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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: MIP Model Parameters :

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Solution Approach: MIP Model (cont’d)Parameters :

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Variables:

Solution Approach: MIP Model (cont’d)

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Solution Approach: MIP Model (cont’d)

Subject to:

Model:

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Solution Approach: MIP Model (cont’d)

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Solution Approach: MIP Model (cont’d)

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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

Parameters:

Solution Approach: Set covering model

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Variables:

Subject to :

λ i

µ d

p

Solution Approach: Set covering model (cont’d)

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p

u k

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.

Thank You Thank You

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