
-
Previous Article
Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points
- JIMO Home
- This Issue
-
Next Article
Designing a hub location and pricing network in a competitive environment
Shipper collaboration in forward and reverse logistics
1. | School of Management, Xi'an Jiaotong University, 710049, NO.28 Xianning Road, Xian Shaanxi, China, ERC for Process Mining of Manufacturing Services in Shaanxi Province |
2. | Industrial Systems Optimization Laboratory, Charles Delaunay Institute and UMR CNRS, 6281, University of Technology of Troyes, 12 rue Marie Curie, CS 42060, 10004 Troyes, France |
In less than truckload transportation, shippers collaborate to reduce their logistics costs by consolidating their transportation requests in the procurement of transportation services from a carrier for serving the requests. In this paper, we study shipper collaboration in forward and reverse logistics, in which multiple shippers with forward or/and reverse logistics operations consolidate their transportation requests. In the forward and reverse logistics, manufacturers deliver new products to their customers and used products are collected from customers and transported to remanufacturers for repair or reproduction. This gives rise to a new vehicle routing problem with pickup and delivery requests and three different types of depots (product depots, vehicle depots and recycle depots). A hybrid approach combining greedy randomized adaptive search procedure (GRASP) and iterated local search (ILS) is proposed to find a near optimal solution of the problem. Numerical experiments on a large set of randomly generated instances with different problem sizes demonstrate that shipper collaboration in forward and reverse logistics can realize significant cost savings compared with the isolated operation of each shipper without cooperation, and the proposed approach is effective in the sense that it can find a high quality solution in a reasonable computation time.
References:
[1] |
C. Archetti and M. G. Speranza,
Vehicle routing problems with split deliveries, International Transactions in Operational Research, 19 (2012), 3-22.
doi: 10.1111/j.1475-3995.2011.00811.x. |
[2] |
J. F. Audy, S. D'Amours and L. M. Rousseau,
Cost allocation in the establishment of a collaborative transportation agreement-an application in the furniture industry, Journal of the Operational Research Society, 62 (2011), 960-970.
|
[3] |
M. Battarra, J. F. Cordeau and M. Iori,
Pickup-and-delivery problems for goods transportation, Vehicle routing: problems, methods, and applications. MOS/SIAM series on optimization, (2014), 161-192.
|
[4] |
R. Bent and P. Van Hentenryck,
A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows, Computers & Operations Research, 33 (2006), 875-893.
|
[5] |
G. Berbeglia, J. F. Cordeau, I. Gribkovskaia and G. Laporte,
Static pickup and delivery problems: a classification scheme and survey, Top, 15 (2007), 1-31.
doi: 10.1007/s11750-007-0009-0. |
[6] |
S. Berger and C. Bierwirth,
Solutions to the request reassignment problem in collaborative carrier networks, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 627-638.
|
[7] |
N. Bianchessi and G. Righini,
Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery, Computers & Operations Research, 34 (2007), 578-594.
|
[8] |
J. Crispim and J. Brandão,
Metaheuristics applied to mixed and simultaneous extensions of vehicle routing problems with backhauls, Journal of the Operational Research Society, 34 (2005), 1296-1302.
|
[9] |
B. Dai and H. Chen,
Mathematical model and solution approach for collaborative logistics in less than truckload (LTL) transportation, Computers & Industrial Engineering, 2009. CIE 2009. International Conference on IEEE, (2009), 767-772.
|
[10] |
J. Dethloff,
Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up, Operations Research-Spektrum, 23 (2001), 79-96.
doi: 10.1007/PL00013346. |
[11] |
M. Dror and P. Trudeau,
Savings by split delivery routing, Transportation Science, 23 (1989), 141-145.
|
[12] |
O. Ergun, G. Kuyzu and M. Savelsbergh,
Shipper collaboration, Computers & Operations Research, 34 (2007a), 1551-1560.
|
[13] |
O. Ergun, G. Kuyzu and M. Savelsbergh,
Reducing truckload transportation costs through collaboration, Transportation Science, 41 (2007b), 206-221.
|
[14] |
T. A. Feo and J. F. Bard,
Flight scheduling and maintenance base planning, Management Science, 35 (1989), 1415-1432.
|
[15] |
M. Frisk, M. G |
[16] |
Y. Gajpal and P. Abad,
An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup, Computers & Operations Research, 36 (2009), 3215-3223.
|
[17] |
F. P. Goksal, I. Karaoglan and F. Altiparmak,
A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery, Computers & Industrial Engineering, 65 (2013), 39-53.
|
[18] |
M. Y. Lai, C. S. Liu and X. J. Tong,
A two-stage hybrid meta-heuristic for pickup and delivery vehicle routing problem with time windows, Journal of Industrial & Management Optimization, 6 (2010), 435-451.
doi: 10.3934/jimo.2010.6.435. |
[19] |
H. Li and A. Lim,
A metaheuristic for the pickup and delivery problem with time windows, International Journal on Artificial Intelligence Tools, 12 (2003), 173-186.
|
[20] |
J. Li, P. M. Pardalos, H. Sun, J. Pei and Y. Zhang,
Iterated local search embedded adaptive neighborhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups, Expert Systems with Applications, 42 (2015), 3551-3561.
|
[21] |
R. Liu, X. Xie, V. Augusto and C. Rodriguez,
Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care, European Journal of Operational Research, 230 (2013), 475-486.
doi: 10.1016/j.ejor.2013.04.044. |
[22] |
H. R. Lourenço, O. C. Martin and T. Stützle, Iterated local search, in In Handbook of metaheuristics, Springer US, 57 (2003), 321–353. |
[23] |
Q. Lu and M. M. Dessouky,
A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows, European Journal of Operational Research, 175 (2006), 672-687.
|
[24] |
H. Min,
The multiple vehicle routing problem with simultaneous delivery and pick-up points, Transportation Research Part A: General, 23 (1989), 377-386.
|
[25] |
S. Mitra,
An algorithm for the generalized vehicle routing problem with backhauling, Asia-Pacific Journal of Operational Research, 22 (2005), 153-169.
doi: 10.1142/S0217595905000522. |
[26] |
S. Mitra,
A parallel clustering technique for the vehicle routing problem with split deliveries and pickups, Journal of the operational Research Society, 59 (2008), 1532-1546.
|
[27] |
G. Nagy and S. Salhi,
Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries, European Journal of Operational Research, 162 (2005), 126-141.
|
[28] |
W. P. Nanry and J. W. Barnes,
Solving the pickup and delivery problem with time windows using reactive tabu search, Transportation Research Part B: Methodological, 34 (2000), 107-121.
|
[29] |
M. Nowak, |
[30] |
M. Nowak, |
[31] |
G. Pankratz,
A grouping genetic algorithm for the pickup and delivery problem with time windows, Or Spectrum, 27 (2005), 21-41.
doi: 10.1007/s00291-004-0173-7. |
[32] |
P. Pelagagge, L. Fratocchi and A. C. Caputo,
A genetic approach for freight transportation planning, Industrial Management & Data Systems, 106 (2006), 719-738.
|
[33] |
D. Pisinger and S. Ropke,
A general heuristic for vehicle routing problems, Computers & operations research, 34 (2007), 2403-2435.
doi: 10.1016/j.cor.2005.09.012. |
[34] |
C. Prins, N. Labadi and M. Reghioui,
Tour splitting algorithms for vehicle routing problems, International Journal of Production Research, 47 (2009), 507-535.
|
[35] |
M. Reghioui, C. Prins and N. Labadi,
GRASP with path relinking for the capacitated arc routing problem with time windows, InWorkshops on Applications of Evolutionary Computation, (2007), 722-731.
|
[36] |
J. Renaud, F. F. Boctor and G. Laporte,
Perturbation heuristics for the pickup and delivery traveling salesman problem, Computers & Operations Research, 29 (2002), 1129-1141.
doi: 10.1016/S0305-0548(99)00066-0. |
[37] |
S. Ropke and D. Pisinger,
An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Transportation Science, 40 (2006a), 455-472.
|
[38] |
S. Ropke and D. Pisinger,
A unified heuristic for a large class of vehicle routing problems with backhauls, European Journal of Operational Research, 171 (2006), 750-775.
doi: 10.1016/j.ejor.2004.09.004. |
[39] |
S. Salhi and G. Nagy,
A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling, Journal of the operational Research Society, 50 (1999), 1034-1042.
|
[40] |
R. Sprenger and L. Monch,
A methodology to solve large-scale cooperative transportation planning problems, European Journal of Operational Research, 223 (2012), 626-636.
|
[41] |
A. Subramanian, L. M. Drummond, L. M. D. A., C. Bentes, L. S. Ochi and R. Farias,
A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery, Computers & Operations Research, 223 (2010), 1899-1911.
|
[42] |
A. Subramanian, E. Uchoa and L. S. Ochi,
A hybrid algorithm for a class of vehicle routing problems, Computers & Operations Research, 40 (2013), 2519-2531.
|
[43] |
A. S. Tasan and M. Gen,
A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries, Computers & Industrial Engineering, 62 (2012), 755-761.
|
[44] |
F. L. Usberti, P. M. França and A. L. M. França,
GRASP with evolutionary path-relinking for the capacitated arc routing problem, Computers & Operations Research, 40 (2013), 3206-3217.
doi: 10.1016/j.cor.2011.10.014. |
[45] |
N. A. Wassan, A. H. Wassan and G. Nagy,
A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries, Journal of Combinatorial Optimization, 15 (2008), 368-386.
doi: 10.1007/s10878-007-9090-4. |
[46] |
O. Yilmaz and S. Savasaneril,
Collaboration among small shippers in a transportation market, European Journal of Operational Research, 218 (2012), 408-415.
doi: 10.1016/j.ejor.2011.11.018. |
[47] |
T. Zhang, W. A. Chaovalitwongse and Y. Zhang,
Integrated ant colony and tabu search approach for time dependent vehicle routing problems with simultaneous pickup and delivery, Journal of Combinatorial Optimization, 28 (2014), 288-309.
doi: 10.1007/s10878-014-9741-1. |
show all references
References:
[1] |
C. Archetti and M. G. Speranza,
Vehicle routing problems with split deliveries, International Transactions in Operational Research, 19 (2012), 3-22.
doi: 10.1111/j.1475-3995.2011.00811.x. |
[2] |
J. F. Audy, S. D'Amours and L. M. Rousseau,
Cost allocation in the establishment of a collaborative transportation agreement-an application in the furniture industry, Journal of the Operational Research Society, 62 (2011), 960-970.
|
[3] |
M. Battarra, J. F. Cordeau and M. Iori,
Pickup-and-delivery problems for goods transportation, Vehicle routing: problems, methods, and applications. MOS/SIAM series on optimization, (2014), 161-192.
|
[4] |
R. Bent and P. Van Hentenryck,
A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows, Computers & Operations Research, 33 (2006), 875-893.
|
[5] |
G. Berbeglia, J. F. Cordeau, I. Gribkovskaia and G. Laporte,
Static pickup and delivery problems: a classification scheme and survey, Top, 15 (2007), 1-31.
doi: 10.1007/s11750-007-0009-0. |
[6] |
S. Berger and C. Bierwirth,
Solutions to the request reassignment problem in collaborative carrier networks, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 627-638.
|
[7] |
N. Bianchessi and G. Righini,
Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery, Computers & Operations Research, 34 (2007), 578-594.
|
[8] |
J. Crispim and J. Brandão,
Metaheuristics applied to mixed and simultaneous extensions of vehicle routing problems with backhauls, Journal of the Operational Research Society, 34 (2005), 1296-1302.
|
[9] |
B. Dai and H. Chen,
Mathematical model and solution approach for collaborative logistics in less than truckload (LTL) transportation, Computers & Industrial Engineering, 2009. CIE 2009. International Conference on IEEE, (2009), 767-772.
|
[10] |
J. Dethloff,
Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up, Operations Research-Spektrum, 23 (2001), 79-96.
doi: 10.1007/PL00013346. |
[11] |
M. Dror and P. Trudeau,
Savings by split delivery routing, Transportation Science, 23 (1989), 141-145.
|
[12] |
O. Ergun, G. Kuyzu and M. Savelsbergh,
Shipper collaboration, Computers & Operations Research, 34 (2007a), 1551-1560.
|
[13] |
O. Ergun, G. Kuyzu and M. Savelsbergh,
Reducing truckload transportation costs through collaboration, Transportation Science, 41 (2007b), 206-221.
|
[14] |
T. A. Feo and J. F. Bard,
Flight scheduling and maintenance base planning, Management Science, 35 (1989), 1415-1432.
|
[15] |
M. Frisk, M. G |
[16] |
Y. Gajpal and P. Abad,
An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup, Computers & Operations Research, 36 (2009), 3215-3223.
|
[17] |
F. P. Goksal, I. Karaoglan and F. Altiparmak,
A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery, Computers & Industrial Engineering, 65 (2013), 39-53.
|
[18] |
M. Y. Lai, C. S. Liu and X. J. Tong,
A two-stage hybrid meta-heuristic for pickup and delivery vehicle routing problem with time windows, Journal of Industrial & Management Optimization, 6 (2010), 435-451.
doi: 10.3934/jimo.2010.6.435. |
[19] |
H. Li and A. Lim,
A metaheuristic for the pickup and delivery problem with time windows, International Journal on Artificial Intelligence Tools, 12 (2003), 173-186.
|
[20] |
J. Li, P. M. Pardalos, H. Sun, J. Pei and Y. Zhang,
Iterated local search embedded adaptive neighborhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups, Expert Systems with Applications, 42 (2015), 3551-3561.
|
[21] |
R. Liu, X. Xie, V. Augusto and C. Rodriguez,
Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care, European Journal of Operational Research, 230 (2013), 475-486.
doi: 10.1016/j.ejor.2013.04.044. |
[22] |
H. R. Lourenço, O. C. Martin and T. Stützle, Iterated local search, in In Handbook of metaheuristics, Springer US, 57 (2003), 321–353. |
[23] |
Q. Lu and M. M. Dessouky,
A new insertion-based construction heuristic for solving the pickup and delivery problem with time windows, European Journal of Operational Research, 175 (2006), 672-687.
|
[24] |
H. Min,
The multiple vehicle routing problem with simultaneous delivery and pick-up points, Transportation Research Part A: General, 23 (1989), 377-386.
|
[25] |
S. Mitra,
An algorithm for the generalized vehicle routing problem with backhauling, Asia-Pacific Journal of Operational Research, 22 (2005), 153-169.
doi: 10.1142/S0217595905000522. |
[26] |
S. Mitra,
A parallel clustering technique for the vehicle routing problem with split deliveries and pickups, Journal of the operational Research Society, 59 (2008), 1532-1546.
|
[27] |
G. Nagy and S. Salhi,
Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries, European Journal of Operational Research, 162 (2005), 126-141.
|
[28] |
W. P. Nanry and J. W. Barnes,
Solving the pickup and delivery problem with time windows using reactive tabu search, Transportation Research Part B: Methodological, 34 (2000), 107-121.
|
[29] |
M. Nowak, |
[30] |
M. Nowak, |
[31] |
G. Pankratz,
A grouping genetic algorithm for the pickup and delivery problem with time windows, Or Spectrum, 27 (2005), 21-41.
doi: 10.1007/s00291-004-0173-7. |
[32] |
P. Pelagagge, L. Fratocchi and A. C. Caputo,
A genetic approach for freight transportation planning, Industrial Management & Data Systems, 106 (2006), 719-738.
|
[33] |
D. Pisinger and S. Ropke,
A general heuristic for vehicle routing problems, Computers & operations research, 34 (2007), 2403-2435.
doi: 10.1016/j.cor.2005.09.012. |
[34] |
C. Prins, N. Labadi and M. Reghioui,
Tour splitting algorithms for vehicle routing problems, International Journal of Production Research, 47 (2009), 507-535.
|
[35] |
M. Reghioui, C. Prins and N. Labadi,
GRASP with path relinking for the capacitated arc routing problem with time windows, InWorkshops on Applications of Evolutionary Computation, (2007), 722-731.
|
[36] |
J. Renaud, F. F. Boctor and G. Laporte,
Perturbation heuristics for the pickup and delivery traveling salesman problem, Computers & Operations Research, 29 (2002), 1129-1141.
doi: 10.1016/S0305-0548(99)00066-0. |
[37] |
S. Ropke and D. Pisinger,
An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Transportation Science, 40 (2006a), 455-472.
|
[38] |
S. Ropke and D. Pisinger,
A unified heuristic for a large class of vehicle routing problems with backhauls, European Journal of Operational Research, 171 (2006), 750-775.
doi: 10.1016/j.ejor.2004.09.004. |
[39] |
S. Salhi and G. Nagy,
A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling, Journal of the operational Research Society, 50 (1999), 1034-1042.
|
[40] |
R. Sprenger and L. Monch,
A methodology to solve large-scale cooperative transportation planning problems, European Journal of Operational Research, 223 (2012), 626-636.
|
[41] |
A. Subramanian, L. M. Drummond, L. M. D. A., C. Bentes, L. S. Ochi and R. Farias,
A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery, Computers & Operations Research, 223 (2010), 1899-1911.
|
[42] |
A. Subramanian, E. Uchoa and L. S. Ochi,
A hybrid algorithm for a class of vehicle routing problems, Computers & Operations Research, 40 (2013), 2519-2531.
|
[43] |
A. S. Tasan and M. Gen,
A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries, Computers & Industrial Engineering, 62 (2012), 755-761.
|
[44] |
F. L. Usberti, P. M. França and A. L. M. França,
GRASP with evolutionary path-relinking for the capacitated arc routing problem, Computers & Operations Research, 40 (2013), 3206-3217.
doi: 10.1016/j.cor.2011.10.014. |
[45] |
N. A. Wassan, A. H. Wassan and G. Nagy,
A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries, Journal of Combinatorial Optimization, 15 (2008), 368-386.
doi: 10.1007/s10878-007-9090-4. |
[46] |
O. Yilmaz and S. Savasaneril,
Collaboration among small shippers in a transportation market, European Journal of Operational Research, 218 (2012), 408-415.
doi: 10.1016/j.ejor.2011.11.018. |
[47] |
T. Zhang, W. A. Chaovalitwongse and Y. Zhang,
Integrated ant colony and tabu search approach for time dependent vehicle routing problems with simultaneous pickup and delivery, Journal of Combinatorial Optimization, 28 (2014), 288-309.
doi: 10.1007/s10878-014-9741-1. |





Instance set | Best improvement | First improvement | ||
CPU | Gap | CPU | Gap | |
I40 | 827.63 | 5.20 | 29.22 | 5.18 |
O40 | 796.54 | 0.62 | 35.18 | 0.58 |
Instance set | Best improvement | First improvement | ||
CPU | Gap | CPU | Gap | |
I40 | 827.63 | 5.20 | 29.22 | 5.18 |
O40 | 796.54 | 0.62 | 35.18 | 0.58 |
Instance set | General strategy | Speedup strategy | ||
CPU | Gap | CPU | Gap | |
I40 | 327.63 | 5.18 | 29.22 | 5.18 |
O40 | 296.54 | 0.61 | 35.18 | 0.58 |
Instance set | General strategy | Speedup strategy | ||
CPU | Gap | CPU | Gap | |
I40 | 327.63 | 5.18 | 29.22 | 5.18 |
O40 | 296.54 | 0.61 | 35.18 | 0.58 |
Description | Parameter | Value | |||
Small instances (20 requests) |
Medium instances (40 requests) |
Large instances (60 requests) |
Large instances (100 requests) | ||
Number of GRASP iterations | np | 10 | 10 | 15 | 15 |
Number of ILS iterations | ni | 5 | 10 | 15 | 20 |
RCL size | nrcl | 3 | 5 | 7 | 7 |
Description | Parameter | Value | |||
Small instances (20 requests) |
Medium instances (40 requests) |
Large instances (60 requests) |
Large instances (100 requests) | ||
Number of GRASP iterations | np | 10 | 10 | 15 | 15 |
Number of ILS iterations | ni | 5 | 10 | 15 | 20 |
RCL size | nrcl | 3 | 5 | 7 | 7 |
Instance set | CPLEX | GRASP-ILS | ||||||
ImpIni | GapLB | CPU | ImpIni | ImpCplex | GapLB | CPU | ||
I20 | -- | 0.00 | 2101.07 | -- | 0.00 | 0.00 | 3.17 | |
O20 | -- | 0.00 | 1077.42 | -- | 0.00 | 0.00 | 1.92 | |
A20 | -- | 0.00 | 1350.15 | -- | 0.00 | 0.00 | 2.49 | |
Average | 0.00 | 1509.55 | 0.00 | 0.00 | 2.53 | |||
I40 | 1.44 | 28.47 | 21600.00 | 6.57 | 5.18 | 24.58 | 29.22 | |
O40 | 6.02 | 10.78 | 21600.00 | 6.37 | 0.58 | 10.27 | 35.18 | |
A40 | 3.33 | 20.89 | 21600.00 | 6.61 | 3.58 | 17.91 | 29.94 | |
Average | 3.60 | 20.05 | 21600.00 | 6.52 | 3.11 | 17.59 | 31.45 | |
I60 | 2.74 | 34.25 | 21600.00 | 12.45 | 9.99 | 26.73 | 125.42 | |
O60 | 4.77 | 28.38 | 21600.00 | 16.85 | 12.63 | 18.00 | 144.84 | |
A60 | 3.35 | 28.74 | 21600.00 | 14.78 | 11.81 | 19.18 | 148.35 | |
Average | 3.62 | 30.46 | 21600.00 | 13.70 | 12.47 | 21.30 | 139.54 | |
I100 | 1.62 | 40.24 | 21600.00 | 16.85 | 13.00 | 31.27 | 246.32 | |
O100 | 2.57 | 38.25 | 21600.00 | 21.11 | 15.24 | 23.55 | 292.72 | |
A100 | 1.83 | 34.56 | 21600.00 | 19.52 | 14.68 | 23.17 | 282.45 | |
Average | 2.01 | 37.68 | 21600.00 | 19.16 | 14.31 | 26.00 | 273.83 |
Instance set | CPLEX | GRASP-ILS | ||||||
ImpIni | GapLB | CPU | ImpIni | ImpCplex | GapLB | CPU | ||
I20 | -- | 0.00 | 2101.07 | -- | 0.00 | 0.00 | 3.17 | |
O20 | -- | 0.00 | 1077.42 | -- | 0.00 | 0.00 | 1.92 | |
A20 | -- | 0.00 | 1350.15 | -- | 0.00 | 0.00 | 2.49 | |
Average | 0.00 | 1509.55 | 0.00 | 0.00 | 2.53 | |||
I40 | 1.44 | 28.47 | 21600.00 | 6.57 | 5.18 | 24.58 | 29.22 | |
O40 | 6.02 | 10.78 | 21600.00 | 6.37 | 0.58 | 10.27 | 35.18 | |
A40 | 3.33 | 20.89 | 21600.00 | 6.61 | 3.58 | 17.91 | 29.94 | |
Average | 3.60 | 20.05 | 21600.00 | 6.52 | 3.11 | 17.59 | 31.45 | |
I60 | 2.74 | 34.25 | 21600.00 | 12.45 | 9.99 | 26.73 | 125.42 | |
O60 | 4.77 | 28.38 | 21600.00 | 16.85 | 12.63 | 18.00 | 144.84 | |
A60 | 3.35 | 28.74 | 21600.00 | 14.78 | 11.81 | 19.18 | 148.35 | |
Average | 3.62 | 30.46 | 21600.00 | 13.70 | 12.47 | 21.30 | 139.54 | |
I100 | 1.62 | 40.24 | 21600.00 | 16.85 | 13.00 | 31.27 | 246.32 | |
O100 | 2.57 | 38.25 | 21600.00 | 21.11 | 15.24 | 23.55 | 292.72 | |
A100 | 1.83 | 34.56 | 21600.00 | 19.52 | 14.68 | 23.17 | 282.45 | |
Average | 2.01 | 37.68 | 21600.00 | 19.16 | 14.31 | 26.00 | 273.83 |
Instance set | ||
ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |
I20 | 6.51 | 3.17 |
O20 | 1.87 | 0.86 |
A20 | 7.65 | 3.68 |
Average | 5.34 | 2.57 |
I40 | 3.95 | 3.71 |
O40 | 3.00 | 3.23 |
A40 | 6.75 | 3.62 |
Average | 4.57 | 3.52 |
I60 | 4.09 | 2.65 |
O60 | 7.42 | 0.73 |
A60 | 6.35 | 4.64 |
Average | 5.95 | 2.67 |
I100 | 7.20 | 4.19 |
O100 | 6.59 | 3.78 |
A100 | 5.00 | 4.06 |
Average | 6.26 | 4.01 |
Instance set | ||
ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |
I20 | 6.51 | 3.17 |
O20 | 1.87 | 0.86 |
A20 | 7.65 | 3.68 |
Average | 5.34 | 2.57 |
I40 | 3.95 | 3.71 |
O40 | 3.00 | 3.23 |
A40 | 6.75 | 3.62 |
Average | 4.57 | 3.52 |
I60 | 4.09 | 2.65 |
O60 | 7.42 | 0.73 |
A60 | 6.35 | 4.64 |
Average | 5.95 | 2.67 |
I100 | 7.20 | 4.19 |
O100 | 6.59 | 3.78 |
A100 | 5.00 | 4.06 |
Average | 6.26 | 4.01 |
Instance set | GRASP | ILS | GRASP-ILS |
Dev | Dev | Dev | |
I20 | 1.93 | 4.31 | 0.37 |
O20 | 0.26 | 0.43 | 0.01 |
A20 | 1.21 | 5.23 | 0.76 |
Average | 1.13 | 3.32 | 0.38 |
I40 | 4.46 | 7.73 | 0.42 |
O40 | 3.81 | 7.01 | 0.44 |
A40 | 3.68 | 8.65 | 0.89 |
Average | 3.98 | 7.80 | 0.58 |
I60 | 6.92 | 11.58 | 0.51 |
O60 | 4.80 | 6.72 | 0.81 |
A60 | 4.09 | 8.66 | 0.92 |
Average | 5.27 | 8.99 | 0.75 |
I100 | 7.04 | 12.38 | 0.88 |
O100 | 5.25 | 8.96 | 1.16 |
A100 | 5.40 | 9.31 | 1.12 |
Average | 5.90 | 10.22 | 1.05 |
Instance set | GRASP | ILS | GRASP-ILS |
Dev | Dev | Dev | |
I20 | 1.93 | 4.31 | 0.37 |
O20 | 0.26 | 0.43 | 0.01 |
A20 | 1.21 | 5.23 | 0.76 |
Average | 1.13 | 3.32 | 0.38 |
I40 | 4.46 | 7.73 | 0.42 |
O40 | 3.81 | 7.01 | 0.44 |
A40 | 3.68 | 8.65 | 0.89 |
Average | 3.98 | 7.80 | 0.58 |
I60 | 6.92 | 11.58 | 0.51 |
O60 | 4.80 | 6.72 | 0.81 |
A60 | 4.09 | 8.66 | 0.92 |
Average | 5.27 | 8.99 | 0.75 |
I100 | 7.04 | 12.38 | 0.88 |
O100 | 5.25 | 8.96 | 1.16 |
A100 | 5.40 | 9.31 | 1.12 |
Average | 5.90 | 10.22 | 1.05 |
Geographical distributions of customers | Non-collaboration Nv | Collaboration Nv | |
I20 | 4.3 | 2.3 | 22.57 |
O20 | 4.1 | 2 | 17.90 |
A20 | 4.2 | 2.1 | 10.76 |
I40 | 8 | 6 | 31.02 |
O40 | 7.3 | 3.5 | 24.19 |
A40 | 7.5 | 3.9 | 16.35 |
I60 | 11 | 6.3 | 33.31 |
O60 | 10.1 | 4.9 | 28.22 |
A60 | 10.1 | 5.2 | 24.42 |
I100 | 17.8 | 9.8 | 41.37 |
O100 | 14.1 | 8.4 | 33.79 |
A100 | 13.8 | 8.7 | 30.96 |
Geographical distributions of customers | Non-collaboration Nv | Collaboration Nv | |
I20 | 4.3 | 2.3 | 22.57 |
O20 | 4.1 | 2 | 17.90 |
A20 | 4.2 | 2.1 | 10.76 |
I40 | 8 | 6 | 31.02 |
O40 | 7.3 | 3.5 | 24.19 |
A40 | 7.5 | 3.9 | 16.35 |
I60 | 11 | 6.3 | 33.31 |
O60 | 10.1 | 4.9 | 28.22 |
A60 | 10.1 | 5.2 | 24.42 |
I100 | 17.8 | 9.8 | 41.37 |
O100 | 14.1 | 8.4 | 33.79 |
A100 | 13.8 | 8.7 | 30.96 |
Customer Requests | Non-collaboration Nv | Collaboration Nv | |
I20 | 4.3 | 2.3 | 22.57 |
I40 | 8 | 6 | 31.02 |
I60 | 11 | 6.3 | 33.31 |
I100 | 17.8 | 9.8 | 41.37 |
Average | 4.2 | 2.1 | 17.08 |
O20 | 4.1 | 2 | 17.90 |
O40 | 7.3 | 3.5 | 24.19 |
O60 | 10.1 | 4.9 | 28.22 |
O100 | 14.1 | 8.4 | 33.79 |
Average | 7.6 | 4.4 | 23.85 |
A20 | 4.2 | 2.1 | 10.76 |
A40 | 7.5 | 3.9 | 16.35 |
A60 | 10.1 | 5.2 | 24.42 |
A100 | 13.8 | 8.7 | 30.96 |
Average | 10.4 | 5.5 | 28.65 |
Customer Requests | Non-collaboration Nv | Collaboration Nv | |
I20 | 4.3 | 2.3 | 22.57 |
I40 | 8 | 6 | 31.02 |
I60 | 11 | 6.3 | 33.31 |
I100 | 17.8 | 9.8 | 41.37 |
Average | 4.2 | 2.1 | 17.08 |
O20 | 4.1 | 2 | 17.90 |
O40 | 7.3 | 3.5 | 24.19 |
O60 | 10.1 | 4.9 | 28.22 |
O100 | 14.1 | 8.4 | 33.79 |
Average | 7.6 | 4.4 | 23.85 |
A20 | 4.2 | 2.1 | 10.76 |
A40 | 7.5 | 3.9 | 16.35 |
A60 | 10.1 | 5.2 | 24.42 |
A100 | 13.8 | 8.7 | 30.96 |
Average | 10.4 | 5.5 | 28.65 |
Instance | CPLEX | GRASP-ILS | ||||||||||
Ini | UB | LB | CPU | GapLB | Zmin | CPU | Zavg | CPUavg | ImpCplex | GapLB | ||
I20-2-1-0 | / | 459.26 | 459.26 | 6727.61 | 0.00 | 459.26 | 6.24 | 459.26 | 7.25 | 0.00 | 0.00 | |
I20-2-1-1 | / | 366.66 | 366.66 | 142.44 | 0.00 | 366.66 | 2.23 | 366.66 | 4.47 | 0.00 | 0.00 | |
I20-2-1-2 | / | 478.19 | 478.19 | 1360.56 | 0.00 | 478.19 | 6.64 | 478.19 | 8.24 | 0.00 | 0.00 | |
I20-2-1-3 | / | 360.24 | 360.24 | 128.19 | 0.00 | 360.24 | 1.86 | 365.33 | 1.89 | 0.00 | 0.00 | |
I20-2-1-4 | / | 383.24 | 383.24 | 8933.10 | 0.00 | 383.24 | 1.67 | 383.24 | 2.01 | 0.00 | 0.00 | |
I20-2-1-5 | / | 343.70 | 343.70 | 369.21 | 0.00 | 343.70 | 1.41 | 350.76 | 1.81 | 0.00 | 0.00 | |
I20-2-1-6 | / | 344.51 | 344.51 | 366.51 | 0.00 | 344.51 | 1.59 | 344.51 | 1.77 | 0.00 | 0.00 | |
I20-2-1-7 | / | 354.59 | 354.59 | 266.03 | 0.00 | 354.59 | 1.75 | 355.59 | 3.11 | 0.00 | 0.00 | |
I20-2-1-8 | / | 351.37 | 351.37 | 2202.84 | 0.00 | 351.37 | 1.40 | 351.37 | 1.77 | 0.00 | 0.00 | |
I20-2-1-9 | / | 476.32 | 476.32 | 514.23 | 0.00 | 476.32 | 6.97 | 476.32 | 8.15 | 0.00 | 0.00 | |
Avg | 2101.07 | 0.00 | 3.17 | |||||||||
O20-2-1-0 | / | 240.46 | 240.46 | 817.75 | 0.00 | 240.46 | 2.18 | 240.46 | 2.51 | 0.00 | 0.00 | |
O20-2-1-1 | / | 260.84 | 260.84 | 727.20 | 0.00 | 260.84 | 1.84 | 260.84 | 2.13 | 0.00 | 0.00 | |
O20-2-1-2 | / | 250.62 | 250.62 | 945.73 | 0.00 | 250.62 | 2.50 | 250.62 | 2.66 | 0.00 | 0.00 | |
O20-2-1-3 | / | 254.79 | 254.79 | 1213.25 | 0.00 | 254.79 | 1.50 | 254.79 | 1.83 | 0.00 | 0.00 | |
O20-2-1-4 | / | 273.79 | 273.79 | 563.98 | 0.00 | 273.79 | 2.03 | 273.85 | 1.99 | 0.00 | 0.00 | |
O20-2-1-5 | / | 269.61 | 269.61 | 2227.00 | 0.00 | 269.61 | 1.46 | 269.61 | 2.05 | 0.00 | 0.00 | |
O20-2-1-6 | / | 260.31 | 260.31 | 1456.89 | 0.00 | 260.31 | 1.64 | 260.41 | 2.33 | 0.00 | 0.00 | |
O20-2-1-7 | / | 245.95 | 245.95 | 1323.50 | 0.00 | 245.95 | 1.69 | 246.06 | 2.32 | 0.00 | 0.00 | |
O20-2-1-8 | / | 240.28 | 240.28 | 685.00 | 0.00 | 240.28 | 1.70 | 240.28 | 2.28 | 0.00 | 0.00 | |
O20-2-1-9 | / | 229.92 | 229.92 | 813.89 | 0.00 | 229.92 | 2.70 | 229.96 | 2.41 | 0.00 | 0.00 | |
Avg | 1077.42 | 0.00 | 1.92 | 0.00 | 0.00 | |||||||
A20-2-1-0 | / | 362.31 | 362.31 | 987.80 | 0.00 | 362.31 | 1.59 | 366.24 | 1.85 | 0.00 | 0.00 | |
A20-2-1-1 | / | 444.80 | 444.80 | 1188.06 | 0.00 | 444.80 | 7.26 | 444.80 | 8.29 | 0.00 | 0.00 | |
A20-2-1-2 | / | 329.67 | 329.67 | 2358.72 | 0.00 | 329.67 | 1.37 | 334.31 | 1.85 | 0.00 | 0.00 | |
A20-2-1-3 | / | 363.62 | 363.62 | 1206.36 | 0.00 | 363.62 | 4.06 | 372.23 | 5.38 | 0.00 | 0.00 | |
A20-2-1-4 | / | 343.77 | 343.77 | 2440.98 | 0.00 | 343.77 | 1.66 | 343.77 | 1.91 | 0.00 | 0.00 | |
A20-2-1-5 | / | 287.74 | 287.74 | 1266.59 | 0.00 | 287.74 | 1.99 | 294.17 | 1.55 | 0.00 | 0.00 | |
A20-2-1-6 | / | 338.23 | 338.23 | 821.69 | 0.00 | 338.23 | 1.56 | 338.23 | 1.70 | 0.00 | 0.00 | |
A20-2-1-7 | / | 290.21 | 290.21 | 985.11 | 0.00 | 290.21 | 1.40 | 292.05 | 1.59 | 0.00 | 0.00 | |
A20-2-1-8 | / | 314.20 | 314.20 | 1324.84 | 0.00 | 314.20 | 2.13 | 314.20 | 1.70 | 0.00 | 0.00 | |
A20-2-1-9 | / | 323.60 | 323.60 | 921.38 | 0.00 | 323.60 | 1.93 | 323.60 | 2.18 | 0.00 | 0.00 | |
Avg | 1350.15 | 0.00 | 2.49 | 0.00 | 0.00 |
Instance | CPLEX | GRASP-ILS | ||||||||||
Ini | UB | LB | CPU | GapLB | Zmin | CPU | Zavg | CPUavg | ImpCplex | GapLB | ||
I20-2-1-0 | / | 459.26 | 459.26 | 6727.61 | 0.00 | 459.26 | 6.24 | 459.26 | 7.25 | 0.00 | 0.00 | |
I20-2-1-1 | / | 366.66 | 366.66 | 142.44 | 0.00 | 366.66 | 2.23 | 366.66 | 4.47 | 0.00 | 0.00 | |
I20-2-1-2 | / | 478.19 | 478.19 | 1360.56 | 0.00 | 478.19 | 6.64 | 478.19 | 8.24 | 0.00 | 0.00 | |
I20-2-1-3 | / | 360.24 | 360.24 | 128.19 | 0.00 | 360.24 | 1.86 | 365.33 | 1.89 | 0.00 | 0.00 | |
I20-2-1-4 | / | 383.24 | 383.24 | 8933.10 | 0.00 | 383.24 | 1.67 | 383.24 | 2.01 | 0.00 | 0.00 | |
I20-2-1-5 | / | 343.70 | 343.70 | 369.21 | 0.00 | 343.70 | 1.41 | 350.76 | 1.81 | 0.00 | 0.00 | |
I20-2-1-6 | / | 344.51 | 344.51 | 366.51 | 0.00 | 344.51 | 1.59 | 344.51 | 1.77 | 0.00 | 0.00 | |
I20-2-1-7 | / | 354.59 | 354.59 | 266.03 | 0.00 | 354.59 | 1.75 | 355.59 | 3.11 | 0.00 | 0.00 | |
I20-2-1-8 | / | 351.37 | 351.37 | 2202.84 | 0.00 | 351.37 | 1.40 | 351.37 | 1.77 | 0.00 | 0.00 | |
I20-2-1-9 | / | 476.32 | 476.32 | 514.23 | 0.00 | 476.32 | 6.97 | 476.32 | 8.15 | 0.00 | 0.00 | |
Avg | 2101.07 | 0.00 | 3.17 | |||||||||
O20-2-1-0 | / | 240.46 | 240.46 | 817.75 | 0.00 | 240.46 | 2.18 | 240.46 | 2.51 | 0.00 | 0.00 | |
O20-2-1-1 | / | 260.84 | 260.84 | 727.20 | 0.00 | 260.84 | 1.84 | 260.84 | 2.13 | 0.00 | 0.00 | |
O20-2-1-2 | / | 250.62 | 250.62 | 945.73 | 0.00 | 250.62 | 2.50 | 250.62 | 2.66 | 0.00 | 0.00 | |
O20-2-1-3 | / | 254.79 | 254.79 | 1213.25 | 0.00 | 254.79 | 1.50 | 254.79 | 1.83 | 0.00 | 0.00 | |
O20-2-1-4 | / | 273.79 | 273.79 | 563.98 | 0.00 | 273.79 | 2.03 | 273.85 | 1.99 | 0.00 | 0.00 | |
O20-2-1-5 | / | 269.61 | 269.61 | 2227.00 | 0.00 | 269.61 | 1.46 | 269.61 | 2.05 | 0.00 | 0.00 | |
O20-2-1-6 | / | 260.31 | 260.31 | 1456.89 | 0.00 | 260.31 | 1.64 | 260.41 | 2.33 | 0.00 | 0.00 | |
O20-2-1-7 | / | 245.95 | 245.95 | 1323.50 | 0.00 | 245.95 | 1.69 | 246.06 | 2.32 | 0.00 | 0.00 | |
O20-2-1-8 | / | 240.28 | 240.28 | 685.00 | 0.00 | 240.28 | 1.70 | 240.28 | 2.28 | 0.00 | 0.00 | |
O20-2-1-9 | / | 229.92 | 229.92 | 813.89 | 0.00 | 229.92 | 2.70 | 229.96 | 2.41 | 0.00 | 0.00 | |
Avg | 1077.42 | 0.00 | 1.92 | 0.00 | 0.00 | |||||||
A20-2-1-0 | / | 362.31 | 362.31 | 987.80 | 0.00 | 362.31 | 1.59 | 366.24 | 1.85 | 0.00 | 0.00 | |
A20-2-1-1 | / | 444.80 | 444.80 | 1188.06 | 0.00 | 444.80 | 7.26 | 444.80 | 8.29 | 0.00 | 0.00 | |
A20-2-1-2 | / | 329.67 | 329.67 | 2358.72 | 0.00 | 329.67 | 1.37 | 334.31 | 1.85 | 0.00 | 0.00 | |
A20-2-1-3 | / | 363.62 | 363.62 | 1206.36 | 0.00 | 363.62 | 4.06 | 372.23 | 5.38 | 0.00 | 0.00 | |
A20-2-1-4 | / | 343.77 | 343.77 | 2440.98 | 0.00 | 343.77 | 1.66 | 343.77 | 1.91 | 0.00 | 0.00 | |
A20-2-1-5 | / | 287.74 | 287.74 | 1266.59 | 0.00 | 287.74 | 1.99 | 294.17 | 1.55 | 0.00 | 0.00 | |
A20-2-1-6 | / | 338.23 | 338.23 | 821.69 | 0.00 | 338.23 | 1.56 | 338.23 | 1.70 | 0.00 | 0.00 | |
A20-2-1-7 | / | 290.21 | 290.21 | 985.11 | 0.00 | 290.21 | 1.40 | 292.05 | 1.59 | 0.00 | 0.00 | |
A20-2-1-8 | / | 314.20 | 314.20 | 1324.84 | 0.00 | 314.20 | 2.13 | 314.20 | 1.70 | 0.00 | 0.00 | |
A20-2-1-9 | / | 323.60 | 323.60 | 921.38 | 0.00 | 323.60 | 1.93 | 323.60 | 2.18 | 0.00 | 0.00 | |
Avg | 1350.15 | 0.00 | 2.49 | 0.00 | 0.00 |
Instance | CPLEX | GRASP-ILS | ||||||||||||
Ini | UB | LB | CPU | ImpIni | GapLB | Zmin | CPU | Zavg | CPUavg | ImpIni | ImpCplex | GapLB | ||
I40-2-1-0 | 764.73 | 733.02 | 554.38 | 21600.00 | 4.15 | 24.37 | 706.64 | 31.77 | 722.04 | 35.64 | 7.60 | 3.60 | 21.55 | |
I40-2-1-1 | 617.81 | 617.81 | 432.47 | 21600.00 | 0.00 | 30.00 | 600.90 | 30.07 | 607.03 | 33.09 | 2.74 | 2.74 | 28.03 | |
I40-2-1-2 | 776.04 | 776.04 | 526.08 | 21600.00 | 0.00 | 32.21 | 729.24 | 31.07 | 729.24 | 33.12 | 6.03 | 6.03 | 27.86 | |
I40-2-1-3 | 718.16 | 702.54 | 545.94 | 21600.00 | 2.18 | 22.29 | 651.55 | 26.00 | 651.55 | 28.16 | 9.28 | 7.26 | 16.21 | |
I40-2-1-4 | 720.41 | 716.43 | 519.91 | 21600.00 | 0.55 | 27.43 | 699.59 | 26.37 | 699.59 | 27.97 | 2.89 | 2.35 | 25.68 | |
I40-2-1-5 | 748.66 | 748.66 | 475.02 | 21600.00 | 0.00 | 36.55 | 647.36 | 27.67 | 647.36 | 31.16 | 13.53 | 13.53 | 26.62 | |
I40-2-1-6 | 615.92 | 615.92 | 435.58 | 21600.00 | 0.00 | 29.28 | 590.24 | 29.90 | 591.42 | 32.15 | 4.17 | 4.17 | 26.20 | |
I40-2-1-7 | 664.83 | 662.64 | 432.11 | 21600.00 | 0.33 | 34.79 | 612.68 | 28.53 | 613.44 | 29.29 | 7.84 | 7.54 | 29.47 | |
I40-2-1-8 | 634.10 | 594.85 | 447.33 | 21600.00 | 6.19 | 24.80 | 573.59 | 32.61 | 574.75 | 34.14 | 9.54 | 3.57 | 22.01 | |
I40-2-1-9 | 611.25 | 604.84 | 466.03 | 21600.00 | 1.05 | 22.95 | 598.44 | 28.16 | 601.82 | 31.40 | 2.10 | 1.06 | 22.13 | |
Avg | 21600.00 | 1.44 | 28.47 | 29.22 | 31.61 | 6.57 | 5.18 | 24.58 | ||||||
O40-2-1-0 | 590.88 | 494.73 | 486.52 | 21600.00 | 16.27 | 1.66 | 494.73 | 30.31 | 497.25 | 32.04 | 16.27 | 0.00 | 1.66 | |
O40-2-1-1 | 484.61 | 443.19 | 390.45 | 21600.00 | 9.99 | 11.90 | 434.04 | 36.80 | 439.23 | 35.30 | 10.44 | 2.06 | 10.04 | |
O40-2-1-2 | 452.71 | 445.80 | 401.58 | 21600.00 | 1.53 | 9.92 | 445.80 | 34.44 | 445.80 | 36.68 | 1.53 | 0.00 | 9.92 | |
O40-2-1-3 | 604.15 | 529.67 | 456.10 | 21600.00 | 12.33 | 13.89 | 523.35 | 36.44 | 523.35 | 37.24 | 13.37 | 1.19 | 12.85 | |
O40-2-1-4 | 551.18 | 550.47 | 458.60 | 21600.00 | 0.13 | 16.69 | 549.35 | 37.96 | 549.35 | 41.00 | 0.33 | 0.20 | 16.52 | |
O40-2-1-5 | 627.43 | 576.14 | 486.90 | 21600.00 | 8.17 | 15.49 | 573.11 | 34.70 | 573.11 | 36.25 | 8.66 | 0.53 | 15.04 | |
O40-2-1-6 | 496.89 | 492.06 | 422.04 | 21600.00 | 0.97 | 14.23 | 489.14 | 39.24 | 489.14 | 41.56 | 1.56 | 0.59 | 13.72 | |
O40-2-1-7 | 545.21 | 532.03 | 492.50 | 21600.00 | 2.78 | 7.43 | 528.80 | 31.72 | 542.87 | 36.13 | 3.01 | 0.61 | 6.86 | |
O40-2-1-8 | 441.62 | 427.55 | 427.55 | 21600.00 | 3.19 | 0.00 | 427.55 | 32.20 | 427.82 | 40.79 | 3.19 | 0.00 | 0.00 | |
O40-2-1-9 | 611.65 | 582.21 | 485.50 | 21600.00 | 4.81 | 16.61 | 578.85 | 37.98 | 579.14 | 37.03 | 5.36 | 0.58 | 16.13 | |
Avg | 21600.00 | 6.02 | 10.78 | 35.18 | 37.40 | 6.37 | 0.58 | 10.27 | ||||||
A40-2-1-0 | 595.16 | 581.93 | 463.33 | 21600.00 | 2.22 | 20.38 | 550.20 | 26.67 | 563.08 | 29.48 | 7.55 | 5.45 | 15.79 | |
A40-2-1-1 | 617.54 | 617.54 | 428.57 | 21600.00 | 0.00 | 30.60 | 597.17 | 29.64 | 601.48 | 32.31 | 3.30 | 3.30 | 28.23 | |
A40-2-1-2 | 685.71 | 593.58 | 508.05 | 21600.00 | 13.44 | 14.41 | 582.03 | 32.10 | 582.03 | 36.22 | 15.12 | 1.95 | 12.71 | |
A40-2-1-3 | 511.22 | 511.22 | 383.62 | 21600.00 | 0.00 | 24.96 | 505.21 | 31.86 | 505.21 | 34.47 | 1.18 | 1.18 | 24.07 | |
A40-2-1-4 | 574.55 | 569.49 | 460.72 | 21600.00 | 0.88 | 19.10 | 567.77 | 33.23 | 568.40 | 33.13 | 1.18 | 0.30 | 18.85 | |
A40-2-1-5 | 626.75 | 626.75 | 484.73 | 21600.00 | 0.00 | 22.66 | 617.34 | 28.18 | 617.38 | 30.09 | 1.50 | 1.50 | 21.48 | |
A40-2-1-6 | 574.52 | 572.59 | 457.56 | 21600.00 | 1.90 | 20.09 | 537.91 | 32.50 | 560.92 | 37.04 | 6.37 | 6.06 | 14.94 | |
A40-2-1-7 | 615.58 | 552.47 | 494.52 | 21600.00 | 10.90 | 10.49 | 542.06 | 30.23 | 548.20 | 28.19 | 11.94 | 1.88 | 8.77 | |
A40-2-1-8 | 642.09 | 630.61 | 480.02 | 21600.00 | 1.79 | 23.88 | 600.61 | 27.93 | 600.61 | 29.57 | 6.46 | 4.76 | 20.08 | |
A40-2-1-9 | 714.16 | 698.33 | 542.39 | 21600.00 | 2.22 | 22.33 | 632.33 | 27.06 | 635.86 | 30.86 | 11.46 | 9.45 | 14.22 | |
Avg | 21600.00 | 3.33 | 20.89 | 29.94 | 32.14 | 6.61 | 3.58 | 17.91 |
Instance | CPLEX | GRASP-ILS | ||||||||||||
Ini | UB | LB | CPU | ImpIni | GapLB | Zmin | CPU | Zavg | CPUavg | ImpIni | ImpCplex | GapLB | ||
I40-2-1-0 | 764.73 | 733.02 | 554.38 | 21600.00 | 4.15 | 24.37 | 706.64 | 31.77 | 722.04 | 35.64 | 7.60 | 3.60 | 21.55 | |
I40-2-1-1 | 617.81 | 617.81 | 432.47 | 21600.00 | 0.00 | 30.00 | 600.90 | 30.07 | 607.03 | 33.09 | 2.74 | 2.74 | 28.03 | |
I40-2-1-2 | 776.04 | 776.04 | 526.08 | 21600.00 | 0.00 | 32.21 | 729.24 | 31.07 | 729.24 | 33.12 | 6.03 | 6.03 | 27.86 | |
I40-2-1-3 | 718.16 | 702.54 | 545.94 | 21600.00 | 2.18 | 22.29 | 651.55 | 26.00 | 651.55 | 28.16 | 9.28 | 7.26 | 16.21 | |
I40-2-1-4 | 720.41 | 716.43 | 519.91 | 21600.00 | 0.55 | 27.43 | 699.59 | 26.37 | 699.59 | 27.97 | 2.89 | 2.35 | 25.68 | |
I40-2-1-5 | 748.66 | 748.66 | 475.02 | 21600.00 | 0.00 | 36.55 | 647.36 | 27.67 | 647.36 | 31.16 | 13.53 | 13.53 | 26.62 | |
I40-2-1-6 | 615.92 | 615.92 | 435.58 | 21600.00 | 0.00 | 29.28 | 590.24 | 29.90 | 591.42 | 32.15 | 4.17 | 4.17 | 26.20 | |
I40-2-1-7 | 664.83 | 662.64 | 432.11 | 21600.00 | 0.33 | 34.79 | 612.68 | 28.53 | 613.44 | 29.29 | 7.84 | 7.54 | 29.47 | |
I40-2-1-8 | 634.10 | 594.85 | 447.33 | 21600.00 | 6.19 | 24.80 | 573.59 | 32.61 | 574.75 | 34.14 | 9.54 | 3.57 | 22.01 | |
I40-2-1-9 | 611.25 | 604.84 | 466.03 | 21600.00 | 1.05 | 22.95 | 598.44 | 28.16 | 601.82 | 31.40 | 2.10 | 1.06 | 22.13 | |
Avg | 21600.00 | 1.44 | 28.47 | 29.22 | 31.61 | 6.57 | 5.18 | 24.58 | ||||||
O40-2-1-0 | 590.88 | 494.73 | 486.52 | 21600.00 | 16.27 | 1.66 | 494.73 | 30.31 | 497.25 | 32.04 | 16.27 | 0.00 | 1.66 | |
O40-2-1-1 | 484.61 | 443.19 | 390.45 | 21600.00 | 9.99 | 11.90 | 434.04 | 36.80 | 439.23 | 35.30 | 10.44 | 2.06 | 10.04 | |
O40-2-1-2 | 452.71 | 445.80 | 401.58 | 21600.00 | 1.53 | 9.92 | 445.80 | 34.44 | 445.80 | 36.68 | 1.53 | 0.00 | 9.92 | |
O40-2-1-3 | 604.15 | 529.67 | 456.10 | 21600.00 | 12.33 | 13.89 | 523.35 | 36.44 | 523.35 | 37.24 | 13.37 | 1.19 | 12.85 | |
O40-2-1-4 | 551.18 | 550.47 | 458.60 | 21600.00 | 0.13 | 16.69 | 549.35 | 37.96 | 549.35 | 41.00 | 0.33 | 0.20 | 16.52 | |
O40-2-1-5 | 627.43 | 576.14 | 486.90 | 21600.00 | 8.17 | 15.49 | 573.11 | 34.70 | 573.11 | 36.25 | 8.66 | 0.53 | 15.04 | |
O40-2-1-6 | 496.89 | 492.06 | 422.04 | 21600.00 | 0.97 | 14.23 | 489.14 | 39.24 | 489.14 | 41.56 | 1.56 | 0.59 | 13.72 | |
O40-2-1-7 | 545.21 | 532.03 | 492.50 | 21600.00 | 2.78 | 7.43 | 528.80 | 31.72 | 542.87 | 36.13 | 3.01 | 0.61 | 6.86 | |
O40-2-1-8 | 441.62 | 427.55 | 427.55 | 21600.00 | 3.19 | 0.00 | 427.55 | 32.20 | 427.82 | 40.79 | 3.19 | 0.00 | 0.00 | |
O40-2-1-9 | 611.65 | 582.21 | 485.50 | 21600.00 | 4.81 | 16.61 | 578.85 | 37.98 | 579.14 | 37.03 | 5.36 | 0.58 | 16.13 | |
Avg | 21600.00 | 6.02 | 10.78 | 35.18 | 37.40 | 6.37 | 0.58 | 10.27 | ||||||
A40-2-1-0 | 595.16 | 581.93 | 463.33 | 21600.00 | 2.22 | 20.38 | 550.20 | 26.67 | 563.08 | 29.48 | 7.55 | 5.45 | 15.79 | |
A40-2-1-1 | 617.54 | 617.54 | 428.57 | 21600.00 | 0.00 | 30.60 | 597.17 | 29.64 | 601.48 | 32.31 | 3.30 | 3.30 | 28.23 | |
A40-2-1-2 | 685.71 | 593.58 | 508.05 | 21600.00 | 13.44 | 14.41 | 582.03 | 32.10 | 582.03 | 36.22 | 15.12 | 1.95 | 12.71 | |
A40-2-1-3 | 511.22 | 511.22 | 383.62 | 21600.00 | 0.00 | 24.96 | 505.21 | 31.86 | 505.21 | 34.47 | 1.18 | 1.18 | 24.07 | |
A40-2-1-4 | 574.55 | 569.49 | 460.72 | 21600.00 | 0.88 | 19.10 | 567.77 | 33.23 | 568.40 | 33.13 | 1.18 | 0.30 | 18.85 | |
A40-2-1-5 | 626.75 | 626.75 | 484.73 | 21600.00 | 0.00 | 22.66 | 617.34 | 28.18 | 617.38 | 30.09 | 1.50 | 1.50 | 21.48 | |
A40-2-1-6 | 574.52 | 572.59 | 457.56 | 21600.00 | 1.90 | 20.09 | 537.91 | 32.50 | 560.92 | 37.04 | 6.37 | 6.06 | 14.94 | |
A40-2-1-7 | 615.58 | 552.47 | 494.52 | 21600.00 | 10.90 | 10.49 | 542.06 | 30.23 | 548.20 | 28.19 | 11.94 | 1.88 | 8.77 | |
A40-2-1-8 | 642.09 | 630.61 | 480.02 | 21600.00 | 1.79 | 23.88 | 600.61 | 27.93 | 600.61 | 29.57 | 6.46 | 4.76 | 20.08 | |
A40-2-1-9 | 714.16 | 698.33 | 542.39 | 21600.00 | 2.22 | 22.33 | 632.33 | 27.06 | 635.86 | 30.86 | 11.46 | 9.45 | 14.22 | |
Avg | 21600.00 | 3.33 | 20.89 | 29.94 | 32.14 | 6.61 | 3.58 | 17.91 |
Instance | CPLEX | GRASP-ILS | ||||||||||||
Ini | UB | LB | CPU | ImpIni | GapLB | Zmin | CPU | Zavg | CPUavg | ImpIni | ImpCplex | GapLB | ||
I60-2-1-0 | 1075.15 | 1011.77 | 647.03 | 21600.00 | 5.89 | 36.05 | 911.77 | 99.40 | 914.95 | 114.83 | 15.20 | 9.88 | 29.04 | |
I60-2-1-1 | 1190.63 | 1187.76 | 774.42 | 21600.00 | 0.24 | 34.80 | 987.76 | 118.70 | 988.14 | 130.24 | 17.04 | 16.84 | 21.60 | |
I60-2-1-2 | 950.96 | 939.23 | 602.05 | 21600.00 | 1.23 | 35.90 | 877.23 | 131.62 | 879.37 | 139.26 | 7.75 | 6.60 | 31.37 | |
I60-2-1-3 | 1088.70 | 1082.44 | 690.16 | 21600.00 | 0.57 | 36.24 | 882.44 | 137.82 | 889.93 | 122.66 | 18.95 | 18.48 | 21.79 | |
I60-2-1-4 | 1047.69 | 1000.73 | 685.00 | 21600.00 | 4.48 | 31.55 | 896.87 | 108.94 | 900.72 | 119.33 | 14.40 | 10.38 | 23.62 | |
I60-2-1-5 | 1026.03 | 1026.03 | 632.75 | 21600.00 | 0.00 | 38.33 | 996.95 | 138.59 | 997.19 | 135.02 | 2.83 | 2.83 | 36.53 | |
I60-2-1-6 | 1214.28 | 1143.88 | 758.39 | 21600.00 | 5.80 | 33.70 | 1043.88 | 119.96 | 1046.20 | 126.73 | 14.03 | 8.74 | 27.35 | |
I60-2-1-7 | 993.02 | 993.02 | 642.58 | 21600.00 | 0.00 | 35.29 | 944.32 | 132.32 | 960.94 | 137.32 | 4.90 | 4.90 | 31.95 | |
I60-2-1-8 | 946.14 | 918.94 | 625.61 | 21600.00 | 2.87 | 31.92 | 818.94 | 132.87 | 826.45 | 119.74 | 13.44 | 10.88 | 23.61 | |
I60-2-1-9 | 1029.63 | 965.24 | 687.93 | 21600.00 | 6.25 | 28.73 | 865.24 | 133.94 | 867.75 | 135.43 | 15.97 | 10.36 | 20.49 | |
Avg | 21600.00 | 2.74 | 34.25 | 125.42 | 12.45 | 9.99 | 26.73 | |||||||
O60-2-1-0 | 778.81 | 742.35 | 556.24 | 21600.00 | 4.68 | 25.07 | 652.35 | 146.37 | 672.06 | 140.72 | 16.24 | 12.12 | 14.73 | |
O60-2-1-1 | 860.37 | 792.55 | 585.30 | 21600.00 | 7.88 | 26.15 | 746.22 | 144.23 | 750.48 | 150.35 | 13.27 | 5.85 | 21.56 | |
O60-2-1-2 | 883.39 | 832.49 | 606.55 | 21600.00 | 5.76 | 27.14 | 732.49 | 138.82 | 736.08 | 137.72 | 17.08 | 12.01 | 17.19 | |
O60-2-1-3 | 975.67 | 897.76 | 686.25 | 21600.00 | 7.99 | 23.56 | 787.76 | 128.96 | 795.54 | 144.19 | 19.26 | 12.25 | 12.89 | |
O60-2-1-4 | 889.25 | 832.01 | 565.60 | 21600.00 | 6.44 | 32.02 | 727.32 | 159.57 | 734.02 | 163.88 | 18.21 | 12.58 | 22.24 | |
O60-2-1-5 | 891.08 | 852.47 | 631.60 | 21600.00 | 4.33 | 25.91 | 752.74 | 150.60 | 755.68 | 145.87 | 15.53 | 11.70 | 16.09 | |
O60-2-1-6 | 813.00 | 813.00 | 542.76 | 21600.00 | 0.00 | 33.24 | 680.46 | 129.71 | 680.46 | 147.45 | 16.30 | 16.30 | 20.24 | |
O60-2-1-7 | 935.69 | 881.76 | 640.60 | 21600.00 | 5.76 | 27.35 | 752.96 | 162.61 | 761.11 | 172.49 | 19.53 | 14.61 | 14.92 | |
O60-2-1-8 | 850.19 | 835.58 | 571.37 | 21600.00 | 1.72 | 31.62 | 695.58 | 134.58 | 696.81 | 139.18 | 18.19 | 16.75 | 17.86 | |
O60-2-1-9 | 850.23 | 823.61 | 562.61 | 21600.00 | 3.13 | 31.69 | 723.61 | 152.90 | 727.63 | 150.04 | 14.89 | 12.14 | 22.25 | |
Avg | 21600.00 | 4.77 | 28.38 | 144.84 | 16.85 | 12.63 | 18.00 | |||||||
A60-2-1-0 | 936.24 | 936.24 | 594.70 | 21600.00 | 0.00 | 36.48 | 836.54 | 161.45 | 836.60 | 163.57 | 10.65 | 10.65 | 28.91 | |
A60-2-1-1 | 1072.31 | 1072.31 | 663.76 | 21600.00 | 0.00 | 38.1 | 911.33 | 161.93 | 941.39 | 158.79 | 15.01 | 15.01 | 27.17 | |
A60-2-1-2 | 859.84 | 803.79 | 620.37 | 21600.00 | 6.52 | 22.82 | 703.79 | 135.40 | 703.85 | 151.11 | 18.15 | 12.44 | 11.85 | |
A60-2-1-3 | 950.17 | 881.73 | 663.68 | 21600.00 | 7.20 | 24.73 | 781.73 | 122.15 | 782.94 | 123.85 | 17.73 | 11.34 | 15.10 | |
A60-2-1-4 | 912.08 | 902.08 | 622.80 | 21600.00 | 1.10 | 30.96 | 793.69 | 148.34 | 806.85 | 147.38 | 12.98 | 12.02 | 21.53 | |
A60-2-1-5 | 908.24 | 908.24 | 611.25 | 21600.00 | 0.00 | 32.7 | 740.28 | 148.01 | 741.38 | 148.81 | 18.49 | 18.49 | 17.43 | |
A60-2-1-6 | 919.06 | 854.71 | 676.50 | 21600.00 | 7.00 | 20.85 | 754.71 | 146.15 | 756.53 | 157.06 | 17.88 | 11.70 | 10.36 | |
A60-2-1-7 | 942.98 | 880.28 | 647.62 | 21600.00 | 6.65 | 26.43 | 780.28 | 155.59 | 796.40 | 155.86 | 17.25 | 11.36 | 17.00 | |
A60-2-1-8 | 799.61 | 799.61 | 594.75 | 21600.00 | 0.00 | 25.62 | 751.38 | 140.81 | 757.58 | 142.27 | 6.03 | 6.03 | 20.85 | |
A60-2-1-9 | 817.71 | 776.45 | 553.61 | 21600.00 | 5.05 | 28.7 | 705.99 | 163.67 | 712.95 | 157.17 | 13.66 | 9.07 | 21.58 | |
Avg | 21600.00 | 3.35 | 28.74 | 148.35 | 14.78 | 11.81 | 19.18 |
Instance | CPLEX | GRASP-ILS | ||||||||||||
Ini | UB | LB | CPU | ImpIni | GapLB | Zmin | CPU | Zavg | CPUavg | ImpIni | ImpCplex | GapLB | ||
I60-2-1-0 | 1075.15 | 1011.77 | 647.03 | 21600.00 | 5.89 | 36.05 | 911.77 | 99.40 | 914.95 | 114.83 | 15.20 | 9.88 | 29.04 | |
I60-2-1-1 | 1190.63 | 1187.76 | 774.42 | 21600.00 | 0.24 | 34.80 | 987.76 | 118.70 | 988.14 | 130.24 | 17.04 | 16.84 | 21.60 | |
I60-2-1-2 | 950.96 | 939.23 | 602.05 | 21600.00 | 1.23 | 35.90 | 877.23 | 131.62 | 879.37 | 139.26 | 7.75 | 6.60 | 31.37 | |
I60-2-1-3 | 1088.70 | 1082.44 | 690.16 | 21600.00 | 0.57 | 36.24 | 882.44 | 137.82 | 889.93 | 122.66 | 18.95 | 18.48 | 21.79 | |
I60-2-1-4 | 1047.69 | 1000.73 | 685.00 | 21600.00 | 4.48 | 31.55 | 896.87 | 108.94 | 900.72 | 119.33 | 14.40 | 10.38 | 23.62 | |
I60-2-1-5 | 1026.03 | 1026.03 | 632.75 | 21600.00 | 0.00 | 38.33 | 996.95 | 138.59 | 997.19 | 135.02 | 2.83 | 2.83 | 36.53 | |
I60-2-1-6 | 1214.28 | 1143.88 | 758.39 | 21600.00 | 5.80 | 33.70 | 1043.88 | 119.96 | 1046.20 | 126.73 | 14.03 | 8.74 | 27.35 | |
I60-2-1-7 | 993.02 | 993.02 | 642.58 | 21600.00 | 0.00 | 35.29 | 944.32 | 132.32 | 960.94 | 137.32 | 4.90 | 4.90 | 31.95 | |
I60-2-1-8 | 946.14 | 918.94 | 625.61 | 21600.00 | 2.87 | 31.92 | 818.94 | 132.87 | 826.45 | 119.74 | 13.44 | 10.88 | 23.61 | |
I60-2-1-9 | 1029.63 | 965.24 | 687.93 | 21600.00 | 6.25 | 28.73 | 865.24 | 133.94 | 867.75 | 135.43 | 15.97 | 10.36 | 20.49 | |
Avg | 21600.00 | 2.74 | 34.25 | 125.42 | 12.45 | 9.99 | 26.73 | |||||||
O60-2-1-0 | 778.81 | 742.35 | 556.24 | 21600.00 | 4.68 | 25.07 | 652.35 | 146.37 | 672.06 | 140.72 | 16.24 | 12.12 | 14.73 | |
O60-2-1-1 | 860.37 | 792.55 | 585.30 | 21600.00 | 7.88 | 26.15 | 746.22 | 144.23 | 750.48 | 150.35 | 13.27 | 5.85 | 21.56 | |
O60-2-1-2 | 883.39 | 832.49 | 606.55 | 21600.00 | 5.76 | 27.14 | 732.49 | 138.82 | 736.08 | 137.72 | 17.08 | 12.01 | 17.19 | |
O60-2-1-3 | 975.67 | 897.76 | 686.25 | 21600.00 | 7.99 | 23.56 | 787.76 | 128.96 | 795.54 | 144.19 | 19.26 | 12.25 | 12.89 | |
O60-2-1-4 | 889.25 | 832.01 | 565.60 | 21600.00 | 6.44 | 32.02 | 727.32 | 159.57 | 734.02 | 163.88 | 18.21 | 12.58 | 22.24 | |
O60-2-1-5 | 891.08 | 852.47 | 631.60 | 21600.00 | 4.33 | 25.91 | 752.74 | 150.60 | 755.68 | 145.87 | 15.53 | 11.70 | 16.09 | |
O60-2-1-6 | 813.00 | 813.00 | 542.76 | 21600.00 | 0.00 | 33.24 | 680.46 | 129.71 | 680.46 | 147.45 | 16.30 | 16.30 | 20.24 | |
O60-2-1-7 | 935.69 | 881.76 | 640.60 | 21600.00 | 5.76 | 27.35 | 752.96 | 162.61 | 761.11 | 172.49 | 19.53 | 14.61 | 14.92 | |
O60-2-1-8 | 850.19 | 835.58 | 571.37 | 21600.00 | 1.72 | 31.62 | 695.58 | 134.58 | 696.81 | 139.18 | 18.19 | 16.75 | 17.86 | |
O60-2-1-9 | 850.23 | 823.61 | 562.61 | 21600.00 | 3.13 | 31.69 | 723.61 | 152.90 | 727.63 | 150.04 | 14.89 | 12.14 | 22.25 | |
Avg | 21600.00 | 4.77 | 28.38 | 144.84 | 16.85 | 12.63 | 18.00 | |||||||
A60-2-1-0 | 936.24 | 936.24 | 594.70 | 21600.00 | 0.00 | 36.48 | 836.54 | 161.45 | 836.60 | 163.57 | 10.65 | 10.65 | 28.91 | |
A60-2-1-1 | 1072.31 | 1072.31 | 663.76 | 21600.00 | 0.00 | 38.1 | 911.33 | 161.93 | 941.39 | 158.79 | 15.01 | 15.01 | 27.17 | |
A60-2-1-2 | 859.84 | 803.79 | 620.37 | 21600.00 | 6.52 | 22.82 | 703.79 | 135.40 | 703.85 | 151.11 | 18.15 | 12.44 | 11.85 | |
A60-2-1-3 | 950.17 | 881.73 | 663.68 | 21600.00 | 7.20 | 24.73 | 781.73 | 122.15 | 782.94 | 123.85 | 17.73 | 11.34 | 15.10 | |
A60-2-1-4 | 912.08 | 902.08 | 622.80 | 21600.00 | 1.10 | 30.96 | 793.69 | 148.34 | 806.85 | 147.38 | 12.98 | 12.02 | 21.53 | |
A60-2-1-5 | 908.24 | 908.24 | 611.25 | 21600.00 | 0.00 | 32.7 | 740.28 | 148.01 | 741.38 | 148.81 | 18.49 | 18.49 | 17.43 | |
A60-2-1-6 | 919.06 | 854.71 | 676.50 | 21600.00 | 7.00 | 20.85 | 754.71 | 146.15 | 756.53 | 157.06 | 17.88 | 11.70 | 10.36 | |
A60-2-1-7 | 942.98 | 880.28 | 647.62 | 21600.00 | 6.65 | 26.43 | 780.28 | 155.59 | 796.40 | 155.86 | 17.25 | 11.36 | 17.00 | |
A60-2-1-8 | 799.61 | 799.61 | 594.75 | 21600.00 | 0.00 | 25.62 | 751.38 | 140.81 | 757.58 | 142.27 | 6.03 | 6.03 | 20.85 | |
A60-2-1-9 | 817.71 | 776.45 | 553.61 | 21600.00 | 5.05 | 28.7 | 705.99 | 163.67 | 712.95 | 157.17 | 13.66 | 9.07 | 21.58 | |
Avg | 21600.00 | 3.35 | 28.74 | 148.35 | 14.78 | 11.81 | 19.18 |
Instance | CPLEX | GRASP-ILS | ||||||||||||
Ini | UB | LB | CPU | ImpIni | GapLB | Zmin | CPU | Zavg | CPUavg | ImpIni | ImpCplex | GapLB | ||
I100-2-1-0 | 1735.62 | 1680.34 | 1041.47 | 21600.00 | 3.29 | 38.02 | 1500.16 | 242.56 | 1509.42 | 254.82 | 15.70 | 10.72 | 30.58 | |
I100-2-1-1 | 1651.57 | 1634.89 | 1015.27 | 21600.00 | 1.02 | 37.90 | 1399.61 | 244.23 | 1409.80 | 271.59 | 18.00 | 14.39 | 27.46 | |
I100-2-1-2 | 1668.99 | 1668.99 | 907.93 | 21600.00 | 0.00 | 45.60 | 1481.37 | 264.12 | 1491.31 | 270.40 | 12.67 | 11.24 | 38.71 | |
I100-2-1-3 | 1764.60 | 1689.42 | 1077.17 | 21600.00 | 4.45 | 36.24 | 1406.15 | 200.51 | 1412.52 | 228.29 | 25.49 | 16.77 | 23.40 | |
I100-2-1-4 | 1686.00 | 1686.00 | 985.47 | 21600.00 | 0.00 | 41.55 | 1471.77 | 231.05 | 1479.38 | 237.84 | 14.56 | 12.71 | 33.04 | |
I100-2-1-5 | 1700.66 | 1700.66 | 878.73 | 21600.00 | 0.00 | 48.33 | 1465.71 | 265.97 | 1488.23 | 273.44 | 16.03 | 13.82 | 40.05 | |
I100-2-1-6 | 1692.38 | 1691.53 | 1017.12 | 21600.00 | 0.05 | 39.87 | 1482.92 | 258.92 | 1503.80 | 271.70 | 14.12 | 12.33 | 31.41 | |
I100-2-1-7 | 1645.66 | 1645.66 | 900.34 | 21600.00 | 0.00 | 45.29 | 1439.77 | 227.63 | 1442.38 | 242.32 | 14.30 | 12.51 | 37.47 | |
I100-2-1-8 | 1505.41 | 1478.50 | 927.61 | 21600.00 | 1.82 | 37.26 | 1277.58 | 261.05 | 1283.99 | 274.56 | 17.83 | 13.59 | 27.39 | |
I100-2-1-9 | 1541.52 | 1460.33 | 987.62 | 21600.00 | 5.56 | 32.37 | 1286.29 | 267.15 | 1315.68 | 277.42 | 19.84 | 11.92 | 23.22 | |
Avg | 21600.00 | 1.62 | 40.24 | 246.32 | 16.85 | 13.00 | 31.27 | |||||||
O100-2-1-0 | 1467.93 | 1420.49 | 950.02 | 21600.00 | 3.34 | 33.12 | 1215.92 | 278.27 | 1225.50 | 288.86 | 20.73 | 14.40 | 21.87 | |
O100-2-1-1 | 1309.79 | 1309.79 | 836.30 | 21600.00 | 0.00 | 36.15 | 1113.13 | 316.97 | 1124.36 | 328.01 | 17.67 | 15.01 | 24.87 | |
O100-2-1-2 | 1283.48 | 1230.45 | 831.54 | 21600.00 | 4.31 | 32.42 | 1066.12 | 254.79 | 1068.68 | 263.26 | 20.39 | 13.36 | 22.00 | |
O100-2-1-3 | 1284.46 | 1321.90 | 810.99 | 21600.00 | 0.00 | 38.65 | 1166.47 | 300.23 | 1186.02 | 278.56 | 13.32 | 11.76 | 30.48 | |
O100-2-1-4 | 1382.26 | 1338.36 | 909.82 | 21600.00 | 3.28 | 32.02 | 1146.62 | 287.89 | 1151.50 | 298.72 | 20.55 | 14.33 | 20.65 | |
O100-2-1-5 | 1494.38 | 1431.12 | 903.18 | 21600.00 | 4.42 | 36.89 | 1223.53 | 294.71 | 1245.41 | 298.48 | 22.14 | 14.51 | 26.18 | |
O100-2-1-6 | 1318.96 | 1264.83 | 831.75 | 21600.00 | 4.28 | 34.24 | 1062.43 | 311.91 | 1064.81 | 321.69 | 24.15 | 16.00 | 21.71 | |
O100-2-1-7 | 1435.95 | 1432.51 | 894.75 | 21600.00 | 0.24 | 37.54 | 1224.31 | 306.67 | 1230.86 | 324.67 | 17.29 | 14.53 | 26.92 | |
O100-2-1-8 | 1254.70 | 1221.48 | 779.18 | 21600.00 | 2.72 | 36.21 | 971.56 | 296.99 | 1002.10 | 317.68 | 29.14 | 20.46 | 19.80 | |
O100-2-1-9 | 1381.18 | 1339.26 | 866.90 | 21600.00 | 3.13 | 35.27 | 1098.25 | 278.80 | 1119.88 | 283.29 | 25.76 | 18.00 | 21.06 | |
Avg | 21600.00 | 2.57 | 35.25 | 292.72 | 21.11 | 15.24 | 23.55 | |||||||
A100-2-1-0 | 1415.28 | 1404.33 | 863.94 | 21600.00 | 0.78 | 38.48 | 1212.68 | 235.67 | 1230.21 | 256.89 | 16.71 | 13.65 | 28.76 | |
A100-2-1-1 | 1696.07 | 1627.24 | 1168.36 | 21600.00 | 4.23 | 28.20 | 1271.73 | 269.87 | 1291.68 | 279.07 | 33.37 | 21.85 | 8.13 | |
A100-2-1-2 | 1328.88 | 1283.69 | 849.55 | 21600.00 | 3.52 | 33.82 | 1129.63 | 308.04 | 1132.34 | 325.42 | 17.64 | 12.00 | 24.79 | |
A100-2-1-3 | 1364.97 | 1360.34 | 865.59 | 21600.00 | 0.34 | 36.37 | 1162.85 | 263.527 | 1179.11 | 269.85 | 17.38 | 14.52 | 25.56 | |
A100-2-1-4 | 1433.15 | 1417.56 | 886.68 | 21600.00 | 1.10 | 37.45 | 1190.23 | 270.33 | 1197.46 | 281.37 | 20.41 | 16.04 | 25.50 | |
A100-2-1-5 | 1320.79 | 1320.79 | 802.64 | 21600.00 | 0.00 | 39.23 | 1093.48 | 267.46 | 1116.72 | 344.65 | 20.79 | 17.21 | 26.60 | |
A100-2-1-6 | 1450.78 | 1400.91 | 972.51 | 21600.00 | 3.56 | 30.58 | 1208.76 | 258.22 | 1212.17 | 356.84 | 20.02 | 13.72 | 19.54 | |
A100-2-1-7 | 1404.69 | 1371.23 | 920.23 | 21600.00 | 2.44 | 32.89 | 1174.24 | 364.28 | 1193.54 | 380.21 | 19.63 | 14.37 | 21.63 | |
A100-2-1-8 | 1334.8 | 1321.19 | 847.28 | 21600.00 | 1.03 | 35.87 | 1154.51 | 266.66 | 1177.15 | 345.79 | 15.62 | 12.62 | 26.61 | |
A100-2-1-9 | 1382.94 | 1365.60 | 918.36 | 21600.00 | 1.27 | 32.75 | 1217.18 | 320.42 | 1218.88 | 329.73 | 13.62 | 10.87 | 24.55 | |
Avg | 21600.00 | 1.83 | 34.56 | 282.45 | 19.52 | 14.68 | 23.17 |
Instance | CPLEX | GRASP-ILS | ||||||||||||
Ini | UB | LB | CPU | ImpIni | GapLB | Zmin | CPU | Zavg | CPUavg | ImpIni | ImpCplex | GapLB | ||
I100-2-1-0 | 1735.62 | 1680.34 | 1041.47 | 21600.00 | 3.29 | 38.02 | 1500.16 | 242.56 | 1509.42 | 254.82 | 15.70 | 10.72 | 30.58 | |
I100-2-1-1 | 1651.57 | 1634.89 | 1015.27 | 21600.00 | 1.02 | 37.90 | 1399.61 | 244.23 | 1409.80 | 271.59 | 18.00 | 14.39 | 27.46 | |
I100-2-1-2 | 1668.99 | 1668.99 | 907.93 | 21600.00 | 0.00 | 45.60 | 1481.37 | 264.12 | 1491.31 | 270.40 | 12.67 | 11.24 | 38.71 | |
I100-2-1-3 | 1764.60 | 1689.42 | 1077.17 | 21600.00 | 4.45 | 36.24 | 1406.15 | 200.51 | 1412.52 | 228.29 | 25.49 | 16.77 | 23.40 | |
I100-2-1-4 | 1686.00 | 1686.00 | 985.47 | 21600.00 | 0.00 | 41.55 | 1471.77 | 231.05 | 1479.38 | 237.84 | 14.56 | 12.71 | 33.04 | |
I100-2-1-5 | 1700.66 | 1700.66 | 878.73 | 21600.00 | 0.00 | 48.33 | 1465.71 | 265.97 | 1488.23 | 273.44 | 16.03 | 13.82 | 40.05 | |
I100-2-1-6 | 1692.38 | 1691.53 | 1017.12 | 21600.00 | 0.05 | 39.87 | 1482.92 | 258.92 | 1503.80 | 271.70 | 14.12 | 12.33 | 31.41 | |
I100-2-1-7 | 1645.66 | 1645.66 | 900.34 | 21600.00 | 0.00 | 45.29 | 1439.77 | 227.63 | 1442.38 | 242.32 | 14.30 | 12.51 | 37.47 | |
I100-2-1-8 | 1505.41 | 1478.50 | 927.61 | 21600.00 | 1.82 | 37.26 | 1277.58 | 261.05 | 1283.99 | 274.56 | 17.83 | 13.59 | 27.39 | |
I100-2-1-9 | 1541.52 | 1460.33 | 987.62 | 21600.00 | 5.56 | 32.37 | 1286.29 | 267.15 | 1315.68 | 277.42 | 19.84 | 11.92 | 23.22 | |
Avg | 21600.00 | 1.62 | 40.24 | 246.32 | 16.85 | 13.00 | 31.27 | |||||||
O100-2-1-0 | 1467.93 | 1420.49 | 950.02 | 21600.00 | 3.34 | 33.12 | 1215.92 | 278.27 | 1225.50 | 288.86 | 20.73 | 14.40 | 21.87 | |
O100-2-1-1 | 1309.79 | 1309.79 | 836.30 | 21600.00 | 0.00 | 36.15 | 1113.13 | 316.97 | 1124.36 | 328.01 | 17.67 | 15.01 | 24.87 | |
O100-2-1-2 | 1283.48 | 1230.45 | 831.54 | 21600.00 | 4.31 | 32.42 | 1066.12 | 254.79 | 1068.68 | 263.26 | 20.39 | 13.36 | 22.00 | |
O100-2-1-3 | 1284.46 | 1321.90 | 810.99 | 21600.00 | 0.00 | 38.65 | 1166.47 | 300.23 | 1186.02 | 278.56 | 13.32 | 11.76 | 30.48 | |
O100-2-1-4 | 1382.26 | 1338.36 | 909.82 | 21600.00 | 3.28 | 32.02 | 1146.62 | 287.89 | 1151.50 | 298.72 | 20.55 | 14.33 | 20.65 | |
O100-2-1-5 | 1494.38 | 1431.12 | 903.18 | 21600.00 | 4.42 | 36.89 | 1223.53 | 294.71 | 1245.41 | 298.48 | 22.14 | 14.51 | 26.18 | |
O100-2-1-6 | 1318.96 | 1264.83 | 831.75 | 21600.00 | 4.28 | 34.24 | 1062.43 | 311.91 | 1064.81 | 321.69 | 24.15 | 16.00 | 21.71 | |
O100-2-1-7 | 1435.95 | 1432.51 | 894.75 | 21600.00 | 0.24 | 37.54 | 1224.31 | 306.67 | 1230.86 | 324.67 | 17.29 | 14.53 | 26.92 | |
O100-2-1-8 | 1254.70 | 1221.48 | 779.18 | 21600.00 | 2.72 | 36.21 | 971.56 | 296.99 | 1002.10 | 317.68 | 29.14 | 20.46 | 19.80 | |
O100-2-1-9 | 1381.18 | 1339.26 | 866.90 | 21600.00 | 3.13 | 35.27 | 1098.25 | 278.80 | 1119.88 | 283.29 | 25.76 | 18.00 | 21.06 | |
Avg | 21600.00 | 2.57 | 35.25 | 292.72 | 21.11 | 15.24 | 23.55 | |||||||
A100-2-1-0 | 1415.28 | 1404.33 | 863.94 | 21600.00 | 0.78 | 38.48 | 1212.68 | 235.67 | 1230.21 | 256.89 | 16.71 | 13.65 | 28.76 | |
A100-2-1-1 | 1696.07 | 1627.24 | 1168.36 | 21600.00 | 4.23 | 28.20 | 1271.73 | 269.87 | 1291.68 | 279.07 | 33.37 | 21.85 | 8.13 | |
A100-2-1-2 | 1328.88 | 1283.69 | 849.55 | 21600.00 | 3.52 | 33.82 | 1129.63 | 308.04 | 1132.34 | 325.42 | 17.64 | 12.00 | 24.79 | |
A100-2-1-3 | 1364.97 | 1360.34 | 865.59 | 21600.00 | 0.34 | 36.37 | 1162.85 | 263.527 | 1179.11 | 269.85 | 17.38 | 14.52 | 25.56 | |
A100-2-1-4 | 1433.15 | 1417.56 | 886.68 | 21600.00 | 1.10 | 37.45 | 1190.23 | 270.33 | 1197.46 | 281.37 | 20.41 | 16.04 | 25.50 | |
A100-2-1-5 | 1320.79 | 1320.79 | 802.64 | 21600.00 | 0.00 | 39.23 | 1093.48 | 267.46 | 1116.72 | 344.65 | 20.79 | 17.21 | 26.60 | |
A100-2-1-6 | 1450.78 | 1400.91 | 972.51 | 21600.00 | 3.56 | 30.58 | 1208.76 | 258.22 | 1212.17 | 356.84 | 20.02 | 13.72 | 19.54 | |
A100-2-1-7 | 1404.69 | 1371.23 | 920.23 | 21600.00 | 2.44 | 32.89 | 1174.24 | 364.28 | 1193.54 | 380.21 | 19.63 | 14.37 | 21.63 | |
A100-2-1-8 | 1334.8 | 1321.19 | 847.28 | 21600.00 | 1.03 | 35.87 | 1154.51 | 266.66 | 1177.15 | 345.79 | 15.62 | 12.62 | 26.61 | |
A100-2-1-9 | 1382.94 | 1365.60 | 918.36 | 21600.00 | 1.27 | 32.75 | 1217.18 | 320.42 | 1218.88 | 329.73 | 13.62 | 10.87 | 24.55 | |
Avg | 21600.00 | 1.83 | 34.56 | 282.45 | 19.52 | 14.68 | 23.17 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I20-2-1-0 | 459.26 | 459.26 | 459.26 | 459.26 | 459.26 | 0.00 | 0.00 | ||
I20-2-1-1 | 449.88 | 449.88 | 366.66 | 366.66 | 366.66 | 22.70 | 0.00 | ||
I20-2-1-2 | 478.19 | 478.19 | 478.19 | 478.19 | 478.19 | 0.00 | 0.00 | ||
I20-2-1-3 | 449.29 | 459.44 | 360.24 | 415.28 | 360.24 | 24.72 | 0.00 | ||
I20-2-1-4 | 387.33 | 413.78 | 387.33 | 412.08 | 383.24 | 1.07 | 1.07 | ||
I20-2-1-5 | 364.89 | 370.22 | 364.89 | 373.59 | 343.70 | 6.17 | 6.17 | ||
I20-2-1-6 | 344.51 | 344.51 | 344.51 | 344.51 | 344.51 | 0.00 | 0.00 | ||
I20-2-1-7 | 379.50 | 407.70 | 426.47 | 479.74 | 354.59 | 7.03 | 20.27 | ||
I20-2-1-8 | 363.34 | 368.28 | 366.19 | 376.44 | 351.37 | 3.41 | 4.22 | ||
I20-2-1-9 | 476.32 | 476.32 | 476.32 | 494.04 | 476.32 | 0.00 | 0.00 | ||
Avg | 6.51 | 3.17 | |||||||
O20-2-1-0 | 240.46 | 240.46 | 240.46 | 240.46 | 240.46 | 0.00 | 0.00 | ||
O20-2-1-1 | 261.02 | 261.02 | 278.50 | 278.56 | 260.84 | 0.07 | 6.77 | ||
O20-2-1-2 | 250.62 | 250.62 | 251.75 | 251.75 | 250.62 | 0.00 | 0.45 | ||
O20-2-1-3 | 254.79 | 254.79 | 254.79 | 254.79 | 254.79 | 0.00 | 0.00 | ||
O20-2-1-4 | 273.98 | 274.99 | 275.45 | 275.56 | 273.79 | 0.07 | 0.61 | ||
O20-2-1-5 | 269.61 | 269.61 | 269.61 | 269.61 | 269.61 | 0.00 | 0.00 | ||
O20-2-1-6 | 260.87 | 260.92 | 260.87 | 261.21 | 260.31 | 0.22 | 0.22 | ||
O20-2-1-7 | 245.95 | 246.37 | 246.97 | 246.97 | 245.95 | 0.00 | 0.41 | ||
O20-2-1-8 | 265.74 | 265.74 | 240.28 | 244.44 | 240.28 | 10.60 | 0.00 | ||
O20-2-1-9 | 247.82 | 247.97 | 230.15 | 235.51 | 229.92 | 7.79 | 0.10 | ||
Avg | 1.87 | 0.86 | |||||||
A20-2-1-0 | 367.97 | 367.97 | 367.91 | 379.79 | 362.31 | 1.56 | 1.55 | ||
A20-2-1-1 | 444.8 | 444.80 | 444.80 | 444.80 | 444.80 | 0.00 | 0.00 | ||
A20-2-1-2 | 364.77 | 375.31 | 364.77 | 404.68 | 329.67 | 10.65 | 10.65 | ||
A20-2-1-3 | 412.44 | 439.21 | 423.93 | 456.66 | 363.62 | 13.43 | 16.59 | ||
A20-2-1-4 | 415.4 | 415.40 | 343.77 | 397.64 | 343.77 | 20.84 | 0.00 | ||
A20-2-1-5 | 295.37 | 297.82 | 299.91 | 305.22 | 287.74 | 2.65 | 4.23 | ||
A20-2-1-6 | 340.74 | 340.74 | 338.23 | 338.74 | 338.23 | 0.74 | 0.00 | ||
A20-2-1-7 | 298.51 | 304.03 | 301.26 | 304.94 | 290.21 | 2.86 | 3.81 | ||
A20-2-1-8 | 314.20 | 314.20 | 314.20 | 314.20 | 314.20 | 0.00 | 0.00 | ||
A20-2-1-9 | 400.40 | 400.40 | 323.60 | 361.33 | 323.60 | 23.73 | 0.00 | ||
Avg | 7.65 | 3.68 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I20-2-1-0 | 459.26 | 459.26 | 459.26 | 459.26 | 459.26 | 0.00 | 0.00 | ||
I20-2-1-1 | 449.88 | 449.88 | 366.66 | 366.66 | 366.66 | 22.70 | 0.00 | ||
I20-2-1-2 | 478.19 | 478.19 | 478.19 | 478.19 | 478.19 | 0.00 | 0.00 | ||
I20-2-1-3 | 449.29 | 459.44 | 360.24 | 415.28 | 360.24 | 24.72 | 0.00 | ||
I20-2-1-4 | 387.33 | 413.78 | 387.33 | 412.08 | 383.24 | 1.07 | 1.07 | ||
I20-2-1-5 | 364.89 | 370.22 | 364.89 | 373.59 | 343.70 | 6.17 | 6.17 | ||
I20-2-1-6 | 344.51 | 344.51 | 344.51 | 344.51 | 344.51 | 0.00 | 0.00 | ||
I20-2-1-7 | 379.50 | 407.70 | 426.47 | 479.74 | 354.59 | 7.03 | 20.27 | ||
I20-2-1-8 | 363.34 | 368.28 | 366.19 | 376.44 | 351.37 | 3.41 | 4.22 | ||
I20-2-1-9 | 476.32 | 476.32 | 476.32 | 494.04 | 476.32 | 0.00 | 0.00 | ||
Avg | 6.51 | 3.17 | |||||||
O20-2-1-0 | 240.46 | 240.46 | 240.46 | 240.46 | 240.46 | 0.00 | 0.00 | ||
O20-2-1-1 | 261.02 | 261.02 | 278.50 | 278.56 | 260.84 | 0.07 | 6.77 | ||
O20-2-1-2 | 250.62 | 250.62 | 251.75 | 251.75 | 250.62 | 0.00 | 0.45 | ||
O20-2-1-3 | 254.79 | 254.79 | 254.79 | 254.79 | 254.79 | 0.00 | 0.00 | ||
O20-2-1-4 | 273.98 | 274.99 | 275.45 | 275.56 | 273.79 | 0.07 | 0.61 | ||
O20-2-1-5 | 269.61 | 269.61 | 269.61 | 269.61 | 269.61 | 0.00 | 0.00 | ||
O20-2-1-6 | 260.87 | 260.92 | 260.87 | 261.21 | 260.31 | 0.22 | 0.22 | ||
O20-2-1-7 | 245.95 | 246.37 | 246.97 | 246.97 | 245.95 | 0.00 | 0.41 | ||
O20-2-1-8 | 265.74 | 265.74 | 240.28 | 244.44 | 240.28 | 10.60 | 0.00 | ||
O20-2-1-9 | 247.82 | 247.97 | 230.15 | 235.51 | 229.92 | 7.79 | 0.10 | ||
Avg | 1.87 | 0.86 | |||||||
A20-2-1-0 | 367.97 | 367.97 | 367.91 | 379.79 | 362.31 | 1.56 | 1.55 | ||
A20-2-1-1 | 444.8 | 444.80 | 444.80 | 444.80 | 444.80 | 0.00 | 0.00 | ||
A20-2-1-2 | 364.77 | 375.31 | 364.77 | 404.68 | 329.67 | 10.65 | 10.65 | ||
A20-2-1-3 | 412.44 | 439.21 | 423.93 | 456.66 | 363.62 | 13.43 | 16.59 | ||
A20-2-1-4 | 415.4 | 415.40 | 343.77 | 397.64 | 343.77 | 20.84 | 0.00 | ||
A20-2-1-5 | 295.37 | 297.82 | 299.91 | 305.22 | 287.74 | 2.65 | 4.23 | ||
A20-2-1-6 | 340.74 | 340.74 | 338.23 | 338.74 | 338.23 | 0.74 | 0.00 | ||
A20-2-1-7 | 298.51 | 304.03 | 301.26 | 304.94 | 290.21 | 2.86 | 3.81 | ||
A20-2-1-8 | 314.20 | 314.20 | 314.20 | 314.20 | 314.20 | 0.00 | 0.00 | ||
A20-2-1-9 | 400.40 | 400.40 | 323.60 | 361.33 | 323.60 | 23.73 | 0.00 | ||
Avg | 7.65 | 3.68 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I40-2-1-0 | 733.03 | 769.61 | 741.58 | 773.84 | 706.64 | 3.73 | 4.94 | ||
I40-2-1-1 | 617.81 | 617.81 | 610.54 | 675.38 | 600.90 | 2.81 | 1.60 | ||
I40-2-1-2 | 756.99 | 806.65 | 755.90 | 772.53 | 729.24 | 3.81 | 3.66 | ||
I40-2-1-3 | 651.55 | 681.20 | 718.16 | 718.16 | 651.55 | 0.00 | 10.22 | ||
I40-2-1-4 | 699.59 | 731.00 | 720.42 | 720.42 | 699.59 | 0.00 | 2.98 | ||
I40-2-1-5 | 718.38 | 761.48 | 672.90 | 771.28 | 647.36 | 10.97 | 3.95 | ||
I40-2-1-6 | 605.91 | 639.66 | 627.27 | 700.22 | 590.24 | 4.35 | 6.27 | ||
I40-2-1-7 | 653.35 | 653.35 | 612.68 | 686.02 | 612.68 | 6.64 | 0.00 | ||
I40-2-1-8 | 601.37 | 635.83 | 582.26 | 645.55 | 573.59 | 4.84 | 1.51 | ||
I40-2-1-9 | 612.71 | 654.01 | 610.28 | 677.78 | 598.44 | 2.38 | 1.98 | ||
Avg | 3.95 | 3.71 | |||||||
O40-2-1-0 | 573.13 | 607.63 | 530.77 | 613.94 | 494.73 | 15.85 | 7.28 | ||
O40-2-1-1 | 451.96 | 479.67 | 476.94 | 535.79 | 434.04 | 4.13 | 9.88 | ||
O40-2-1-2 | 465.61 | 486.61 | 452.72 | 499.94 | 445.80 | 4.44 | 1.55 | ||
O40-2-1-3 | 523.35 | 523.35 | 523.35 | 523.35 | 523.35 | 0.00 | 0.00 | ||
O40-2-1-4 | 549.35 | 549.35 | 549.35 | 549.35 | 549.35 | 0.00 | 0.00 | ||
O40-2-1-5 | 577.85 | 601.43 | 603.35 | 666.88 | 573.11 | 0.83 | 5.28 | ||
O40-2-1-6 | 492.06 | 525.27 | 492.06 | 492.06 | 489.14 | 0.60 | 0.60 | ||
O40-2-1-7 | 545.21 | 550.93 | 545.21 | 545.21 | 528.80 | 3.10 | 3.10 | ||
O40-2-1-8 | 431.92 | 455.46 | 430.07 | 473.46 | 427.55 | 1.02 | 0.59 | ||
O40-2-1-9 | 579.27 | 602.79 | 601.79 | 668.05 | 578.85 | 0.07 | 3.96 | ||
Avg | 3.00 | 3.23 | |||||||
A40-2-1-0 | 636.15 | 636.28 | 551.33 | 631.55 | 550.20 | 15.62 | 0.21 | ||
A40-2-1-1 | 606.64 | 644.56 | 616.86 | 622.47 | 597.17 | 1.59 | 3.30 | ||
A40-2-1-2 | 587.75 | 587.75 | 582.03 | 583.37 | 582.03 | 0.98 | 0.00 | ||
A40-2-1-3 | 506.85 | 506.85 | 508.34 | 559.68 | 505.21 | 0.32 | 0.62 | ||
A40-2-1-4 | 573.67 | 573.78 | 568.42 | 570.30 | 567.77 | 1.04 | 0.11 | ||
A40-2-1-5 | 683.98 | 697.73 | 617.34 | 703.95 | 617.34 | 10.79 | 0.00 | ||
A40-2-1-6 | 587.71 | 660.17 | 569.77 | 572.96 | 537.91 | 9.26 | 5.92 | ||
A40-2-1-7 | 615.47 | 645.69 | 605.92 | 703.23 | 542.06 | 13.54 | 11.78 | ||
A40-2-1-8 | 624.30 | 670.44 | 624.30 | 702.84 | 600.61 | 3.94 | 3.94 | ||
A40-2-1-9 | 697.84 | 724.57 | 697.60 | 816.89 | 632.33 | 10.36 | 10.32 | ||
Avg | 6.75 | 3.62 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I40-2-1-0 | 733.03 | 769.61 | 741.58 | 773.84 | 706.64 | 3.73 | 4.94 | ||
I40-2-1-1 | 617.81 | 617.81 | 610.54 | 675.38 | 600.90 | 2.81 | 1.60 | ||
I40-2-1-2 | 756.99 | 806.65 | 755.90 | 772.53 | 729.24 | 3.81 | 3.66 | ||
I40-2-1-3 | 651.55 | 681.20 | 718.16 | 718.16 | 651.55 | 0.00 | 10.22 | ||
I40-2-1-4 | 699.59 | 731.00 | 720.42 | 720.42 | 699.59 | 0.00 | 2.98 | ||
I40-2-1-5 | 718.38 | 761.48 | 672.90 | 771.28 | 647.36 | 10.97 | 3.95 | ||
I40-2-1-6 | 605.91 | 639.66 | 627.27 | 700.22 | 590.24 | 4.35 | 6.27 | ||
I40-2-1-7 | 653.35 | 653.35 | 612.68 | 686.02 | 612.68 | 6.64 | 0.00 | ||
I40-2-1-8 | 601.37 | 635.83 | 582.26 | 645.55 | 573.59 | 4.84 | 1.51 | ||
I40-2-1-9 | 612.71 | 654.01 | 610.28 | 677.78 | 598.44 | 2.38 | 1.98 | ||
Avg | 3.95 | 3.71 | |||||||
O40-2-1-0 | 573.13 | 607.63 | 530.77 | 613.94 | 494.73 | 15.85 | 7.28 | ||
O40-2-1-1 | 451.96 | 479.67 | 476.94 | 535.79 | 434.04 | 4.13 | 9.88 | ||
O40-2-1-2 | 465.61 | 486.61 | 452.72 | 499.94 | 445.80 | 4.44 | 1.55 | ||
O40-2-1-3 | 523.35 | 523.35 | 523.35 | 523.35 | 523.35 | 0.00 | 0.00 | ||
O40-2-1-4 | 549.35 | 549.35 | 549.35 | 549.35 | 549.35 | 0.00 | 0.00 | ||
O40-2-1-5 | 577.85 | 601.43 | 603.35 | 666.88 | 573.11 | 0.83 | 5.28 | ||
O40-2-1-6 | 492.06 | 525.27 | 492.06 | 492.06 | 489.14 | 0.60 | 0.60 | ||
O40-2-1-7 | 545.21 | 550.93 | 545.21 | 545.21 | 528.80 | 3.10 | 3.10 | ||
O40-2-1-8 | 431.92 | 455.46 | 430.07 | 473.46 | 427.55 | 1.02 | 0.59 | ||
O40-2-1-9 | 579.27 | 602.79 | 601.79 | 668.05 | 578.85 | 0.07 | 3.96 | ||
Avg | 3.00 | 3.23 | |||||||
A40-2-1-0 | 636.15 | 636.28 | 551.33 | 631.55 | 550.20 | 15.62 | 0.21 | ||
A40-2-1-1 | 606.64 | 644.56 | 616.86 | 622.47 | 597.17 | 1.59 | 3.30 | ||
A40-2-1-2 | 587.75 | 587.75 | 582.03 | 583.37 | 582.03 | 0.98 | 0.00 | ||
A40-2-1-3 | 506.85 | 506.85 | 508.34 | 559.68 | 505.21 | 0.32 | 0.62 | ||
A40-2-1-4 | 573.67 | 573.78 | 568.42 | 570.30 | 567.77 | 1.04 | 0.11 | ||
A40-2-1-5 | 683.98 | 697.73 | 617.34 | 703.95 | 617.34 | 10.79 | 0.00 | ||
A40-2-1-6 | 587.71 | 660.17 | 569.77 | 572.96 | 537.91 | 9.26 | 5.92 | ||
A40-2-1-7 | 615.47 | 645.69 | 605.92 | 703.23 | 542.06 | 13.54 | 11.78 | ||
A40-2-1-8 | 624.30 | 670.44 | 624.30 | 702.84 | 600.61 | 3.94 | 3.94 | ||
A40-2-1-9 | 697.84 | 724.57 | 697.60 | 816.89 | 632.33 | 10.36 | 10.32 | ||
Avg | 6.75 | 3.62 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I60-2-1-0 | 971.76 | 930.24 | 954.90 | 1040.17 | 911.77 | 6.58 | 4.73 | ||
I60-2-1-1 | 997.55 | 990.98 | 997.55 | 1070.57 | 987.76 | 0.99 | 0.99 | ||
I60-2-1-2 | 893.43 | 879.02 | 897.08 | 1033.44 | 877.23 | 1.85 | 2.26 | ||
I60-2-1-3 | 907.53 | 902.23 | 901.81 | 1008.95 | 882.44 | 2.84 | 2.20 | ||
I60-2-1-4 | 979.14 | 967.49 | 975.61 | 1121.17 | 896.87 | 9.17 | 8.78 | ||
I60-2-1-5 | 1004.53 | 997.95 | 1004.53 | 1065.50 | 996.95 | 0.76 | 0.76 | ||
I60-2-1-6 | 1061.43 | 1051.96 | 1056.81 | 1093.90 | 1043.88 | 1.68 | 1.24 | ||
I60-2-1-7 | 1005.16 | 981.49 | 950.37 | 1110.89 | 944.32 | 6.44 | 0.64 | ||
I60-2-1-8 | 882.39 | 854.26 | 854.36 | 965.17 | 818.94 | 7.75 | 4.33 | ||
I60-2-1-9 | 890.19 | 877.62 | 870.52 | 1028.26 | 865.24 | 2.88 | 0.61 | ||
Avg | 4.09 | 2.65 | |||||||
O60-2-1-0 | 713.15 | 746.03 | 703.50 | 758.65 | 652.35 | 9.32 | 3.73 | ||
O60-2-1-1 | 820.25 | 872.50 | 782.50 | 820.53 | 746.22 | 9.92 | 0.55 | ||
O60-2-1-2 | 782.26 | 799.70 | 761.74 | 868.31 | 732.49 | 6.79 | 0.15 | ||
O60-2-1-3 | 847.18 | 875.98 | 820.05 | 853.67 | 787.76 | 7.54 | 0.52 | ||
O60-2-1-4 | 776.48 | 845.20 | 771.15 | 817.65 | 727.32 | 6.76 | 0.64 | ||
O60-2-1-5 | 820.66 | 851.19 | 763.93 | 844.07 | 752.74 | 9.02 | 0.40 | ||
O60-2-1-6 | 708.48 | 714.50 | 680.46 | 680.46 | 680.46 | 4.12 | 0.00 | ||
O60-2-1-7 | 816.27 | 830.39 | 781.70 | 811.56 | 752.96 | 8.41 | 1.16 | ||
O60-2-1-8 | 723.94 | 759.78 | 715.02 | 806.47 | 695.58 | 4.08 | 0.00 | ||
O60-2-1-9 | 783.28 | 871.56 | 747.26 | 771.70 | 723.61 | 8.25 | 0.18 | ||
Avg | 7.42 | 0.73 | |||||||
A60-2-1-0 | 858.31 | 858.31 | 836.63 | 929.83 | 836.54 | 2.60 | 0.01 | ||
A60-2-1-1 | 956.96 | 1024.04 | 952.71 | 1049.60 | 911.33 | 5.01 | 4.54 | ||
A60-2-1-2 | 719.41 | 741.14 | 776.51 | 778.37 | 703.79 | 2.22 | 10.33 | ||
A60-2-1-3 | 849.45 | 928.96 | 802.22 | 912.04 | 781.73 | 8.66 | 2.62 | ||
A60-2-1-4 | 857.32 | 880.81 | 841.54 | 899.44 | 793.69 | 8.02 | 6.03 | ||
A60-2-1-5 | 808.57 | 830.08 | 761.17 | 803.11 | 740.28 | 9.22 | 2.82 | ||
A60-2-1-6 | 803.29 | 862.81 | 803.29 | 871.89 | 754.71 | 6.44 | 6.44 | ||
A60-2-1-7 | 853.23 | 853.23 | 802.72 | 905.31 | 780.28 | 9.35 | 2.88 | ||
A60-2-1-8 | 780.61 | 815.35 | 772.43 | 843.73 | 751.38 | 3.89 | 2.80 | ||
A60-2-1-9 | 763.12 | 795.25 | 762.09 | 825.88 | 705.99 | 8.09 | 7.95 | ||
Avg | 6.35 | 4.64 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I60-2-1-0 | 971.76 | 930.24 | 954.90 | 1040.17 | 911.77 | 6.58 | 4.73 | ||
I60-2-1-1 | 997.55 | 990.98 | 997.55 | 1070.57 | 987.76 | 0.99 | 0.99 | ||
I60-2-1-2 | 893.43 | 879.02 | 897.08 | 1033.44 | 877.23 | 1.85 | 2.26 | ||
I60-2-1-3 | 907.53 | 902.23 | 901.81 | 1008.95 | 882.44 | 2.84 | 2.20 | ||
I60-2-1-4 | 979.14 | 967.49 | 975.61 | 1121.17 | 896.87 | 9.17 | 8.78 | ||
I60-2-1-5 | 1004.53 | 997.95 | 1004.53 | 1065.50 | 996.95 | 0.76 | 0.76 | ||
I60-2-1-6 | 1061.43 | 1051.96 | 1056.81 | 1093.90 | 1043.88 | 1.68 | 1.24 | ||
I60-2-1-7 | 1005.16 | 981.49 | 950.37 | 1110.89 | 944.32 | 6.44 | 0.64 | ||
I60-2-1-8 | 882.39 | 854.26 | 854.36 | 965.17 | 818.94 | 7.75 | 4.33 | ||
I60-2-1-9 | 890.19 | 877.62 | 870.52 | 1028.26 | 865.24 | 2.88 | 0.61 | ||
Avg | 4.09 | 2.65 | |||||||
O60-2-1-0 | 713.15 | 746.03 | 703.50 | 758.65 | 652.35 | 9.32 | 3.73 | ||
O60-2-1-1 | 820.25 | 872.50 | 782.50 | 820.53 | 746.22 | 9.92 | 0.55 | ||
O60-2-1-2 | 782.26 | 799.70 | 761.74 | 868.31 | 732.49 | 6.79 | 0.15 | ||
O60-2-1-3 | 847.18 | 875.98 | 820.05 | 853.67 | 787.76 | 7.54 | 0.52 | ||
O60-2-1-4 | 776.48 | 845.20 | 771.15 | 817.65 | 727.32 | 6.76 | 0.64 | ||
O60-2-1-5 | 820.66 | 851.19 | 763.93 | 844.07 | 752.74 | 9.02 | 0.40 | ||
O60-2-1-6 | 708.48 | 714.50 | 680.46 | 680.46 | 680.46 | 4.12 | 0.00 | ||
O60-2-1-7 | 816.27 | 830.39 | 781.70 | 811.56 | 752.96 | 8.41 | 1.16 | ||
O60-2-1-8 | 723.94 | 759.78 | 715.02 | 806.47 | 695.58 | 4.08 | 0.00 | ||
O60-2-1-9 | 783.28 | 871.56 | 747.26 | 771.70 | 723.61 | 8.25 | 0.18 | ||
Avg | 7.42 | 0.73 | |||||||
A60-2-1-0 | 858.31 | 858.31 | 836.63 | 929.83 | 836.54 | 2.60 | 0.01 | ||
A60-2-1-1 | 956.96 | 1024.04 | 952.71 | 1049.60 | 911.33 | 5.01 | 4.54 | ||
A60-2-1-2 | 719.41 | 741.14 | 776.51 | 778.37 | 703.79 | 2.22 | 10.33 | ||
A60-2-1-3 | 849.45 | 928.96 | 802.22 | 912.04 | 781.73 | 8.66 | 2.62 | ||
A60-2-1-4 | 857.32 | 880.81 | 841.54 | 899.44 | 793.69 | 8.02 | 6.03 | ||
A60-2-1-5 | 808.57 | 830.08 | 761.17 | 803.11 | 740.28 | 9.22 | 2.82 | ||
A60-2-1-6 | 803.29 | 862.81 | 803.29 | 871.89 | 754.71 | 6.44 | 6.44 | ||
A60-2-1-7 | 853.23 | 853.23 | 802.72 | 905.31 | 780.28 | 9.35 | 2.88 | ||
A60-2-1-8 | 780.61 | 815.35 | 772.43 | 843.73 | 751.38 | 3.89 | 2.80 | ||
A60-2-1-9 | 763.12 | 795.25 | 762.09 | 825.88 | 705.99 | 8.09 | 7.95 | ||
Avg | 6.35 | 4.64 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I100-2-1-0 | 1638.35 | 1704.61 | 1609.09 | 1890.61 | 1500.16 | 9.21 | 7.26 | ||
I100-2-1-1 | 1475.76 | 1550.51 | 1462.03 | 1720.88 | 1399.61 | 5.44 | 4.46 | ||
I100-2-1-2 | 1549.56 | 1714.37 | 1519.43 | 1792.65 | 1481.37 | 4.60 | 2.57 | ||
I100-2-1-3 | 1541.71 | 1630.81 | 1516.8 | 1799.58 | 1406.15 | 9.64 | 7.87 | ||
I100-2-1-4 | 1586.41 | 1607.53 | 1501.97 | 1774.75 | 1471.77 | 7.79 | 2.05 | ||
I100-2-1-5 | 1547.53 | 1591.87 | 1476.42 | 1763.20 | 1465.71 | 5.58 | 0.73 | ||
I100-2-1-6 | 1594.07 | 1622.95 | 1501.05 | 1791.06 | 1482.92 | 7.50 | 1.22 | ||
I100-2-1-7 | 1568.12 | 1653.99 | 1508.18 | 1741.59 | 1439.77 | 8.91 | 4.75 | ||
I100-2-1-8 | 1340.87 | 1424.62 | 1358.42 | 1513.15 | 1277.58 | 4.95 | 6.33 | ||
I100-2-1-9 | 1393.89 | 1430.99 | 1346.03 | 1604.42 | 1286.29 | 8.37 | 4.64 | ||
Avg | 7.20 | 4.19 | |||||||
O100-2-1-0 | 1279.18 | 1347.70 | 1252.87 | 1352.97 | 1215.92 | 5.20 | 3.04 | ||
O100-2-1-1 | 1169.86 | 1255.83 | 1149.36 | 1236.94 | 1113.13 | 5.10 | 3.25 | ||
O100-2-1-2 | 1123.63 | 1191.98 | 1098.08 | 1156.11 | 1066.12 | 5.39 | 3.00 | ||
O100-2-1-3 | 1272.18 | 1320.34 | 1209.93 | 1297.75 | 1166.47 | 9.06 | 3.73 | ||
O100-2-1-4 | 1278.7 | 1376.42 | 1206.94 | 1273.12 | 1146.62 | 11.52 | 5.26 | ||
O100-2-1-5 | 1282.2 | 1310.21 | 1264.78 | 1444.76 | 1223.53 | 4.80 | 3.37 | ||
O100-2-1-6 | 1112.92 | 1195.06 | 1099.75 | 1266.59 | 1062.43 | 4.75 | 3.51 | ||
O100-2-1-7 | 1271.97 | 1338.24 | 1231.68 | 1310.19 | 1224.31 | 3.89 | 0.60 | ||
O100-2-1-8 | 1071.1 | 1141.54 | 1000.51 | 1190.17 | 971.56 | 10.25 | 2.98 | ||
O100-2-1-9 | 1163.25 | 1211.45 | 1197.58 | 1339.77 | 1098.25 | 5.92 | 9.04 | ||
Avg | 6.59 | 3.78 | |||||||
A100-2-1-0 | 1280.19 | 1361.66 | 1265.52 | 1359.89 | 1212.68 | 5.57 | 4.36 | ||
A100-2-1-1 | 1362.77 | 1431.84 | 1362.04 | 1541.04 | 1271.73 | 7.16 | 7.10 | ||
A100-2-1-2 | 1183.91 | 1240.90 | 1159.67 | 1326.68 | 1129.63 | 4.81 | 2.66 | ||
A100-2-1-3 | 1214.65 | 1288.61 | 1198.17 | 1355.01 | 1162.85 | 2.73 | 3.04 | ||
A100-2-1-4 | 1236.76 | 1325.19 | 1243.54 | 1400.64 | 1190.23 | 3.91 | 4.48 | ||
A100-2-1-5 | 1177.71 | 1241.31 | 1144.83 | 1228.66 | 1093.48 | 7.70 | 4.70 | ||
A100-2-1-6 | 1270.56 | 1328.54 | 1256.54 | 1336.74 | 1208.76 | 5.11 | 3.95 | ||
A100-2-1-7 | 1227.98 | 1308.64 | 1221.57 | 1316.30 | 1174.24 | 4.58 | 4.03 | ||
A100-2-1-8 | 1210.54 | 1298.73 | 1192.27 | 1288.85 | 1154.51 | 3.99 | 3.27 | ||
A100-2-1-9 | 1271.11 | 1320.95 | 1253.95 | 1419.94 | 1217.18 | 4.43 | 3.02 | ||
Avg | 5.00 | 4.06 |
Instance | GRASP | ILS | GRASP-ILS | ||||||
Zmin | Zavg | Zmin | Zavg | Zmin | ImpGRASP-ILS, GRASP | ImpGRASP-ILS, ILS | |||
I100-2-1-0 | 1638.35 | 1704.61 | 1609.09 | 1890.61 | 1500.16 | 9.21 | 7.26 | ||
I100-2-1-1 | 1475.76 | 1550.51 | 1462.03 | 1720.88 | 1399.61 | 5.44 | 4.46 | ||
I100-2-1-2 | 1549.56 | 1714.37 | 1519.43 | 1792.65 | 1481.37 | 4.60 | 2.57 | ||
I100-2-1-3 | 1541.71 | 1630.81 | 1516.8 | 1799.58 | 1406.15 | 9.64 | 7.87 | ||
I100-2-1-4 | 1586.41 | 1607.53 | 1501.97 | 1774.75 | 1471.77 | 7.79 | 2.05 | ||
I100-2-1-5 | 1547.53 | 1591.87 | 1476.42 | 1763.20 | 1465.71 | 5.58 | 0.73 | ||
I100-2-1-6 | 1594.07 | 1622.95 | 1501.05 | 1791.06 | 1482.92 | 7.50 | 1.22 | ||
I100-2-1-7 | 1568.12 | 1653.99 | 1508.18 | 1741.59 | 1439.77 | 8.91 | 4.75 | ||
I100-2-1-8 | 1340.87 | 1424.62 | 1358.42 | 1513.15 | 1277.58 | 4.95 | 6.33 | ||
I100-2-1-9 | 1393.89 | 1430.99 | 1346.03 | 1604.42 | 1286.29 | 8.37 | 4.64 | ||
Avg | 7.20 | 4.19 | |||||||
O100-2-1-0 | 1279.18 | 1347.70 | 1252.87 | 1352.97 | 1215.92 | 5.20 | 3.04 | ||
O100-2-1-1 | 1169.86 | 1255.83 | 1149.36 | 1236.94 | 1113.13 | 5.10 | 3.25 | ||
O100-2-1-2 | 1123.63 | 1191.98 | 1098.08 | 1156.11 | 1066.12 | 5.39 | 3.00 | ||
O100-2-1-3 | 1272.18 | 1320.34 | 1209.93 | 1297.75 | 1166.47 | 9.06 | 3.73 | ||
O100-2-1-4 | 1278.7 | 1376.42 | 1206.94 | 1273.12 | 1146.62 | 11.52 | 5.26 | ||
O100-2-1-5 | 1282.2 | 1310.21 | 1264.78 | 1444.76 | 1223.53 | 4.80 | 3.37 | ||
O100-2-1-6 | 1112.92 | 1195.06 | 1099.75 | 1266.59 | 1062.43 | 4.75 | 3.51 | ||
O100-2-1-7 | 1271.97 | 1338.24 | 1231.68 | 1310.19 | 1224.31 | 3.89 | 0.60 | ||
O100-2-1-8 | 1071.1 | 1141.54 | 1000.51 | 1190.17 | 971.56 | 10.25 | 2.98 | ||
O100-2-1-9 | 1163.25 | 1211.45 | 1197.58 | 1339.77 | 1098.25 | 5.92 | 9.04 | ||
Avg | 6.59 | 3.78 | |||||||
A100-2-1-0 | 1280.19 | 1361.66 | 1265.52 | 1359.89 | 1212.68 | 5.57 | 4.36 | ||
A100-2-1-1 | 1362.77 | 1431.84 | 1362.04 | 1541.04 | 1271.73 | 7.16 | 7.10 | ||
A100-2-1-2 | 1183.91 | 1240.90 | 1159.67 | 1326.68 | 1129.63 | 4.81 | 2.66 | ||
A100-2-1-3 | 1214.65 | 1288.61 | 1198.17 | 1355.01 | 1162.85 | 2.73 | 3.04 | ||
A100-2-1-4 | 1236.76 | 1325.19 | 1243.54 | 1400.64 | 1190.23 | 3.91 | 4.48 | ||
A100-2-1-5 | 1177.71 | 1241.31 | 1144.83 | 1228.66 | 1093.48 | 7.70 | 4.70 | ||
A100-2-1-6 | 1270.56 | 1328.54 | 1256.54 | 1336.74 | 1208.76 | 5.11 | 3.95 | ||
A100-2-1-7 | 1227.98 | 1308.64 | 1221.57 | 1316.30 | 1174.24 | 4.58 | 4.03 | ||
A100-2-1-8 | 1210.54 | 1298.73 | 1192.27 | 1288.85 | 1154.51 | 3.99 | 3.27 | ||
A100-2-1-9 | 1271.11 | 1320.95 | 1253.95 | 1419.94 | 1217.18 | 4.43 | 3.02 | ||
Avg | 5.00 | 4.06 |
Instance | Non-collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I20-2-1-0 | 528.74 | 5 | 459.26 | 3 | 13.14 |
I20-2-1-1 | 477.54 | 4 | 366.66 | 2 | 23.22 |
I20-2-1-2 | 612.48 | 4 | 478.19 | 3 | 21.93 |
I20-2-1-3 | 481.75 | 4 | 360.24 | 2 | 25.22 |
I20-2-1-4 | 491.83 | 4 | 383.24 | 2 | 22.08 |
I20-2-1-5 | 427.16 | 4 | 343.7 | 2 | 19.54 |
I20-2-1-6 | 453.01 | 5 | 344.51 | 2 | 23.95 |
I20-2-1-7 | 476.59 | 4 | 354.59 | 2 | 25.60 |
I20-2-1-8 | 484.62 | 4 | 351.37 | 2 | 27.50 |
I20-2-1-9 | 622.55 | 5 | 476.32 | 3 | 23.49 |
Avg | 4.3 | 2.3 | 22.57 | ||
O20-2-1-0 | 283.63 | 4 | 240.46 | 2 | 15.22 |
O20-2-1-1 | 299.27 | 4 | 260.84 | 2 | 12.84 |
O20-2-1-2 | 336.31 | 4 | 250.62 | 2 | 25.48 |
O20-2-1-3 | 316.26 | 4 | 254.79 | 2 | 19.44 |
O20-2-1-4 | 329.42 | 5 | 273.79 | 2 | 16.89 |
O20-2-1-5 | 323.26 | 4 | 269.61 | 2 | 16.60 |
O20-2-1-6 | 293.28 | 4 | 260.31 | 2 | 11.24 |
O20-2-1-7 | 348.76 | 4 | 245.95 | 2 | 29.48 |
O20-2-1-8 | 296.46 | 4 | 240.28 | 2 | 18.95 |
O20-2-1-9 | 263.93 | 4 | 229.92 | 2 | 12.89 |
Avg | 4.1 | 2 | 17.90 | ||
A20-2-1-0 | 403.54 | 4 | 362.31 | 2 | 10.22 |
A20-2-1-1 | 494.62 | 4 | 444.8 | 3 | 10.07 |
A20-2-1-2 | 383.46 | 5 | 329.67 | 2 | 14.03 |
A20-2-1-3 | 410.31 | 5 | 363.62 | 2 | 11.38 |
A20-2-1-4 | 386.48 | 4 | 343.77 | 2 | 11.05 |
A20-2-1-5 | 302.36 | 4 | 287.74 | 2 | 4.83 |
A20-2-1-6 | 371.57 | 4 | 338.23 | 2 | 8.97 |
A20-2-1-7 | 333.01 | 4 | 290.21 | 2 | 12.85 |
A20-2-1-8 | 358.15 | 4 | 314.2 | 2 | 12.27 |
A20-2-1-9 | 367.36 | 4 | 323.6 | 2 | 11.91 |
Avg | 4.2 | 10.76 |
Instance | Non-collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I20-2-1-0 | 528.74 | 5 | 459.26 | 3 | 13.14 |
I20-2-1-1 | 477.54 | 4 | 366.66 | 2 | 23.22 |
I20-2-1-2 | 612.48 | 4 | 478.19 | 3 | 21.93 |
I20-2-1-3 | 481.75 | 4 | 360.24 | 2 | 25.22 |
I20-2-1-4 | 491.83 | 4 | 383.24 | 2 | 22.08 |
I20-2-1-5 | 427.16 | 4 | 343.7 | 2 | 19.54 |
I20-2-1-6 | 453.01 | 5 | 344.51 | 2 | 23.95 |
I20-2-1-7 | 476.59 | 4 | 354.59 | 2 | 25.60 |
I20-2-1-8 | 484.62 | 4 | 351.37 | 2 | 27.50 |
I20-2-1-9 | 622.55 | 5 | 476.32 | 3 | 23.49 |
Avg | 4.3 | 2.3 | 22.57 | ||
O20-2-1-0 | 283.63 | 4 | 240.46 | 2 | 15.22 |
O20-2-1-1 | 299.27 | 4 | 260.84 | 2 | 12.84 |
O20-2-1-2 | 336.31 | 4 | 250.62 | 2 | 25.48 |
O20-2-1-3 | 316.26 | 4 | 254.79 | 2 | 19.44 |
O20-2-1-4 | 329.42 | 5 | 273.79 | 2 | 16.89 |
O20-2-1-5 | 323.26 | 4 | 269.61 | 2 | 16.60 |
O20-2-1-6 | 293.28 | 4 | 260.31 | 2 | 11.24 |
O20-2-1-7 | 348.76 | 4 | 245.95 | 2 | 29.48 |
O20-2-1-8 | 296.46 | 4 | 240.28 | 2 | 18.95 |
O20-2-1-9 | 263.93 | 4 | 229.92 | 2 | 12.89 |
Avg | 4.1 | 2 | 17.90 | ||
A20-2-1-0 | 403.54 | 4 | 362.31 | 2 | 10.22 |
A20-2-1-1 | 494.62 | 4 | 444.8 | 3 | 10.07 |
A20-2-1-2 | 383.46 | 5 | 329.67 | 2 | 14.03 |
A20-2-1-3 | 410.31 | 5 | 363.62 | 2 | 11.38 |
A20-2-1-4 | 386.48 | 4 | 343.77 | 2 | 11.05 |
A20-2-1-5 | 302.36 | 4 | 287.74 | 2 | 4.83 |
A20-2-1-6 | 371.57 | 4 | 338.23 | 2 | 8.97 |
A20-2-1-7 | 333.01 | 4 | 290.21 | 2 | 12.85 |
A20-2-1-8 | 358.15 | 4 | 314.2 | 2 | 12.27 |
A20-2-1-9 | 367.36 | 4 | 323.6 | 2 | 11.91 |
Avg | 4.2 | 10.76 |
Instance | Non- collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I40-2-1-0 | 1021.39 | 8 | 706.64 | 6 | 30.82 |
I40-2-1-1 | 861.87 | 8 | 600.90 | 6 | 30.28 |
I40-2-1-2 | 1006.32 | 8 | 729.24 | 6 | 27.53 |
I40-2-1-3 | 943.17 | 8 | 651.55 | 6 | 30.92 |
I40-2-1-4 | 1062.08 | 8 | 699.59 | 6 | 34.13 |
I40-2-1-5 | 930.23 | 8 | 647.36 | 6 | 30.41 |
I40-2-1-6 | 874.73 | 8 | 590.24 | 6 | 32.52 |
I40-2-1-7 | 910.38 | 8 | 612.68 | 6 | 32.70 |
I40-2-1-8 | 841.23 | 8 | 573.59 | 6 | 31.82 |
I40-2-1-9 | 843.80 | 8 | 598.44 | 6 | 29.08 |
Avg | 8 | 6 | 31.02 | ||
O40-2-1-0 | 650.32 | 7 | 494.73 | 3 | 23.93 |
O40-2-1-1 | 574.51 | 7 | 434.04 | 3 | 24.45 |
O40-2-1-2 | 578.02 | 7 | 445.80 | 3 | 22.87 |
O40-2-1-3 | 692.40 | 8 | 523.35 | 4 | 24.42 |
O40-2-1-4 | 749.51 | 7 | 549.35 | 4 | 26.71 |
O40-2-1-5 | 750.72 | 8 | 573.11 | 4 | 23.66 |
O40-2-1-6 | 636.65 | 7 | 492.06 | 4 | 22.71 |
O40-2-1-7 | 734.12 | 7 | 528.80 | 3 | 27.97 |
O40-2-1-8 | 553.40 | 7 | 427.55 | 3 | 22.74 |
O40-2-1-9 | 746.28 | 8 | 578.85 | 4 | 22.43 |
Avg | 7.3 | 3.5 | 24.19 | ||
A40-2-1-0 | 686.52 | 8 | 550.2 | 4 | 19.86 |
A40-2-1-1 | 730.78 | 7 | 597.17 | 4 | 18.28 |
A40-2-1-2 | 708.31 | 8 | 582.03 | 4 | 17.83 |
A40-2-1-3 | 662.45 | 8 | 505.21 | 4 | 23.74 |
A40-2-1-4 | 667.54 | 8 | 567.77 | 4 | 14.95 |
A40-2-1-5 | 714.79 | 7 | 617.34 | 4 | 13.63 |
A40-2-1-6 | 610.43 | 7 | 537.91 | 3 | 11.88 |
A40-2-1-7 | 639.30 | 7 | 542.06 | 4 | 15.21 |
A40-2-1-8 | 695.09 | 7 | 600.61 | 4 | 13.59 |
A40-2-1-9 | 739.69 | 8 | 632.33 | 4 | 14.51 |
Avg | 7.5 | 3.9 | 16.35 |
Instance | Non- collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I40-2-1-0 | 1021.39 | 8 | 706.64 | 6 | 30.82 |
I40-2-1-1 | 861.87 | 8 | 600.90 | 6 | 30.28 |
I40-2-1-2 | 1006.32 | 8 | 729.24 | 6 | 27.53 |
I40-2-1-3 | 943.17 | 8 | 651.55 | 6 | 30.92 |
I40-2-1-4 | 1062.08 | 8 | 699.59 | 6 | 34.13 |
I40-2-1-5 | 930.23 | 8 | 647.36 | 6 | 30.41 |
I40-2-1-6 | 874.73 | 8 | 590.24 | 6 | 32.52 |
I40-2-1-7 | 910.38 | 8 | 612.68 | 6 | 32.70 |
I40-2-1-8 | 841.23 | 8 | 573.59 | 6 | 31.82 |
I40-2-1-9 | 843.80 | 8 | 598.44 | 6 | 29.08 |
Avg | 8 | 6 | 31.02 | ||
O40-2-1-0 | 650.32 | 7 | 494.73 | 3 | 23.93 |
O40-2-1-1 | 574.51 | 7 | 434.04 | 3 | 24.45 |
O40-2-1-2 | 578.02 | 7 | 445.80 | 3 | 22.87 |
O40-2-1-3 | 692.40 | 8 | 523.35 | 4 | 24.42 |
O40-2-1-4 | 749.51 | 7 | 549.35 | 4 | 26.71 |
O40-2-1-5 | 750.72 | 8 | 573.11 | 4 | 23.66 |
O40-2-1-6 | 636.65 | 7 | 492.06 | 4 | 22.71 |
O40-2-1-7 | 734.12 | 7 | 528.80 | 3 | 27.97 |
O40-2-1-8 | 553.40 | 7 | 427.55 | 3 | 22.74 |
O40-2-1-9 | 746.28 | 8 | 578.85 | 4 | 22.43 |
Avg | 7.3 | 3.5 | 24.19 | ||
A40-2-1-0 | 686.52 | 8 | 550.2 | 4 | 19.86 |
A40-2-1-1 | 730.78 | 7 | 597.17 | 4 | 18.28 |
A40-2-1-2 | 708.31 | 8 | 582.03 | 4 | 17.83 |
A40-2-1-3 | 662.45 | 8 | 505.21 | 4 | 23.74 |
A40-2-1-4 | 667.54 | 8 | 567.77 | 4 | 14.95 |
A40-2-1-5 | 714.79 | 7 | 617.34 | 4 | 13.63 |
A40-2-1-6 | 610.43 | 7 | 537.91 | 3 | 11.88 |
A40-2-1-7 | 639.30 | 7 | 542.06 | 4 | 15.21 |
A40-2-1-8 | 695.09 | 7 | 600.61 | 4 | 13.59 |
A40-2-1-9 | 739.69 | 8 | 632.33 | 4 | 14.51 |
Avg | 7.5 | 3.9 | 16.35 |
Instance | Non- collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I60-2-1-0 | 1405.67 | 11 | 911.77 | 6 | 35.14 |
I60-2-1-1 | 1466.10 | 10 | 987.76 | 7 | 32.63 |
I60-2-1-2 | 1326.57 | 12 | 877.23 | 6 | 33.87 |
I60-2-1-3 | 1381.98 | 12 | 882.44 | 6 | 36.15 |
I60-2-1-4 | 1341.28 | 11 | 896.87 | 5 | 33.13 |
I60-2-1-5 | 1438.62 | 11 | 996.95 | 7 | 30.70 |
I60-2-1-6 | 1575.24 | 13 | 1043.88 | 7 | 33.73 |
I60-2-1-7 | 1384.43 | 10 | 944.32 | 6 | 31.79 |
I60-2-1-8 | 1245.97 | 10 | 818.94 | 5 | 34.27 |
I60-2-1-9 | 1266.52 | 10 | 865.24 | 8 | 31.68 |
Avg | 11 | 6.3 | 33.31 | ||
O60-2-1-0 | 920.63 | 8 | 652.35 | 5 | 29.14 |
O60-2-1-1 | 1049.04 | 11 | 742.55 | 4 | 29.22 |
O60-2-1-2 | 1092.15 | 11 | 732.49 | 5 | 32.93 |
O60-2-1-3 | 1083.86 | 11 | 787.76 | 5 | 27.32 |
O60-2-1-4 | 1031.74 | 11 | 727.32 | 5 | 29.51 |
O60-2-1-5 | 981.97 | 10 | 752.74 | 5 | 23.34 |
O60-2-1-6 | 956.39 | 9 | 680.46 | 5 | 28.85 |
O60-2-1-7 | 1052.40 | 11 | 752.96 | 5 | 28.45 |
O60-2-1-8 | 977.50 | 9 | 695.58 | 5 | 28.84 |
O60-2-1-9 | 959.39 | 10 | 723.61 | 5 | 24.58 |
Avg | 10.1 | 4.9 | 4.9 | 28.22 | |
A60-2-1-0 | 1133.63 | 11 | 836.54 | 6 | 26.21 |
A60-2-1-1 | 1187.66 | 10 | 911.33 | 6 | 23.27 |
A60-2-1-2 | 956.53 | 10 | 703.79 | 5 | 26.42 |
A60-2-1-3 | 969.58 | 10 | 781.73 | 5 | 19.37 |
A60-2-1-4 | 1074.74 | 10 | 793.69 | 5 | 26.15 |
A60-2-1-5 | 984.88 | 9 | 740.28 | 5 | 24.84 |
A60-2-1-6 | 999.87 | 10 | 754.71 | 5 | 24.52 |
A60-2-1-7 | 1061.10 | 11 | 780.28 | 5 | 26.46 |
A60-2-1-8 | 962.43 | 11 | 751.38 | 5 | 21.93 |
A60-2-1-9 | 941.98 | 9 | 705.99 | 5 | 25.05 |
Avg | 10.1 | 5.2 | 5.2 | 24.42 |
Instance | Non- collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I60-2-1-0 | 1405.67 | 11 | 911.77 | 6 | 35.14 |
I60-2-1-1 | 1466.10 | 10 | 987.76 | 7 | 32.63 |
I60-2-1-2 | 1326.57 | 12 | 877.23 | 6 | 33.87 |
I60-2-1-3 | 1381.98 | 12 | 882.44 | 6 | 36.15 |
I60-2-1-4 | 1341.28 | 11 | 896.87 | 5 | 33.13 |
I60-2-1-5 | 1438.62 | 11 | 996.95 | 7 | 30.70 |
I60-2-1-6 | 1575.24 | 13 | 1043.88 | 7 | 33.73 |
I60-2-1-7 | 1384.43 | 10 | 944.32 | 6 | 31.79 |
I60-2-1-8 | 1245.97 | 10 | 818.94 | 5 | 34.27 |
I60-2-1-9 | 1266.52 | 10 | 865.24 | 8 | 31.68 |
Avg | 11 | 6.3 | 33.31 | ||
O60-2-1-0 | 920.63 | 8 | 652.35 | 5 | 29.14 |
O60-2-1-1 | 1049.04 | 11 | 742.55 | 4 | 29.22 |
O60-2-1-2 | 1092.15 | 11 | 732.49 | 5 | 32.93 |
O60-2-1-3 | 1083.86 | 11 | 787.76 | 5 | 27.32 |
O60-2-1-4 | 1031.74 | 11 | 727.32 | 5 | 29.51 |
O60-2-1-5 | 981.97 | 10 | 752.74 | 5 | 23.34 |
O60-2-1-6 | 956.39 | 9 | 680.46 | 5 | 28.85 |
O60-2-1-7 | 1052.40 | 11 | 752.96 | 5 | 28.45 |
O60-2-1-8 | 977.50 | 9 | 695.58 | 5 | 28.84 |
O60-2-1-9 | 959.39 | 10 | 723.61 | 5 | 24.58 |
Avg | 10.1 | 4.9 | 4.9 | 28.22 | |
A60-2-1-0 | 1133.63 | 11 | 836.54 | 6 | 26.21 |
A60-2-1-1 | 1187.66 | 10 | 911.33 | 6 | 23.27 |
A60-2-1-2 | 956.53 | 10 | 703.79 | 5 | 26.42 |
A60-2-1-3 | 969.58 | 10 | 781.73 | 5 | 19.37 |
A60-2-1-4 | 1074.74 | 10 | 793.69 | 5 | 26.15 |
A60-2-1-5 | 984.88 | 9 | 740.28 | 5 | 24.84 |
A60-2-1-6 | 999.87 | 10 | 754.71 | 5 | 24.52 |
A60-2-1-7 | 1061.10 | 11 | 780.28 | 5 | 26.46 |
A60-2-1-8 | 962.43 | 11 | 751.38 | 5 | 21.93 |
A60-2-1-9 | 941.98 | 9 | 705.99 | 5 | 25.05 |
Avg | 10.1 | 5.2 | 5.2 | 24.42 |
Instance | Non- collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I100-2-1-0 | 2741.02 | 20 | 1500.16 | 10 | 45.27 |
I100-2-1-1 | 2308.06 | 17 | 1399.61 | 10 | 39.36 |
I100-2-1-2 | 2634.95 | 19 | 1481.37 | 10 | 43.78 |
I100-2-1-3 | 2517.73 | 18 | 1406.15 | 10 | 44.15 |
I100-2-1-4 | 2275.46 | 17 | 1471.77 | 9 | 35.32 |
I100-2-1-5 | 2393.39 | 17 | 1465.71 | 10 | 38.76 |
I100-2-1-6 | 2635.37 | 19 | 1482.92 | 10 | 43.73 |
I100-2-1-7 | 2628.76 | 19 | 1439.77 | 10 | 45.23 |
I100-2-1-8 | 1910.26 | 15 | 1277.58 | 9 | 33.12 |
I100-2-1-9 | 2337.01 | 17 | 1286.29 | 10 | 44.96 |
Avg | 17.8 | 9.8 | 41.37 | ||
O100-2-1-0 | 1791.81 | 15 | 1215.92 | 9 | 32.14 |
O100-2-1-1 | 1692.20 | 14 | 1113.13 | 8 | 34.22 |
O100-2-1-2 | 1690.38 | 14 | 1066.12 | 8 | 36.93 |
O100-2-1-3 | 1803.45 | 15 | 1166.47 | 9 | 35.32 |
O100-2-1-4 | 1641.55 | 14 | 1146.62 | 9 | 30.15 |
O100-2-1-5 | 1924.70 | 15 | 1223.53 | 9 | 36.43 |
O100-2-1-6 | 1606.09 | 14 | 1062.43 | 8 | 33.85 |
O100-2-1-7 | 1786.01 | 14 | 1224.31 | 9 | 31.45 |
O100-2-1-8 | 1538.25 | 13 | 971.56 | 7 | 36.84 |
O100-2-1-9 | 1582.04 | 13 | 1098.25 | 8 | 30.58 |
Avg | 14.1 | 8.4 | 33.79 | ||
A100-2-1-0 | 1760.57 | 14 | 1212.68 | 9 | 31.12 |
A100-2-1-1 | 1809.52 | 15 | 1271.73 | 9 | 29.72 |
A100-2-1-2 | 1717.81 | 14 | 1129.63 | 8 | 34.24 |
A100-2-1-3 | 1497.94 | 10 | 1162.85 | 8 | 22.37 |
A100-2-1-4 | 1611.69 | 14 | 1190.23 | 9 | 26.15 |
A100-2-1-5 | 1613.52 | 14 | 1093.48 | 8 | 32.23 |
A100-2-1-6 | 1895.50 | 15 | 1208.76 | 9 | 36.23 |
A100-2-1-7 | 1764.98 | 14 | 1174.24 | 8 | 33.47 |
A100-2-1-8 | 1764.23 | 14 | 1154.51 | 9 | 34.56 |
A100-2-1-9 | 1727.48 | 14 | 1217.18 | 10 | 29.54 |
Avg | 13.8 | 8.7 | 30.96 |
Instance | Non- collaboration | Collaboration | |||
Cost | NV | Cost | NV | ||
I100-2-1-0 | 2741.02 | 20 | 1500.16 | 10 | 45.27 |
I100-2-1-1 | 2308.06 | 17 | 1399.61 | 10 | 39.36 |
I100-2-1-2 | 2634.95 | 19 | 1481.37 | 10 | 43.78 |
I100-2-1-3 | 2517.73 | 18 | 1406.15 | 10 | 44.15 |
I100-2-1-4 | 2275.46 | 17 | 1471.77 | 9 | 35.32 |
I100-2-1-5 | 2393.39 | 17 | 1465.71 | 10 | 38.76 |
I100-2-1-6 | 2635.37 | 19 | 1482.92 | 10 | 43.73 |
I100-2-1-7 | 2628.76 | 19 | 1439.77 | 10 | 45.23 |
I100-2-1-8 | 1910.26 | 15 | 1277.58 | 9 | 33.12 |
I100-2-1-9 | 2337.01 | 17 | 1286.29 | 10 | 44.96 |
Avg | 17.8 | 9.8 | 41.37 | ||
O100-2-1-0 | 1791.81 | 15 | 1215.92 | 9 | 32.14 |
O100-2-1-1 | 1692.20 | 14 | 1113.13 | 8 | 34.22 |
O100-2-1-2 | 1690.38 | 14 | 1066.12 | 8 | 36.93 |
O100-2-1-3 | 1803.45 | 15 | 1166.47 | 9 | 35.32 |
O100-2-1-4 | 1641.55 | 14 | 1146.62 | 9 | 30.15 |
O100-2-1-5 | 1924.70 | 15 | 1223.53 | 9 | 36.43 |
O100-2-1-6 | 1606.09 | 14 | 1062.43 | 8 | 33.85 |
O100-2-1-7 | 1786.01 | 14 | 1224.31 | 9 | 31.45 |
O100-2-1-8 | 1538.25 | 13 | 971.56 | 7 | 36.84 |
O100-2-1-9 | 1582.04 | 13 | 1098.25 | 8 | 30.58 |
Avg | 14.1 | 8.4 | 33.79 | ||
A100-2-1-0 | 1760.57 | 14 | 1212.68 | 9 | 31.12 |
A100-2-1-1 | 1809.52 | 15 | 1271.73 | 9 | 29.72 |
A100-2-1-2 | 1717.81 | 14 | 1129.63 | 8 | 34.24 |
A100-2-1-3 | 1497.94 | 10 | 1162.85 | 8 | 22.37 |
A100-2-1-4 | 1611.69 | 14 | 1190.23 | 9 | 26.15 |
A100-2-1-5 | 1613.52 | 14 | 1093.48 | 8 | 32.23 |
A100-2-1-6 | 1895.50 | 15 | 1208.76 | 9 | 36.23 |
A100-2-1-7 | 1764.98 | 14 | 1174.24 | 8 | 33.47 |
A100-2-1-8 | 1764.23 | 14 | 1154.51 | 9 | 34.56 |
A100-2-1-9 | 1727.48 | 14 | 1217.18 | 10 | 29.54 |
Avg | 13.8 | 8.7 | 30.96 |
Notations | Description |
UB | The best cost obtained by CPLEX solver in a preset running time. |
LB | The lower bound obtained by CPLEX solver in a preset running time |
Ini | The cost of the best initial solution obtained by GRASP-ILS |
Zmin | The best cost of 10 runs for each meta-heuristic |
Zavg | The average cost of 10 runs for each meta-heuristic |
Dev | The standard deviation of the costs obtained in ten runs by each meta-heuristic. |
The improvement of best cost over Ini. For CPLEX solver For meta-heuristics, | |
The percentage gap between the best cost and LB. For CPLEX solver, For meta-heuristics, | |
The improvement of the best cost obtained by meta-heuristics over the best cost obtained by CPLEX solver. | |
The improvement of over. It is calculated as: | |
The improvement of over. It is calculated as: | |
NV | The average total number of vehicles used in the transportation |
The total transportation cost of the shippers without collaboration obtained by CPLEX solver. | |
The total transportation cost of the shippers with collaboration, which is the best objective value of CPLEX solver and GRASP-ILS. | |
The cost savings in percentage achieved by the collaboration among the shippers. is defined as: | |
The average execution time in seconds for meta-heuristics |
Notations | Description |
UB | The best cost obtained by CPLEX solver in a preset running time. |
LB | The lower bound obtained by CPLEX solver in a preset running time |
Ini | The cost of the best initial solution obtained by GRASP-ILS |
Zmin | The best cost of 10 runs for each meta-heuristic |
Zavg | The average cost of 10 runs for each meta-heuristic |
Dev | The standard deviation of the costs obtained in ten runs by each meta-heuristic. |
The improvement of best cost over Ini. For CPLEX solver For meta-heuristics, | |
The percentage gap between the best cost and LB. For CPLEX solver, For meta-heuristics, | |
The improvement of the best cost obtained by meta-heuristics over the best cost obtained by CPLEX solver. | |
The improvement of over. It is calculated as: | |
The improvement of over. It is calculated as: | |
NV | The average total number of vehicles used in the transportation |
The total transportation cost of the shippers without collaboration obtained by CPLEX solver. | |
The total transportation cost of the shippers with collaboration, which is the best objective value of CPLEX solver and GRASP-ILS. | |
The cost savings in percentage achieved by the collaboration among the shippers. is defined as: | |
The average execution time in seconds for meta-heuristics |
[1] |
T. W. Leung, Chi Kin Chan, Marvin D. Troutt. A mixed simulated annealing-genetic algorithm approach to the multi-buyer multi-item joint replenishment problem: advantages of meta-heuristics. Journal of Industrial and Management Optimization, 2008, 4 (1) : 53-66. doi: 10.3934/jimo.2008.4.53 |
[2] |
Mingyong Lai, Hongming Yang, Songping Yang, Junhua Zhao, Yan Xu. Cyber-physical logistics system-based vehicle routing optimization. Journal of Industrial and Management Optimization, 2014, 10 (3) : 701-715. doi: 10.3934/jimo.2014.10.701 |
[3] |
Ming-Yong Lai, Chang-Shi Liu, Xiao-Jiao Tong. A two-stage hybrid meta-heuristic for pickup and delivery vehicle routing problem with time windows. Journal of Industrial and Management Optimization, 2010, 6 (2) : 435-451. doi: 10.3934/jimo.2010.6.435 |
[4] |
Abdelghani Bouras, Ramdane Hedjar, Lotfi Tadj. Production planning in a three-stock reverse-logistics system with deteriorating items under a periodic review policy. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1075-1089. doi: 10.3934/jimo.2016.12.1075 |
[5] |
Abdelghani Bouras, Lotfi Tadj. Production planning in a three-stock reverse-logistics system with deteriorating items under a continuous review policy. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1041-1058. doi: 10.3934/jimo.2015.11.1041 |
[6] |
David Kinderlehrer, Adrian Tudorascu. Transport via mass transportation. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 311-338. doi: 10.3934/dcdsb.2006.6.311 |
[7] |
G.S. Liu, J.Z. Zhang. Decision making of transportation plan, a bilevel transportation problem approach. Journal of Industrial and Management Optimization, 2005, 1 (3) : 305-314. doi: 10.3934/jimo.2005.1.305 |
[8] |
Lorenzo Brasco, Filippo Santambrogio. An equivalent path functional formulation of branched transportation problems. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 845-871. doi: 10.3934/dcds.2011.29.845 |
[9] |
Gershon Wolansky. Limit theorems for optimal mass transportation and applications to networks. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 365-374. doi: 10.3934/dcds.2011.30.365 |
[10] |
Jaimie W. Lien, Vladimir V. Mazalov, Jie Zheng. Pricing equilibrium of transportation systems with behavioral commuters. Journal of Dynamics and Games, 2020, 7 (4) : 335-350. doi: 10.3934/jdg.2020026 |
[11] |
Ş. İlker Birbil, Kerem Bülbül, J. B. G. Frenk, H. M. Mulder. On EOQ cost models with arbitrary purchase and transportation costs. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1211-1245. doi: 10.3934/jimo.2015.11.1211 |
[12] |
Jun Pei, Panos M. Pardalos, Xinbao Liu, Wenjuan Fan, Shanlin Yang, Ling Wang. Coordination of production and transportation in supply chain scheduling. Journal of Industrial and Management Optimization, 2015, 11 (2) : 399-419. doi: 10.3934/jimo.2015.11.399 |
[13] |
Massimiliano Caramia, Giovanni Storchi. Evaluating the effects of parking price and location in multi-modal transportation networks. Networks and Heterogeneous Media, 2006, 1 (3) : 441-465. doi: 10.3934/nhm.2006.1.441 |
[14] |
A. Daducci, A. Marigonda, G. Orlandi, R. Posenato. Neuronal Fiber--tracking via optimal mass transportation. Communications on Pure and Applied Analysis, 2012, 11 (5) : 2157-2177. doi: 10.3934/cpaa.2012.11.2157 |
[15] |
Paulina Ávila-Torres, Fernando López-Irarragorri, Rafael Caballero, Yasmín Ríos-Solís. The multimodal and multiperiod urban transportation integrated timetable construction problem with demand uncertainty. Journal of Industrial and Management Optimization, 2018, 14 (2) : 447-472. doi: 10.3934/jimo.2017055 |
[16] |
Gbeminiyi John Oyewole, Olufemi Adetunji. Solving the facility location and fixed charge solid transportation problem. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1557-1575. doi: 10.3934/jimo.2020034 |
[17] |
Eva Barrena, Alicia De-Los-Santos, Gilbert Laporte, Juan A. Mesa. Transferability of collective transportation line networks from a topological and passenger demand perspective. Networks and Heterogeneous Media, 2015, 10 (1) : 1-16. doi: 10.3934/nhm.2015.10.1 |
[18] |
Deqiang Qu, Youlin Shang, Dan Wu, Guanglei Sun. Filled function method to optimize supply chain transportation costs. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021115 |
[19] |
Nan Liu, Yong Ye. Humanitarian logistics planning for natural disaster response with Bayesian information updates. Journal of Industrial and Management Optimization, 2014, 10 (3) : 665-689. doi: 10.3934/jimo.2014.10.665 |
[20] |
Yaw Chang, Lin Chen. Solve the vehicle routing problem with time windows via a genetic algorithm. Conference Publications, 2007, 2007 (Special) : 240-249. doi: 10.3934/proc.2007.2007.240 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]