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Optimization methods for solving transportation problems on networks
Katja Prnaver, 2011, dissertation

Abstract: 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.
Keywords: graph theory, networks, optimization, shortest path problem, traveling salesman problem, algorithms, metaheuristics, order batching
Published: 03.06.2011; Views: 3822; Downloads: 149
.pdf Full text (925,86 KB)

3.
Izdelava in uporaba dinamičnih nalog pri pouku matematike
Katja Prnaver, Igor Pesek, Samo Repolusk, 2009, published scientific conference contribution

Abstract: V šolah se učitelji nemalokrat srečujejo s težavami pri sestavljanju nalog. V ekipi E-um smo zato razvili aplikacijo, ki učiteljem omogoča pripravo dinamičnih nalog. S pojmom dinamične naloge mislimo na naloge, ki ob vnovičnem nalaganju ohranijo strukturo, razlikujejo pa se v podatkih. Naloge lahko učitelji uporabijo bodisi med šolsko uro bodisi pri preverjanju znanja. Ker je naloge mogoče shraniti v SCORM-paket in jih kot takšne vnesti v orodje Moodle, lahko izjemno nadgradijo že obstoječe vsebine. Prispevek opisuje didaktične smernice za uporabo dinamičnih nalog, postopek priprave takšnih nalog in možnosti njihove uporabe pri pouku matematike.
Keywords: računalništvo, informacijska tehnologija, matematika, dinamične naloge, spletne naloge, e-gradivo
Published: 07.06.2012; Views: 938; Downloads: 46
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4.
On total chromatic number of direct product graphs
Katja Prnaver, Blaž Zmazek, 2009, original scientific article

Keywords: graph theory, total chromatic number, direct product, tensor product
Published: 07.06.2012; Views: 1141; Downloads: 51
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