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2. Synthesis of regional networks for biomass and biofuel production Hon Loong Lam, 2010, doktorska disertacija Opis: This thesis presents two different approaches to the synthesis of regional networks for biomass and biofuel production and supply: Mathematical Programming and Graph Theoretic approach. The optimisation criterion for both approaches is the maximisation of profit.
The first approach is based on a generic optimisation model of biomass production and supply networks. This superstructure approach is based on a flexible number of network layers: plantation, collection using a pre-treatment, process, and consumption. A Mixed Integer Linear Programming (MILP) model has been successfully developed during this work.
However, the solution of this biomass production network model is very challenging due to the large sizes of the networks and the number of interconnections. The huge number of redundant variables reduces model efficiency (time taken to solve the model and the interpretation of the results). This model when representing very large size networks cannot be solved over a reasonable time even by professional mathematical programming software tools. Several model-size reduction techniques are therefore proposed for the solution of large-scale networks. In particular, methods are proposed for (i) reducing the connectivity within a biomass supply chain network by setting the maximum allowable distance between the supply zones to the collection centres, (ii) eliminating unnecessary variables and constrains to reduce the zero-flows in the full model, and (iii) aggregating the network and hence the synthesis process by merging the collection centres.
The network synthesis is also carried out by P-graph (Process Graph) tools. P-graph is a directed bipartite graph, having two types of vertices — one for operating units and another for those objects representing material or energy flows/quantities. In this procedure, firstly a maximum feasible superstructure for biomass production network is generated from which the optimal structure is then selected by the Branch and Bound method. This graph-based method clearly shows where, how, and what kind of material and energy carriers will be transferred from one supply chain layer to another.
In order to test the efficiency of the model, a small regional renewable network problem was solved using both methods. Their performances were tested and the results confirmed the applicability on a regional scale. The proposed model-size reduction techniques were also tested. A large-scale regional case study was created to demonstrate these techniques. The results are very positive and some suggestions for future work are given in the conclusion. Ključne besede: Biomass and bioenergy network synthesis, Model-size reduction
techniques, Mathematical Programming, MILP, P-Graph Objavljeno: 06.01.2011; Ogledov: 2483; Prenosov: 84 Celotno besedilo (4,25 MB) |
3. Optimization methods for solving transportation problems on networksKatja Prnaver, 2011, doktorska disertacija Opis: In this thesis we study problems from real situations, which can be applied to network
graphs and solved using mathematical graph theory.
We start with the problem of oriented network design. The problem originates from
networks, where the flow over the arcs is important and many times limited with the capacity
of the networks. There are several techniques and results on the problem of assigning the
flow through the network channels. In our problem, we try to find the optimal network
structure, which could be used in the design phase of the network. With metaheuristics,
we search for optimal network structures for a given number of nodes. We define triangle
neighborhood and compare the results of the algorithm with the conjecture by Choplin et
al. [8].
Further, we study the problem of order picking and order batching in block structured
warehouses. For order picking problem, we present the extension of a dynamic programming
algorithm by Ratliff and Rosenthal [42], which enables the development of an algorithm for
an unlimited number of blocks. In order to achieve this, a new presentation of states and
transitions of dynamic programming algorithm is given. We prove that the resulting path is
optimal for the given structure. We compare the optimal path lengths to the results found in
literature and also investigate the impact of warehouse layout parameters onto the routing.
Closely related to the problem of order picking, we investigate the order batching problem.
We discuss the variation of the order batching problem with time windows and present
the algorithmic approach to solving the problem. The previously presented optimal path
algorithm is applied in the algorithm to ensure even better quality of results. We introduce
the evaluation function of a batch and compare the results of the algorithm with the test
data from the literature as well as with data from the real warehouse.
We conclude by summarizing the results and stating some possible extensions and further
work. Ključne besede: graph theory, networks, optimization, shortest path problem, traveling salesman problem, algorithms, metaheuristics, order batching Objavljeno: 03.06.2011; Ogledov: 3726; Prenosov: 146 Celotno besedilo (925,86 KB) |
4. Chepoi Victor, Dragan Feodor F., Vaxes Yann: Distance and routing labeling schemes for non-positively curved plane graphs. J. Algorithms 61 (2006), no. 2, 60-88.Boštjan Brešar, 2006, recenzija, prikaz knjige, kritika Ključne besede: mathematics, graph theory, distance labeling scheme, routing labeling scheme, efficient algorithms Objavljeno: 31.05.2012; Ogledov: 966; Prenosov: 10 Povezava na celotno besedilo |
5. Nebesk'y Ladislav: Signpost systems and spanning trees of graphs, Czechoslovak Math. J. 56(131) (2006), no. 3, 885-893.Boštjan Brešar, 2006, recenzija, prikaz knjige, kritika Ključne besede: signpost system, path, connected graph, tree, spanning tree Objavljeno: 31.05.2012; Ogledov: 556; Prenosov: 15 Povezava na celotno besedilo |
6. Chastand Marc, Polat Norbert: On geodesic structures of weakly median graphs.II. Compactness, the role of isometric rays. Discrete Math. 306 (2006), no. 16, 1846-1861.Boštjan Brešar, 2006, recenzija, prikaz knjige, kritika Ključne besede: infinite graph, weakly median graph, geodesic topology, ray, hyperinterval Objavljeno: 31.05.2012; Ogledov: 679; Prenosov: 14 Povezava na celotno besedilo |
7. Chastand Marc, Polat Norbert: On geodesic structures of weakly median graphs.I. Decomposition and octahedral graphs. Discrete Math. 306 (2006), no. 13, 1272-1284Boštjan Brešar, 2006, recenzija, prikaz knjige, kritika Ključne besede: infinite graph, weakly median graph, octahedral graph, eodesic convexity Objavljeno: 31.05.2012; Ogledov: 510; Prenosov: 10 Povezava na celotno besedilo |
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