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 - 1 2 Koşucuoğlu, Aksen, Savaş
Maps of the Travels of Odysseus - 2 3 Koşucuoğlu, Aksen, Savaş Maps of the Travels of Odysseus - 3 4 Koşucuoğlu, Aksen, Savaş
Maps of the Travels of Odysseus - 4 5 Koşucuoğlu, Aksen, Savaş Maps of the Travels of Odysseus - 5 6 Koşucuoğlu, Aksen, Savaş
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
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): 2918 2930. 9 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): 85 91. 10 Koşucuoğlu, Aksen, Savaş
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): 1223 1234 11 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): 588 596 12 Koşucuoğlu, Aksen, Savaş
OVRP LITERATURE pioneers L Schrage (1981). Formulation and structure of more complex/realistic routing and scheduling problems. Networks 11: 229 232. 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):63 211. D Sariklis, S Powell (2000). A heuristic method for the open vehicle routing problem. Journal of the Operational Research Society 51(5):564 573. CD Tarantilis and CT Kiranoudis (2002). Distribution of fresh meat. Journal of Food Engineering 51(1): 85 91. 13 Koşucuoğlu, Aksen, Savaş OVRP LITERATURE easy to compile JORS 2000 - A heuristic method for OVRP - Sariklis, Powell JFE 2002 - Distribution of Fresh Meat - Tarantilis, Kiranoudis JORS 2002 - The school bus routing problem- a case study- Li, Fu EJOR 2004 - A tabu search for OVRP - Brandão JORS 2005 - A new tabu search heuristic for OVRP - Fu, Eglese, Li JORS 2005 - Solving OVRP via a single parameter metaheuristic - Tarantilis, Ioannou, Kiranoudis, Prastacos LNCS 2006 - An Ant Colony System for OVRP - Li, Tian LNCS 2006 - Particle Swarm Optimization for OVRP - Wang, Wu, Zhao, Feng JORS 2007 - A Branch-and-Cut Algorithm for the capacitated OVRP - Letchford, Lysgaard, Eglese JORS 2007 - OVRP with driver nodes and time deadlines - Aksen, Özyurt, Aras JORS 2007 - OVRPTW - Repoussis, Tarantilis, Ioannou JORS 2007 - Solving school bus routing problems through IP - Bektaş, Elmastaş Comp&OR 2007 - OVRP Algorithms large-scale test problems computational results - Li, Golden, Wasil 17th World Congress IFAC 2008 - PSO for OVRP with time dependent travel time - Yanwei, Bin, Wanliang, Jingling EJOR 2009 - VNS for OVRP - Fleszar, Osman, Hindi JORS 2009 - ACO metaheuristic hybridized with TS for OVRP - Li, Tian, Leung 14 Koşucuoğlu, Aksen, Savaş
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
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
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 + 2-2 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-p01 5 417.5 5 413.0 6 Tarantilis et al. AMP, LBTA, BATA 416.1 5 Osman-Hindi / Pisinger and Ropke ORTR / VNS / ALNS 25K, ALNS 50K 416.1 5 0.3% CMT-p02 10 580.2 10 564.1 11 Tarantilis et al. AMP, LBTA, BATA 567.1 10 CMT-p03 8 651.6 8 639.6 9 Tarantilis et al. LBTA 639.7 8 Fu-Eglese-Li / Li-Tian-Leung / Li- TSR / ACO / ORTR / Golden-Wasil / Fleszar-Osman- VNS / ALNS 25K, Hindi / Pisinger and Ropke ALNS 50K 567.1 10 2.3% Li-Tian-Leung / Li-Golden-Wasil / Fleszar-Osman-Hindi ACO / ORTR / VNS 639.7 8 1.8% CMT-p04 12 751.3 12 733.1 12 Li-Golden-Wasil / Pisinger and Ropke / Li-Tian-Leung / ORTR / ALNS 25K, ALNS Fleszar-Osman-Hindi 50K / ACO / VNS 733.1 12 2.5% CMT-p05 16 954.1 16 870.3 17 Tarantilis et al. LBTA 879.4 16 Tarantilis et al. BATA 879.4 16 8.5% CMT-p06 5 413.7 6 413.0 6 CMT-p07 10 568.9 11 568.5 11 CMT-p08 8 657.7 9 644.6 9 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 413.0 6 0.2% Fu-Eglese-Li / Li-Tian-Leung / Li-Golden-Wasil TSR / ACO / ORTR 583.2 10 Pisinger and Ropke ALNS 50K 568.5 11 0.1% Brandão / Li-Tian-Leung / Li- Golden-Wasil / Fleszar- Osman-Hindi TSAK / ACO / ORTR / VNS 644.6 9 2.0% CMT-p09 12 772.8 14 756.4 14 Li-Golden-Wasil ORTR 757.8 13 Pisinger and Ropke ALNS 50K 756.4 14 2.2% Pisinger and Ropke / Fleszar- ALNS 25K, ALNS 50K / CMT-p10 16 915.1 18 875.7 17 Osman-Hindi VNS 875.7 17 4.5% CMT-p11 7 688.2 7 678.5 10 Tarantilis et al. LBTA 679.6 9 Tarantilis et al. BATA 682.1 7 0.9% CMT-p12 10 535.5 10 534.2 10 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 534.2 10 0.2% CMT-p13 7 914.9 12 896.5 12 Li-Golden-Wasil ORTR 904.0 11 Fleszar-Osman-Hindi VNS 896.5 12 2.0% CMT-p14 10 590.5 12 591.9 11 Fisher-prob11 4 178.2 4 177.0 4 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 591.9 11-0.2% TSR / ACO / ALNS 25K, ALNS 50K / ORTR 177.0 4 0.7% Fisher-prob12 7 772.9 7 769.7 7 Li-Golden-Wasil / Fleszar- Osman-Hindi ORTR / VNS 769.7 7 0.4% Average Best Results 647.7 632.9 678.4 634.1 2.15%
Performance of OTS + 2-2 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-p01 5 417.5 5 416.1 5 0.3% CMT-p02 10 580.2 10 567.1 10 2.3% CMT-p03 8 651.6 8 639.7 8 1.8% CMT-p04 12 751.3 12 733.1 12 2.5% CMT-p05 16 954.1 16 879.4 16 8.5% CMT-p06 5 413.7 6 413.0 6 0.2% CMT-p07 10 568.9 11 568.5 11 0.1% CMT-p08 8 657.7 9 644.6 9 2.0% CMT-p09 12 772.8 14 756.4 14 2.2% CMT-p10 16 915.1 18 875.7 17 4.5% CMT-p11 7 688.2 7 682.1 7 0.9% CMT-p12 10 535.5 10 534.2 10 0.2% CMT-p13 7 914.9 12 896.5 12 2.0% CMT-p14 10 590.5 12 591.9 11-0.2% Fisher-prob11 4 178.2 4 177.0 4 0.7% Fisher-prob12 7 772.9 7 769.7 7 0.4% Average Best Results 647.7 634.1 2.15% 21 Koşucuoğlu, Aksen, Savaş Performance of OTS + 2-2 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 O1 5 6040.10 5 6018.52 5 Li-Golden-Wasil ORTR 0.4% O2 9 4672.36 10 4584.55 10 Li-Golden-Wasil ORTR 1.9% O3 7 7752.08 7 7732.85 7 Li-Golden-Wasil ORTR 0.2% O4 10 7352.73 10 7291.89 10 Li-Golden-Wasil ORTR 0.8% O5 8 9223.84 9 9197.61 9 Li-Golden-Wasil ORTR 0.3% O6 9 9891.41 9 9803.80 10 Li-Golden-Wasil ORTR 0.9% O7 10 10449.60 10 10374.97 11 Li-Golden-Wasil ORTR 0.7% O8 10 12491.58 10 12429.56 10 Li-Golden-Wasil ORTR 0.5% Average Best Results 8484.21 8429.22 0.65% 22 Koşucuoğlu, Aksen, Savaş
Performance of OTS + 2-2 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 0 3.21% 2 2.82% 2 3.34% 2 3.09% 1 2.68% 1 2.57% 1 1 3.32% 1 2.59% 3 3.83% 1 2.33% 1 2.61% 1 2.70% 1 2 3.27% 1 2.63% 2 3.47% 1 2.48% 2 2.63% 1 2.71% 2 3 3.29% 1 3.20% 2 3.40% 2 2.95% 2 2.15% 2 2.55% 1 4 3.20% 1 2.82% 1 2.76% 1 3.08% 1 2.84% 1 2.76% 1 5 3.14% 1 3.04% 0 2.90% 1 3.15% 0 2.58% 1 2.22% 1 6 3.00% 2 2.35% 0 3.02% 2 2.63% 2 2.53% 1 2.72% 1 7 3.30% 1 3.58% 2 3.40% 0 2.62% 1 2.24% 1 2.82% 1 8 3.11% 0 3.22% 2 3.46% 0 2.82% 1 2.45% 1 2.58% 1 9 2.65% 0 3.15% 0 3.54% 0 3.12% 0 2.56% 2 2.53% 2 10 3.23% 0 2.98% 2 3.44% 1 2.95% 0 2.30% 1 2.66% 2 11 3.57% 0 2.82% 0 2.96% 0 2.98% 0 2.43% 1 2.57% 1 12 3.23% 0 2.58% 1 3.16% 0 3.09% 1 2.48% 1 2.66% 1 13 2.89% 1 2.51% 3 3.02% 0 2.92% 2 2.57% 1 2.69% 1 BEST's 2.65% 2 2.35% 3 2.76% 2 2.33% 2 2.15% 2 2.22% 2 23 Koşucuoğlu, Aksen, Savaş Finansbank Call Center in İstanbul 24 Koşucuoğlu, Aksen, Savaş
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
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
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 111 30 Koşucuoğlu, Aksen, Savaş
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
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
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
Screenshots of the Software (cont.) Database Editor 37 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) 38 Koşucuoğlu, Aksen, Savaş
Screenshots of the Software (cont.) 39 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) 40 Koşucuoğlu, Aksen, Savaş
Screenshots of the Software (cont.) 41 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) 42 Koşucuoğlu, Aksen, Savaş
Screenshots of the Software (cont.) CMT-p12.ovrp 43 Koşucuoğlu, Aksen, Savaş Screenshots of the Software (cont.) CMT-p02.ovrp 44 Koşucuoğlu, Aksen, Savaş
Questions & Comments? 45 Koşucuoğlu, Aksen, Savaş