Browsing Mathematical Sciences by Title
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Vujić, Slobodan; Ivić, Aleksandar (Beograd , 1991)[more][less]
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Fragović, Hristina (Beograd , 2014)[more][less]
URI: http://hdl.handle.net/123456789/3898 Files in this item: 1
masterHristinaFaragovic.pdf ( 755.9Kb ) -
Srbulović, Tamara (Beograd , 2012)[more][less]
URI: http://hdl.handle.net/123456789/2426 Files in this item: 1
Master rad, Mat ... anja, Tamara Srbulovic.pdf ( 1.057Mb ) -
Srbulović, Tamara (Beograd , 2012)[more][less]
URI: http://hdl.handle.net/123456789/4955 Files in this item: 1
Master rad, Mat ... anja, Tamara Srbulovic.pdf ( 1.057Mb ) -
Todorov, Pavel; Pejović, Stanislav; Karanikolov, Chr; Martić, Branislav; Adamović, Dušan; Stanilov, Grozljo; Makowski, Andrzej; Sidrpinski, I. W. (MATEMATIČKI VESNIK , 1965)[more][less]
URI: http://hdl.handle.net/123456789/1614 Files in this item: 1
PavelTodorovStanislavPejovicMatematickeNote.pdf ( 179.9Kb ) -
Vlajčić Gašić, Milica (b , 2023)[more][less]
URI: http://hdl.handle.net/123456789/5667 Files in this item: 1
v1_masterMilicaVlajcic Gasic.pdf ( 600.3Kb ) -
Redakcijski odbor (Beograd , 1968)[more][less]
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Redakcijski odbor (Beograd , 1968)[more][less]
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Redakcijski odbor (Beograd , 1968)[more][less]
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Redakcijski odbor (Beograd , 1969)[more][less]
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Redakcijski odbor (Beograd , 1969)[more][less]
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Redakcijski odbor (Beograd , 1969)[more][less]
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Redakcijski odbor (Beograd , 1970)[more][less]
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Redakcijski odbor (Beograd , 1970)[more][less]
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Anokić, Ana (Beograd , 2017)[more][less]
Abstract: Optimization problems arise from many real-life situations. The development of adequate mathematical models of optimization problems and appropriate solution methods are of great importance for performance of real systems. The subject of this doctoral dissertation is a novel vehicle scheduling problem (VSP) that arises from optimizing the transport of agricultural raw materials. The organization of transport of raw materials is of great importance in the initial phase of production. This is particularly evident in the case of agricultural raw materials, because their price in the market is very low, and therefore, the costs of their transport represent the largest part of the total production cost. For this reason, any reduction of time and money spent in this early production stage directly increases the company’s profitability. The considered variant of VSP arises from optimizing the transport of sugar beet in a factory for sugar production in Serbia, but it can also be applied in a wider context, i.e., to optimize the transport of raw materials or goods in large companies under the same or similar conditions. The considered problem involves a number of specific constraints that distinguish it from existing variants of the vehicle scheduling problem. Therefore, mathematical models proposed in the literature for other variants of VSP do not describe adequately the considered problem. The complexity of the newly introduced VSP is analyzed. It is proven that the introduced VSP belongs to the class of NP-hard problems by comparing its relaxation with the Parallel Machine Scheduling Problem (PMSP). PMSP is known to be NP-hard, as it is equivalent to the Partitioning problem. From the established analogy between the relaxation of the considered VSP and PMSP, it is concluded that the VSP introduced in this dissertation is NP-hard. New mathematical models of the considered problem that involve all problem specific properties, are developed. The proposed mathematical models are compared in sense of efficiency by using Lingo 17 and CPLEX MIP 12.6.2 solvers. Experimental results showed that both exact solvers provided optimal or feasible solutions only for small-size real-life problem instances. However, this was expectable, having in mind the NP-hardness of the considered problem. Therefore, heuristic and metaheuristic method seem to be appropriate approaches for solving problem instances of larger dimension. Due to specific properties of the considered problem, the existing implementations of heuristic and metaheuristic methods for vehicle routing and scheduling problems can not be directly applied. For this reason, different variants of well-known Variable Neighborhood Search (VNS) metaheuristic, as well as Greedy Randomized Adaptive Search Procedure (GRASP), are designed. The constructive elements of the proposed VNS and GRASP implementations are adapted to the characteristics of the considered vehicle scheduling problem. A subproblem of the proposed variant of vehicle scheduling problem, denoted as VSP-P is considered first. VSP-P is obtained from the initial VSP by excluding problem specific constraints regarding vehicle arriving times to each location and to the factory area. Two metaheuristic algorithms are designed as solution methods for this subproblem: Basic Variable Neighborhood Search - BVNS, and Greedy Randomized Adaptive Search Procedure - GRASP. Both proposed approaches were tested on instances based on real-life data and on the set of generated instances of lager dimensions. Experimental results show that BVNS and GRASP reached all optimal solutions obtained by exact solvers on small-size real-life problem instances. On medium-size real-life instances, BVNS reached or improved upper bounds obtained by CPLEX solver under time limit of 5 hours. BVNS showed to be superior compared to GRASP in the sense of solution quality on medium size real-life instances, as well as on generated large-size problem instances. However, general conclusion is that both proposed methods represent adequate solution approaches for the subproblem VSP-P. BVNS provides solutions of better quality compared to GRASP, while GRASP outperforms BVNS regarding the average CPU time required to produce its best solutions. For the initial vehicle scheduling problem (VSP) that includes all problem specific constraints, three VNS-based metaheuristic methods are designed and implemented: Basic Variable Neighborhood Search - BVNS, Skewed Variable Neighborhood Search - SVNS, and Improved Basic Variable Neighborhood Search - BVNSi. BVNS and SVNS use the same neighborhood structures, but different search strategies in local search phase: BVNS uses Best improvement strategy, while SVNS uses First improvement strategy. All three VNS-based methods are tested on real-life and generated problem instances. As it was expected, experimental results showed that BVNS outperformed SVNS regarding solution quality, while SVNS running time was significantly shorter compared to BVNS. The third designed algorithm BVNSi represents a variant of BVNS that uses more general neighborhood structures compared to the ones used in BVNS and SVNS. The use of such neighborhood structures lead to the simplicity of BVNSi and shorter running times compared to BVNS. Two variants of BVNSi method that exploit different strategies in Local search phase are designed: BVNSiB with best improvement strategy and BVNSiF with First improvement strategy. The results of computational experiments for all proposed VNS-based methods for VSP are analyzed and compared. Regarding the quality of the obtained solutions, BVNS method shows the best performance, while SVNS needed the shortest average running times to produce its best solutions. Two variants of BVNSi method succeeded to find new best solutions on two medium size real life instances and to solve large size instances in shorter running time compared to BVNS and SVNS, respectively. However, both BVNSiB and BVNSiF turn out to be less stabile than BVNS and SVNS on real-life and generated inatances. In the case of one large-size generated instance, both BVNSi variants had significantly worse performance compared to BVNS and SVNS, which had negative impact on their average objective values and average running times. The proposed vehicle scheduling problem is of great practical importance for optimizing the transport of agricultural raw materials. It is planned to use the obtained results in practice (partially or completely), as a support to decision makers who organize transportation of in the early production phase. From the theoretical point of view, the developed mathematical models represent a scientific contribution to the fields of optimization and mathematical modeling. The variants of VNS methods that are developed and adapted to the problem, as well as comparison of their performances, represent a scientific contribution to the field of metaheuristic methods for solving NP-hard optimization problems. URI: http://hdl.handle.net/123456789/4664 Files in this item: 1
Anokic_Ana_disertacija.pdf ( 2.688Mb ) -
Stakić, Đorđe (Beograd , 2022)[more][less]
Abstract: Intermodal transport involves traffic with more than one type of trans port. Its presence in practice has become very significant. Bearing in mind that these are mostly long distances, optimization has become important in this area. By default, three standard types of containers of different sizes are used for the transport. In accordance with the given criteria adequate mathematical models have been developed. Based on the model, the exact solver CPLEX was programmed, which succeeds to find the optimal solutions for lesser values of the input parameters. For a number of models, solutions have been implemented in the C programming language. The input data for smaller instances was taken from the practice. To test instances of larger size, the input data is randomly generated from the selected domain. In the first part of this work the main focus is the search for the optimal route in transportation, according to the given criteria, which includes ocean and mainland transport. The problem becomes more complex by increasing the number of shipping companies, the number of side ports, as well as the number of modes of transport on land. In the second part of the paper, additional problems related to the optimization of intermodal transport are considered. More attention is paid to the individual packages by considering the mass and volume of the package, and sub sequently the limits of mass and volume of the containers. One of solved problems is related to the deployment of a large pack in several containers, then the selection of optimal allocation in accordance with the set criteria. The second solved problem is from the aggregate container transport and it is related to the deployment of a large number of packages into containers, taking the constraints of mass and volume into consideration. Here we also seek an optimal allocation in accordance with the set criteria, eg. the total minimum price. The problem thus considered to belong to the heterogeneous and homogeneous vector bin packing. The numerous com puter implementations of exact and approximate methods for the different models are made. Variant methods of Variable Neighborhood Search (VNS) and GRASP (Greedy Randomized Adaptive Search Procedures) have been designed to optimize the aggregate container transport. These approximation methods were compared with each other as well as with solutions obtained by exact solver CPLEX. URI: http://hdl.handle.net/123456789/5377 Files in this item: 1
DjordjeStakicDisertacija.pdf ( 1.629Mb ) -
Milošević, Katarina (Beograd , 2013)[more][less]
URI: http://hdl.handle.net/123456789/4912 Files in this item: 1
Master teza Katarina Milosevic.pdf ( 1.290Mb ) -
Stanojević, Mirjana (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4830 Files in this item: 1
masStanojevicMirjana.pdf ( 658.3Kb ) -
Lazić, Nenad (Beograd , 2017)[more][less]
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Kubura, Jovana (Beograd , 2018)[more][less]