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A Branch-and-Price Algorithm for a Multi-Attribute Technician Routing and Scheduling Problem

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  1. 1. 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,Canada b MAGI, Ecole Polytechnique, Montreal, QC, Canada c CIRRELT,C.P.8888, succ. Centre-ville, Montreal, Qc, Canada H3C 3P8 INFORMS/CORS Montreal June 2015
  2. 2. Outline I. Context II. Problem Description III. Solution Approach IV. Computational Experiments V. Conclusion 2
  3. 3. Context : Technician Routing and Scheduling Problem TRSP Pickup Pickup Pickup Skills Tools Spare parts Depot 3
  4. 4. Static TRSPs: Xu et al. [2001]: Technicians routing problem encountered in the field of telecommunications; Allocation of technicians taking into account time slots; 4 heuristics: Greedy, Greedy-Plus, Local search, GRASP. Context: Related Works 4 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.
  5. 5. Corts et al. [2014]: Technician routing problem for Xerox ; Allocation of technicians taking into account call priority; Column generation approach; Context: Related Works (contd) 5 Column generation approach;
  6. 6. Dynamic TRSPs : Bostel et al. [2008]: Dynamic TRSPs; Assigning technicians over a period of one week for repairs or maintenance; Memetic algorithm; Context: Related Works (contd) 6 Memetic algorithm; Column generation. Pillac et al. [2012]: TRSP with subset of dynamic tasks; Adaptive large neighborhood search method;
  7. 7. Problem Description Between 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 7 Client Sub-clients 100 Depots Scoring system Model of the service area for distances and travel times. Service in major centers across Canada 150 Technicians
  8. 8. Shelf Problem Description: (contd) Spare parts Shelf Pickup Depot Break -Skills; -Inventory; -Breaks. -Spare parts; -Shelf parts; -Time windows; -Skills. 8
  9. 9. Solution Approach: MIP Model Parameters : 9
  10. 10. Solution Approach: MIP Model (contd) Parameters : 10
  11. 11. Variables: Solution Approach: MIP Model (contd) 11
  12. 12. Solution Approach: MIP Model (contd) Subject to: Model: 12
  13. 13. Solution Approach: MIP Model (contd) 13
  14. 14. Solution Approach: MIP Model (contd) 14
  15. 15. Solution Approach: Column generation Exact method; Requires a path formulation ; Column generations iteration: Master problem: Set covering problem; 15 Set covering 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
  16. 16. Parameters: Solution Approach: Set covering model 16 Variables:
  17. 17. Subject to : i d p Solution Approach: Set covering model (contd) 17 p u k
  18. 18. 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 18
  19. 19. 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; 19
  20. 20. 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 ; 20
  21. 21. Computational Experiments: Data (contd) Instance Nb.Tasks Technician Depot Shelf Part Area %tasks need shelf parts Technicians versatility (100%, 50%,25%) of tasks InstP 25 3 2 1 1600 km 12% (33.33%, 33.33%, 33.33%) 21 InstS 25 3 2 1 1600km 25% (33%,33%,34%) InstSk 25 3 2 1 1600km 12% (50%,25%,25%)
  22. 22. Instance LB Average of Tasks per Technican ESPPRC Time Iterations Branch 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 22 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 - - - -
  23. 23. 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 computationPromising 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. 23
  24. 24. 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.),TheVehicle 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 SixthTriennial Symposium onTransportation Analysis. Feillet, D. Dejax, P. Gendreau, M. Gueguen, C. 2004.An exact algorithm for the elementary 24 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) :216229. Pillac,V., Gueret, C., Medaglia,A., May 2012. On the dynamic technician routing and scheduling problem. In: Proceedings of the 5th InternationalWorkshop on FreightTransportation 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.
  25. 25. Thank YouThank You 25
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