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Probabilistic robust anti-disturbance control of uncertain systems
Tabu search and simulated annealing for resource-constrained multi-project scheduling to minimize maximal cash flow gap
1. | School of Engineering and Applied Science, Aston University, Birmingham, B4 7ET, United Kingdom |
2. | School of management, Xi'an Jiaotong University, Xi'an 710049, China |
In reality, a contractor may implement multiple projects simultaneously and in such an environment, how to achieve a positive balance between cash outflow and inflow by scheduling is an important problem for the contractor has to tackle. For this fact, this paper investigates a resource-constrained multi-project scheduling problem with the objective of minimizing the contractor's maximal cash flow gap under the constraint of a project deadline and renewable resource. In the paper, we construct a non-linear integer programming optimization model for the studied problem at first. Then, for the NP-hardness of the problem, we design three metaheuristic algorithms to solve the model: tabu search (TS), simulated annealing (SA), and an algorithm comprising both TS and SA (SA-TS). Finally, we conduct a computational experiment on a data set coming from existing literature to evaluate the performance of the developed algorithms and analyze the effects of key parameters on the objective function. Based on the computational results, the following conclusions are drawn: Among the designed algorithms, the SA-TS with an improvement measure is the most promising for solving the problem under study. Some parameters may exert an important effect on the contractor's maximal cash flow gap.
References:
[1] |
A. Alghazi, A. Elazouni and S. Selim,
Improved genetic algorithm for finance-based scheduling, J. Comput. Civil Engineering, 27 (2013), 379-394.
doi: 10.1061/(ASCE)CP.1943-5487.0000227. |
[2] |
M. M. Ali and A. Elazouni,
Finance-based CPM/LOB scheduling of projects with repetitive non-serial activities, Construction Management Economics, 27 (2009), 839-856.
doi: 10.1080/01446190903191764. |
[3] |
M. Abido and A. Elazouni,
Multiobjective evolutionary finance-based scheduling: Entire projects' portfolio, J. Comput. Civil Engineering, 25 (2011), 85-97.
doi: 10.1061/(ASCE)CP.1943-5487.0000070. |
[4] |
S. T. Al-Shihabi and M. M. AlDurgam,
A max-min ant system for the finance-based scheduling problem, Comput. Industrial Engineering, 110 (2017), 264-276.
doi: 10.1016/j.cie.2017.06.016. |
[5] |
J. Blazewicz, J. K. Lenstra and K. A. H. G. Rinnooy,
Scheduling subject to resource constraints: Classification and complexity, Discrete Appl. Math., 5 (1983), 11-24.
doi: 10.1016/0166-218X(83)90012-4. |
[6] |
T. R. Browning and A. A. Yassine,
A random generator of resource-constrained multi-project network problems, J. Scheduling, 13 (2010), 143-161.
doi: 10.1007/s10951-009-0131-y. |
[7] |
T. R. Browning and A. A. Yassine,
Resource-constrained multi-project scheduling: Priority rule performance revised, Internat. J. Production Economics, 126 (2010), 212-228.
doi: 10.1016/j.ijpe.2010.03.009. |
[8] |
R. H. Doersch and J. H. Patterson,
Scheduling a project to maximize its present value: A zero-one programming approach, Management Science, 23 (1977), 882-889.
doi: 10.1287/mnsc.23.8.882. |
[9] |
M. Engwall and A. Jerbrant,
The resource allocation syndrome: The prime challenge of multi-project management?, Internat. J. Project Management, 21 (2003), 403-409.
doi: 10.1016/S0263-7863(02)00113-8. |
[10] |
A. M. Elazouni and A. A. Gab-Allah,
Finance-based scheduling of construction projects using integer programming, J. Construction Engineering Management, 130 (2004), 15-24.
doi: 10.1061/(ASCE)0733-9364(2004)130:1(15). |
[11] |
A. Elazouni, A. Alghazi and S. Selim,
Finance-based scheduling using meta-heuristics: Discrete versus continuous optimization problems, J. Finance Management Property Construction, 20 (2015), 85-104.
doi: 10.1108/JFMPC-07-2014-0013. |
[12] |
A. Elazouni,
Heuristic method for multi-project finance-based scheduling, Construction Management Economics, 27 (2009), 199-211.
doi: 10.1080/01446190802673110. |
[13] |
A. Elazouni and M. Abido,
Multiobjective evolutionary finance-based scheduling: Individual projects within a portfolio, Automat. Construction, 20 (2011), 755-766.
doi: 10.1016/j.autcon.2011.03.010. |
[14] |
M. S. El-Abbasy, A. Elazouni and T. Z. F. ASCE, Generic scheduling optimization model for multiple construction projects, J. Comput. Civil Engineering, 31 (2017).
doi: 10.1061/(ASCE)CP.1943-5487.0000659. |
[15] |
H. Fathi and A. Afshar,
GA-based multi-objective optimization of finance-based construction project scheduling, KSCE J. Civil Engineering, 14 (2010), 627-638.
doi: 10.1007/s12205-010-0849-2. |
[16] |
F. Glover,
Future path for integer programming and links to artificial intelligence, Comput. Oper. Res., 13 (1986), 533-549.
doi: 10.1016/0305-0548(86)90048-1. |
[17] |
W. S. Herroelen, P. Dommelen and E. L. Demeulemeester,
Project network models with discounted cash flows: A guided tour through recent developments, European J. Oper. Res., 100 (1997), 97-121.
doi: 10.1016/S0377-2217(96)00112-9. |
[18] |
Z. He, R. Liu and T. Jia,
Metaheuristics for multi-mode capital-constrained project payment scheduling, European J. Oper. Res., 223 (2012), 605-613.
doi: 10.1016/j.ejor.2012.07.014. |
[19] |
Z. He, H. He, R. Liu and N. Wang,
Variable neighbourhood search and tabu search for a discrete time/cost trade-off problem to minimize the maximal cash flow gap, Comput. Oper. Res., 78 (2017), 564-577.
doi: 10.1016/j.cor.2016.07.013. |
[20] |
A. Jiang, R. R. A. Issa and M. Malek,
Construction project cash flow planning using the Pareto optimality efficiency network model, J. Construction Engineering Management, 17 (2011), 510-519.
doi: 10.3846/13923730.2011.604537. |
[21] |
P. Leyman and M. Vanhoucke,
A new scheduling technique for the resource–constrained project scheduling problem with discounted cash flows, Internat. J. Prod. Res., 53 (2015), 2771-2786.
doi: 10.1080/00207543.2014.980463. |
[22] |
P. Leyman and M. Vanhoucke,
Payment models and net present value optimization for resource-constrained project scheduling, Comput. Industrial Engineering, 91 (2016), 139-153.
doi: 10.1016/j.cie.2015.11.008. |
[23] |
P. Leyman and M. Vanhoucke,
Capital- and resource-constrained project scheduling with net present value optimization, European J. Oper. Res., 256 (2017), 757-776.
doi: 10.1016/j.ejor.2016.07.019. |
[24] |
S. S. Liu and C. J. Wang,
Profit optimization for multiproject scheduling problems considering cash flow, J. Construction Engineering Management, 136 (2010), 1268-1278.
doi: 10.1061/(ASCE)CO.1943-7862.0000235. |
[25] |
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller,
Equation of state calculations by fast computing machines, J. Chemical Physics, 21 (1953), 1087-1092.
doi: 10.2172/4390578. |
[26] |
M. Ning, Z. He, T. Jia and N. Wang,
Metaheuristics for multi-mode cash flow balanced project scheduling with stochastic duration of activities, Automat. Construction, 81 (2017), 224-233.
doi: 10.1016/j.autcon.2017.06.011. |
[27] |
M. Ning, Z. He, N. Wang and R. Liu,
Metaheuristic algorithms for proactive and reactive project scheduling to minimize contractor's cash flow gap under random activity duration, IEEE Access, 6 (2018), 30547-30558.
doi: 10.1109/ACCESS.2018.2828037. |
[28] |
L. Özdamar and H. Dündar,
A flexible heuristic for a multi-mode capital constrained project scheduling problem with probabilistic cash inflows, Comput. Opera. Res., 24 (1997), 1187-1200.
doi: 10.1016/S0305-0548(96)00058-5. |
[29] |
L. Özdamar,
On scheduling project activities with variable expenditure rates, IIE Transactions, 30 (1998), 695-704.
doi: 10.1023/A:1007598405238. |
[30] |
C. Schwindt and J. Zimmermann, Handbook of Project Management and Scheduling, Springer International Publishing AG, Berlin, 2014.
doi: 10.1007/978-3-319-05443-8. |
[31] |
D. E. Smith-Daniels and V. L. Smith-Daniels,
Maximizing the net present value of a project subject to materials and capital constraints, J. Oper. Management, 7 (1987), 33-45.
doi: 10.1016/0272-6963(87)90005-2. |
[32] |
D. E. Smith-Daniels, R. Padman and V. L. Smith-Daniels,
Heuristic scheduling of capital constrained projects, J. Oper. Management, 14 (1996), 241-254.
doi: 10.1016/0272-6963(96)00004-6. |
show all references
References:
[1] |
A. Alghazi, A. Elazouni and S. Selim,
Improved genetic algorithm for finance-based scheduling, J. Comput. Civil Engineering, 27 (2013), 379-394.
doi: 10.1061/(ASCE)CP.1943-5487.0000227. |
[2] |
M. M. Ali and A. Elazouni,
Finance-based CPM/LOB scheduling of projects with repetitive non-serial activities, Construction Management Economics, 27 (2009), 839-856.
doi: 10.1080/01446190903191764. |
[3] |
M. Abido and A. Elazouni,
Multiobjective evolutionary finance-based scheduling: Entire projects' portfolio, J. Comput. Civil Engineering, 25 (2011), 85-97.
doi: 10.1061/(ASCE)CP.1943-5487.0000070. |
[4] |
S. T. Al-Shihabi and M. M. AlDurgam,
A max-min ant system for the finance-based scheduling problem, Comput. Industrial Engineering, 110 (2017), 264-276.
doi: 10.1016/j.cie.2017.06.016. |
[5] |
J. Blazewicz, J. K. Lenstra and K. A. H. G. Rinnooy,
Scheduling subject to resource constraints: Classification and complexity, Discrete Appl. Math., 5 (1983), 11-24.
doi: 10.1016/0166-218X(83)90012-4. |
[6] |
T. R. Browning and A. A. Yassine,
A random generator of resource-constrained multi-project network problems, J. Scheduling, 13 (2010), 143-161.
doi: 10.1007/s10951-009-0131-y. |
[7] |
T. R. Browning and A. A. Yassine,
Resource-constrained multi-project scheduling: Priority rule performance revised, Internat. J. Production Economics, 126 (2010), 212-228.
doi: 10.1016/j.ijpe.2010.03.009. |
[8] |
R. H. Doersch and J. H. Patterson,
Scheduling a project to maximize its present value: A zero-one programming approach, Management Science, 23 (1977), 882-889.
doi: 10.1287/mnsc.23.8.882. |
[9] |
M. Engwall and A. Jerbrant,
The resource allocation syndrome: The prime challenge of multi-project management?, Internat. J. Project Management, 21 (2003), 403-409.
doi: 10.1016/S0263-7863(02)00113-8. |
[10] |
A. M. Elazouni and A. A. Gab-Allah,
Finance-based scheduling of construction projects using integer programming, J. Construction Engineering Management, 130 (2004), 15-24.
doi: 10.1061/(ASCE)0733-9364(2004)130:1(15). |
[11] |
A. Elazouni, A. Alghazi and S. Selim,
Finance-based scheduling using meta-heuristics: Discrete versus continuous optimization problems, J. Finance Management Property Construction, 20 (2015), 85-104.
doi: 10.1108/JFMPC-07-2014-0013. |
[12] |
A. Elazouni,
Heuristic method for multi-project finance-based scheduling, Construction Management Economics, 27 (2009), 199-211.
doi: 10.1080/01446190802673110. |
[13] |
A. Elazouni and M. Abido,
Multiobjective evolutionary finance-based scheduling: Individual projects within a portfolio, Automat. Construction, 20 (2011), 755-766.
doi: 10.1016/j.autcon.2011.03.010. |
[14] |
M. S. El-Abbasy, A. Elazouni and T. Z. F. ASCE, Generic scheduling optimization model for multiple construction projects, J. Comput. Civil Engineering, 31 (2017).
doi: 10.1061/(ASCE)CP.1943-5487.0000659. |
[15] |
H. Fathi and A. Afshar,
GA-based multi-objective optimization of finance-based construction project scheduling, KSCE J. Civil Engineering, 14 (2010), 627-638.
doi: 10.1007/s12205-010-0849-2. |
[16] |
F. Glover,
Future path for integer programming and links to artificial intelligence, Comput. Oper. Res., 13 (1986), 533-549.
doi: 10.1016/0305-0548(86)90048-1. |
[17] |
W. S. Herroelen, P. Dommelen and E. L. Demeulemeester,
Project network models with discounted cash flows: A guided tour through recent developments, European J. Oper. Res., 100 (1997), 97-121.
doi: 10.1016/S0377-2217(96)00112-9. |
[18] |
Z. He, R. Liu and T. Jia,
Metaheuristics for multi-mode capital-constrained project payment scheduling, European J. Oper. Res., 223 (2012), 605-613.
doi: 10.1016/j.ejor.2012.07.014. |
[19] |
Z. He, H. He, R. Liu and N. Wang,
Variable neighbourhood search and tabu search for a discrete time/cost trade-off problem to minimize the maximal cash flow gap, Comput. Oper. Res., 78 (2017), 564-577.
doi: 10.1016/j.cor.2016.07.013. |
[20] |
A. Jiang, R. R. A. Issa and M. Malek,
Construction project cash flow planning using the Pareto optimality efficiency network model, J. Construction Engineering Management, 17 (2011), 510-519.
doi: 10.3846/13923730.2011.604537. |
[21] |
P. Leyman and M. Vanhoucke,
A new scheduling technique for the resource–constrained project scheduling problem with discounted cash flows, Internat. J. Prod. Res., 53 (2015), 2771-2786.
doi: 10.1080/00207543.2014.980463. |
[22] |
P. Leyman and M. Vanhoucke,
Payment models and net present value optimization for resource-constrained project scheduling, Comput. Industrial Engineering, 91 (2016), 139-153.
doi: 10.1016/j.cie.2015.11.008. |
[23] |
P. Leyman and M. Vanhoucke,
Capital- and resource-constrained project scheduling with net present value optimization, European J. Oper. Res., 256 (2017), 757-776.
doi: 10.1016/j.ejor.2016.07.019. |
[24] |
S. S. Liu and C. J. Wang,
Profit optimization for multiproject scheduling problems considering cash flow, J. Construction Engineering Management, 136 (2010), 1268-1278.
doi: 10.1061/(ASCE)CO.1943-7862.0000235. |
[25] |
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller,
Equation of state calculations by fast computing machines, J. Chemical Physics, 21 (1953), 1087-1092.
doi: 10.2172/4390578. |
[26] |
M. Ning, Z. He, T. Jia and N. Wang,
Metaheuristics for multi-mode cash flow balanced project scheduling with stochastic duration of activities, Automat. Construction, 81 (2017), 224-233.
doi: 10.1016/j.autcon.2017.06.011. |
[27] |
M. Ning, Z. He, N. Wang and R. Liu,
Metaheuristic algorithms for proactive and reactive project scheduling to minimize contractor's cash flow gap under random activity duration, IEEE Access, 6 (2018), 30547-30558.
doi: 10.1109/ACCESS.2018.2828037. |
[28] |
L. Özdamar and H. Dündar,
A flexible heuristic for a multi-mode capital constrained project scheduling problem with probabilistic cash inflows, Comput. Opera. Res., 24 (1997), 1187-1200.
doi: 10.1016/S0305-0548(96)00058-5. |
[29] |
L. Özdamar,
On scheduling project activities with variable expenditure rates, IIE Transactions, 30 (1998), 695-704.
doi: 10.1023/A:1007598405238. |
[30] |
C. Schwindt and J. Zimmermann, Handbook of Project Management and Scheduling, Springer International Publishing AG, Berlin, 2014.
doi: 10.1007/978-3-319-05443-8. |
[31] |
D. E. Smith-Daniels and V. L. Smith-Daniels,
Maximizing the net present value of a project subject to materials and capital constraints, J. Oper. Management, 7 (1987), 33-45.
doi: 10.1016/0272-6963(87)90005-2. |
[32] |
D. E. Smith-Daniels, R. Padman and V. L. Smith-Daniels,
Heuristic scheduling of capital constrained projects, J. Oper. Management, 14 (1996), 241-254.
doi: 10.1016/0272-6963(96)00004-6. |









The positive cash flow balance is taken as a constraint | The positive cash flow balance is taken as an objective | ||||
The objective is to maximize project profit | The objective is to minimize project duration | The objective is the optimal trade-off among multiple objectives | The activity durations are constants | The activity durations are stochastic variables | |
A contractor needs to implement a single project | Doersch and Patterson ([8]); Smith-Daniels and Smith-Daniels ([31]); Smith-Daniels et al. ([32]); Özdamar and Dündar ([28]); Özdamar ([29]); He et al. ([18]); Leyman and Vanhoucke ([21]); Leyman and Vanhoucke ([22]); Leyman and Vanhoucke ([23]) | Elazouni and Gab-Allah ([10]); Alghazi et al. ([1]); Ali and Elazouni ([2]); Elazouni et al. ([11]); Al-Shihabi and AlDurgam ([4]) | Fathi and Afshar ([15]) | He et al. ([19]) | Ning et al. ([26]); Ning et al. ([27]) |
A contractor needs to implement multiple projects concurrently | Liu and Wang ([24]) | Elazouni ([12]) | Elazouni and Abido ([13]); Abido and Elazouni ([3]); El-Abbasy et al. ([14]) | This paper |
The positive cash flow balance is taken as a constraint | The positive cash flow balance is taken as an objective | ||||
The objective is to maximize project profit | The objective is to minimize project duration | The objective is the optimal trade-off among multiple objectives | The activity durations are constants | The activity durations are stochastic variables | |
A contractor needs to implement a single project | Doersch and Patterson ([8]); Smith-Daniels and Smith-Daniels ([31]); Smith-Daniels et al. ([32]); Özdamar and Dündar ([28]); Özdamar ([29]); He et al. ([18]); Leyman and Vanhoucke ([21]); Leyman and Vanhoucke ([22]); Leyman and Vanhoucke ([23]) | Elazouni and Gab-Allah ([10]); Alghazi et al. ([1]); Ali and Elazouni ([2]); Elazouni et al. ([11]); Al-Shihabi and AlDurgam ([4]) | Fathi and Afshar ([15]) | He et al. ([19]) | Ning et al. ([26]); Ning et al. ([27]) |
A contractor needs to implement multiple projects concurrently | Liu and Wang ([24]) | Elazouni ([12]) | Elazouni and Abido ([13]); Abido and Elazouni ([3]); El-Abbasy et al. ([14]) | This paper |
Project 1 | Project 2 | |||||||
Cash outflow | Cash inflow | Cash outflow | Cash inflow | |||||
Cash flows under the |
||||||||
0 | 4 | / | / | / | 4 | 0 | 4 | |
2 | 4 | 8 | 0 | 8 | ||||
3 | 2 | 5.4 | 10 | 5.4 | 4.6 | |||
4 | 2 | 5 | 5.1 | 17 | 10.5 | 6.5 | ||
5 | 3 | 5.4 | 20 | 15.9 | 4.1 | |||
7 | 2.55 | 20 | 18.45 | 1.55 | ||||
9 | 6.2 | 20 | 24.65 | –4.65 | ||||
10 | 6.35 | 20 | 31 | –11 | ||||
Cash flows under the |
||||||||
0 | 6 | 6 | 0 | 6 | ||||
2 | 7 | 13 | 0 | 13 | ||||
3 | 2 | 8.1 | 15 | 8.1 | 6.9 | |||
4 | 2 | 5.1 | 17 | 13.2 | 3.8 | |||
5 | 3 | 2.7 | 20 | 15.9 | 4.1 | |||
7 | 2.55 | 20 | 18.45 | 1.55 | ||||
8 | 6.35 | 20 | 24.8 | –4.8 | ||||
9 | 6.2 | 20 | 31 | –11 |
Project 1 | Project 2 | |||||||
Cash outflow | Cash inflow | Cash outflow | Cash inflow | |||||
Cash flows under the |
||||||||
0 | 4 | / | / | / | 4 | 0 | 4 | |
2 | 4 | 8 | 0 | 8 | ||||
3 | 2 | 5.4 | 10 | 5.4 | 4.6 | |||
4 | 2 | 5 | 5.1 | 17 | 10.5 | 6.5 | ||
5 | 3 | 5.4 | 20 | 15.9 | 4.1 | |||
7 | 2.55 | 20 | 18.45 | 1.55 | ||||
9 | 6.2 | 20 | 24.65 | –4.65 | ||||
10 | 6.35 | 20 | 31 | –11 | ||||
Cash flows under the |
||||||||
0 | 6 | 6 | 0 | 6 | ||||
2 | 7 | 13 | 0 | 13 | ||||
3 | 2 | 8.1 | 15 | 8.1 | 6.9 | |||
4 | 2 | 5.1 | 17 | 13.2 | 3.8 | |||
5 | 3 | 2.7 | 20 | 15.9 | 4.1 | |||
7 | 2.55 | 20 | 18.45 | 1.55 | ||||
8 | 6.35 | 20 | 24.8 | –4.8 | ||||
9 | 6.2 | 20 | 31 | –11 |
Parameter | Setting |
Number of projects, |
3 |
Number of non-dummy activities in projects, |
20 |
Network complexity of multiple projects, |
LLL, HLL, HHL, HHH, where "L" and "H" represent the network complexity of an individual project. "L" means that the network complexity of the project equals 0.14 while "H" implies it is 0.69 |
Number of resource types, |
4 |
Normalized average resource loading factor, |
–2, 0, 2 |
Modified average utilization factor, |
0.8, 1.0, 1.2 |
Variance in |
0, 0.25 |
Cost of activities, |
Randomly selected from U[1, 9] |
Earned value of activities, |
|
Number of milestone activities, |
4, 5, 6, where the dummy end activity must be a milestone activity while other milestone activities are randomly selected from all the non-dummy activities |
Compensation proportion of projects, |
0.7, 0.8, 0.9 |
Earliest start time of projects, |
Randomly selected from U[1, 5] |
Deadline of projects, |
1.1 |
Parameter | Setting |
Number of projects, |
3 |
Number of non-dummy activities in projects, |
20 |
Network complexity of multiple projects, |
LLL, HLL, HHL, HHH, where "L" and "H" represent the network complexity of an individual project. "L" means that the network complexity of the project equals 0.14 while "H" implies it is 0.69 |
Number of resource types, |
4 |
Normalized average resource loading factor, |
–2, 0, 2 |
Modified average utilization factor, |
0.8, 1.0, 1.2 |
Variance in |
0, 0.25 |
Cost of activities, |
Randomly selected from U[1, 9] |
Earned value of activities, |
|
Number of milestone activities, |
4, 5, 6, where the dummy end activity must be a milestone activity while other milestone activities are randomly selected from all the non-dummy activities |
Compensation proportion of projects, |
0.7, 0.8, 0.9 |
Earliest start time of projects, |
Randomly selected from U[1, 5] |
Deadline of projects, |
1.1 |
Parameter | Value | SA- |
SA- |
||||
LLL | 8.26 | 3.30 | 7.36 | 2.18 | 6.23 | 1.46 | |
HLL | 7.57 | 2.63 | 7.15 | 2.04 | 6.10 | 1.35 | |
HHL | 7.13 | 2.47 | 6.84 | 1.91 | 5.41 | 1.40 | |
HHH | 6.28 | 1.77 | 5.97 | 1.67 | 5.13 | 1.23 | |
–2 | 7.06 | 2.36 | 6.62 | 1.80 | 5.55 | 1.24 | |
0 | 7.38 | 2.61 | 6.70 | 1.90 | 5.75 | 1.39 | |
2 | 7.49 | 2.65 | 7.18 | 2.16 | 5.86 | 1.45 | |
0.8 | 8.20 | 3.00 | 7.57 | 2.46 | 6.23 | 1.52 | |
1.0 | 7.33 | 2.70 | 6.74 | 1.88 | 5.67 | 1.35 | |
1.2 | 6.41 | 1.93 | 6.18 | 1.51 | 5.26 | 1.20 | |
0 | 7.13 | 2.42 | 6.71 | 1.89 | 5.54 | 1.19 | |
0.25 | 7.49 | 2.67 | 6.94 | 2.01 | 5.90 | 1.53 | |
1.1 |
6.05 | 1.84 | 5.85 | 1.54 | 5.07 | 1.13 | |
1.3 |
7.25 | 2.45 | 6.76 | 1.96 | 5.61 | 1.35 | |
1.5 |
8.63 | 3.33 | 7.89 | 2.35 | 6.47 | 1.60 |
Parameter | Value | SA- |
SA- |
||||
LLL | 8.26 | 3.30 | 7.36 | 2.18 | 6.23 | 1.46 | |
HLL | 7.57 | 2.63 | 7.15 | 2.04 | 6.10 | 1.35 | |
HHL | 7.13 | 2.47 | 6.84 | 1.91 | 5.41 | 1.40 | |
HHH | 6.28 | 1.77 | 5.97 | 1.67 | 5.13 | 1.23 | |
–2 | 7.06 | 2.36 | 6.62 | 1.80 | 5.55 | 1.24 | |
0 | 7.38 | 2.61 | 6.70 | 1.90 | 5.75 | 1.39 | |
2 | 7.49 | 2.65 | 7.18 | 2.16 | 5.86 | 1.45 | |
0.8 | 8.20 | 3.00 | 7.57 | 2.46 | 6.23 | 1.52 | |
1.0 | 7.33 | 2.70 | 6.74 | 1.88 | 5.67 | 1.35 | |
1.2 | 6.41 | 1.93 | 6.18 | 1.51 | 5.26 | 1.20 | |
0 | 7.13 | 2.42 | 6.71 | 1.89 | 5.54 | 1.19 | |
0.25 | 7.49 | 2.67 | 6.94 | 2.01 | 5.90 | 1.53 | |
1.1 |
6.05 | 1.84 | 5.85 | 1.54 | 5.07 | 1.13 | |
1.3 |
7.25 | 2.45 | 6.76 | 1.96 | 5.61 | 1.35 | |
1.5 |
8.63 | 3.33 | 7.89 | 2.35 | 6.47 | 1.60 |
Parameter | Value | Parameter | Value | ||
LLL | 66.06 | 0 | 70.37 | ||
HLL | 67.34 | 0.25 | 66.86 | ||
HHL | 69.66 | 4 | 81.48 | ||
HHH | 71.43 | 5 | 67.12 | ||
–2 | 70.63 | 6 | 57.26 | ||
0 | 68.51 | 0.7 | 83.76 | ||
2 | 66.73 | 0.8 | 68.73 | ||
0.8 | 65.57 | 0.9 | 53.36 | ||
1.0 | 68.44 | 1.1 |
72.88 | ||
1.2 | 71.86 | 1.3 |
67.66 | ||
1.5 |
65.33 |
Parameter | Value | Parameter | Value | ||
LLL | 66.06 | 0 | 70.37 | ||
HLL | 67.34 | 0.25 | 66.86 | ||
HHL | 69.66 | 4 | 81.48 | ||
HHH | 71.43 | 5 | 67.12 | ||
–2 | 70.63 | 6 | 57.26 | ||
0 | 68.51 | 0.7 | 83.76 | ||
2 | 66.73 | 0.8 | 68.73 | ||
0.8 | 65.57 | 0.9 | 53.36 | ||
1.0 | 68.44 | 1.1 |
72.88 | ||
1.2 | 71.86 | 1.3 |
67.66 | ||
1.5 |
65.33 |
|
|||||||||||
0.8 | LLL | 61.8 | 0.8 | –2 | 66.96 | 0.8 | 0 | 66.67 | 0.8 | 1.1 |
71.33 |
HLL | 64.29 | 0 | 65.46 | 0.25 | 64.46 | 1.3 |
64.61 | ||||
HHL | 66.6 | 2 | 64.28 | 1.0 | 0 | 69.99 | 1.5 |
60.78 | |||
HHH | 69.58 | 1.0 | –2 | 70.3 | 0.25 | 66.88 | 1.0 | 1.1 |
72.2 | ||
1.0 | LLL | 66.08 | 0 | 68.33 | 1.2 | 0 | 74.46 | 1.3 |
67.46 | ||
HLL | 67.16 | 2 | 66.7 | 0.25 | 69.25 | 1.5 |
65.65 | ||||
HHL | 69.48 | 1.2 | –2 | 74.62 | 1.2 | 1.1 |
75.12 | ||||
HHH | 71.05 | 0 | 71.75 | 1.3 |
70.9 | ||||||
1.2 | LLL | 70.3 | 2 | 69.21 | 1.5 |
69.57 | |||||
HLL | 70.58 | ||||||||||
HHL | 72.9 | ||||||||||
HHH | 73.67 |
|
|||||||||||
0.8 | LLL | 61.8 | 0.8 | –2 | 66.96 | 0.8 | 0 | 66.67 | 0.8 | 1.1 |
71.33 |
HLL | 64.29 | 0 | 65.46 | 0.25 | 64.46 | 1.3 |
64.61 | ||||
HHL | 66.6 | 2 | 64.28 | 1.0 | 0 | 69.99 | 1.5 |
60.78 | |||
HHH | 69.58 | 1.0 | –2 | 70.3 | 0.25 | 66.88 | 1.0 | 1.1 |
72.2 | ||
1.0 | LLL | 66.08 | 0 | 68.33 | 1.2 | 0 | 74.46 | 1.3 |
67.46 | ||
HLL | 67.16 | 2 | 66.7 | 0.25 | 69.25 | 1.5 |
65.65 | ||||
HHL | 69.48 | 1.2 | –2 | 74.62 | 1.2 | 1.1 |
75.12 | ||||
HHH | 71.05 | 0 | 71.75 | 1.3 |
70.9 | ||||||
1.2 | LLL | 70.3 | 2 | 69.21 | 1.5 |
69.57 | |||||
HLL | 70.58 | ||||||||||
HHL | 72.9 | ||||||||||
HHH | 73.67 |
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