This dissertation has three contributions in the area of path planning for Unmanned Aerial Vehicle (UAV) Search And Track (SAT) missions. These contributions are: (a) the study of a novel metric, G, used to quantify the value of the target information gained during a search and track mission, (b) an optimal planning horizon that minimizes time-error of a planning horizon when interrupted by Poisson random events, and (c) a modified Particle Swarm Optimization (PSO) algorithm for search missions that uses the prior target distribution in the generation of paths rather than just in the evaluation of them. UAV route planning is an important topic with many applications. Of these, military applications are the best known. This dissertation focuses on route planning for SAT missions that jointly optimize the conflicting objectives of detecting new targets and monitoring previously detected targets. The information theoretic approach proposed here is different from and is superior to existing approaches. One of the main differences is that G quantifies the value of the target information rather than the information itself. Several examples are provided to highlight G’s desirable properties. Another important component of path planning is the selection of a planning horizon, which specifies the amount of time to include in a plan. Unfortunately, little research is available to aid in the selection of a planning horizon. The proposed planning horizon is derived in the context of plan updates triggered by Poisson random events. To our knowledge, it is the only theoretically derived horizon available making it an important contribution. While the proposed horizon is optimal in minimizing planning time errors, simulation results show that it is also near optimal in minimizing the average time needed to capture an evasive target. The final contribution is the modified PSO. Our modification is based on the idea that PSO should be provided with the target distribution for path generation. This allows the algorithm to create candidate path plans in target rich regions. The modified PSO is studied using a search mission and is used in the study of G.

In this thesis, we study a series of closely related multi-stage stochastic programming models in production planning, from both a modeling and an algorithmic point of view. We first consider a very simple multi-stage stochastic lot-sizing problem, involving a single item with no fixed charge and capacity constraint. Although a multi-stage stochastic integer program, this problem can be shown to have a totally unimodular constraint matrix. We develop primal and dual algorithms by exploiting the problem structure. Both algorithms are strongly polynomial, and therefore much more efficient than the Simplex method. Next, motivated by applications in semiconductor tool planning, we develop a general capacity planning problem under uncertainty. Using a scenario tree to model the evolution of the uncertainties, we present a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier two-stage approaches, the multi-stage model allows for revision of the capacity expansion plan as more information regarding the uncertainties is revealed. We provide analytical bounds for the value of multi-stage stochastic programming over the two-stage approach. By exploiting the special simple stochastic lot-sizing substructure inherent in the problem, we design an efficient approximation scheme and show that the proposed scheme is asymptotically optimal. We conduct a computational study with respect to a semiconductor-tool-planning problem. Numerical results indicate that even an approximate solution to the multi-stage model is far superior to any optimal solution to the two-stage model. These results show that the value of multi-stage stochastic programming for this class of problem is extremely high. Next, we extend the simple stochastic lot-sizing model to an infinite horizon problem to study the planning horizon of this problem. We show that an optimal solution of the infinite horizon problem can be approximated by optimal solutions of a series of finite horizon problems, which implies the existence of a planning horizon. We also provide a useful upper bound for the planning horizon.

The purpose of this thesis is to develop a model that will guide a company towards a decision of whether to change the current due date of work orders or not. The model will help the company to reveal the technical and financial factors that will be affected and how these factors can be assessed. After accomplishing a thorough literature review, we found no existing practical models in this specific area. We developed a model to cover this gap in the existing theories. A case study approach was used to test the developed model on our case company Elitfönster in Lenhovda who manufactures windows. We applied our model at the processing department and the change concerned going from a weekly to a daily due date of work orders. The technical factors that would be affected by the change of the due date are; setup times, lead time and output of components. The financial factors that will be affected are the tied-up capital and the manning. We found that a change could not be carried through without a purchase of an extra plane. The model also showed that the financial benefits that the change generated could not surpass the costs that an extra plane would cause. Thereby, our recommendations to the case company are to keep the current due date of work orders until the rest of the company can handle the extra components that can be produced after the change. / Syftet med denna uppsats är att utveckla en modell som ska vägleda ett företag mot ett beslut om man ska ändra den nuvarande tidpunkt när en arbetsorder ska vara färdigställd, eller inte. Modellen kommer att hjälpa företaget att påvisa de tekniska och finansiella faktorer som kommer att påverkas och hur dessa kan bedömas. Efter att ha gjort en grundlig litteraturstudie kunde vi inte hitta några existerande modeller inom detta specifika område. Vi utvecklade en modell för att täcka denna brist i den existerande teorin. Vi använde oss av en fallstudie för att testa vår utvecklade modell på Elitfönster i Lenhovda som tillverkar fönster. Vi applicerade vår modell på maskinverkstaden och förändringen handlade om att gå från att färdigställa arbetsorder på en vecka till att färdigställa dem på en dag. De tekniska faktorer som skulle påverkas av en förändring är; ställtiderna, ledtiden och mängden producerade komponenter. De finansiella faktorerna som kommer att påverkas är mängden bundet kapital samt bemanningen. Vi kom fram till att en förändring inte kunde genomföras utan att köpa in en extra hyvel. Modellen visade också att de finansiella fördelarna som en förändring skulle generera inte skulle motsvara de kostnader som den extra hyveln skulle orsaka. Våra rekommendationer till företaget är således att fortsätta med den nuvarande tidpunkt när en arbetsorder ska vara färdigställd tills resten av företaget kan hantera de extra komponenter som skulle kunna bli producerade efter förändringen.

<p>The purpose of this thesis is to develop a model that will guide a company towards a decision of whether to</p><p>change the current due date of work orders or not. The model will help the company to reveal the technical and</p><p>financial factors that will be affected and how these factors can be assessed. After accomplishing a thorough</p><p>literature review, we found no existing practical models in this specific area. We developed a model to cover this</p><p>gap in the existing theories. A case study approach was used to test the developed model on our case company</p><p>Elitfönster in Lenhovda who manufactures windows. We applied our model at the processing department and the</p><p>change concerned going from a weekly to a daily due date of work orders. The technical factors that would be</p><p>affected by the change of the due date are; setup times, lead time and output of components. The financial</p><p>factors that will be affected are the tied-up capital and the manning. We found that a change could not be carried</p><p>through without a purchase of an extra plane. The model also showed that the financial benefits that the change</p><p>generated could not surpass the costs that an extra plane would cause. Thereby, our recommendations to the</p><p>case company are to keep the current due date of work orders until the rest of the company can handle the extra</p><p>components that can be produced after the change.</p> / <p>Syftet med denna uppsats är att utveckla en modell som ska vägleda ett företag mot ett beslut om man ska</p><p>ändra den nuvarande tidpunkt när en arbetsorder ska vara färdigställd, eller inte. Modellen kommer att hjälpa</p><p>företaget att påvisa de tekniska och finansiella faktorer som kommer att påverkas och hur dessa kan bedömas.</p><p>Efter att ha gjort en grundlig litteraturstudie kunde vi inte hitta några existerande modeller inom detta specifika</p><p>område. Vi utvecklade en modell för att täcka denna brist i den existerande teorin. Vi använde oss av en</p><p>fallstudie för att testa vår utvecklade modell på Elitfönster i Lenhovda som tillverkar fönster. Vi applicerade vår</p><p>modell på maskinverkstaden och förändringen handlade om att gå från att färdigställa arbetsorder på en vecka</p><p>till att färdigställa dem på en dag. De tekniska faktorer som skulle påverkas av en förändring är; ställtiderna,</p><p>ledtiden och mängden producerade komponenter. De finansiella faktorerna som kommer att påverkas är</p><p>mängden bundet kapital samt bemanningen. Vi kom fram till att en förändring inte kunde genomföras utan att</p><p>köpa in en extra hyvel. Modellen visade också att de finansiella fördelarna som en förändring skulle generera</p><p>inte skulle motsvara de kostnader som den extra hyveln skulle orsaka. Våra rekommendationer till företaget är</p><p>således att fortsätta med den nuvarande tidpunkt när en arbetsorder ska vara färdigställd tills resten av företaget</p><p>kan hantera de extra komponenter som skulle kunna bli producerade efter förändringen.</p>

We consider a class of periodic preventive maintenance (PM) optimization problems, for a single piece of equipment that deteriorates with time or use, and can be repaired upon failure, through corrective maintenance (CM). We develop analytical and simulation-based optimization models that seek an optimal periodic PM policy, which minimizes the sum of the expected total cost of PMs and the risk-averse cost of CMs, over a finite planning horizon. In the simulation-based models, we assume that both types of maintenance actions are imperfect, whereas our analytical models consider imperfect PMs with minimal CMs. The effectiveness of maintenance actions is modeled using age reduction factors. For a repairable unit of equipment, its virtual age, and not its calendar age, determines the associated failure rate. Therefore, two sets of parameters, one describing the effectiveness of maintenance actions, and the other that defines the underlying failure rate of a piece of equipment, are critical to our models. Under a given maintenance policy, the two sets of parameters and a virtual-age-based age-reduction model, completely define the failure process of a piece of equipment. In practice, the true failure rate, and exact quality of the maintenance actions, cannot be determined, and are often estimated from the equipment failure history. We use a Bayesian approach to parameter estimation, under which a random-walk-based Gibbs sampler provides posterior estimates for the parameters of interest. Our posterior estimates for a few datasets from the literature, are consistent with published results. Furthermore, our computational results successfully demonstrate that our Gibbs sampler is arguably the obvious choice over a general rejection sampling-based parameter estimation method, for this class of problems. We present a general simulation-based periodic PM optimization model, which uses the posterior estimates to simulate the number of operational equipment failures, under a given periodic PM policy. Optimal periodic PM policies, under the classical maximum likelihood (ML) and Bayesian estimates are obtained for a few datasets. Limitations of the ML approach are revealed for a dataset from the literature, in which the use of ML estimates of the parameters, in the maintenance optimization model, fails to capture a trivial optimal PM policy. Finally, we introduce a single-stage and a two-stage formulation of the risk-averse periodic PM optimization model, with imperfect PMs and minimal CMs. Such models apply to a class of complex equipment with many parts, operational failures of which are addressed by replacing or repairing a few parts, thereby not affecting the failure rate of the equipment under consideration. For general values of PM age reduction factors, we provide sufficient conditions to establish the convexity of the first and second moments of the number of failures, and the risk-averse expected total maintenance cost, over a finite planning horizon. For increasing Weibull rates and a general class of increasing and convex failure rates, we show that these convexity results are independent of the PM age reduction factors. In general, the optimal periodic PM policy under the single-stage model is no better than the optimal two-stage policy. But if PMs are assumed perfect, then we establish that the single-stage and the two-stage optimization models are equivalent. / text