The main goal is to develop decision policies for individual forest stand management. It addresses three major areas of interest in the optimal management of individual forest stands: incorporating a two-species growth and yield model into a single stand management model, incorporating a comprehensive list of management options into a single stand management model, and incorporating uncertainty into a single stand management model. Dynamic programming (DP) is a natural framework to study forest management with uncertainty. The forest stand management problem, as modelled in this thesis, has a large dimensional state space with a mix of discrete and continuous state variables. The DP model used to study this problem is solved by value iteration with the objective of understanding infinite horizon policies. However, since some of the state variables are continuous, all states can’t be examined in an attempt to create the cost-to-go function. Therefore, the cost-to-go function value is calculated at a given stage of the algorithm at a finite set of state points and then the cost-to-go values are approximated on the continuous portion of the state space using a continuous function. All of this is done with random processes impacting state transitions. With the mixed-species growth model developed in this thesis, a comprehensive list of management options can be incorporated into the DP model and, with the addition of uncertainty from sources such as market prices and natural disasters, near optimal stand management policies are developed. Solving the DP model with the required level of detail lead to the development of insight into function fitting on continuous state spaces and to the development of cost-to-go function approximation bounds. Studying the policies shows that the addition of uncertainty to the model captures the dynamics between market prices and stand definitions, and leads to policies that are better suited to decision making in a stochastic environment, when compared with policies that are developed with a deterministic model. Enough precision is built into the DP model to give answers to typical questions forest managers would ask.

Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 197-202). / Also available by subscription via World Wide Web / xi, 202 leaves, bound ill. 29 cm

Thesis (Ph. D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1985. / Includes bibliographical references.

Thesis (Ph. D.)--University of New South Wales, 2004. / Also available online.

Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 197-202).

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xxi, 200 p.; also includes graphics. Includes bibliographical references (p. 194-200). Available online via OhioLINK's ETD Center.

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Computer Science, 2009. / Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

In the past few years, there has been a strong and growing interest in evaluating the expected behavior of what we call combinatorial bin packing problems. A combinatorial bin packing problem consists of a number of items of various sizes and value ratios (value per unit of size) along with a collection of bins of fixed capacity into which the items are to be packed. The packing must be done in such a way that the sum of the sizes of the items into a given bin does not exceed the capacity of that bin. Moreover, an item must either be packed into a bin in its entirety or not at all: this "all or nothing" requirement is why these problems are characterized as being combinatorial. The objective of the packing is to optimize a given criterion Junction. Here optimize means either maximize or minimize, depending on the problem. We study two problems that fit into this framework: the Knapsack Problem and the Minimum Sum of Squares Problem. Both of these problems are known to be in the class of NP-hard problems and there is ample reason to suspect that these problems do not admit of efficient exact solution. We obtain results concerning the performance of heuristics under the assumption that the inputs are random samples from some distribution. For the Knapsack Problem, we develop four heuristics, two of which are on-line and two off-line. All four heuristics are shown to be asymptotically optimal in expectation when the item sizes and value ratios are assumed to be independent and uniform. One heuristic is shown to be asymptotically optimal in expectation when the item sizes are uniformly distributed and the value ratios are exponentially distributed. The amount of time required by these heuristics is no more than proportional to the amount of time required to sort the items in order of nonincreasing value ratios. For the Minimum Sum of Squares Problem, we develop two heuristics, both of which are off-line. Both of these heuristics are shown to be asymptotically optimal in expectation when the sizes of the items input are assumed uniformly distributed.

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