This dissertation presents various aspects of the solution of the linear multi-period stochastic programming problem. Under relatively mild assumptions on the structure of the random variables present in the problem, the value function at every time stage is shown to be jointly convex in the history of the process, namely the random variables observed so far as well as the decisions taken up to that point. Convexity enables the construction of both upper and lower bounds on the value of the entire problem by suitable discretization of the random variables. These bounds are developed in Chapter 2, where it is also demonstrated how the bounds can be made arbitrarily sharp if the discretizations are chosen sufficiently fine. The chapter emphasizes computability of the bounds, but does not concern itself with finding the discretizations themselves. The practise commonly followed to obtain a discretization of a random variable is to partition its support, usually into rectangular subsets. In order to apply the bounds of Chapter 2, one needs to determine the probability mass and weighted centroid for each element of the partition. This is a hard problem in itself, since in the continuous case it amounts to a multi-dimensional integration. Chapter 3 describes some Monte-Carlo techniques which can be used for normal distributions. These methods require random sampling, and the two main issues addressed are efficiency and accuracy. It turns out that the optimal method to use depends somewhat on the probability mass of the set in question. Having obtained a suitable discretization, one can then solve the resulting large scale linear program which approximates the original problem. Its constraint matrix is highly structured, and Chapter 4 describes one algorithm which attempts to utilize this structure. The algorithm uses the Dantzig-Wolfe decomposition principle, nesting decomposition levels one inside the other. Many of the subproblems generated in the course of this decomposition share the same constraint matrices and can thus be solved simultaneously. Numerical results show that the algorithm may out-perform a linear programming package on some simple problems. Chapter 5, finally, combines all these ideas and applies them to a problem in forest management. Here it is required to find logging levels in each of several time periods to maximize the expected revenue, computed as the volume cut times an appropriate discount factor. Uncertainty enters into the model in the form of the risk of forest fires and other environmental hazards, which may destroy a fraction of the existing forest. Several discretizations are used to formulate both upper and lower bound approximations to the original problem. / Business, Sauder School of / Graduate

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Fjärrvärmebranschen i Sverige har sedan mitten av 1990-talet varit i en stagnationsfas, där mängden producerad och förbrukad energi i stort sett varit konstant, trots stora investeringar i fjärrvärmenätet. Samtidigt har den höga andelen återvinning gjort att det råder brist på avfallsbränsle till energiåtervinning i Sverige. I kombination med hög konkurrens om avfallsbränslet har detta medfört att aktörerna på marknaden tvingats se sig om efter nya vägar att tillfredsställa behovet av bränsle, vilket lett till att det idag importeras stora mängder avfall för energiåtervinning från utlandet. Vid Vattenfalls fjärrvärmeverk i Uppsala har det mellan åren 2006-2013 återvunnits i snitt drygt 360 000 ton avfall per år. En stor del av detta hämtas in från lokala kunder, både kommuner och privata aktörer, men man har på senare tid även behövt börja importera avfall för att tillfredsställa energibehovet. Vattenfall i Uppsala har valt att framför allt rikta blickarna mot de brittiska öarna, varifrån avfall levereras med fartyg till hamnen i Hargshamn. Anläggningen består av tre förbränningsugnar, block 1, 4 och 5, där block 1 och 4 har en gemensam bunker där avfall förvaras innan förbränning, och den nyare block 5 har en egen bunker. I detta arbete har ett planeringsverktyg skapats i Microsoft Excel. Planeringsverktyget, Fuel Logistics Optimal Planner (FLOP), använder linjärprogrammering för att generera en optimal avfallsblandning som givet ugnarnas effekt maximerar anläggningens intäkter från kunderna. Det ger även svar på frågorna i vilken bunker en given kund ska tippa sitt avfall en given vecka, ger en optimal lagernivå för lagret i Hargshamn, samt information om under vilka veckor båtar med avfall bör anlända hamnen. FLOP stöttar logistikansvarige vid anläggningen i arbetet att skapa en veckoplanering som ligger till grund för hur mycket avfall som ska beställas från de individuella kunderna under nästkommande vecka. En jämförelse mot planeringen och utfallet för 2013 visar att FLOP genererar 2,97 % högre intäkter än den tidigare planeringen, och 0,17 % högre intäkter gentemot det verkliga utfallet för året. Detta trots att en ugn, block 3, togs ur bruk under året och således inte används i FLOP. Under 2013 stod block 3 för ungefär 3,4 % av all förbränning som skedde vid anläggningen. / The first district heating-system in Sweden was implemented in the city of Karlstad in 1948 and the favorable environment for this technology lead to a quick expansion that lasted all the way to the mid 1990’s. Since then, however, the industry has stagnated due to climate change, an increase in energy efficient buildings and market saturation. This has led to the need for new strategies for the parties involved with district heating. In Sweden, many of the incinerators used for district heating use waste fuel as the main fuel source. The increased recycling of mainly household waste and the high competition on the waste incineration market has forced the affected parties to look abroad for waste fuel. Vattenfall’s waste incineration plant in Uppsala uses waste fuel and peat as main fuel for the incinerators, and between the years 2006-2013 the average annual amount of waste fuel incinerated amounted to around 360 000 metric tons. There are three incinerators, block 1, 4 and 5, connected to two bunkers storing waste fuel. Blocks 1 and 4 get their fuel from one bunker, and the newer block 5 has its own bunker attached. From the bunkers, the fuel is distributed to the incinerators by an overhead crane. The fuel is brought in from local customers at the customer’s expense for energy recovery. On top of this, Vattenfall also owns a storage facility in Hargshamn, to which it imports waste fuel from customers predominantly from the British Isles. Vattenfall then transports this waste fuel to the incineration plant whenever there is a shortage of fuel from local customers. Today, the logistics manager at the facility receives a yearly plan of all the local, contracted customers with information on how much waste each individual customer should deliver each month of the year. Every week, the logistics manager then breaks down this plan into a weekly plan, before sending out an order to each customer detailing how much waste they are expected to deliver during the subsequent week. The customers then deliver the specified amount of waste and tip it into either of the two bunkers at the facility. If one bunker is being utilized more than the other, the operators of the overhead cranes can signal to the drivers of the waste fuel trucks not to use that bunker for the time being. It is also up to the operators to make sure they feed the incinerators with an appropriate mix of fuel to keep the incinerators operating at a suitable rate. In this work, we have created a planning tool, Fuel Logistics Optimal Planner (FLOP), using Microsoft Excel and the OpenSolver add-in to yield an optimal fuel mix in the respective bunkers in regard to maximizing the overall revenue from the customers. FLOP also presents the user with an optimal storage level of waste fuel at the storage facility in Hargshamn, and informs the logistics manager about which weeks new shipments of waste fuel should arrive at the warehouse. A linear programming model was created to answer these questions. The model is based on the blending problem to get the optimal waste fuel mix to the bunkers, but it has also been influenced by the inventory management problem to make sure the storage level in Hargshamn is optimal. Backtesting FLOP against the planned and actual revenue of 2013 shows that FLOP increases the planned revenue by 2.97 % and surpasses the actual revenue by 0.17 %. During parts of 2013 a fourth incinerator, block 3, was operative at the plant, responsible for about 3.4 % of the total weight of waste incinerated. This incinerator has been omitted in the comparison.

The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-sparse linear system solution technique, efficient approaches to updating LU factors and sophisticated dual simplex pivoting rules. These techniques, some of which are novel, lead to serial performance which is comparable with the best public domain dual simplex solver, providing a solid foundation for the simplex parallelization. During the implementation of the sequential dual simplex solver, the study of classic LU factor update techniques leads to the development of three novel update variants. One of them is comparable to the most efficient established approach but is much simpler in terms of implementation, and the other two are specially useful for one of the parallel simplex solvers. In addition, the study of the dual simplex pivoting rules identifies and motivates further investigation of how hyper-sparsity maybe promoted. In parallel, two high performance simplex solvers are designed and developed. One approach, based on a less-known dual pivoting rule called suboptimization, exploits parallelism across multiple iterations (PAMI). The other, based on the regular dual pivoting rule, exploits purely single iteration parallelism (SIP). The performance of PAMI is comparable to a world-leading commercial simplex solver. SIP is frequently complementary to PAMI in achieving speedup when PAMI results in slowdown.

During the 2005 North Atlantic hurricane season, an objective tropical cyclone vortex identification and tracking technique was applied to analyzed and forecast fields of three global operational numerical models- the National Centers for Environmental Prediction Global Forecast System (GFS), the Navy Operational Global Atmospheric Prediction System (NOGAPS), and the United Kingdom Meteorological Office model (UKMET). For the purpose of evaluating each model's performance with respect to forecasting tropical cyclone formation, 14 relevant parameters are cataloged for every tropical vortex. In this study, nine of the fourteen parameters are subjected to a linear discriminant analysis applied to all forecast vortices that exceed vorticity and warm core thresholds. The goal is to determine the combination of parameters for each model, at each 12-h forecast period to 120h, that best discriminates between a vortex that is correctly forecast to intensify into a tropical cyclone (developer) and a vortex that is forecast to intensify into a tropical cyclone, but does not (false alarm). The performance of the resulting discriminant functions are then assessed using the Heidke Skill Score and Receiver Operating Characteristic curves. Overall, the methodology applied to forecasts from the UKMET model shows the most skill with regard to identifying correct forecasts of tropical cyclone formation. / US Navy (USN) author.

This thesis examines linear programming problems, the theoretical foundations of the simplex method, and how a liner programming problem can be solved with the simplex method.

Master of Science / Department of Electrical and Computer Engineering / Anil Pahwa / Due to the ongoing changes in the structure of the electricity markets, distribution networks have developed an appealing potential for housing distributed generation (DG). In order to make the most out of the present distribution network, this project report verifies the results and method developed in a paper (Optimal Allocation of Embedded Generation on Distribution Networks) by A. Kean and M. O’Malley, which discusses an efficient way of incorporating DG in the current power system. The methodology under consideration elaborates on how certain constraints should be adopted that will lead toward optimally sizing and placing DG in the network under examination. Along with that, the effect of voltage rise and short circuit current are observed which shows that a certain allocation to some buses will cause a sudden rise in voltage and short circuit levels throughout the network. Furthermore, the adopted methodology with its relative constraints is solved using linear programming. Linear programming provides a more accurate allocation than its heuristic counterparts when it comes to embedding DG in smaller networks. The adopted methodology is then applied to a section of the Irish rural distribution network and the results pinpoint that appropriate placement of the DG will pave the way toward higher levels of penetration. The results obtained showed the same pattern as those recorded in the aforementioned source paper, there were only minor differences that are the result of using different software’s than those that were used by the authors of the paper.

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Original typescript. / Digitized by Kansas Correctional Industries

Typescript. / Digitized by Kansas Correctional Industries