Approved for public release; distribution is unlimited / The U.S. Army Wartime Ammunition Distribution System (WADS) will experience an unprecedented demand for ammunition under the operational concept of Airland Battle. To meet demand, proper storage facility location and an efficient flow through the distribution network will be required. Using information from Army Field Manuals, maps and simulation data for demand, both a mixed integer program (MIP) and a sequential, optimization-based heuristic are developed to model the WADS. The Generalized Algebraic Modelling System is used to implement both models. The sequential heuristic locates ammunition facilities with a binary integer program and then directs ammunition through those facilities utilizing a network flow model with side constraints. The MIP integrates location and flow decisions in the same model. For a general scenario, the sequential heuristic locates a 21 node, 30 arc network with ammunition flows over 30 time periods in 22 CPU seconds on an IBM 3033AP. For the same scenario the MIP obtains a solution for only a 3 time period problem in 87 CPU seconds. Keywords: Ammunition, Integer programming, Heuristic, Networks / http://archive.org/details/gamsbasedmodelof00cain / Captain, United States Army

A dissertation submitted to the Faculty of Science School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg. April 27, 2013. / In a number of situations the derivative of the objective function of an optimization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region methodology. Three implementations of the algorithm are developed and deterministic proofs of convergence to local minima are provided for two of the implementations. In the development of the algorithm several other contributions are made. The derivative free algorithm requires the solution of several mixed integer quadratic programming subproblems and novel methods for solving nonconvex instances of these problems are developed in this thesis. Additionally, it is shown that the current definitions of local minima for mixed integer programs are deficient and a rigorous approach to developing possible definitions is proposed. Using this approach we propose a new definition which improves on those currently used in the literature. Other components of this thesis are an overview of derivative based mixed integer non-linear programming, extensive reviews of mixed integer quadratic programming and deterministic derivative free optimization and extensive computational results illustrating the effectiveness of the contributions mentioned in the previous paragraphs.

Wang, Chongyu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 74-78). / Abstract also in Chinese. / Abstract --- p.1 / Abstract in Chinese --- p.3 / Acknowledgement --- p.4 / Contents --- p.5 / List of Tables --- p.7 / List of Figures --- p.8 / Chapter 1. --- Introduction --- p.9 / Chapter 2. --- Conventional Dynamic Programming --- p.15 / Chapter 2.1. --- Principle of optimality and decomposition --- p.15 / Chapter 2.2. --- Backward dynamic programming --- p.17 / Chapter 2.3. --- Forward dynamic programming --- p.20 / Chapter 2.4. --- Curse of dimensionality --- p.23 / Chapter 3. --- Surrogate Constraint Formulation --- p.26 / Chapter 3.1. --- Surrogate constraint formulation --- p.26 / Chapter 3.2. --- Singly constrained dynamic programming --- p.28 / Chapter 3.3. --- Surrogate dual search --- p.29 / Chapter 4. --- Distance Confined Path Algorithm --- p.34 / Chapter 4.1. --- Yen´ةs algorithm for the kth shortest path problem --- p.35 / Chapter 4.2. --- Application of Yen´ةs method to integer programming --- p.36 / Chapter 4.3. --- Distance confined path problem --- p.42 / Chapter 4.4. --- Application of distance confined path formulation to integer programming --- p.50 / Chapter 5. --- Convergent Surrogate Dual Search --- p.59 / Chapter 5.1. --- Algorithm for convergent surrogate dual search --- p.62 / Chapter 5.2. --- "Solution schemes for (Pμ{αk,αβ)) and f(x) = αk" --- p.63 / Chapter 5.3. --- Computational Results and Analysis --- p.68 / Chapter 6. --- Conclusions --- p.72 / Bibliography --- p.74

Generating employee rosters on a 24 hour, 7 day per week basis taking into account fluctuating demand for employees, employee skills, working conditions, training and employee preferences, while ensuring efficiency and equity between the employees is a very difficult task due to the very large number of possible rostering combinations available. The research done in this thesis sets to solve this exact problem for CS Energy's Swanbank Power Station located in Queensland, Australia. / thesis (PhDMathematics)--University of South Australia, 2002.

The acquisition and elimination of products and the resources needed to create them constitutes an important part of the business decision-making process. Activity-based costing (ABC) supports this process by providing a tool for evaluating the relative profitability of various products. It accomplishes this by allocating costs to products based on the activities, and in turn the resources demanded by those activities, required to produce them. In allocating indirect costs traditionally considered "fixed," such as equipment, administrative overhead, and support staff salaries, ABC treats all costs as variable in the long-run. However, many costs can only vary in discrete steps. For example, one usually cannot purchase a fractional piece of equipment; one chooses either to buy it or not to buy it. Also, in adding support staff, one will typically find that people demand full-time positions, so increments will come in discrete amounts. This stairstep semivariable nature of many costs runs counter to ABC's treatment of all costs as variable. In addition, different products often draw upon the same resources. This creates complex interactions, making it difficult to predict the ultimate consequences of adding or eliminating a particular product. Mixed integer programming (MIP) provides another tool for making these product/resource mix decisions. Unlike ABC, however, it can handle variables that take on integer values, and hence deal appropriately with stairstep semivariable costs. It also ensures that the decision recommended by the model will optimize profitability, given that a solution exists and the underlying assumptions hold true. In doing this, MIP automatically adjusts for all of the complex interactions that exist among the various products and resources. Using a simplified two product/two resource model, one can detail the mathematics behind ABC and MIP, and then link the two approaches through a common variable. This allows one to establish the conditions under which ABC and MIP will yield the same results, and those under which they will differ. Since MW produces an optimal solution, the fact that ABC yields a different result under specific circumstances underscores the danger of relying solely on the product margins generated by an ABC model. / Graduation date: 1998

Given an undirected network with L possible facility types for each edge, and a partition of the nodes into L levels, the Multi-level Network Design (MLND) problem seeks a fixed cost minimizing design that spans all the nodes and connects the nodes at each level by facilities of the corresponding or higher type. This problem generalizes the well-known Steiner network problem and the hierarchical network design problem, and has applications in telecommunication, transportation, and electric power distribution network design. In a companion paper we introduced the problem, studied alternative model formulations, and analyzed the worst-case performance of heuristics based on Steiner network and spanning tree solutions. This paper develops and tests a dual-based algorithm for the Multi-level Network Design (MLND) problem. The method first performs problem preprocessing to fix certain design variables, and then applies a dual ascent procedure to generate upper and lower bounds on the optimal value. We report extensive computational results on large, random networks (containing up to 500 nodes, and 5000 edges) with varying cost structures. The integer programming formulation of the largest of these problems has 20,000 integer variables and over 5 million constraints. Our tests indicate that the dualbased algorithm is very effective, producing solutions guaranteed to be within 0 to 0.9% of optimality.

Thesis (M.S.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaves 74-78).

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The Time-Dependent Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem, where the cost for travel between two nodes is dependent on the nodes and their position in the tour. Inequalities for the Asymmetric TSP can be easily extended to the TDTSP, but the added time information can be used to strengthen these inequalities. We look at extending the Lifted Cycle Inequalities, a large family of inequalities for the ATSP. We define a new inequality, the Extended Cycle (X-cycle) Inequality, based on cycles in the graph. We extend the results of Balas and Fischetti for Lifted Cycle Inequalities to define Lifted X-cycle Inequalities. We show that the Lifted X-cycle Inequalities include some inequalities which define facets of the submissive of the TDTS Polytope.

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