Browsing by Subject "Linear programming"
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Item A group theoretic partial enumeration algorithm for all-integer programming(Texas Tech University, 1985-08) Zaatari, Abbas TNot availableItem A particular reflexive generalized inverse and its use in finding integral solutions to systems of linear equations(1971-05) Hurt, Michiel FrancisNot AvailableItem A simulation approach to stochastic linear programming(Texas Tech University, 1973-05) Armstrong, Walter PatrickNot availableItem An all-integer cutting plane algorithm with an advanced start(Texas Tech University, 1981-08) Hanna, Michael EdwardNot availableItem An application of linear predictor theory(Texas Tech University, 1972-08) Wester, John BascomeNot availableItem An investigation of an algorithm for decomposition of large angular linear programs(Texas Tech University, 1967-05) Hancock, Charles CavanaughNot availableItem Application of empirical Bayes decision procedures to discrete time linear filtering(Texas Tech University, 1970-12) Kamat, Satish JanardanNot availableItem An average cost Markov decision process model to decide when to challenge a call in a tennis match(2010-08) Nadimpalli, Vamsi Krishna; Hasenbein, John J.; Bickel, J. E.In a standard tennis match each player has an unlimited opportunity to challenge an umpire’s call, but if three incorrect challenges are made in a set he is not allowed to challenge anymore in that set. If the set goes into a tie break the limit on incorrect challenges increases by one. These limited incorrect challenges are not carried over from one set to another. So this is kind of a limited resource available to the player and if he knows how to use this resource in a best possible way, there is a scope for increasing his overall chances of winning a match. With the motive of gaining insight on when to challenge a call, we have modeled a single game in a tennis match as a Markov decision process. We have also studied the impact of variables like player’s probability of winning a point, the player’s perception of the challengability of a call and proportion of challengable calls on the decision making process.Item Branch-and-cut for piecewise linear optimization(2012-05) Rajat, Gupta; Farias, Ismael R. d.; Simonton, James L.; Matis, Timothy I.; Smith, Phillip; Zhang, YuanlinIn this research we report and analyze the results of our extensive testing of branch-and- cut for piecewise linear optimization using the cutting planes. We tested large instances for transshipment problem using MIP, LOG and SOS2 formulations. Besides analysis of the performance of the cuts, we also analyze the effect of formulation of the performance of branch-and-cut. These tests were conducted using callable libraries of CPLEX and GUROBI. Finally, we also analyzed the results of piecewise linear optimization problems with semi- continuous constraints.Item Integrated mathematical and financial modeling with applications to product distribution, warehouse location and capacity problems(Texas Tech University, 1985-05) Cokelez, SadikThe main objective of this study is to develop effective integrated models in product distribution system design. The integrated mixed Integer linear programming model developed in this paper concurrently assesses the optimal solution of interrelated problems. Conventional optimization models treat such problems separately. This research has combined the existing models of subproblems with minor modifications to achieve an overall objective. Existing models were drawn from the areas of production operations management, operations research, finance, and statistics. The research has produced general guidelines for: 1. formulation of integrated decision models and their applications to product mix and distribution system design, 2. warehouse location and capacity under diverse situations. This thesis has contributed to production operations management and operations research decisions by developing integrated models with capabilities that serve to: 1. provide a high degree of coordination, adaptability, and flexibility, 2. provide cost-effective model usage, 3. prevent suboptimality caused by treating the individual models separately. The integrated decisions regarding which warehouses to operate and what quantity to ship from each warehouse have been the cornerstones of product distribution system design. The warehouse location problem has attracted much attention. Without warehouses, shipping direct from factory to customers may result in higher costs due to the inability to ship bulk and in long shipping time. Also, the warehouses act as collection points for several factories, thereby enabling a mix of products to be shipped to customers. Existing warehouse location models do not integrate production decisions and are useful only to agencies or middlemen who are in the transportation or warehousing businesses, not producers themselves. The models that treat production problems individually may give suboptimal results and artificially-generated subjective supply figures; they suffer from the artificial restrictions Imposed by individual models such as subjectively predetermined supply figures, subjectively predetermined warehouse capacity ranges or meeting all the demand even when it is not profitable to do so. The integrated mixed Integer linear model developed in this research is more comprehensive. For this reason, there was a need for a more sophisticated and realistic integrated model capable of handling diverse problems without imposing the artificial restrictions mentioned above. This research developed a unified and highly coordinated mixed integer programming model to address product mix, transportation, warehouse location, warehouse capacity and overcapacity Issues concurrently. This unified model allows insertion, deletion, and choice of individual models and it is very flexible. It has also been shown through test problems that profits were much higher using the integrated decision model developed in this paper than using conventional optimization techniques. Finally, this study extended the warehouse location problem by analyzing various factors affecting warehouse location and distribution Analyzing techniques required experiments on the computer, followed by comprehensive mathematical proofs. The effects of an Increase or decrease in distances among possible warehouse sites on the degree of warehouse centralization were analyzed. In addition, the effects of changes in resource consumption of products were studied. The analysis ended with a study of relationship between warehouse location costs and warehouse distribution and appropriate conclusions were drawn.Item On a linear estimator for continuous data(Texas Tech University, 1967-08) Sommers, John PaulNOT AVAILABLEItem Optimization of production allocation under price uncertainty : relating price model assumptions to decisions(2011-08) Bukhari, Abdulwahab Abdullatif; Jablonowski, Christopher J.; Lasdon, Leon S.; Dyer, James S.Allocating production volumes across a portfolio of producing assets is a complex optimization problem. Each producing asset possesses different technical attributes (e.g. crude type), facility constraints, and costs. In addition, there are corporate objectives and constraints (e.g. contract delivery requirements). While complex, such a problem can be specified and solved using conventional deterministic optimization methods. However, there is often uncertainty in many of the inputs, and in these cases the appropriate approach is neither obvious nor straightforward. One of the major uncertainties in the oil and gas industry is the commodity price assumption(s). This paper investigates this problem in three major sections: (1) We specify an integrated stochastic optimization model that solves for the optimal production allocation for a portfolio of producing assets when there is uncertainty in commodity prices, (2) We then compare the solutions that result when different price models are used, and (3) We perform a value of information analysis to estimate the value of more accurate price models. The results show that the optimum production allocation is a function of the price model assumptions. However, the differences between models are minor, and thus the value of choosing the “correct” price model, or similarly of estimating a more accurate model, is small. This work falls in the emerging research area of decision-oriented assessments of information value.Item Performance Guarantee of a Sub-Optimal Policy for a Discrete Markov Decision Process and Its Application to a Robotic Surveillance Problem(2014-04-24) Park, MyoungkukThis dissertation deals with the development and analysis of sub-optimal decision algorithms for a collection of robots that assist a remotely located operator in perimeter surveillance. The operator is tasked with the classification of incursions across the perimeter. Whenever there is an incursion into the perimeter, a nearby Unattended Ground Sensor (UGS) signals an alert. A robot services the alert by visiting the alert location, collecting evidence in the form of video imagery, and transmitting it to the operator. The accuracy of operator's classification depends on the volume and freshness of information gathered and provided by the robots at locations where incursions occur. There are two competing needs for a robot: it needs to spend adequate time at an alert location to collect evidence for aiding the operator in accurate classification but it also needs to service other alerts as soon as possible, so that the evidence collected is relevant. The control problem is to determine the optimal amount of time a robot must spend servicing an alert. The incursions are stochastic and their statistics are assumed to be known. The control problem may be posed as a Markov Decision Problem (MDP). Dynamic Programming(DP) provides the optimal policy to the MDP. However, because of the "curse of dimensionality" of DP, finding the optimal policy is not practical in many applications. For a perimeter surveillance problem with two robots and five UGS locations, the number of states is of the order of billions. Approximate Dynamic Programming (ADP) via Linear Programming (LP) provides a way to approximate the value function and derive sub-optimal strategies. Using state partitioning and ADP, this dissertation provides different LP formulations for upper and lower bounds to the value function of the MDP, and shows the relationship between LPs and MDP. The novel features of this dissertation are (1) the derivation of a tractable lower bound via LP and state partitioning, (2) the construction of a sub-optimal policy whose performance exceeds the lower bound, and (3) the derivation of an upper bound using a non-linear programming formuation. The upper and lower bounds provides approximation ratio to the value function. Finally, illustrative perimeter surveillance examples corroborate the results derived in this dissertation.Item Quadratic programming with linear inequality constraints(Texas Tech University, 1969-08) Pore, Michael DavidThe least-squares method of optimization of quadratic functions is the most common and widely practiced. The exact procedure in matrix form, is described by Boot, p.25 [2]. Some of the merits of the least-squares method are discussed in [1]. This thesis discusses this least-squares method of optimization in several restricted cases. The matrix format is used throughout, and the less than full rank case (the matrix in the quadratic part of the objective function is of less than full rank) is of particular interest. It is taken up in Chapter II along with the case of linear restrictions.Item Robust algorithms for area and power optimization of digital integrated circuits under variability(2008-12) Mani, Murari, 1981-; Orshansky, MichaelAs device geometries shrink, variability of process parameters becomes pronounced, resulting in a significant impact on the power and timing performance of integrated circuits. Deterministic optimization algorithms for power and area lack capabilities for handling uncertainty, and may lead to over-conservative solutions. As a result, there is an increasing need for statistical algorithms that can take into account the probabilistic nature of process parameters. Statistical optimization techniques however suffer from the limitation of high computational complexity. The objective of this work is to develop efficient algorithms for optimization of area and power under process variability while guaranteeing high yield. The first half of the dissertation focuses on two design-time techniques: (i) a gate sizing approach for area minimization under timing variability; (ii) an algorithm for total power minimization considering variability in timing and power. Design-time methods impose an overhead on each instance of the fabricated chip since they lack the ability to react to the actual conditions on the chip. In the second half of the dissertation we develop joint design-time and post-silicon co-optimization techniques which are superior to design-time only optimization methods. Specifically, we develop (i) a methodology for optimization of leakage power using design-time sizing and post silicon tuning using adaptive body bias; (ii) an optimization technique to minimize the total power of a buffer chain while considering the finite nature of adaptability afforded. The developed algorithms effectively improve the overconservatism of the corner-based deterministic algorithms and permit us to target a specified yield level accurately. As the magnitude of variability increases, it is expected that statistical algorithms will become increasingly important in future technology generations.Item Selection of the design matrix in linear models(Texas Tech University, 1969-05) Reynolds, Roy FarestNot availableItem Smooth Empirical Bayes Estimation of Observation Error Variances in Linear Systems(Texas Tech University, 1971-12) Lian, Mingwei GeorgeNot Available.Item Use of linear programming in least cost ration formulations.(Texas Tech University, 1974-08) Thompson, Phillip VincentNot available