1. Koordinacija blagovnega toka v maloprodajni oskrbovalni verigiTea Vizinger, 2019, doktorska disertacija Opis: Disertacija obravnava koordinacijo blagovnih tokov v maloprodajnih oziroma
trgovinskih oskrbovalnih verigah. Zanje je značilno, da delujejo v nenehno spreminjajočem se okolju ter so močno odvisne od povpraševanja končnih odjemalcev. Tipično maloprodajno oskrbovalno verigo sestavlja več trgovin, ki so oskrbovane iz vsaj enega skladišča izbranega trgovca. Da dosežemo usklajenost zalog med objekti dane oskrbovalne verige, je zagotovo najprej potrebno doseči primerno koordinacijo vseh povezanih in odvisnih si aktivnosti, ki spremljajo blagovni tok. Pri gradnji matematičnega modela smo se najprej osredotočili na analizo povpraševanja, medtem ko so dinamično prilagajanje cen, upoštevanje pokvarljivosti itd. predmet nadaljnih raziskav, povezanih s komplementarnim modelom za operativno planiranje blagovnega toka. Idejno je pristop zasnovan tako, da se najprej poišče primerni distribucijski plan (taktični plan) z minimalnimi pričakovanimi stroški distribucije, kot tudi z minimalnimi pričakovanimi stroški rizikov. Problem predstavljamo kot večkriterijski problem optimizacije, predlagani stohastični model za dosego koordinacije pa pri tem kombinira več metod in postopkov iz področij teorije grafov, teorije verjetnosti in operacijskih raziskav. Ker je izbrani problem računsko kompleksen, za njegovo reševanje uporabimo nekaj hevrističnih postopkov lokalnega iskanja ter tudi predlagamo robustni optimizacijski pristop
reševanja danega problema. Eksperimentalna študija pokaže, da je za optimizacijski problem mogoče implementirati algoritem, ki da uporabne rešitve.
Ključne besede: Distribucija, Zaloge, Optimizacija, Hevristike, Stohastično programiranje
Objavljeno: 01.10.2019; Ogledov: 680; Prenosov: 89
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2. Heuristics for NP-hard optimization problemsJanez Žerovnik, 2015, izvirni znanstveni članek Opis: We provide several examples showing that local search, the most basic metaheuristics, may be a very competitive choice for solving computationally hard optimization problems. In addition, generation of starting solutions by greedy heuristics should be at least considered as one of very natural possibilities. In this critical survey, selected examples discussed include the traveling salesman, the resource-constrained project scheduling, the channel assignment, and computation of bounds for the Shannon capacity.
Ključne besede: optimization, metaheuristics, local search, greedy construction, traveling salesman problem
Objavljeno: 17.11.2017; Ogledov: 702; Prenosov: 127
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3. Roman domination number of the Cartesian products of paths and cyclesPolona Repolusk, Janez Žerovnik, 2012, izvirni znanstveni članek Opis: Roman domination is a historically inspired variety of general domination such that every vertex is labeled with labels from $\{0,1,2\}$. Roman domination number is the smallest of the sums of labels fulfilling condition that every vertex, labeled 0, has a neighbor, labeled 2. Using algebraic approach we give ▫$O(C)$▫ time algorithm for computing Roman domination number of special classes of polygraphs (rota- and fasciagraphs). By implementing the algorithm we give formulas for Roman domination number of the Cartesian products of paths and cycles ▫$P_n \Box P_k$▫, ▫$P_n \Box C_k$▫ for ▫$k \leq 8$▫ and ▫$n \in {\mathbb N}$▫ and for ▫$C_n \Box P_k$▫ and ▫$C_n \Box C_k$▫ for ▫$k \leq 5$▫, ▫$n \in {\mathbb N}$▫. We also give a list of Roman graphs among investigated families.
Ključne besede: graph theory, Roman domination number, Cartesian product, polygraphs, path algebra
Objavljeno: 23.08.2017; Ogledov: 651; Prenosov: 153
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4. Altered Wiener indicesDamir Vukičević, Janez Žerovnik, 2005, izvirni znanstveni članek Opis: Recently Nikolić, Trinajstić and Randić put forward a novel modification ▫$^mW(G)$▫ of the Wiener number ▫$W(G)$▫, called modified Wiener index, which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as ▫$W_{min,λ}(G) = ∑(V(G)^λm_G(u,ν)^λ−m_G(u,ν)^{2λ})$▫ and show that some of the important properties of ▫$W(G)$▫, ▫$^mW(G)$▫ and ▫$^λW(G)$▫ are also properties of ▫$W_{min,λ}(G)$▫, valid for most values of the parameter λ. In particular, if ▫$T_n$▫ is any n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex star ▫$S_n$▫, then for any λ ≥ 1 or λ < 0, ▫$^W_{min,λ}(P_n) > W_{min,λ}(T_n)>W_{min,λ}(S_n)$▫. Thus for these values of the parameter λ, ▫$W_{min,λ}(G)$▫ provides a novel class of structure-descriptors, suitable for modeling branching-dependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to ▫$W_{min,λ}(G)$▫ then, in the general case, this ordering is different for different λ.
Ključne besede: mathematics, chemical graph theory, Wiener index, modified Wiener index
Objavljeno: 17.08.2017; Ogledov: 528; Prenosov: 78
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5. On vulnerability measures of networksRija Erveš, Darja Rupnik Poklukar, Janez Žerovnik, 2013, objavljeni znanstveni prispevek na konferenci Opis: As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication networks are discussed including the connectivities, fault diameters, and measures based on Hosoya- Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved.
Ključne besede: discrete optimization, communication network, vulnerability
Objavljeno: 21.07.2017; Ogledov: 551; Prenosov: 76
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6. The Hosoya-Wiener polynomial of weighted treesBlaž Zmazek, Janez Žerovnik, 2007, izvirni znanstveni članek Opis: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.
Ključne besede: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs
Objavljeno: 05.07.2017; Ogledov: 599; Prenosov: 60
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7. Simplified computation of matchings in polygraphsAnte Graovac, Damir Vukičević, Damir Ježek, Janez Žerovnik, 2005, izvirni znanstveni članek Opis: Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when twoor more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry.
Ključne besede: polygraphs, matching polynomial, matchings, perfect matchings, Kekulé structures, extended structures, recursive enumeration, transfer matrix method
Objavljeno: 05.07.2017; Ogledov: 620; Prenosov: 58
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8. On algebraic and geometric Kekulé structures in benzenoid rotagraphsAnte Graovac, Damir Vukičević, Janez Žerovnik, 2006, izvirni znanstveni članek Opis: Recently introduced algebraic Kekulé structures (AKS) describe the ▫$\pi$▫-electron distribution within rings of a conjugated network. The ratio of the AKS countto the classical Kekulé structures count was studied in benzenoid rotagraphs. By considering three representative classes of such rotagraphs, it was shown that this ratio tends towards either 1 or 0, or its value lies between 0 and 1.
Ključne besede: Kekulé structures, Kekulé structure count, geometric and algebraic Kekulé structures, benzenoids, rotagraph
Objavljeno: 05.07.2017; Ogledov: 595; Prenosov: 69
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9. Corroborating a modification of the Wiener indexIvan Gutman, Janez Žerovnik, 2002, kratki znanstveni prispevek Opis: In a recent work [Chem. Phys. Lett. 333 (2001) 319-321] Nikolić, Trinajstić, and Randie put forward a novel modification ▫$^m$▫W of the Wiener index. We now show that ▫$^m$▫W possesses the basic properties required by a topological index to be acceptable as a measure of the extent of branching of the carbon-atom skeleton of the respective molecule (and therefore to be a structure-descriptor, potentially applicable in QSPR and QSAR studies). In particular, if ▫$T_n$▫ is any n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex star ▫$S_n$▫, then mw(Pn) < mW(Tn) < mW(Sn). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs.
Ključne besede: graph theory, distance, molecular graphs, modified Wiener index, weigted modified Wiener index, branching, chemical graph theory
Objavljeno: 05.07.2017; Ogledov: 571; Prenosov: 57
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