ROUTING OF PERSONNEL SHUTTLES FOR A CALL CENTER:

Transcription

1 ODYSSEUS 2009 Workshop in Çeşme - İZMİR May 27th 2009 ROUTING OF PERSONNEL SHUTTLES FOR A CALL CENTER: AN OPEN VEHICLE ROUTING APPLICATION Deniz Koşucuoğlu 1, Deniz Aksen 2, Selçuk Savaş 3 1 Dept. of Industrial Engineering, Boğaziçi University 2 CASE, Koç University 3 Industrial Engineering Dept., Işık University Çeşme, İZMİR, May 27th 2009 Maps of the Travels of Odysseus Koşucuoğlu, Aksen, Savaş

2 Maps of the Travels of Odysseus Koşucuoğlu, Aksen, Savaş Maps of the Travels of Odysseus Koşucuoğlu, Aksen, Savaş

3 Maps of the Travels of Odysseus Koşucuoğlu, Aksen, Savaş Maps of the Travels of Odysseus Koşucuoğlu, Aksen, Savaş

4 Intro: Capacitated Open Vehicle Routing NP-hard problem as a total distance / traveling cost minimization problem. OPEN ROUTE Single Tour: Hamiltonian Path (each and every node visited at most once) Orienteering Problem (OP) Multiple Tours Team Orienteering Problem (TOP) 7 Koşucuoğlu, Aksen, Savaş CLOSED ROUTE Single Tour: Hamiltonian Cycle (each and every node visited exactly once) Traveling Salesman Problem (TSP) Multiple Tours Multiple Traveling Salesman Problem (m-tsp) Intro: Capacitated Open Vehicle Routing OPEN ROUTE Multiple Capacitated Tours: (each and every node visited exactly once) Open Vehicle Routing Problem (OVRP) Multiple Capacitated Tours served from multiple depots: Multi-Depot Open Vehicle Routing Problem (MDOVRP) CLOSED ROUTE Multiple Capacitated Tours: (each and every node visited exactly once) Vehicle Routing Problem (VRP) Multiple Capacitated Tours: served from multiple depots: Multi-Depot Vehicle Routing Problem (MDVRP) 8 Koşucuoğlu, Aksen, Savaş

5 Sample OVRP Routes 1) Source: Feiyue Li, Bruce Golden, Edward Wasil (2007) The open vehicle routing problem: Algorithms, large-scale test problems, and computational results. Computers & Operations Research 34 (10): Koşucuoğlu, Aksen, Savaş Sample OVRP Routes 2) Source: Christos D. Tarantilis, Chris T. Kiranoudis (2002) Distribution of fresh meat. Journal of Food Engineering 51 (1): Koşucuoğlu, Aksen, Savaş

6 Sample OVRP Routes 3) Source: Deniz Aksen, Zeynep Özyurt, Necati Aras (2007) Open vehicle routing problem with driver nodes and time deadlines Journal of the Operational Research Society 58 (9): Koşucuoğlu, Aksen, Savaş Sample OVRP Routes 4) Source: CD Tarantilis, G Ioannou, CT Kiranoudis and GP Prastacos (2007) Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm Journal of the Operational Research Society 56 (5): Koşucuoğlu, Aksen, Savaş

7 OVRP LITERATURE pioneers L Schrage (1981). Formulation and structure of more complex/realistic routing and scheduling problems. Networks 11: L Bodin, B Golden, A Assad, M Ball (1983). Routing and scheduling of vehicles and crews: the state of the art. Computers & Operations Research 10(2): D Sariklis, S Powell (2000). A heuristic method for the open vehicle routing problem. Journal of the Operational Research Society 51(5): CD Tarantilis and CT Kiranoudis (2002). Distribution of fresh meat. Journal of Food Engineering 51(1): Koşucuoğlu, Aksen, Savaş OVRP LITERATURE easy to compile JORS A heuristic method for OVRP - Sariklis, Powell JFE Distribution of Fresh Meat - Tarantilis, Kiranoudis JORS The school bus routing problem- a case study- Li, Fu EJOR A tabu search for OVRP - Brandão JORS A new tabu search heuristic for OVRP - Fu, Eglese, Li JORS Solving OVRP via a single parameter metaheuristic - Tarantilis, Ioannou, Kiranoudis, Prastacos LNCS An Ant Colony System for OVRP - Li, Tian LNCS Particle Swarm Optimization for OVRP - Wang, Wu, Zhao, Feng JORS A Branch-and-Cut Algorithm for the capacitated OVRP - Letchford, Lysgaard, Eglese JORS OVRP with driver nodes and time deadlines - Aksen, Özyurt, Aras JORS OVRPTW - Repoussis, Tarantilis, Ioannou JORS Solving school bus routing problems through IP - Bektaş, Elmastaş Comp&OR OVRP Algorithms large-scale test problems computational results - Li, Golden, Wasil 17th World Congress IFAC PSO for OVRP with time dependent travel time - Yanwei, Bin, Wanliang, Jingling EJOR VNS for OVRP - Fleszar, Osman, Hindi JORS ACO metaheuristic hybridized with TS for OVRP - Li, Tian, Leung 14 Koşucuoğlu, Aksen, Savaş

8 OVRP for a Call Center Solving VRP and OVRP with Classical Heuristics Classical Heuristics preferred when solution time is more critical than solution quality. (Parallel) Savings Algorithm by Clarke and Wright (1964) Sweep Algorithm by Gillett and Miller (1974) Push-Forward-Insertion by Solomon (1987), by Thangiah et al. (1993) Nearest Neighbourhood Search by Rosenkratz, Stearns and Lewis (1977), Solomon (1987), Fisher (1994). 15 Koşucuoğlu, Aksen, Savaş OVRP for a Call Center (cont.) Solving VRP and OVRP with Classical Heuristics Local Post Optimization (LPO) Procedures a.k.a. Local Improvement Heuristics (Parallel) 1-0 move (1-Opt) of Golden, Magnanti and Nguyen (1977) 1-1 exchange of Waters (1987) 2-2 exchange 2-opt of Croes (1958), Lin (1965) 3-opt of Lin (1965), of Lin and Kernighan (1973) 4-opt * of Renaud, Laporte and Boctor (1996) Or-opt of Or (1976) 16 Koşucuoğlu, Aksen, Savaş

9 OVRP for a Call Center (cont.) Solving VRP and OVRP with a Tabu Search Allowing Infeasible Solutions (Strategic Oscillation) Based on the Tabu Search Algorithm OTS described in Aksen, Özyurt and Aras (JORS, 2007). Can tackle a heterogeneous vehicle fleet as well. Enhanced with the 2-2 Exchange heuristic implemented as an intensification method (LPO) rather than diversification (neighborhood structure) 17 Koşucuoğlu, Aksen, Savaş LPO Analysis of the Proposed OTS INITIAL SOLUTION: CLARKE-WRIGHT PARALLEL SAVINGS WITHOUT LPO PROBLEMS SOLVED: 16 Benchmarks & O1, O2, O3, O4, O5, O6, O7, O8 LPO Frequency on the Current Solution: Inclusion of the 2-2 Exchange in the neighborhood search during the TS: Abbreviations Move Code Move Application type 1E 1-0 move exhaustively all possible best improvements with restart 1S 1-0 move sequentially all possible best improvements without restart 2E 1-1 exchange exhaustively all possible best improvements with restart 2S 1-1 exchange sequentially all possible best improvements without restart 3S 2-Opt sequentially all possible best improvements without restart 3E 2-Opt exhaustively all possible best improvements with restart 4S 2-2 exchange sequentially all possible best improvements without restart 4E 2-2 exchange exhaustively all possible best improvements without restart 100 YES 18 Koşucuoğlu, Aksen, Savaş

10 LPO Analysis of the Proposed OTS LPO Sequences No. Type A: Applied to the Current Solution every 100 iterations for intensification Type B: Applied to the Incumbent Solution every time it is improved Type A Type B 0 1S 3S 2S 3S 1S 3S 1S-3S 2S-3S-1S-3S 1 1S 3S 2S 3S 1S 1S-3S 2S-3S-1S 2 3S 1S 2S 3S 1S 3S-1S 2S-3S-1S 3 3S 2S 3S 1S 3S 3S 2S-3S-1S-3S 4 1S 3S 2S 1S 3S 4S 1S-3S 2S-1S-3S-4S 5 1S 3S 2S 1S 3S 1S-3S 2S-1S-3S 6 1S 3S 2S 3S 1S 4S 1S-3S 2S-3S-1S-4S 7 1E 3E 2E 3E 1E 3E 1E-3E 2E-3E-1E-3E 8 1E 3E 2E 3E 1E 1E-3E 2E-3E-1E 9 3E 1E 2E 3E 1E 3E-1E 2E-3E-1E 10 3E 2E 3E 1E 3E 3E 2E-3E-1E-3E 11 1E 3E 2E 1E 3E 4E 1E-3E 2E-1E-3E-4E 12 1E 3E 2E 1E 3E 1E-3E 2E-1E-3E 13 1E 3E 2E 3E 1E 4E 1E-3E 2E-3E-1E-4E 19 Koşucuoğlu, Aksen, Savaş Performance of OTS Exchange Result-I Result-II Result-III Result-V Problem name Our study with LPO Seq. 3 Best in literature (Alternative-a) Best in literature (Alternative-b) Best in literature with our number of vehicles Percent differrence between Result-IV and Result-I K_min Distance # Vehc. Distance # Vehc. Authors Description Distance # Vehc. Authors Description Distance # Vehc. Brandão / Fu-Eglese-Li / Li-Tian- Leung / Li-Golden-Wasil / Fleszar- TSAK / TSR / ACO / CMT-p Tarantilis et al. AMP, LBTA, BATA Osman-Hindi / Pisinger and Ropke ORTR / VNS / ALNS 25K, ALNS 50K % CMT-p Tarantilis et al. AMP, LBTA, BATA CMT-p Tarantilis et al. LBTA Fu-Eglese-Li / Li-Tian-Leung / Li- TSR / ACO / ORTR / Golden-Wasil / Fleszar-Osman- VNS / ALNS 25K, Hindi / Pisinger and Ropke ALNS 50K % Li-Tian-Leung / Li-Golden-Wasil / Fleszar-Osman-Hindi ACO / ORTR / VNS % CMT-p Li-Golden-Wasil / Pisinger and Ropke / Li-Tian-Leung / ORTR / ALNS 25K, ALNS Fleszar-Osman-Hindi 50K / ACO / VNS % CMT-p Tarantilis et al. LBTA Tarantilis et al. BATA % CMT-p CMT-p CMT-p Brandão / Fu-Eglese-Li / Li- Tian-Leung / Li-Golden- TSAK / TSR / ACO / Wasil / Fleszar-Osman-Hindi ORTR / VNS / ALNS 25K, / Pisinger and Ropke ALNS 50K % Fu-Eglese-Li / Li-Tian-Leung / Li-Golden-Wasil TSR / ACO / ORTR Pisinger and Ropke ALNS 50K % Brandão / Li-Tian-Leung / Li- Golden-Wasil / Fleszar- Osman-Hindi TSAK / ACO / ORTR / VNS % CMT-p Li-Golden-Wasil ORTR Pisinger and Ropke ALNS 50K % Pisinger and Ropke / Fleszar- ALNS 25K, ALNS 50K / CMT-p Osman-Hindi VNS % CMT-p Tarantilis et al. LBTA Tarantilis et al. BATA % CMT-p Tarantilis et al. / Li-Tian- Leung / Pisinger and Ropke / Li-Golden-Wasil / Fleszar- Osman-Hindi AMP, LBTA, BATA / ACO / ALNS 25K, ALNS 50K / ORTR / VNS % CMT-p Li-Golden-Wasil ORTR Fleszar-Osman-Hindi VNS % CMT-p Fisher-prob Li-Tian-Leung / Pisinger and Ropke / Li-Golden-Wasil / Fleszar-Osman-Hindi Fu-Eglese-Li / Li-Tian-Leung / Pisinger and Ropke / Li- Golden-Wasil 20 Koşucuoğlu, Aksen, Savaş ACO / ALNS 25K, ALNS 50K / ORTR / VNS % TSR / ACO / ALNS 25K, ALNS 50K / ORTR % Fisher-prob Li-Golden-Wasil / Fleszar- Osman-Hindi ORTR / VNS % Average Best Results %

11 Performance of OTS Exchange Problem name Our study with LPO Seq. 3 Best in literature with our number of vehicles K_min Distance # Vehc. Distance # Vehc. Percent differrence between Result-IV and Result-I CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % CMT-p % Fisher-prob % Fisher-prob % Average Best Results % 21 Koşucuoğlu, Aksen, Savaş Performance of OTS Exchange Result-I Result-II Problem name Our study Percent differrence with between Result-IV LPO Seq. 10 Best in literature and Result-I K_min Distance # Vehc. Distance # Vehc. Authors Description O Li-Golden-Wasil ORTR 0.4% O Li-Golden-Wasil ORTR 1.9% O Li-Golden-Wasil ORTR 0.2% O Li-Golden-Wasil ORTR 0.8% O Li-Golden-Wasil ORTR 0.3% O Li-Golden-Wasil ORTR 0.9% O Li-Golden-Wasil ORTR 0.7% O Li-Golden-Wasil ORTR 0.5% Average Best Results % 22 Koşucuoğlu, Aksen, Savaş

12 Performance of OTS Exchange OVRP LPO Setting No. OTS with Nearest Insertion Heuristic as initial solution 100-NO 100-YES 200-NO 200-YES OTS with C-W Parallel Savings Heuristic as initial solution 100-YES 200-YES No. Matches No. Matches or No. Matches No. Matches No. Matches No. Matches Avg. Dev. or Better Avg. Dev. Better Avg. Dev. or Better Avg. Dev. or Better Avg. Dev. or Better Avg. Dev. or Better % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % 1 BEST's 2.65% % % % % % 2 23 Koşucuoğlu, Aksen, Savaş Finansbank Call Center in İstanbul 24 Koşucuoğlu, Aksen, Savaş

13 Çeşme, İZMİR, May 27th 2009 Finansbank Call Center in İstanbul 25 Koşucuoğlu, Aksen, Savaş Çeşme, İZMİR, May 27th 2009 Finansbank Call Center in İstanbul 26 Koşucuoğlu, Aksen, Savaş

14 Finansbank Call Center in Ümraniye, İstanbul 27 Koşucuoğlu, Aksen, Savaş Personnel Buses of a Call Center Why do call centers in Istanbul heavily rely on personnel buses and minibuses? Which routes are modeled as open route? Which routes as closed route? Why? 28 Koşucuoğlu, Aksen, Savaş

15 A Software Application: SOLVER A decision support system (DSS) developed in Microsoft Visual Studio.NET environment using C#. Tailored for the call center s OVRP / VRP based on the daily shift schedules of 341 agents. Finansbank Call Center HQ, 20 Drivers, 341 Agents, 177 Pickup Points: - All coordinates obtained from Google Earth in degrees, minutes, and seconds with double decimal point precision. 29 Koşucuoğlu, Aksen, Savaş Solver.exe: an application SW - Google Earth coordinates then converted into 2-dimensional planar coordinates with the HQ being the origin. - The distance matrix is calculated using Euclidean distances except for arcs connecting intercontinental O/D pairs. X_coord = {([Latitude deg] + [Latitude min]/60 + [Latitude sec]/3600) [HQ s X_coord]} x 84 Y_coord = {([Longitude degrees] + [Longitude minutes]/60 + [Longitude seconds]/3600) [HQ s Y_coord] } x Koşucuoğlu, Aksen, Savaş

16 Features of the Software Capability of dealing with both VRP and OVRP subject to an optional Maximum Tour Duration constraint. Vehicles of non-uniform passenger capacities (Heterogeneous Fleet) The two Bosphorus Bridges represented with a pair of nodes each, one node for the European foot and one for the Asian foot. - Arcs connecting intercontinental nodes must pass through either bridge, whichever has the shortest perpendicular distance to the arc. Choice between Pickup Point Routing vs. Home Address Routing Manual modification of the distance matrix possible to account for traffic density or blocked roads. 31 Koşucuoğlu, Aksen, Savaş Features of the Software (cont.) At the end of the routing, agents drop-off times (in case of HQ transfers) and pickup times (in case of home transfers) can be obtained from the output file. A database editing utility (Editor.exe) allows modification, deletion, and addition of agent, pickup point, and driver location data. The software can read shift schedules either from XML files created a priori or from MS-Excel worksheets put together in a standard format. The software can also be used to create ad-hoc problem instances with an arbitrary selection of individual agents and drivers in the database. 32 Koşucuoğlu, Aksen, Savaş

17 Features of the Software (cont.) The software (Solver.exe) can be used to generate new large-scale problem instances using the pseudo code described in Li, Golden and Wasil (Comp. & OR, 2007). When multiple OVRP instances are to be solved as a batch job, the software can read data input files of the batch that are created according to Markus Solomon s VRPTW file format (OR, 1987). Each instance is then solved 20 times using different initial random number seeds. By the end of the batch run, a solution is double-checked for overcapacity and possible maximum tour length infeasibilities. 33 Koşucuoğlu, Aksen, Savaş Features of the Software (cont.) Results such as objective values, solution times, no. used drivers (vehicles), and infeasibility status can be read from the output files that are saved as text, and can be automatically tabulated in a MS-Excel worksheet. 34 Koşucuoğlu, Aksen, Savaş

18 Çeşme, İZMİR, May 27th 2009 MS- Excel Worksheet of Agents Shift Schedules for two weeks 35 Koşucuoğlu, Aksen, Savaş Çeşme, İZMİR, May 27th 2009 Screenshots of the Software Database Editor 36 Koşucuoğlu, Aksen, Savaş

19 Screenshots of the Software (cont.) Database Editor 37 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) 38 Koşucuoğlu, Aksen, Savaş

20 Screenshots of the Software (cont.) 39 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) 40 Koşucuoğlu, Aksen, Savaş

21 Screenshots of the Software (cont.) 41 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) 42 Koşucuoğlu, Aksen, Savaş

22 Screenshots of the Software (cont.) CMT-p12.ovrp 43 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) CMT-p02.ovrp 44 Koşucuoğlu, Aksen, Savaş

23 Questions & Comments? 45 Koşucuoğlu, Aksen, Savaş