Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
A HEURISTIC FOR THE SOLUTION OF VEHICLE
ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
Dirk Sackmann, University of Applied Sciences Merseburg, Germany
Dirk Sackmann 3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
Dirk Sackmann 3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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.
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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)
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
A capacitated k-means algorithm:
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Capacitated k-means algorithm
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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:
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Capacitated savings algorithm
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
Restrictions: § time windows § shift duration and § capacity constraints of the vehicles § waiting times
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
Computations of savings:
§ savings according to CLARKE, G. & WRIGHT, J.W (1964), (Algorithm 1):
§ savings taking waiting times into account
(Algorithm 2):
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
𝑠↓𝑖𝑗 = 𝑡↓𝑖0 + 𝑡↓0𝑗 − 𝑡↓𝑖𝑗 −∆𝑤 ∀𝑖,𝑗
𝑠↓𝑖𝑗 = 𝑡↓𝑖0 + 𝑡↓0𝑗 − 𝑡↓𝑖𝑗 ∀𝑖,𝑗
The saving increases, if the waiting time is reduced.
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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.
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
Results:
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Number of clusters per day for residual waste
Number of clusters per day for organic waste
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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)
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Number of vehicles for residual waste in k-means clusters
Number of vehicles for organic waste in k-means clusters
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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)
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Table 1: Total time [hours] for residual waste in k-means clusters
Day Algorithm 1 Algorithm 2 Without TW 1 51.63 50.22 51.25 2 53.98 53.98 50.68 3 54.45 55.22 52.29 4 51.21 51.26 51.24 5 47.88 47.88 47.84
Total 259.15 258.56 253.30
Table 3: Total time [hours] for organic waste in k-means clusters
Day Algorithm 1 Algorithm 2 Without TW 1 19.68 20.13 19.15 2 20.92 20.63 19.85 3 14.45 14.45 14.42 4 15.62 15.62 15.63 5 18.00 18.00 18.00
Total 88.67 88.83 87.05
Total time [hours] for residual waste in k-means clusters
Total time [hours] for organic waste in k-means clusters
Day Algorithm 1 Algorithm 2 Without TW 1 19.68 20.13 19.15 2 20.92 20.63 19.85 3 14.45 14.45 14.42 4 15.62 15.62 15.63 5 18.00 18.00 18.00
Total 88.67 88.83 87.05
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
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
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
Prof. Dr.-Ing. Jörg Kirbs - Hochschule Merseburg
DIE HOCHSCHULE MERSEBURG ALS FLEXIBLER PARTNER DER INDUSTRIE
Prof. Dr. Dirk Sackmann, Prorektor für Forschung, Wissenstransfer und Existenzgründung
Thank you very much for your attention!
Dirk Sackmann
A HEURISTIC FOR THE SOLUTION OF VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS AND MULTIPLE DUMPING SITES IN WASTE COLLECTION
3rd Traveling Conference February 13-17, Zhengzhou, Busan, Manila
