A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION

Transcription

1 A HEURISTIC FOR THE SOLUTION OF VEHICLE, University of Applied Sciences Merseburg, Germany

2 1 Problem statement 2 A cluster first route second approach 2.1 A capacitated k-means algorithm 2.2 A capacitated savings algorithm with time windows 3 Numerical example 4 Conclusion and further research

3 Problem Statement (I) Managing the daily residential waste collection problem Waste collection vehicle routing problem with time windows (WCVRPTW) Differs from the traditional VRPTW by that the waste collecting vehicles must empty their load at multiple disposal sites

4 Problem Statement (II) Vehicles leave the depot at the start of the day and must return there before the end of the day. At the end of the day or in between, the vehicle is unloaded at a waste disposal site or at the depot. There are a limited number of identical vehicles available with given capacity to collect the waste, and each tour is served by one vehicle

5 Problem Statement (III): Our real world problem is determined by the following issues: one depot, multiple dumping sites, a given shift duration, a given vehicle capacity and, given time windows for the requesters.

6 A cluster first route second approach: Cluster first (assign a number of requesters to a vehicle that has to serve them within a given shift duration) Route second (build sequences of requesters within each cluster)

7 A capacitated k-means algorithm: Capacitated k-means algorithm

8 A capacitated savings algorithm with time windows: choose the valid combination of two subtours out of a set of subtours, which lead to the highest saving of travel distance: Capacitated savings algorithm

9 Restrictions: time windows shift duration and capacity constraints of the vehicles waiting times

10 Computations of savings: savings according to CLARKE, G. & WRIGHT, J.W (1964), (Algorithm 1): s ij = t i0 + t 0j t ij i,j savings taking waiting times into account (Algorithm 2): s ij = t i0 + t 0j t ij w i,j The saving increases, if the waiting time is reduced.

11 Numerical Examples: two types of waste (organic waste, residual waste) of five days in one week: 750 demands including 5130 single bins of residual waste are served each day. That means about 750 nodes. The mean value for the number of demands of organic waste is approximately 250 per day. Around 150 different locations for this type are visited daily on average.

12 Results: Number of clusters per day for residual waste Number of clusters per day for organic waste

13 Results: Algorithm 1 (savings according to CLARKE, G. & WRIGHT, J.W) Algorithm 2 (modified savings taking waiting times into account) Algorithm 3 (neglecting TW, lower bound) Number of vehicles for residual waste in k-means clusters Number of vehicles for organic waste in k-means clusters

14 Results: Algorithm 1 (savings according to CLARKE, G. & WRIGHT, J.W) Algorithm 2 (modified savings taking waiting times into account) Algorithm 3 (neglecting TW, lower bound) Day Algorithm 1 Algorithm 2 Without TW Total Total time [hours] for residual waste in k-means clusters Day Algorithm 1 Algorithm 2 Without TW Total Total time [hours] for organic waste in k-means clusters

15 Conclusion and further Research: Time based savings heuristic including waiting times seems the most promising approach Get more experienced with the application and optimize parameter Test metaheuristics to overcome local optima Use and analyze process data to get better knowledge about: Demand of vertex i: di Driving time: tij Service time: ts

16 Thank you very much for your attention!