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Hadrianty Ramly
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Mathematics

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Algoritma Warshall untuk Penyelesaian Masalah Vehicle Routing (Studi Kasus : Pendistribusian PT Semen Bosowa di Makassar) Syafruddin Side; Maya Sari Wahyuni; Hadrianty Ramly
Journal of Mathematics, Computations and Statistics Vol. 1 No. 01 (2018): Volume 01 Nomor 01 (April 2018)
Publisher : Jurusan Matematika FMIPA UNM

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Abstract

Warshall is an algorithm to calculate the shortest distance for every pair of points in a locationthat can be converted into a directed and weighted graph, in the form of vertex (V) and edges (E), and mosthave at least one side at any vertex. Vehicle Routing Problem (VRP) is included in the class of NP-hardproblem in combinatorial optimization, making it difficult to solve with exact methods applicable ingeneral. This study beginning with mathematical concepts Implementation of Algorithms Warshall, whichis taking the data distribution from the Company, the search for weight trajectory, changing into a matrixwith n × n squares in this case matrix used measuring 11 x 11, apply the algorithm Warshall in the matrixobtained, the second is the implementation of Algorithms Warshall using Microsoft Visual Basicprogramming language. The equation used is the first representation of the graph to a weighted matrix D= [dij] ie the distance from the vertex i to j; The second order decomposition with dij(k). D (k) be the nxnmatrix [dij(k)] so that the limit k to n for k = 0, 1, ..., n; Third observation structures shortest path done intwo ways: if k is not a vertex on the path (the shortest path length dij (k-1)) and k is the vertex on the path(the shortest path length dij (k-1) + dij (k -1)), it contains a subpath from i to k and a subpath from k to j.The fourth iteration numbered 0 through n. The result showed that the method Warshall algorithm cansolve the problems of determining the shortest route in the distribution of PT Semen Bosowa by calculatingthe distance of the entire passage is in the distribution of cement Bosowa in Makassar
Co-Authors Syafruddin Side Wahyuni, Maya Sari