We examine the Rayleigh–Bénard convection as modelled by the Boussinesq equation. Our aim is at deriving bounds for the heat enhancement factor in the vertical direction, the Nusselt number, which reproduce physical scalings. In the first part of the dissertation, we examine the the simpler model when the acceleration of the fluid is neglected (Pr=∞) and prove the non-optimality of the temperature background field method by showing a lower bound for the Nusselt number associated to it. In the second part we consider the full model (Pr<∞) and we prove a new upper bound which improve the existing ones (for large Pr numbers) and catches a transition at Pr~Ra^(1/3).

This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context. In the proof we make use of the Yosida approximation of maximal monotone operators to achieve stochastic differential equations which are solvable by a theorem of Krylov and Rozovskij [7]. The selection property is verified with certain properties of the considered set-valued maps. Concerning Lipschitz continuous set-valued diffusion terms, uniqueness holds. At last two examples for application are given.

Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.

<p>Cilj ovo rada je da obezbedi informacije o apstraktnim osobinama<br />klonova ko-operacija, mrezi klonova operacija, ali i ostalim objektima koji<br />prate pojam klona. U Uvodu je pokazano kako je nastao pojam ko-algebraske strukture. Kratko se razmatraju i dva pristupa ko-algebrama: Kleislijev, koji je potekao iz konteksta teorije kategorija [Kle 65], i Drbohlavov, koji je po osnovnoj ideji blizi<br />univerzalnoj algebri, i koji je usvojen u ovom radu. Glava 0 sadrzi spisak osnovnih pojmova i oznaka vezanih za skupove, preslikavanja, relacije, mreze i particije koji se koriste u celom radu, dok se u Glavama 1 i 2 uvode standardni termini teorije klonova operacija i ko-operacija i daje pregled poznatih rezultata. Originalni rezultati rada sadrzani su u Glavama 3&ndash;7. Glava 3 sadrzi osnovni rezultat rada. Pomocu kontravarijantnog liftinga kooperacija uspostavlja se izomorfizam izmedju klona svih ko-operacija skupa X s jedne strane i jednog posebnog klona operacija skupa P(X) sa druge strane. Pokazuje se da je isto preslikavanje ujedno i potapanje algebre kooperacija skupa X u algebru operacija skupa P(X) koja je standardna u teoriji klonova. Takodje se pokazuje da je kontravarijantni lifting klonova ujedno i izomorfizam mreze klonova ko-operacija skupa X i jednog glavnog ideala u mrezi klonova na P(X). Nakon ispitivanja lokalno ko-zatvorenih klonova ko-operacija pokazujemo u u kakvom odnosu stoje reprezentacije klonova ko-operacija selektivnim operacijama s jedne strane [Cs&acute;a 85], i operacijama na partitivnom skupu s druge strane. Reprezentaciju operacijama na partitivnom skupu, mada izomorfna jednom specijalnom slucaju reprezentacije selektivnim operacijama, smatramo bitnom, zato sto se njome klonovi ko-operacija smestaju u poznati ambijent skupovnih Booleovih algebri, umesto u prilicno opskuran prostor selektivnih operacija. U pretposlednjem odeljku se razmatra odnos klonova ko-operacija i klonova operacija kroz proces liftinga, sto je omoguceno cinjenicom da i kontravarijantni lifting klona svih ko-operacija i kovarijantni lifting klona svih operacija skupa X odredjuju klon operacija skupa P X. Na samom kraju ove pomalo dugacke glave se ispituju odnosi klonova ko-relacija i klonova relacija kroz prizmu monoida<br />transformacija. U Glavi 4 se izlazu neke osobine mreze klonova ko-operacija kao parcijalno uredjenog skupa. Opisani su intervali Int(M) za neke posebne monoide transformacija M. Pokazano je da u slucaju M = TX u mrezi klonova ko-operacijane postoji &ldquo;Burlova anomalija&rdquo; (ispitivanja kolapsirajucih monoida su, medjutim, odlozena do Glave 5). Nakon toga je predlozena jedna konstrukcija skupa nezavisnih ko-operacija na osnovu koje je dobijena donja granica za broj klonova ko-operacija na konacnom skupu i tacan broj klonova ko-operacija na beskonacnom skupu. Iako je dobijena donja granica prilicno neprecizna, na osnovu nje se sasvim jasno uocava &ldquo;veoma eksponencijalna priroda&rdquo; ovog broja. Ispitivanja jednog posebnog glavnog filtera mreze klonova ko-operacija nam daju gornju granicu za visinu mreze. Glava 5 je posve&acute;cena ispitivanjima maksimalnih klonova ko-operacija na kona-cnom skupu. Maksimalni klonovi ko-operacija su opisani u radu [Sz&acute;ek 89] kao skupovi operacija koji slabo cuvaju regularne familije skupova. Prvo se daje interpretacija ovog rezultata u terminima ko-relacija i pokazuje se da je ovakav opis najbolji moguci kada se u obzir uzme arnost dobijenih ko-relacija. Nakon toga se pokazuje da nijedan maksimalan klon nema Shefferovu ko-operaciju i daje se opis U&rdquo;&iexcl;1-maksimalnih klonova ko-operacija. Paznja se dalje prenosi na preseke maksimalnih klonova ko-operacija. Prvo se razmatraju preseci nekih parova maksimalnih klonova i pokazuje se da to ne mora uvek biti maksimalni klon, a kasnije se konstruiˇse potapanje mreze cLB1 &pound; : : : &pound; cLBk u mrezu cLX. Potom se pokazuje da je mreza cLX komplementirana, a na samom kraju se razmatraju kolapsirajuci klonovi ko-operacija i monoidi. Glava 6 je posvecena opisu minimalnih klonova ko-operacija i svih supminimalnih klonova ko-operacija koji nisu esencijalno unarni. Uvid u strukturu supminimalnih klonova omogucuje izvodjenje donje granice za visinu mreze klonova ko-operacija. Glava sadrzi i kratak komentar o asocijativnosti kooperacija. U Glavi 7 se razmatraju enumerativne osobine mreze klonova ko-operacija na troelementnom skupu, kao i nekih njenih pratecih objekata. Osim utvrdjivanja kardinalnosti mreze na skupu f0; 1; 2g, odredjena je njena visina, kao<br />i svi submaksimalni klonovi. Poseban odeljak je posvecen enumeraciji baz&macr;a<br />klona svih ko-operacija i svih maksimalnih klonova, klasicnoj temi u teoriji<br />klonova. U dodacima su navedene tabele kojima se sumarizuju rezultati ove<br />glave i dat je opis jednostavnog softverskog alata koji ima ulogu &ldquo;raˇcunarskog<br />atlasa&rdquo; mreˇze cL3. S obzirom da mreza ima previse elemenata da bi se mogao<br />dati njen Hasse dijagram, &ldquo;racunarski atlas&rdquo; se pokazao kao najjednostavniji<br />i najefikasniji nacin da se dodje do informacija o mrezi. Napomenimo da su mnogi rezultati u ovom radu dobijeni uopstavanjem osobina mreze koje su otkrivene &ldquo;prelistavanjem atlasa&rdquo;. Navedimo kao primer strukturu U&rdquo;&iexcl;1- maksimalnih klonova, gornju i donju granicu za visinu mreze, cinjenicu da je mreza komplementirana, kao i to da maksimalni klonovi nemaju Shefferovu ko-operaciju.</p> / <p>The aim of this thesis is to provide information on abstract properties of clones of co- operations, the lattice of clones of co-operations and other accompanying objects.&nbsp; Introduction to the thesis demonstrates in short the genesis of concepts of co-operation and co-algebra and presents two approaches to the topic: the Kleisli&nbsp; approach which originated in the category theory, and the approach<br />of Drbohlav which is more in the spirit of universal algebra and which is adopted in the thesis.<br />Chapter 0 is a short display of standard set-theoretic terminology and notation which is used in the thesis.<br />Chapters 1 and 2 present standard notions of theory of clones of operations and co-operations, respectively. They contain lists of the most important known results. The original contribution of this thesis is contained in Chapters 3&ndash;7.<br />Chapter 3 contains the basic result of the thesis. By means of contravariant lifting of co-operations we establish an isomorphism between the clone&nbsp; of all co-operations on a set X and one special clone of operations on the set P(X). This isomorphism is not only the abstract clone isomorphism, but also a lattice isomorphism between the lattice of all clones of co-operations on X and a principal ideal in the lattice of all clones of operations on P(X). The same mapping is an embedding of the algebra of co-operations on X into the algebra of operations on P(X). Locally co-closed clones of operations are also characterised via this most useful mapping. Representation of clones of co-operations by operations on the powerset is compared to the representation by selective operations. Although isomorphic to a special case of the representation by selective operations, representation by operations on the powerset is highly important because it places clones of co-operations into a familiar setting of set-theoretic Boolean algebras, rather then in the quite obscure setting of selective algebras. At the end of this lengthy chapter, we investigate the relationship of corresponding liftings of the clone of all operations and the clone of all co-operations, and ellaborate the lifting proces and the interplay between description of transformation monoids by relations and co-relations.<br />Chapter 4 exibits some order-theoretic properties of the lattice of clones of co-operations. Intervals of the form Int(M) are described for some special transformation monoids M. In case M = TX it is demonstrated that the socalled &ldquo;Burle anomaly&rdquo; does not occur in the lattice of clones of co-operations. The investigation of collapsing clones and monoids is, however, deferred until&nbsp; Chapter 5. After that a construction of an independent set of co-operations is presented, based on which a lower bound for the number of clones of cooperations is obtained. Although pretty rough, this lower bound shows that the number of clones of co-operations on a finite set is of a &ldquo;very exponental nature&rdquo;. The number of clones of operations on an infinite set is also obtained. The investigations of a particular principal filter of the lattice provide an upper bound for the height of the lattice. Chapter 5 is devoted to the investigation of maximal clones of co-operations on a finite set. All the maximal clones of co-operations are described in [Sz&acute;ek 89] in terms of regular families. We first reinterpret that result in terms of co-relations and show that the description is the best possible as far as arities of co-relations involved are considered. After that we supply some more information on the maximal clones. We show that no maximal clone of co-operations has a Sheffer co-operation and describe clones covered by U&rdquo;&iexcl;1.<br />Then we turn to intersections of maximal clones of co-operations. First we consider intersections of some special pairs of maximal clones and show that in some cases this is not a maximal clone. As for the intersection of several maximal clones of co-operations, we show how to embed cLB1 &pound; : : : &pound; cLBk<br />in cLX. Using results on the structure of maximal clones we show that the lattice cLX is complemented. The chaptr ends with a note on collapsing clones of co-operations.<br />Chapter 6 provides the description of minimal clones of co-operations and those supminimal clones of co-operations which are not essentially unary. The structure of supminimal clones of co-operations provides a lower bound for the height of the lattice of clones of co-operations. As a spin-off, there is<br />a brief discussion on associativity.<br />Chapter 7 is devoted to enumerations of various objects connected to the lattice of clones of co-operations on a three element set. Besides the enumeration of the lattice itself, the submaximal clones have been listed and the height of the lattice on a three element set is determined. A separate section deals with a classical clone-theoretic topic of enumerating the bases for the clone of all co-operations and for the maximal clones of co-operations. The Appendices to this chapter contain some tables that summarize various enumerations, as well as a description of a modest software tool that palys the role of the &ldquo;computer atlas&rdquo; of cL3. Since the lattice has too many elements to be drawn explicitely, this was the simplest and the most efficient way to handle it. Let us remark that many results of this thesis were obtained by gathering the information on the particular case from the &ldquo;computer atlas&rdquo;<br />and by generalisation, such as: the structure of U&rdquo;&iexcl;1 maximal clones, the bounds for the height of the lattice, the fact that maximal clones have noSheffer co-operation and the fact that cLX is complemented.</p>

In Sweden, the rock mass is commonly used for construction of tunnels and caverns. The rockmass is also used as a foundation for large structures such as bridge abutments and dams. Forthese structures, the understanding of the rock mechanical properties play a key role for reachingan acceptable safety level and minimizing cost. One of the properties that has a high uncertaintyis the shear strength of rock joints. These rock joints constitute the weakest link in the rock massand often govern it´s strength. The uncertainty lies in the amount of factors that affect the shearstrength such as the degree of weathering, the matedness, the roughness of the surface and thescale. Various authors have tried to develop a failure criterion that can predict the peak shearstrength of rock joints and takes into account the influence of the various factors.The aim of this thesis is to evaluate the ability of the newly developed Casagrande et al.criterion to determine the peak shear strength for perfectly mated and natural rock joints withdifferent degrees of matedness. All samples analyzed in this thesis have been scanned andcustomized to run in the programmed version of the Casagrande et al. criterion. This iterativeprocess will stop as the application reach the apparent dip angle where the total shearing force issmaller than the total sliding force. This angle combined with the basic friction angle gives thepeak friction angle for calculations of the peak shear strength.The result show that the Casagrande et al. criterion can predict the peak shear strength forperfectly mated joint. However, for the natural rock joint, as the degree of matedness decreases,the accuracy of the prediction of the peak shear strength decreases. The conclusion of this studyis that the Casagrande’s criterion cannot determine the peak shear strength of natural rock jointsand that further development of the Casagrande et al. criterion is needed taking this parameterinto account. / Sverige är berg ett vanligt material för byggande av tunnlar och bergrum. För dessakonstruktioner spelar bergegenskaperna en nyckelroll för att nå en acceptabel säkerhetsnivåoch minimera kostnaden. En av de egenskaper som har stor osäkerhet är skjuvhållfastheten förbergsprickor. Osäkerheten ligger i de många faktorer som påverkar skjuvhållfastheten, såsomgraden av vittring, passning, ytans råhet och skala. Olika författare har försökt att anpassa ettbrottkriterium för bergsprickor som tar hänsyn till faktorernas inflytande och som kan användastill att uppskatta den maximala skjuvhållfastheten.Syftet med detta examensarbete är att utvärdera förmågan hos det nyligen utveckladebrottkriteriet av Casagrande et al. att bestämma den maximala skjuvhållfastheten för perfektpassade sprickor och naturliga sprickor med olika grad av passning. Alla prover i detta arbetehar skannats in och anpassats för att köras i den programmerade algoritmen som beräknar denmaximala skjuvhållfastheten enligt kriteriet av Casagrande et al.. Kriteriet använder sig av eniterativ process som pågår tills algoritmen når den vinkel där den totala skjuvkraften är mindreän den totala glidkraften. Denna vinkel kombinerad med sprickans basfriktionsvinkeln ger denmaximala friktionsvinkeln för beräkning av skjuvhållfastheten.Resultaten visar att Casagrande et al. kan förutspå den maximala skjuvhållfastheten förperfekt passade sprickor. När passningsgraden minskar för naturliga bergsprickor minskar kriterietsförmåga att prediktera den maximala skjuvhållfastheten. Slutsatsen från detta arbete äratt kriteriet av Casagrande et al. kan prediktera skjuvhållfastheten för perfekt passade sprickormen saknar förmågan att beakta inverkan från passning, vilket leder till att skjuvhållfasthetenöverskattas om kriteriet användas på naturliga sprickor som inte är perfekt passade. Fortsattforskning krävs för att vidareutveckla kriteriet så att graden av passning kan beaktas.

When the low voltage electric grid is dimensioned electric loads are predicted by analyzing the area by certain factors such as geographical data, customer type, heating method etc. So far, the charging of Plugin Electric Vehicles (PEVs) is not considered as one of these factors. Approximately 30% of the distribution grid in Sweden is projected to need reinforcements due to the increased loads from PEVs during winters if the charging isn’t controlled. In addition to this Stockholm face the problem of capacity shortage from the transmission grid, limiting the flow of electricity into the city. This research is therefore conducted to analyze the impact that the increase of PEVs will have on the distribution grid in the future. This thesis simulates the electric grid for three substations located in Hammarby Sjöstad by using power flow analysis and electric grid data from 2016. To approach this problem a method to disaggregate the total power consumption per substation into power consumption responding to each building was developed. In addition to this the number of PEVs in the future was projected. Nine different scenarios were used to compare different outcomes for the future, namely the years of 2025 and 2040. In order to simulate the worst possible case for the electric grid all the PEVs were assumed to be charged at the same time, directly when arriving home on the Sunday when the power demand peaks in 2016. The results indicate that PEVs can have a considerable impact on the components of the low voltage distribution network and controlled charging should be implemented. By examining the impact on the simulated electric grid from the different scenarios the limit of PEV penetration is found. In the area of Hammarby this limit seems to be around 30 % of the total cars if there is no controlled charging. Without any controlled charging the peak power demand increases by 30% with a 30% share of PEVs, which is projected to happen in 2025. In 2040 when share of PEVs is projected to be about 95% the peak power is instead increased by more than 100% which shows the impact that PEVs can exert on the electric grid. Utilizing a simple method of controlled charging where the PEVs are instead charged during the night when the power demand is low, the peak power is not increased at all. This also results in the small cost benefit for PEV owners since the electricity is cheaper during the night and controlled charging can therefore save about 15% of the electricity charging cost. However, the main savings are for the grid owners since the need to reinforce the grid is heavily reduced. In addition to this the power losses are reduced heavily from about 14% down to 5% in the electric grid that is simulated. / När dimensioneringen av distributionsnätet utförs analyseras området genom att räkna med elektriska laster som till exempel kan bero på geografiska data, typ av konsument, uppvärmningsmetod etcetera. Än så länge har laddningen av elbilar (PEVs) inte varit en av dessa faktorer trots den förväntade tillväxten av elbilar. Ungefär 30% av Sveriges distributionsnät förväntas behöva förstärkningar på grund av den ökade elkonsumtionen från elbilar under vintrarna om laddningen inte kontrolleras. Utöver detta står Stockholm inför problemet med effektbrist från elöverföringsnätet. Denna uppsats genomförs således för att analysera påverkan från elbilar på fördelningsnätet i framtiden. Denna masteruppsats simulerar det elektriska nätet för tre nätstationer i Hammarby Sjöstad genom en analys av effektflödet. En metod för att disaggregera elkonsumtionen per nätstation ned till elkonsumtionen per byggnad utvecklades och antalet elbilar i framtiden uppskattades. För att utvärdera elbilars påverkan skapades nio olika scenarion för framtiden genom att undersöka hur det kommer att se ut år 2025 och år 2040. Genom att anta att laddningen av alla elbilar i området sker samtidigt, samma tid som den maximala förbrukningen av el sker under en söndag 2016, analyseras det värsta möjliga scenario för det elektriska nätet. Resultaten visar att elbilar kan ha enorm påverkan på de maximala lasterna för ett lågspänningsnät och därför kommer kontroll av laddningen behövas. Genom att undersöka elnätets påverkan i de olika scenariona uppskattades gränsen för hur många elbilar det modellerade elnätet klarar av. I Hammarby Sjöstad ligger denna gräns på ungefär 30% elbilar. Utan kontrollerad laddning ökar maxlasten med 30% år 2025 då antalet elbilar förväntas vara 30% av alla bilar i Hammarby Sjöstad. År 2040 då antalet elbilar uppnår ungefär 95 % av alla bilar ökar maxlasterna med mer än 100% vilket visar den enorma påverkan elbilar kan ha på elnätet. Genom att använda en simpel modell av kontrollerad laddning som består av att flytta laddningen från eftermiddagen till natten, då förbrukningen av elektricitet är låg, ökar inte maxlasten för dygnet alls jämfört med scenariot utan elbilar. Detta resulterar också i besparingen av elektricitetskostnad för elbilsägaren med cirka 15% eftersom elektriciteten ofta är billigare under natten jämfört med kvällens elpriser. Detta är dock små summor jämfört med besparingar elnätsägarna kan göra då elnätet inte behöver förstärkas lika mycket som skulle behövas utan kontroll av laddningen. Utöver detta så sänks även förlusterna av elektricitet i det simulerade nätet från 14% ned till 5% genom att utnyttja denna modell av kontrollerad laddning.

Object detection has been a fundamental part of many emerging technologies, such as autonomous vehicles, robotics, and security. As deep learning is the main reason behind the leap of performance in object detection, it has mostly been associated with a post-processing step of non-maximum suppression (NMS) to reduce the number of resulting bounding boxes output from the network to, ideally, one box per object. As non-maximum suppression blindly suppress the overlap with a pre-defined threshold, it introduces the problem of suppressing false negatives in crowded scenes by choosing a high threshold, or vice versa. This problem is critical, especially in the autonomous vehicle industry, as this concerns the safety of passengers. The problem of the machine understanding whether these bounding boxes belong to the same object or two near-by objects is still not directly solvable. Although a lot of previous research tried to invent a new box-reduction method, every method has its own drawbacks while solving the problem. That is why, until now, many researchers are still using non‐maximum suppression. In this research, a literature review was carried out to determine the best NMS alternatives. Then, an approach for box reduction based on determinantal point process (DPP) was implemented. Furthermore, an evaluation pipeline was introduced for experimental analysis for the differences between NMS and DPP. Although NMS shows a better performance in terms of precision and recall, DPP chooses better fitting bounding boxes. / Objektdetektering har varit en grundläggande del av många nya tekniker, t.ex. autonoma fordon, robotik och säkerhet. Eftersom djupinlärning är den främsta orsaken till den stora prestandaskillnaden vid objektsdetektering har den oftast varit förknippad med ett efterbehandlingssteg med icke-maximal undertryckning (NMS) för att minska antalet resulterande avgränsande rutor som produceras av nätverket till, idealt sett, en ruta per objekt. Eftersom icke-maximal undertryckning blint undertrycker överlappningen med ett fördefinierat tröskelvärde, uppstår problemet med att undertrycka falskt negativa resultat i överfulla scener genom att välja ett högt tröskelvärde, eller tvärtom. Detta problem är kritiskt, särskilt inom industrin för autonoma fordon, eftersom det gäller passagerarnas säkerhet. Problemet med att maskinen ska förstå om dessa avgränsande rutor tillhör samma objekt eller två närliggande objekt är fortfarande inte direkt lösbart. Även om man i tidigare forskning har försökt hitta en ny metod för att reducera boxar, har varje metod sina egna nackdelar när den löser problemet. Det är därför som många forskare fram till nu fortfarande använder sig av icke-maximalt undertryckande. I denna forskning gjordes en litteraturstudie för att fastställa de bästa NMS-alternativen. Därefter implementerades en metod för boxförminskning baserad på determinant punktprocess (DPP). Dessutom infördes en utvärderingsledning för experimentell analys av skillnaderna mellan NMS och DPP. Även om NMS visar en bättre prestanda när det gäller precision och återkallande, väljer DPP bättre passande avgränsande lådor.

<p>This thesis is devoted to introducing new problem formulations and exact solution methods for a class of continuous covering location models. The manuscript includes three self-contained studies which are organized as in the following. </p> <p> In the first study, we introduce the planar expropriation problem with non-rigid rectangular facilities which has many applications in regional planning and undesirable facility location domains. This model is proposed for determining the locations and formations of two-dimensional rectangular facilities. Based on the geometric properties of such facilities, we developed a new formulation which does not require employing distance measures. The resulting model is a mixed integer nonlinear program. For solving this new model, we derived a continuous branch-and-bound framework utilizing linear approximations for the tradeoff curve associated with the facility formation alternatives. Further, we developed new problem generation and bounding strategies suitable for this particular branch-and-bound procedure. We designed a computational study where we compared this algorithm with two well-known mixed integer nonlinear programming solvers. Computational experience showed that the branch-and-bound procedure we developed performs better than BARON and SBB both in terms of processing time and size of the branching tree.</p> <p> The second study is referred to as the planar maximal covering problem with single convex polygonal shapes and it has ample applications in transmitter location, inspection of geometric shapes and directional antenna location. In this study, we investigated maximal point containment by any convex polygonal shape in the Euclidean plane. Using a fundamental separation property of convex sets, we derived a mixed integer linear formulation for this problem. We were able to identify two types of special cuts based on the geometric properties of the shapes under study, which were later employed for developing a branch-and-cut procedure for solving this particular location model. We also evaluated the resultant bound quality after employing the afore-mentioned cuts. </p> <p> In the third study, we discuss the dynamic planar expropriation problem with single convex polygonal shapes. We showed how the basic problem formulations discussed in the first two studies extend to their diametric opposites, and further to models in higher dimensions. Subsequently, we allowed a dynamic setting where the shape under study is expected to function over a finite planning horizon and the system parameters such as the fixed point locations and expropriation costs are subject to change. The shape was permitted to relocate at the beginning of each time period according to particular relocation costs. We showed that this dynamic problem structure can be decomposed into a set of static problems under a particular vector of relocations. We discussed the solution of this model by two enumeration procedures. Subsequently, we derived an incomplete dynamic programming procedure which is suitable for this distinct problem structure. In this method, there is no need to evaluate all the branches of the branching tree and one proceeds with keeping the minimum stage cost. The evaluation of a branch is postponed until relocation takes place in the lower-level problems. With this postponing structure, the procedure turned out to be superior to the two enumeration procedures in terms of tree size. </p> / Thesis / Doctor of Philosophy (PhD)

No description available.

No description available.