The purpose of this dissertation is to address risk and consequences of and effective mitigation strategies for urban fire events involving two critical infrastructures- water distribution and emergency services. Water systems have been identified as one of the United States' critical infrastructures and are vulnerable to various threats caused by natural disasters or malevolent actions. The primary goals of urban water distribution systems are reliable delivery of water during normal and emergency conditions (such as fires), ensuring this water is of acceptable quality, and accomplishing these tasks in a cost-effective manner. Due to interdependency of water systems with other critical infrastructures-e.g., energy, public health, and emergency services (including fire response)- water systems planning and management offers numerous challenges to water utilities and affiliated decision makers. The dissertation is divided into three major sections, each of which presents and demonstrates a methodological innovation applied to the above problem. First, a risk based dynamic programming modeling approach is developed to identify the critical components of a water distribution system during fire events under three failure scenarios: (1) accidental failure due to soil-pipe interaction, (2) accidental failure due to a seismic activity, and (3) intentional failure or malevolent attack. Second, a novel evolutionary computation based multi-objective optimization technique, Non-dominated Sorting Evolution Strategy (NSES), is developed for systematic generation of optimal mitigation strategies for urban fire events for water distribution systems with three competing objectives: (1) minimizing fire damages, (2) minimizing water quality deficiencies, and (3) minimizing the cost of mitigation. Third, a stochastic modeling approach is developed to assess urban fire risk for the coupled water distribution and fire response systems that includes probabilistic expressions for building ignition, WDS failure, and wind direction. Urban fire consequences are evaluated in terms of number of people displaced and cost of property damage. To reduce the assessed urban fire risk, the NSES multi-objective approach is utilized to generate Pareto-optimal solutions that express the tradeoff relationship between risk reduction, mitigation cost, and water quality objectives. The new methodologies are demonstrated through successful application to a realistic case study in water systems planning and management.

A generalized dynamic programming based algorithm and a local search heuristic are used to solve the Two Runway Departure Scheduling Problem that arises at an airport. The objective of this work is to assign the departing aircraft to one of the runways and find a departing time for each aircraft so that the overall delay is minimized subject to the timing, safety, and the ordering constraints. A reduction in the overall delay of the departing aircraft at an airport can improve the airport surface operations and aircraft scheduling. The generalized dynamic programming algorithm is an exact algorithm, and it finds the optimal solution for the two runway scheduling problem. The performance of the generalized dynamic programming algorithm is assessed by comparing its running time with a published dynamic programming algorithm for the two runway scheduling problem. The results from the generalized dynamic programming algorithm show that this algorithm runs much faster than the dynamic programming algorithm. The local search heuristic with k − exchange neighborhoods has a short running time in the order of seconds, and it finds an approximate solution. The performance of this heuristic is assessed based on the quality of the solution found by the heuristic and its running time. The results show that the solution found by the heuristic for a 25 aircraft problem has an average savings of approximately 15 percent in delays with respect to a first come-first served solution. Also, the solutions produced by a 3-opt heuristic for a 25 aircraft scheduling problem has an average quality of 8 percent with respect to the optimal solution found by the generalized dynamic programming algorithm. The heuristic can be used for both real-time and fast-time simulations of airport surface operations, and it can also provide an upper limit for an exact algorithm. Aircraft arrival scheduling problems may also be addressed using the generalized dynamic programming algorithm and the local search heuristic with slight modification to the constraints.

This research introduces a general approach for integrating a probabilistic model of the changes in the committed orders with an analytical model of production and inventory planning under multi-period Quantity Flexibility contracts. We study a decentralized structure where a capacitated manufacturer, capable of subcontracting, serves multiple contract buyers who actually perform forecasts on a rolling horizon basis. We model the evolution of buyers&#039 / commitments as a multiplicative forecast evolution process accommodating contract revision limits. A finite Markovian approximation to this sophisticated evolution model is introduced for facilitating the associated complex probability modeling. We implement computational dynamic programming and introduce an effective approach for reducing state-space dimensionality building upon our forecast evolution structure. Computational investigation demonstrates how the manufacturer benefits from the existence of order commitments and subcontracting option by analyzing the interplay of decisions.

Vendor Managed Inventory (VMI) policy has been widely used in various supply chains due to the benefits such as lower inventory levels and costs of retailer, and less frequent stock outs. In this study, the benefits of VMI policy in a manufacturer-retailer setting are analyzed under three different scenarios (Traditional Decision Making, VMI agreement and Centralized Decision Making). A manufacturer that produces a particular product is considered and that product is sold to a retailer operating under known demand forecasts. Under Traditional Decision Making System, each party is responsible for its own costs. Under VMI, manufacturer controls the replenishment decisions of the retailer and solves a Constrained Two-Echelon Lot Sizing Problem with Backordering. Under Centralized Decision Making, manufacturer and retailer act like merged, the problem under consideration is Two-Echelon Single Item Lot Sizing with Backordering. Through an extensive numerical study, three different scenarios&rsquo / results are compared and the conditions beneficial under VMI are identified. Under VMI, a Lagrangean Relaxation algorithm is proposed to reduce solution time. In terms of computational effort, solution times of proposed algorithm and MIP model are compared.

The objective of this thesis is to design a system that can be used to retrieve the music songs by acoustic input. The system listens to the melody or the partial song singing by the Karaoke users, and then prompts them the whole song paragraphs. Note segmentation is completed by both the magnitude of the song and the k-Nearest Neighbor technique. In order to speed up our system, the pitch period estimation algorithm is rewritten by a theory in communications. Besides, a large popular music database is built to make this system more practical.

Future ambitious solar system exploration missions are likely to require ever larger propulsion capabilities and involve innovative interplanetary trajectories in order to accommodate the increasingly complex mission scenarios. Two recent advances in trajectory design can be exploited to meet those new requirements: the use of low-thrust propulsion which enables larger cumulative momentum exchange relative to chemical propulsion; and the consideration of low-energy transfers relying on full multi-body dynamics. Yet the resulting optimal control problems are hypersensitive, time-consuming and extremely difficult to tackle with current optimization tools. Therefore, the goal of the thesis is to develop a methodology that facilitates and simplifies the solution finding process of low-thrust optimization problems in multi-body environments. Emphasis is placed on robust techniques to produce good solutions for a wide range of cases despite the strong nonlinearities of the problems. The complete trajectory is broken down into different component phases, which facilitates the modeling of the effects of multiple bodies and makes the process less sensitive to the initial guess. A unified optimization framework is created to solve the resulting multi-phase optimal control problems. Interfaces to state-of-the-art solvers SNOPT and IPOPT are included. In addition, a new, robust Hybrid Differential Dynamic Programming (HDDP) algorithm is developed. HDDP is based on differential dynamic programming, a proven robust second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. HDDP also incorporates nonlinear mathematical programming techniques to increase efficiency, and decouples the optimization from the dynamics using first- and second-order state transition matrices. Crucial to this optimization procedure is the generation of the sensitivities with respect to the variables of the system. In the context of trajectory optimization, these derivatives are often tedious and cumbersome to estimate analytically, especially when complex multi-body dynamics are considered. To produce a solution with minimal effort, an new approach is derived that computes automatically first- and high-order derivatives via multicomplex numbers. Another important aspect of the methodology is the representation of low-thrust trajectories by different dynamical models with varying degrees of fidelity. Emphasis is given on analytical expressions to speed up the optimization process. In particular, one novelty of the framework is the derivation and implementation of analytic expressions for motion subjected to Newtonian gravitation plus an additional constant inertial force. Example applications include low-thrust asteroid tour design, multiple flyby trajectories, and planetary inter-moon transfers. In the latter case, we generate good initial guesses using dynamical systems theory to exploit the chaotic nature of these multi-body systems. The developed optimization framework is then used to generate low-energy, inter-moon trajectories with multiple resonant gravity assists.

Many supply chain problems involve discrete decisions in a dynamic environment. The inventory routing problem is an example that combines the dynamic control of inventory at various facilities in a supply chain with the discrete routing decisions of a fleet of vehicles that moves product between the facilities. We study these problems modeled as mixed-integer programs and propose a time decomposition based on approximate inventory valuation. We generate the approximate value function with an algorithm that combines data fitting, discrete optimization and dynamic programming methodology. Our framework allows the user to specify a class of piecewise linear, concave functions from which the algorithm chooses the value function. The use of piecewise linear concave functions is motivated by intuition, theory and practice. Intuitively, concavity reflects the notion that inventory is marginally more valuable the closer one is to a stock-out. Theoretically, piecewise linear concave functions have certain structural properties that also hold for finite mixed-integer program value functions. (Whether the same properties hold in the infinite case is an open question, to our knowledge.) Practically, piecewise linear concave functions are easily embedded in the objective function of a maximization mixed-integer or linear program, with only a few additional auxiliary continuous variables. We evaluate the solutions generated by our value functions in a case study using maritime inventory routing instances inspired by the petrochemical industry. The thesis also includes two other contributions. First, we review various data fitting optimization models related to piecewise linear concave functions, and introduce new mixed-integer programming formulations for some cases. The formulations may be of independent interest, with applications in engineering, mixed-integer non-linear programming, and other areas. Second, we study a discounted, infinite-horizon version of the canonical single-item lot-sizing problem and characterize its value function, proving that it inherits all properties of interest from its finite counterpart. We then compare its optimal policies to our algorithm's solutions as a proof of concept.

In einer von Vernetzung und Globalisierung geprägten Umwelt wächst der Wettbewerbsdruck auf die Unternehmen am Markt stetig. Die effektive Nutzung der Ressourcen einerseits und die enge Zusammenarbeit mit Lieferanten und Kunden andererseits führen für nicht wenige Unternehmen des industriellen Sektors zu entscheidenden Wettbewerbsvorteilen, die das Fortbestehen jener Unternehmen am Markt sichern. Viele Unternehmen verstehen sich aus diesem Grund als Bestandteil so genannter Supply Chains. Die unternehmensübergreifende Steuerung und Optimierung des Wertschöpfungsprozesses stellt ein charakteristisches Problem des Supply Chain Managements dar und besitzt zur Erzielung von Wettbewerbsvorteilen hohes Potential. Produktionsnetzwerke sind ein wesentlicher Forschungsschwerpunkt der Professur für Produktionswirtschaft und Industriebetriebslehre an der TU Chemnitz. Das Extended Value Chain Management (EVCM) stellt ein kompetenzorientiertes Konzept für die Bildung und zum Betrieb hierarchieloser temporärer regionaler Produktionsnetzwerke im Sinne virtueller Unternehmen dar. Gegenstand dieser Arbeit ist ein diskretes Optimierungsproblem, dass einen mehrstufigen Entscheidungsprozesses unter Berücksichtigung mehrerer Ziele abbildet, der sich bei der Auswahl möglicher Partner in einem Produktionsnetzwerk nach dem Betreiberkonzept des EVCM ergibt. Da mehrere Zielstellungen bestehen, werden grundlegende Methoden der mehrkriteriellen Optimierung und Entscheidung erörtert. Neben der Vorstellung des Problems sollen mehrzielorientierte Ansätze im Sinne einer Pareto-Optimierung auf Basis des Dynamic Programmings als Verfahren zur Bestimmung von Optimallösungen sowie Ant Colony Optimization zur näherungsweisen Lösung vorgestellt werden. Darauf aufbauend werden verschiedene Möglichkeiten der Hybridisierung beider Methoden diskutiert. Die entwickelten Ansätze werden auf ihre Eignung im Rahmen der informationstechnischen Umsetzung des EVCM-Konzepts untersucht und einer Evaluierung unterzogen. Hierzu werden verschiedene Kennzahlen zur Beurteilung der Verfahren entwickelt. Die modellierten Algorithmen und entwickelten Konzepte beschränken sich nicht ausschließlich auf das betrachtete Problem, sondern können leicht auf Probleme mit ähnlichen Eigenschaften übertragen werden. Insbesondere das NP-vollständige mehrkriterielle Kürzeste-Wege-Problem stellt einen Spezialfall des behandelten Optimierungsproblems dar.

The purpose of this research is to develop a model and solution methodology for selecting and scheduling timely and cost-effective maintenance, rehabilitation, and reconstruction activities (M & R) for each pavement section in a highway network and allocating the funding levels through a finite multi-period horizon within the constraints imposed by budget availability in each period, frequency availability of activities, and specified minimum pavement quality requirements. M & R is defined as a chronological sequence of reconstruction, rehabilitation, and major/minor maintenance, including a "do nothing" activity. A procedure is developed for selecting an M & R activity for each pavement section in each period of a specified extended planning horizon. Each activity in the sequence consumes a known amount of capital and generates a known amount of effectiveness measured in pavement quality. The effectiveness of an activity is the expected value of the overall gains in pavement quality rating due to the activity performed on a highway network over an analysis period. It is assumed that the unused portion of the budget for one period can be carried over to subsequent periods. Dynamic Programming (DP) and Branch-and-Bound (B-and-B) approaches are combined to produce a hybrid algorithm for solving the problem under consideratioin. The algorithm is essentially a DP approach in the sense that the problem is divided into smaller subproblems corresponding to each single period problem. However, the idea of fathoming partial solutions that could not lead to an optimal solution is incorporated within the algorithm to reduce storage and computational requirements in the DP frame using the B-and-B approach. The imbedded-state approach is used to reduce a multi-dimensional DP to a one-dimensional DP. For bounding at each stage, the problem is relaxed in a Lagrangean fashion so that it separates into longest-path network model subproblems. The values of the Lagrangean multipliers are found by a subgradient optimization method, while the Ford-Bellman network algorithm is employed at each iteration of the subgradient optimization procedure to solve the longest-path network problem as well as to obtain an improved lower and upper bound. If the gap between lower and upper bound is sufficiently small, then we may choose to accept the best known solutions as being sufficiently close to optimal and terminate the algorithm rather than continue to the final stage.

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