Optimization of the municipal waste collection route based on the method of the minimum pairing

Abstract

In the present article is shown the use of Maple program for processing of data describing the position of municipal waste sources and topology of collecting area. The data are further processed through the use of graph theory algorithms, which enable creation of collection round proposal. In this case study is described method of waste pick-up solution in a certain village of approx. 1,600 inhabitants and built-up area of approx. 30 hectares. Village has approx. 11.5 kilometers of ride able routes, with approx. 1 kilometer without waste source. The first part shows topology of the village in light of location of waste sources and capacity of the routes. In the second part are topological data converted into data that can be processed by use of the Graph Theory and the correspondent graph is shown. Optimizing collection route in a certain graph means to find the Euler circle. However, this circle can be constructed only on condition that all the vertices of the graph are of an even degree. Practically this means that is necessary to introduce auxiliary edges - paths that will be passed twice. These paths will connect vertices with odd values. The optimal solution then requires that the total length of the inserted edges was minimal possible, which corresponds to the minimum pairing method. As it is a problem of exponential complexity, it is necessary to make some simplifications. These simplifications are depicted graphically and the results are displayed in the conclusion. The resulting graph with embedded auxiliary edges can be used as a basic decision making material for creation of real collection round that respects local limitations such as one way streets or streets where is the waste collection is not possible from both sides at the same time.