Thesis (PhD (Logistics))--University of Stellenbosch, 2007. / In this dissertation original algorithms are introduced to solve separable resource allocation problems (RAPs) with increasing nonlinear functions in the objective function, and lower and upper bounds on each variable. Algorithms are introduced in three special cases. The first case arises when the objective function of the RAP consists of the sum of convex functions and all the variables for these functions range over the same interval. In the second case RAPs with the sum of convex functions in the objective function are considered, but the variables of these functions can range over different intervals. In the last special case RAPs with an objective function comprising the sum of convex and concave functions are considered. In this case the intervals of the variables can range over different values. In the first case two new algorithms, namely the fraction and the slope algorithm are presented to solve the RAPs adhering to the conditions of the case. Both these algorithms yield far better solution times than the existing branch and bound algorithm. A new heuristic and three new algorithms are presented to solve RAPs falling into the second case. The iso-bound heuristic yields, on average, good solutions relative to the optimal objective function value in faster times than exact algorithms. The three algorithms, namely the iso-bound algorithm, the branch and cut algorithm and the iso-bound branch and cut algorithm also yield considerably beter solution times than the existing branch and bound algorithm. It is shown that, on average, the iso-bound branch and cut algorithm yields the fastest solution times, followed by the iso-bound algorithm and then by die branch and cut algorithm. In the third case the necessary and sufficient conditions for optimality are considered. From this, the conclusion is drawn that search techniques for points complying with the necessary conditions will take too long relative to branch and bound techniques. Thus three new algorithms, namely the KL, SKL and IKL algorithms are introduced to solve RAPs falling into this case. These algorithms are generalisations of the branch and bound, branch and cut, and iso-bound algorithms respectively. The KL algorithm was then used as a benchmark. Only the IKL algorithm yields a considerable improvement on the KL algorithm.

Nesse trabalho, estudamos um problema de otimização combinatorial conhecido por Problema da Mochila Compartimentada, que é uma extensão do clássico Problema da Mochila. O problema consiste em determinar as capacidades adequadas de vários compartimentos que podem vir a ser alocados em uma mochila e como esses compartimentos devem ser carregados, respeitando as restrições de capacidades dos compartimentos e da mochila. Busca-se maximizar o valor de utilidade total. O problema é muito pouco estudado na literatura, apesar de surgir naturalmente em aplicações práticas. Nesse estudo, propomos uma modelagem matemática não linear para o problema e verificamos algumas heurísticas para sua resolução. / In this work, we studied a combinatorial optimization problem called the Clustered Knapsack Problem, that is an extension of the standard Knapsack Problem. The problem is to determine the right capacities of several clusters which can be allocated in a knapsack and how these clusters should be placed so as to respect the constraints on the capacities of the clusters and the knapsack. The objective is to maximize a total utility value. The problem has seldom been studied in the literature, even though it appears naturally in practical applications. In this study, we propose a non-linear model for the problem and we insert some heuristics for its resolution.

Uma revisão dos algoritmos e conjuntos de instâncias presentes na literatura do Problema da Mochila com Repetições (PMR) é apresentada nessa dissertação de mestrado. Os algoritmos e conjuntos de instâncias usados são brevemente descritos nesse trabalho, afim de que o leitor tenha base para entender as discussões. Algumas propriedades bem conhecidas e específicas do PMR, como a dominância e a periodicidade, são explicadas com detalhes. O PMR é também superficialmente estudado no contexto de problemas de avaliação gerados pela abordagem de geração de colunas aplicada na relaxação contínua do Bin Packing Problem (BPP) e o Cutting Stock Problem (CSP). Múltiplos experimentos computacionais e comparações são realizadas. Para os conjuntos de instâncias artificiais mais recentes da literatura, um simples algoritmo de programação dinâmica, e uma variante do mesmo, parecem superar o desempenho do resto dos algoritmos, incluindo aquele que era estado-da-arte. O modo que relações de dominância é aplicado por esses algoritmos de programação dinâmica têm algumas implicações para as relações de dominância previamente estudadas na literatura. O autor dessa dissertação defende a tese de que a escolha dos conjuntos de instâncias artificiais definiu o que foi considerado o melhor algoritmo nos trabalhos anteriores. O autor dessa dissertação disponibilizou publicamente todos os códigos e conjuntos de instâncias referenciados nesse trabalho. / A review of the algorithms and datasets in the literature of the Unbounded Knapsack Problem (UKP) is presented in this master's thesis. The algorithms and datasets used are brie y described in this work to provide the reader with basis for understanding the discussions. Some well-known UKP-speci c properties, such as dominance and periodicity, are described. The UKP is also super cially studied in the context of pricing problems generated by the column generation approach applied to the continuous relaxation of the Bin Packing Problem (BPP) and Cutting Stock Problem (CSP). Multiple computational experiments and comparisons are performed. For the most recent arti cial datasets in the literature, a simple dynamic programming algorithm, and its variant, seems to outperform the remaining algorithms, including the previous state-of-the-art algorithm. The way dominance is applied by these dynamic programming algorithms has some implications for the dominance relations previously studied in the literature. In this master's thesis we defend that choosing sets of arti cial instances has de ned what was considered the best algorithm in previous works. We made available all codes and datasets referenced in this master's thesis.

One of the most remarkable theories in probability and statistics is the law of large numbers. Law of large numbers describes the behavior of random phenomena when they are reiterated infinitely or in very large trials. Apart from the mathematical exposition of the law of large numbers, its theory and applications have been widely used in gambling houses, financial sectors, and healthcare insurance where uncertainties deteriorate prediction and financial strength. However, the applications of the law of large numbers are not confined to the referred sectors and could be widely applied to industrial organizations and service provider companies in which large number of stochastic phenomena incorporate in their planning. In this thesis, the applications of the law of large numbers are studied in relation to logistics and transportation under conditions of operating in large networks. The results of this study assert that transportation companies can benefit from operating in large networks to increase the filling performance of their vehicles, fleet, etc. Equivalently, according to the law of large numbers the inferior capacity utilization in unit loads, containers, etc. converges to 0 with probability 1 as the size of the network grows. / Uppsatsnivå: D

Modern routers use specialized hardware, such as Ternary Content Addressable Memory (TCAM), to solve the Longest Prefix Matching Problem (LPMP) quickly. Due to the fact that TCAM is a non-standard type of memory and inherently parallel, there are concerns about its cost and power consumption. This problem is exacerbated by the growth in routing tables, which demands ever larger TCAMs. To reduce the size of the TCAMs in a distributed forwarding environment, a batch caching model is proposed and analyzed. The problem of determining which routing prefixes to store in the TCAMs reduces to the In-tree Knapsack Problem (ITKP) for unit weight vertices in this model. Several algorithms are analysed for solving the ITKP, both in the general case and when the problem is restricted to unit weight vertices. Additionally, a variant problem is proposed and analyzed, which exploits the caching model to provide better solutions. This thesis concludes with discussion of open problems and future experimental work.

Modern routers use specialized hardware, such as Ternary Content Addressable Memory (TCAM), to solve the Longest Prefix Matching Problem (LPMP) quickly. Due to the fact that TCAM is a non-standard type of memory and inherently parallel, there are concerns about its cost and power consumption. This problem is exacerbated by the growth in routing tables, which demands ever larger TCAMs. To reduce the size of the TCAMs in a distributed forwarding environment, a batch caching model is proposed and analyzed. The problem of determining which routing prefixes to store in the TCAMs reduces to the In-tree Knapsack Problem (ITKP) for unit weight vertices in this model. Several algorithms are analysed for solving the ITKP, both in the general case and when the problem is restricted to unit weight vertices. Additionally, a variant problem is proposed and analyzed, which exploits the caching model to provide better solutions. This thesis concludes with discussion of open problems and future experimental work.

The purpose of this dissertation is to synthesize a methodology to prescribe a strategic design of a surveillance system to provide the required level of surveillance for ports and waterways. The method of approach to this problem is to formulate a linear integer programming model to prescribe a strategic surveillance system design (SSD) for ports or waterways, to devise branch-and-price decomposition (B

The classical multiple knapsack problem selects a set of items and assigns each to one of the knapsacks so as to maximize the total profit. The knapsacks have limited capacities. The cardinality constrained multiple knapsack problem assumes limits on the number of items that are to be put in each knapsack, as well. Despite many efforts on the classical multiple knapsack problem, the research on the cardinality constrained multiple knapsack problem is scarce. In this study we consider the cardinality constrained multiple knapsack problem. We propose heuristic and optimization procedures that rely on the optimal solutions of the linear programming relaxation problem. Our computational results on the large-sized problem instances have shown the satisfactory performances of our algorithms.

Thesis (Ph.D)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Dr. Dimitri N. Mavris; Committee Member: Dr. Brian J. German; Committee Member: Dr. Daniel P. Schrage; Committee Member: Dr. Frederic Villeneuve; Committee Member: Dr. Michelle R. Kirby; Committee Member: Ms. Antje Lembcke. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Knapsack problem has been widely studied in computer science for years. There exist several variants of the problem, with zero-one maximum knapsack in one dimension being the simplest one. In this thesis we study several existing approximation algorithms for the minimization version of the problem and propose a scaling based fully polynomial time approximation scheme for the minimum knapsack problem. We compare the performance of this algorithm with existing algorithms. Our experiments show that, the proposed algorithm runs fast and has a good performance ratio in practice. We also conduct extensive experiments on the data provided by Canadian Pacific Logistics Solutions during the MITACS internship program. We propose a scaling based e-approximation scheme for the multidimensional (d-dimensional) minimum knapsack problem and compare its performance with a generalization of a greedy algorithm for minimum knapsack in d dimensions. Our experiments show that the e- approximation scheme exhibits good performance ratio in practice. / x, 85 leaves ; 29 cm