spontaneously within a numerical model. Methods of numerically computing correlated random variables are implemented in software and represented. The major contribution of this work is a methodology for the numerical computation of models under uncertainty that expresses no preference for unlikelihood of model input combinations. The methodology presented here serves a sharp contrast to traditional Monte Carlo methods that implicitly equate likelihood of model input values with importance of results. The new methodology herein shifts the computational burden from likelihood of inputs to resolution of input space.

Thesis (Ph.D.)--McMaster University, 2006. / Supervisor: Tamás Terlaky. Includes bibliographical references (p. 181-190).

Dimitri P. Bertsekas. / Bibliography: leaf 6. / Caption title. "August 1981." / NSF Grant No. NSF/ECS 79-20834 DOE Contract no. DE-AC01-79ET29243

by Dimitri P. Bertsekas and Eli M. Gafni. / Bibliography: p. 26-28. / "August 1981." / Partial support provided by the National Science Foundation Grant ECS-79-20834 Defense Advanced Research Project Agency Grant ONR-N00014-75-C-1183

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