The aim in this thesis is to develop efficient enumeration algorithms to solve certain strongly NP-hard scheduling problems. These algorithms were developed using a combination of ideas from Integer Programming, Constraint Programming and Scheduling Theory. In order to combine different techniques in one algorithm, decomposition methods are applied. The main idea on which the first part of our results is based is to separate the optimality and feasibility components of the problem and let different methods tackle these components. Then IP is ``responsible' for optimization, whereas specific combinatorial algorithms tackle the feasibility aspect. Branch-and-cut and branch-and-price algorithms based on this idea are proposed to solve the single-machine and multi-machine variants of the scheduling problem to minimize the sum of the weights of late jobs. Experimental research shows that the algorithms proposed outperform other algorithms available in the literature. Also, it is shown that these algorithms can be used, after some modification, to solve the problem of minimizing the maximum tardiness on unrelated machines. The second part of the thesis deals with the one-machine scheduling problem to minimize the weighted total tardiness. To tackle this problem, the idea of a partition of the time horizon into intervals is used. A particularity of this approach is that we exploit the structure of the problem to partition the time horizon. This particularity allowed us to propose two new Mixed Integer Programming formulations for the problem. The first one is a compact formulation and can be used to solve the problem using a standard MIP solver. The second formulation can be used to derive lower bounds on the value of the optimal solution of the problem. These lower bounds are of a good quality, and they can be obtained relatively fast.

This dissertation focuses on extending solution methods in the area of stochastic optimization. Attention is focused to three specific problems in the field. First, a solution method for mixed integer programs subject to chance constraints is discussed. This class of problems serves as an effective modeling framework for a wide variety of applied problems. Unfortunately, chance constrained mixed integer programs tend to be very challenging to solve. Thus, the aim of this work is to address some of these challenges by exploiting the structure of the deterministic reformulation for the problem. Second, a stochastic program for integrating renewable energy sources into traditional energy systems is developed. As the global push for higher utilization of such green resources increases, such models will prove invaluable to energy system designers. Finally, a process for transforming clinical medical data into a model to assist decision making during the treatment planning phase for palliative chemotherapy is outlined. This work will likely provide decision support tools for oncologists. Moreover, given the new requirements for the usage electronic medical records, such techniques will have applicability to other treatment planning applications in the future.

This diploma thesis has been elaborated within the Master's study of department 2307 that submits a production hooped component. The material of the component is steel ČSN 15 130. Single – part as far as small–lot production. On the basis of the literary study problems bend tubing was sugested the method: rotary draw bending. For this method was sugested mechanical bending machine with mandrel support arm, for bending with mandrel and exact bends in three – dimensional.

In this dissertation, we address three different combinatorial optimization problems (COPs), each of which has specific real-life applications. Owning to their specific nature, these problems are different from those discussed in the literature. For each of these problems, we present a mathematical programming formulation, analyze the problem to determine its useful, inherent structural properties, and develop an efficient methodology for its solution by exploiting these properties. The first problem that we address is the course timetabling problem encountered at Virginia Tech. The course timetabling problem for a university is a difficult problem and has been studied by many researchers over the years. As a result, a plethora of models and approaches have been reported in the literature. However, most of these studies have focused on applications pertaining to course scheduling for a single or at most few departments of a university. The sheer size of the university-wide timetabling problem that we address, involving thousands of courses to be scheduled in hundreds of classrooms in each semester, makes it a challenging problem. We employ an appropriate decomposition technique that relies on some inherent structural properties of the problem both during the modeling and algorithmic development phases. We show the superiority of the schedules generated by our methodology over those that are currently being used. Also, our methodology requires only a reasonable amount of computational time in solving this large-size problem. A facility layout problem involving arbitrary-shaped departments is the second problem that we investigate in this dissertation. We designate this problem as the arbitrary-shaped facility layout problem (ASFLP). The ASFLP deals with arranging a given set of departments (facilities, workstations, machines) within the confines of a given floor space, in order to optimize a desired metric, which invariably relates to the material handling cost. The topic of facility planning has been addressed rather extensively in the literature. However, a major limitation of most of the work reported in the literature is that they assume the shape of a department to be a rectangle (or even a square). The approach that relies on approximating an arbitrary-shaped department by a rectangle might result in an unattractive solution. The key research questions for the ASFLP are: (1) how to accurately model the arbitrary-shaped departments, and (2) how to effectively and efficiently determine the desired layout. We present a mixed-integer programming model that maintains the arbitrary shapes of the departments. We use a meta-heuristic to solve the large-size instances of the ASFLP in a reasonable amount of time. The third problem that we investigate is a supply chain scheduling problem. This problem involves two stages of a supply chain, specifically, a manufacturer and one or more customers. The key issue is to achieve an appropriate coordination between the production and distribution functions of the manufacturer so as to minimize the sum of the shipping and job tardiness costs. We, first, address a single customer problem, and then, extend our analysis to the case of multiple customers. For the single-customer problem, we present a polynomial-time algorithm to solve it to optimality. For the multiple-customer problem, we prove that this problem is NP-hard and solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. We propose a branch-and-bound-based methodology for this problem that exploits its structural properties. Results of an extensive computational experimentation are presented that show the following: (1) our algorithms are efficient to use and effective to implement; and (2) significant benefits accrue as a result of integrating the production and distribution functions. / Ph. D.

This dissertation develops mathematical models to efficiently manage the inland waterway port operations while minimizing the overall supply chain cost. In the first part, a capacitated, multi-commodity, multi-period mixed-integer linear programming model is proposed capturing diversified inland waterway transportation network related properties. We developed an accelerated Benders decomposition algorithm to solve this challenging NP-hard problem. The next study develops a two-stage stochastic mixed-integer nonlinear programming model to manage congestion in an inland waterway transportation network under stochastic commodity supply and water-level fluctuation scenarios. The model also jointly optimizes trip-wise towboat and barge assignment decisions and different supply chain decisions (e.g., inventory management, transportation decisions) in such a way that the overall system cost can be minimized. We develop a parallelized hybrid decomposition algorithm, combining Constraint Generation algorithm, Sample Average Approximation (SAA), and an enhanced variant of the L-shaped algorithm, to effectively solve our proposed optimization model in a timely fashion. While the first two parts develop models from the supply chain network design viewpoint, the next two parts propose mathematical models to emphasize the port and waterway transportation related operations. Two two-stage, stochastic, mixed-integer linear programming (MILP) models are proposed under stochastic commodity supply and water level fluctuations scenarios. The last one puts the specific focus in modeling perishable inventories. To solve the third model we propose to develop a highly customized parallelized hybrid decomposition algorithm that combines SAA with an enhanced Progressive Hedging and Nested Decomposition algorithm. Similarly, to solve the last mathematical model we propose a hybrid decomposition algorithm combining the enhanced Benders decomposition algorithm and SAA to solve the large size of test instances of this complex, NP-hard problem. Both proposed approaches are highly efficient in solving the real-life test instances of the model to desired quality within a reasonable time frame. All the four developed models are validated a real-life case study focusing on the inland waterway transportation network along the Mississippi River. A number of managerial insights are drawn for different key input parameters that impact port operations. These insights will essentially help decisions makers to effectively and efficiently manage an inland waterway-based transportation network.

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Logic-based Benders decomposition (LBBD) is a strategy for solving discrete optimisation problems. In LBBD, the optimisation problem is divided into a master problem and a subproblem and each part is solved separately. LBBD methods that combine mixed-integer programming and constraint programming have been successfully applied to solve large-scale scheduling and resource allocation problems. Such combinations typically solve an assignment-type master problem and a scheduling-type subproblem. However, a challenge with LBBD methods that have feasibility subproblems are that they do not provide a feasible solution until an optimal solution is found.  In this thesis, we show that feasible solutions can be obtained by finding and combining feasible parts of an infeasible master problem assignment. We use these insights to develop an acceleration technique for LBBD that solves a series of subproblems, according to algorithms for constructing a maximal feasible subset of constraints (MaFS). Using a multiprocessor scheduling problem as a benchmark, we study the computational impact from using this technique. We evaluate three variants of LBBD schemes. The first uses MaFS, the second uses irreducible subset of constraints (IIS) and the third combines MaFS with IIS. Computational tests were performed on an instance set of multiprocessor scheduling problems. In total, 83 instances were tested, and their number of tasks varied between 2794 and 10,661. The results showed that when applying our acceleration technique in the decomposition scheme, the pessimistic bounds were strong, but the convergence was slow. The decomposition scheme combining our acceleration technique with the acceleration technique using IIS showed potential to accelerate the method.

With the rise of online retailer giants like Amazon, and enhancements in internet and mobile technologies, online shopping is becoming increasingly popular. This has lead to new opportunities in online price optimization. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions. In Chapter 2 a multi-period revenue maximization and pricing optimization problem in the presence of reference prices is formulated as a mixed integer nonlinear program. Two algorithms are developed to solve the optimization problem: a generalized Benders' decomposition algorithm and a myopic heuristic. This is followed by numerical computations to illustrate the effciency of the solution approaches as well as some managerial pricing insights. In Chapter 3 a data-driven quadratic programming optimization model for online pricing in the presence of customer ratings is proposed. A new demand function is developed for a multi-product, nite horizon, online retail environment. To solve the optimization problem, a myopic pricing heuristic as well as exact solution approaches are introduced. Using customer reviews ratings data from Amazon.com, a new customer rating forecasting model is validated. This is followed by several analytical and numerical insights. In Chapter 4 a multinomial choice model is used for customer purchase decision to find optimal personalized price discounts for an online retailer that incorporates customer locations and feedback from their reviews. Closed form solutions are derived for two special cases of this problem. To gain some analytical insights extensive numerical experiments are carried followed by several analytical and numerical insights. / Thesis / Doctor of Philosophy (PhD) / The increase in online retail and the improvements in mobile technologies has lead to advantages and opportunities for both customers and retailers. One of these advantages is the ability to keep and efficiently access records of historical orders for both customers and retailers. In addition, online retailing has dramatically decreased the cost of price adjustments and discounts compared to the brick and mortar environment. At the same time, with the increase in online retailing we are witnessing proliferations of online reviews in e-commerce platforms. Given this availability of data and the new capabilities in an online retail environment, there is a need to develop pricing optimization models that integrate all these new features. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions.

In this work, we address a variety of problems with applications to `ethanol production from biomass', `agile manufacturing' and `mass customization' domains. Our motivation stems from the potential use of biomass as an alternative to non-renewable fuels, the prevalence of `flexible manufacturing systems', and the popularity of `mass customization' in today's highly competitive markets. Production scheduling and design and optimization of logistics network mark the underlying topics of our work. In particular, we address three problems, Biomass Logistics Problem, Hybrid Flow Shop Scheduling Problem, and Stochastic Demand Assembly Job Scheduling Problem. The Biomass Logistics Problem is a strategic cost analysis for setup and operation of a biomass supply chain network that is aimed at the production of ethanol from switchgrass. We discuss the structural components and operations for such a network. We incorporate real-life GIS data of a geographical region in a model that captures this problem. Consequently, we develop and demonstrate the effectiveness of a `Nested Benders' based algorithm for an efficient solution to this problem. The Hybrid Flow Shop Scheduling Problem concerns with production scheduling of a lot over a two-stage hybrid flow shop configuration of machines, and is often encountered in `flexible manufacturing systems'. We incorporate the use of `lot-streaming' in order to minimize the makespan value. Although a general case of this problem is NP-hard, we develop a pseudo-polynomial time algorithm for a special case of this problem when the sublot sizes are treated to be continuous. The case of discrete sublot sizes is also discussed for which we develop a branch-and-bound-based method and experimentally demonstrate its effectiveness in obtaining a near-optimal solution. The Stochastic Demand Assembly Job Scheduling Problem deals with the scheduling of a set of products in a production setting where manufacturers seek to fulfill multiple objectives such as `economy of scale' together with achieving the flexibility to produce a variety of products for their customers while minimizing delivery lead times. We design a novel methodology that is geared towards these objectives and propose a Lagrangian relaxation-based algorithm for efficient computation. / Doctor of Philosophy / In this work, we organize our research efforts in three broad areas - Biomass Supply Chain, Hybrid Flow Shop, and Assembly Job Shop, which are separate in terms of their application but connected by scheduling and logistics as the underlying functions. For each of them, we formulate the problem statement and identify the challenges and opportunities from the viewpoint of mathematical decision making. We use some of the well known results from the theory of optimization and linear algebra to design effective algorithms in solving these specific problems within a reasonable time limit. Even though the emphasis is on conducting an algorithmic analysis of the proposed solution methods and in solving the problems analytically, we strive to capture all the relevant and practical features of the problems during formulation of each of the problem statement, thereby maintaining their applicability. The Biomass Supply Chain pertains to the production of fuel grade ethanol from naturally occurring biomass in the form of switchgrass. Such a system requires establishment of a supply chain and logistics network that connects the production fields at its source, the intermediate points for temporary storage of the biomass, and bio-energy plant and refinery at its end for conversion of the cellulosic content in the biomass to crude oil and ethanol, respectively. We define the components and operations necessary for functioning of such a supply chain. The Biomass Logistics Problem that we address is a strategic cost analysis for setup and operation of such a biomass supply chain network. We focus our attention to a region in South Central Virginia and use the detailed geographic map data to obtain land use pattern in the region. We conduct survey of existing literature to obtain various transportation related cost factors and costs associated with the use of equipment. Our ultimate aim here is to understand the feasibility of running a biomass supply chain in the region of interest from an economic standpoint. As such, we represent the Biomass Logistics Problem with a cost-based optimization model and solve it in a series of smaller problems. A Hybrid Flow Shop (HFS) is a configuration of machines that is often encountered in the flexible manufacturing systems, wherein a particular station of machines can execute processing of jobs/tasks simultaneously. In our work, we approach a specific type of HFS, with a single machine at the first stage and multiple identical machines at the second stage. A batch or lot of jobs/items is considered for scheduling over such an HFS. Depending upon the area of application, such a batch is either allowed to be split into continuous sections or restricted to be split in discrete sizes only. The objective is to minimize the completion time of the last job on its assigned machine at the second stage. We call this problem, Hybrid Flow Shop Scheduling Problem, which is known to be a hard problem in literature. We aim to derive the results which will reduce the complexity of this problem, and develop both exact as well as heuristic methods in order to obtain near-optimal solution to this problem. An Assembly Job Shop is a variant of the classical Job Shop which considers scheduling a set of assembly operations over a set of assembly machines. Each operation can only be started once all the other operations in its precedence relationship are completed. Assembly Job Shop are at the core of some of the highly competitive manufacturing facilities that are principled on the philosophy of Mass Customization. Assuming an inherent nature of demand uncertainty, this philosophy aims to achieve ‘economy of scale’ together with flexibility to produce a variety of products for the customers while minimizing the delivery lead times simultaneously. We incorporate some of these challenges in a concise framework of production scheduling and call this problem as Stochastic Demand Assembly Job Scheduling Problem. We design a novel methodology that is geared towards achieving the set objectives and propose an effective algorithm for efficient computation.

On se propose d'intégrer un type particulier de contrainte logique dans les problèmes de contrôle optimal à coût quadratique. Une approche numérique directe par collocation conduit à des problèmes de programmation mathématique en variables mixtes. S'intéressant d'abord au cas des systèmes à dynamique linéaire, on propose une variante de la Décomposition de Benders qui nous permet de résoudre des problèmes mixtes de taille importante (au delà de mille variables binaires). Ces résultats sont obtenus grâce aux propriétés induites par la contrainte logique. Dans le cas des problèmes mixtes issus d'une dynamique non-linéaire, la démarche proposée (Branch and Reduce) traite de façon analogue les problèmes d'optimisation globale et ceux en variables mixtes. On s'est limité à l'optimisation globale sur le problème de transfert orbital, étudiant notamment les questions de la convexification et de la réduction du domaine. Les résultats obtenus sont partiels, seuls des problèmes de petite taille ayant été traités.