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Five years of multi-depot vehicle routing problems

Jayarathna Nuwan, Lanel Jayantha, Juman Z. A. M. S.

Journal of Sustainable Development of Transport and Logistics

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2020

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Vol. 5, No. 2

109--123

EN

With vast range of applications in real life situations, the Vehicle Routing Problems (VRPs) have been the subject of countless studies since the late 1950s. However, a more realistic version of the classical VRP, where the distribution of goods is done from several depots is the Multi-Depot Vehicle Routing Problem (MDVRP), which has been the central attraction of recent researches. The objective of this problem is to find the routes for vehicles to serve all the customers at a minimal cost in terms of the number of routes and the total distance travelled without violating the capacity and travel time constraints of the vehicles, and it is handled with a variety of assumptions and constraints in the existing literature. This survey reviews the current status of the MDVRP and discuss the future direction regarding this problem.

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Graphs different category of subsystem as models to synthesis of transverse vibrating beam - system

Buchacz A.

Journal of Achievements in Materials and Manufacturing Engineering

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2010

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Vol. 43, nr 2

644--650

EN

Purpose: of this paper is modeling by different categorygraphs and analysis of vibrating clamped - free beam as subsystem of transverse vibrating beam-system by the exact and approximate methods and creating the hypergraphs of the beams in case of presented methods of analysis. Design/methodology/approach: was to nominate the relevance or irrelevance between the characteristics obtained by considered methods - especially concerning the relevance of the natural frequencies-poles of characteristics of considered beam. The main subject of the research is the continuous clamped - free beam with constant cross sections as a subsystem of transverse vibrating beam - system. Findings: this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and can be introduction to synthesis of these systems modeled by different category graphs. Research limitations/implications: is that linear continuous transverse vibrating clamped-free beam is considered. Practical implications: of this study is the main point is the introduction to synthesis of transverse vibrating continuous beam-systems with constant changeable cross-section. Originality/value: of this approach relies on application approximate methods of analysis of clamped - free beam and modeling the one of transformed hypergraph.

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Comparison of solutions obtained by exact and approximate methods for vibrating shafts

Buchacz A.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 23, nr 1

63-66

EN

Purpose: The purpose of this paper is to compare the transients of characteristics obtained by the approximate and exact method and to answer to the question - if the method can be used to nominate the characteristics of mechatronic systems. Design/methodology/approach: The main approach to the problem is to nominate the relevance or irrelevance between the characteristics obtained by different methods - especially the relevance of the pole values of characteristics. The main subject of the research is the continuous torsionally vibrating bar considered as a mechanical subsystem of the mechatronic system. Findings: The values of zeroes and poles of continuous mechanical system depend on the boundary conditions. Foreseeing approximate solutions fulfill some conditions only, particularly for flexibly vibrating beams. Research limitations/implications: The linear continuous torsionally vibrating bar is considered. Practical implications: The main point is the analysis and the examination of torsionaly vibrating continuous mechatronic systems which characteristics can be nominated with approximate methods only. Originality/value: The originality of the approach relies on the comparisation of the compatibility of the characteristics of the mechatronic and mechanical systems with demanded accuracy, nominated with the same approximate method.