Application Of Max-Plus Algebra In Determining The Shortest Route Of Goods Distribution On Jalur Nugraha Ekakurir (JNE) In Palu City

Abstract

Determining the shortest route is a solution that is needed for companies engaged in the distribution of goods, because the shortest route can help companies optimize the distance traveled and streamline the time needed. Therefore, this study aims to apply max-plus algebra to determine the shortest route for the distribution of goods on the Jalur Nugraha Ekakurir (JNE) in Palu City. This method was chosen because Max-Plus Algebra can find more optimal results from the matrix exponentiation operation of a weighted graph. The data used were obtained from previous research which consisted of 13 JNE warehouse points along with the distance between these points. The results to be obtained are in the form of the shortest route between one point and another which is represented in a graph path with each path length and weight obtained based on the results of max-plus algebraic calculations. Of all the possible route, obtained the route with the minimum weight for distribution of goods from JNE main warehouse dewi sartika (v_1) to JNE tondo mantikulore (v_13), that is JNE main warehouse dewi sartika (v_1) → to JNE basuki rahmat (v_4) → JNE Sisingamangaraja palu (v_8) → JNE tondo mantikulore (v_13) with a total distance of 13.3 km.