a branch-and-price algorithm for a multi-attribute technician routing and scheduling problem
TRANSCRIPT
A Branch-and-Price Algorithm for a Multi-Attribute Technician Routing and Scheduling Problem
Ines Methlouthia,c, Jean-Yves Potvina,c, Michel Gendreaua,b
a Diro, Universite de Montreal, Montreal,Qc,Canadab MAGI, Ecole Polytechnique, Montreal, QC, Canada
c CIRRELT,C.P.8888, succ. Centre-ville, Montreal, Qc, Canada H3C 3P8
INFORMS/CORS Montreal June 2015
Outline
I. Context
II. Problem Description
III. Solution Approach
IV. Computational Experiments
V. Conclusion
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Context : Technician Routing and Scheduling Problem «TRSP»
Pickup
Pickup
Pickup
Skills
Tools
Spare parts
Depot
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� Static TRSPs:� Xu et al. [2001]:
� Technicians routing problem encountered in the field oftelecommunications;
� Allocation of technicians taking into account time slots;� 4 heuristics: Greedy, Greedy-Plus, Local search, GRASP.
Context:Related Works
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� Cordeau et al. [2010]:� Technician routing problem (ROADEF competition).� Assignment of technician teams on a multi-day interval, taking into
account three different task priority levels.� The objective is to minimize the total time to finalize the last task
for each priority level and for all tours;� A construction heuristic is used to identify a first feasible solution;� The solution found is then modified by a destruction-reconstruction
method.
� Cortés et al. [2014]:� Technician routing problem for Xerox ;
� Allocation of technicians taking into account call priority;
� Columngenerationapproach;
Context: Related Works (cont’d)
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� Columngenerationapproach;
� Dynamic TRSPs :� Bostel et al. [2008]:
� Dynamic TRSPs;
� Assigning technicians over a period of one week for repairsor maintenance;
� Memeticalgorithm;
Context:Related Works (cont’d)
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� Memeticalgorithm;
� Column generation.
� Pillac et al. [2012]:
� TRSP with subset of dynamic tasks;
� Adaptive large neighborhood search method;
Problem DescriptionBetween 300 and 600 calls are processed per day. These calls can be either planned or received during the day. A priority is assigned to each call, depending on the emergency of the call and the SLA.
The dispatcher distributes these calls to the company's technicians
Dispatcher
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Client
Sub-clients
100 Depots
Scoring systemModel of the service area for distances and travel times.
Service in major centers across Canada 150 Technicians
Shelf
Problem Description: (cont’d)
Spare partsShelf
Pickup
Depot
Break
-Skills;-Inventory;-Breaks.
-Spare parts;-Shelf parts;-Time windows;-Skills.
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Solution Approach: Column generation
� Exact method;
� Requires a path formulation ;� Column generation’s iteration:
� Master problem:� Setcovering problem;
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� Setcovering problem;� Solve the relaxed problem with a subset of tours(columns, variables);
� Sub-problem: find the best tours with negative reduced cost;� Add those columns to the master problem ;� Stop: no column with negative reduced cost can be found;
Add columns with negative reduced cost
Dual values
Solution Approach: Pricing problem
� Initial solution: Nearest neighbor� Generate Column: ESPPRC
� Label:
� Dominance rules: � For and the labels of
two partial paths from a technician's home position to a given task:
� Solve with Cplex 12.6
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Solution Approach: Branching strategy
� Branching by technician task:� Branch on the technician-task candidate with flow closest to 0.5;
� Branching by tour:� Branch on the tour candidate closest to 0.5;
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Computational Experiments: Data
� New test problems:� Narrow and wide time windows;
� Tasks, depots and technicians’ home positions are randomly located in an area of 40kms*40kms ;located in an area of 40kms*40kms ;
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Computational Experiments: Data (cont’d)
Instance Nb.Tasks Technician DepotShelf Part
Area
%tasks need shelf parts
Technicians versatility
(100%, 50%,25%) of tasks
InstP 25 3 2 1 1600 km² 12%(33.33%, 33.33%,
33.33%)
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InstS 25 3 2 1 1600km² 25% (33%,33%,34%)
InstSk 25 3 2 1 1600km² 12% (50%,25%,25%)
Instance LBAverage of Tasks per Technican
ESPPRC
Time IterationsBranch 1 Branch 2
Time Tree Time Tree
InstP1 119.41 118.13 7.33 03:52:09 27 00:00:09 516 00:00:29 3.60E+16
Computational Experiments: Results
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InstP2 119.42 118.14 7.33 03:31:01 27 00:00:08 516 00:00:21 3.60E+16
InstS1 117.60 116.72 7.67 02:46:31 30 00:00:02 18 00:00:28 3.60E+16
InstS2 117.60 116.60 7.67 02:55:22 30 00:00:02 18 00:00:28 3.60E+16
InstSk1 121.01 121.01 8.33 08:52:37 30 - - - -
Conclusion
� New variant of technician routing and scheduling problem;
� New set covering model;
� New branching strategy exploiting the special structure of the problem;
Promising results in terms of solution quality and computation � Promising results in terms of solution quality and computation time;
� Implement DSSR to decrease computational time;
� Further research will focus on the dynamic version of this problem.
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References� Bostel, N., Dejax, P., Guez, P., Tricoire, F., 2008. Multi-period planning and routing on a rolling
horizon for field force optimization logistics. In: Golden, B., Raghavan, S., Wasil, E. (Eds.), The Vehicle Routing
Problem: Latest Advances and New Challenges. Vol. 43 of Operations Research/Computer Science Interfaces. Springer US, pp. 503-525.
� Cordeau, J.-F., Laporte, G., Pasin, F., Ropke, S., 2010. Scheduling technicians and tasks in a telecommunications company. Journal of Scheduling 13 (4), 393-409.
� Cortes, C. Ordonez, F. Sebastian, S. Weintraub, A. 2014. Routing technicians under stochastic service times : A robust optimization approach. The Sixth Triennial Symposium on Transportation Analysis.
Feillet, D. Dejax, P. Gendreau, M. Gueguen, C. 2004. An exact algorithm for the elementary
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� Feillet, D. Dejax, P. Gendreau, M. Gueguen, C. 2004. An exact algorithm for the elementary shortest path problem with resource constraints : Application to some vehicle routing problems. Networks, 44(3) :216–229.
� Pillac, V., Gueret, C., Medaglia, A., May 2012. On the dynamic technician routing and scheduling problem. In: Proceedings of the 5th International Workshop on Freight Transportation and Logistics (ODYSSEUS
2012). Mikonos, Greece.
� Xu, J., Chiu, S., 2001. Effective heuristic procedures for a Field technician scheduling problem. Journal of Heuristics 7, 495-509.