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A time-dependent scheduling problem to minimize the sum of the total weighted tardiness among two agents
1. | Department of Business Administration, Kang-Ning Junior College of Medical Care and Management, Taipei, Taiwan, Taiwan |
2. | College of Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China |
3. | Department of Healthcare Management, Yuanpei University, Hsinchu, Taiwan |
4. | Department of Statistics, Feng Chia University, Taichung, Taiwan |
References:
[1] |
A. Agnetis, P. B. Mirchandani, D. Pacciarelli and A. Pacifici, Scheduling problems with two competing agents, Operations Research, 52 (2004), 229-242.
doi: 10.1287/opre.1030.0092. |
[2] |
A. Agnetis, D. Pacciarelli and A. Pacifici, Multi-agent single machine scheduling, Annals of Operations Research, 150 (2007), 3-15.
doi: 10.1007/s10479-006-0164-y. |
[3] |
B. Alidaee and N. K. Womer, Scheduling with time dependent processing times: Review and extensions, Journal of the Operational Research Society, 50 (1999), 711-729. |
[4] |
A. Allahverdi and F. S. Al-Anzi, Using two-machine flowshop with maximum lateness objective to model multimedia data objects scheduling problem for WWW applications, Computers and Operations Research, 29 (2002), 971-994.
doi: 10.1016/S0305-0548(00)00097-6. |
[5] |
A. Bachman and A. Janiak, Scheduling Jobs with Special Type of Start Time Dependent Processing Times, Report No 34/97, Institute of Engineering Cybernetics, Wroclaw University of Technology, 1997. |
[6] |
K. R. Baker and J. C. Smith, A multiple-criterion model for machine scheduling, Journal of Scheduling, 6 (2003), 7-16.
doi: 10.1023/A:1022231419049. |
[7] |
D. Ben-Arieh and O. Maimon, Annealing method for PCB assembly scheduling on two sequential machines, International Journal of Computer Integrated Manufacturing, 5 (1992), 361-367.
doi: 10.1080/09511929208944543. |
[8] |
S. Browne and U. Yechiali, Scheduling deteriorating jobs on a single processor, Operations Research, 38 (1990), 495-498.
doi: 10.1287/opre.38.3.495. |
[9] |
S. R. Cheng, A single-machine two-agent scheduling problem by GA approach, Asia-Pacific Journal of Operational Research, 29 (2012), 1250013, 22 pp.
doi: 10.1142/S0217595912500133. |
[10] |
T. C. E. Cheng, Q. Ding and B. M. T. Lin, A concise survey of scheduling with time-dependent processing times, European Journal of Operational Research, 152 (2004), 1-13.
doi: 10.1016/S0377-2217(02)00909-8. |
[11] |
T. C. E. Cheng, C. T. Ng and J. J. Yuan, Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs, Theoretical Computer Science, 362 (2006), 273-281.
doi: 10.1016/j.tcs.2006.07.011. |
[12] |
T. C. E. Cheng, C. T. Ng and J. J. Yuan, Multi-agent scheduling on a single machine with max-form criteria, European Journal of Operational Research, 188 (2008), 603-609.
doi: 10.1016/j.ejor.2007.04.040. |
[13] |
T. C. E. Cheng, S. R. Cheng, W. H. Wu, P. H. Hsu and C. C. Wu, A two-agent single- machine scheduling problem with truncated sum-of-processing-times-based learning considerations, Computers & Industrial Engineering, 60 (2011), 534-541.
doi: 10.1016/j.cie.2010.12.008. |
[14] |
T. C. E. Cheng, W. H. Wu, S. R. Cheng and C. C. Wu, Two-agent scheduling with position- based deteriorating jobs and learning effects, Applied Mathematics and Computation, 217 (2011), 8804-8824.
doi: 10.1016/j.amc.2011.04.005. |
[15] |
T. C. E. Cheng, Y. H. Chung, S. C. Liao and W. C Lee, Two-agent singe-machine scheduling with release times to minimize the total weighted completion time, Computers & Operations Research, 40 (2013), 353-361.
doi: 10.1016/j.cor.2012.07.013. |
[16] |
C. Chu, A branch-and-bound algorithm to minimize total tardiness with different release dates, Naval Research Logistics, 39 (1992), 859-875. |
[17] |
A. Colorni, M. Dorigo, M. Maniezzo, I. F. J. Varela and P. Bourgine, Distributed Optimization by Ant Colonies, Proceedings of the first European Conference on Artificial Life, Pairs, 1991. |
[18] |
A. Colorni, M. Dorigo, V. Maniezzo and M. Trubian, Ant system for job-shop scheduling, Belgian Journal of Operations Research, 34 (1994), 39-53. |
[19] |
M. Dorigo, Di Caro G and L. M. Gambardella, Ant algorithms for discrete optimization, Artificial Life, 5 (1999), 137-172.
doi: 10.1162/106454699568728. |
[20] |
M. Dorigo and L. M. Gambardella, Ant colony system: A cooperative learning approach to travel salesman problem, IEEE Trans Evol Computing, 1 (1997), 53-66.
doi: 10.1109/4235.585892. |
[21] |
M. L. Fisher, A dual algorithm for the one-machine scheduling problem, Math Programming, 11 (1976/77), 229-251.
doi: 10.1007/BF01580393. |
[22] |
R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and heuristic in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics, 5 (1979), 287-326.
doi: 10.1016/S0167-5060(08)70356-X. |
[23] |
A. Janiak, T. Krysiak and R. Trela, Scheduling problems with learning and aging effects: A survey, Decision Making in Manufacturing and Services, 5 (2011), 19-36. |
[24] |
S. Kirkpatrick, C. Gelatt and M. Vecchi, Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[25] |
A. S. Kunnathur and S. K. Gupta, Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem, European Journal of Operation Research, 47 (1990), 56-64.
doi: 10.1016/0377-2217(90)90089-T. |
[26] |
K. Lee, B. C. Choi, J. Y. T. Leung and M. L. Pinedo, Approximation algorithms for multi-agent scheduling to minimize total weighted completion time, Information Processing Letters, 109 (2009), 913-917.
doi: 10.1016/j.ipl.2009.04.018. |
[27] |
J. Lenstra, A. H. G. Rinnooy Kan and P. Brucker, Complexity of Machine Scheduling Problems, Annals of Discrete Mathematics, 1 (1977), 343-362. |
[28] |
M. Lai and X. Tong, A metaheuristic method for vehicle routing problem based on improved ant colony optimization and Tabu search, Journal of Industrial and Management Optimization, 8 (2012), 469-484.
doi: 10.3934/jimo.2012.8.469. |
[29] |
P. Liu and L. Tang, Two-agent scheduling with linear deteriorating jobs on a single machine, Lecture Notes in Computer Science, 5092 (2008), 642-650. |
[30] |
P. Liu, X. Y. Zhou and L. X. Tang, Two-agent single-machine scheduling with position-dependent processing times, International Journal of Advanced Manufacturing Technology, 48 (2010), 325-331.
doi: 10.1007/s00170-009-2259-5. |
[31] |
D. C. Li and P. H. Hsu, Solving a two-agent single-machine scheduling problem considering learning effect, Computers & Operations Research, 39 (2012), 1644-1651.
doi: 10.1016/j.cor.2011.09.018. |
[32] |
W. Luo, L. Chen and G. Zhang, Approximation schemes for two-machine flow shop scheduling with two agents, Journal of Combinatorial Optimization, 24 (2012), 229-239.
doi: 10.1007/s10878-011-9378-2. |
[33] |
W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs, Journal of Industrial and Management Optimization, 8 (2012), 271-283.
doi: 10.3934/jimo.2012.8.271. |
[34] |
E. Mokotoff, Algorithms for bicriteria minimization in the permutation flow shop scheduling problem, Journal of Industrial and Management Optimization, 7 (2011), 253-282.
doi: 10.3934/jimo.2011.7.253. |
[35] |
G. Mosheiov, $V$-shaped policies for scheduling deteriorating jobs, Operations Research, 39 (1991), 979-991.
doi: 10.1287/opre.39.6.979. |
[36] |
G. Mosheiov, Scheduling jobs under simple linear deterioration, Computers & Operations Research, 21 (1994), 653-659.
doi: 10.1016/0305-0548(94)90080-9. |
[37] |
B. Mor and G. Mosheiov, Scheduling problems with two competing agents to minimize minmax and minsum earliness measures, European Journal of Operational Research, 206 (2010), 540-546.
doi: 10.1016/j.ejor.2010.03.003. |
[38] |
C. T. Ng, T. C. E. Cheng and J. J. Yuan, A note on the complexity of the problem of two-agent scheduling on a single machine, Journal of Combinatorial Optimization, 12 (2006), 387-394.
doi: 10.1007/s10878-006-9001-0. |
[39] |
Q. Q. Nong, T. C. E. Cheng and C. T. Ng, Two-agent scheduling to minimize the total cost, European Journal of Operational Research, 215 (2011), 39-44.
doi: 10.1016/j.ejor.2011.05.041. |
[40] |
J. B. Wang and T. C. E. Cheng, Scheduling problems with the effects of deterioration and learning, Asia-Pacific Journal of Operational Research, 24 (2007), 245-261.
doi: 10.1142/S021759590700122X. |
[41] |
J. B. Wang and Q. Guo, A due-date assignment problem with learning effect and deteriorating jobs, Applied Mathematical Modelling, 34 (2010), 309-313.
doi: 10.1016/j.apm.2009.04.020. |
[42] |
J. B. Wang, L. H. Sun and L. Y. Sun, Single-machine total completion time scheduling with a time-dependent deterioration, Applied Mathematical Modelling, 35 (2011), 1506-1511.
doi: 10.1016/j.apm.2010.09.028. |
[43] |
G. Wan, R. S. Vakati, J. Y. T. Leung and M. Pinedo, Scheduling two agents with controllable processing times, European Journal of Operational Research, 205 (2010), 528-539.
doi: 10.1016/j.ejor.2010.01.005. |
[44] |
W. H. Wu, S. R. Cheng, C. C. Wu and Y. Yin, Ant colony algorithms for a two-agent scheduling with sum-of processing times-based learning and deteriorating considerations, Journal of Intelligent Manufacturing, 23 (2012), 1985-1993.
doi: 10.1007/s10845-011-0525-5. |
[45] |
C. C. Wu, S. K. Huang and W. C. Lee, Two-agent scheduling with learning consideration, Computers & Industrial Engineering, 61 (2011), 1324-1335.
doi: 10.1016/j.cie.2011.08.007. |
[46] |
D. L. Yang and W. H. Kuo, Single-machine scheduling with both deterioration and learning effects, Annals of Operations Research, 172 (2009), 315-327.
doi: 10.1007/s10479-009-0615-3. |
[47] |
D. L. Yang and W. H. Kuo, Scheduling with deteriorating jobs and learning effects, Applied Mathematics and Computation, 218 (2011), 2069-2073.
doi: 10.1016/j.amc.2011.07.023. |
[48] |
S. H. Yang and J. B. Wang, Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration, Applied Mathematics and Computation, 217 (2011), 4819-4826.
doi: 10.1016/j.amc.2010.11.037. |
[49] |
S. H. Yang and D. L. Yang, Minimizing the total completion time in single-machine scheduling with aging/deteriorating effects and deteriorating maintenance activities, Computers and Mathematics with Applications, 60 (2010), 2161-2169.
doi: 10.1016/j.camwa.2010.08.003. |
[50] |
Y. Yin and D. Xu, Some single-machine scheduling problems with general effects of learning and deterioration, Computers and Mathematics with Applications, 61 (2011), 100-108.
doi: 10.1016/j.camwa.2010.10.036. |
[51] |
Y. Yin, S. R. Cheng and C. C. Wu, Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties, Information Sciences, 189 (2012), 282-292.
doi: 10.1016/j.ins.2011.11.035. |
[52] |
Y. Yin, S. R. Cheng, T. C. E. Cheng, W. H. Wu and C. C. Wu, Two-agent single-machine scheduling with release times and deadlines, International Journal of Shipping and Transport Logistics, 5 (2013), 75-94.
doi: 10.1504/IJSTL.2013.050590. |
[53] |
Y. Yin, T. C. E. Cheng, J. Xu, S. R. Cheng and C. C. Wu, Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration, Journal of Industrial and Management Optimization, 9 (2013), 323-339.
doi: 10.3934/jimo.2013.9.323. |
[54] |
C. L. Zhao, Q. L. Zhang and H. Y. Tang, Scheduling problems under linear deterioration, Acta Automatica Sinica, 29 (2003), 531-535. |
show all references
References:
[1] |
A. Agnetis, P. B. Mirchandani, D. Pacciarelli and A. Pacifici, Scheduling problems with two competing agents, Operations Research, 52 (2004), 229-242.
doi: 10.1287/opre.1030.0092. |
[2] |
A. Agnetis, D. Pacciarelli and A. Pacifici, Multi-agent single machine scheduling, Annals of Operations Research, 150 (2007), 3-15.
doi: 10.1007/s10479-006-0164-y. |
[3] |
B. Alidaee and N. K. Womer, Scheduling with time dependent processing times: Review and extensions, Journal of the Operational Research Society, 50 (1999), 711-729. |
[4] |
A. Allahverdi and F. S. Al-Anzi, Using two-machine flowshop with maximum lateness objective to model multimedia data objects scheduling problem for WWW applications, Computers and Operations Research, 29 (2002), 971-994.
doi: 10.1016/S0305-0548(00)00097-6. |
[5] |
A. Bachman and A. Janiak, Scheduling Jobs with Special Type of Start Time Dependent Processing Times, Report No 34/97, Institute of Engineering Cybernetics, Wroclaw University of Technology, 1997. |
[6] |
K. R. Baker and J. C. Smith, A multiple-criterion model for machine scheduling, Journal of Scheduling, 6 (2003), 7-16.
doi: 10.1023/A:1022231419049. |
[7] |
D. Ben-Arieh and O. Maimon, Annealing method for PCB assembly scheduling on two sequential machines, International Journal of Computer Integrated Manufacturing, 5 (1992), 361-367.
doi: 10.1080/09511929208944543. |
[8] |
S. Browne and U. Yechiali, Scheduling deteriorating jobs on a single processor, Operations Research, 38 (1990), 495-498.
doi: 10.1287/opre.38.3.495. |
[9] |
S. R. Cheng, A single-machine two-agent scheduling problem by GA approach, Asia-Pacific Journal of Operational Research, 29 (2012), 1250013, 22 pp.
doi: 10.1142/S0217595912500133. |
[10] |
T. C. E. Cheng, Q. Ding and B. M. T. Lin, A concise survey of scheduling with time-dependent processing times, European Journal of Operational Research, 152 (2004), 1-13.
doi: 10.1016/S0377-2217(02)00909-8. |
[11] |
T. C. E. Cheng, C. T. Ng and J. J. Yuan, Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs, Theoretical Computer Science, 362 (2006), 273-281.
doi: 10.1016/j.tcs.2006.07.011. |
[12] |
T. C. E. Cheng, C. T. Ng and J. J. Yuan, Multi-agent scheduling on a single machine with max-form criteria, European Journal of Operational Research, 188 (2008), 603-609.
doi: 10.1016/j.ejor.2007.04.040. |
[13] |
T. C. E. Cheng, S. R. Cheng, W. H. Wu, P. H. Hsu and C. C. Wu, A two-agent single- machine scheduling problem with truncated sum-of-processing-times-based learning considerations, Computers & Industrial Engineering, 60 (2011), 534-541.
doi: 10.1016/j.cie.2010.12.008. |
[14] |
T. C. E. Cheng, W. H. Wu, S. R. Cheng and C. C. Wu, Two-agent scheduling with position- based deteriorating jobs and learning effects, Applied Mathematics and Computation, 217 (2011), 8804-8824.
doi: 10.1016/j.amc.2011.04.005. |
[15] |
T. C. E. Cheng, Y. H. Chung, S. C. Liao and W. C Lee, Two-agent singe-machine scheduling with release times to minimize the total weighted completion time, Computers & Operations Research, 40 (2013), 353-361.
doi: 10.1016/j.cor.2012.07.013. |
[16] |
C. Chu, A branch-and-bound algorithm to minimize total tardiness with different release dates, Naval Research Logistics, 39 (1992), 859-875. |
[17] |
A. Colorni, M. Dorigo, M. Maniezzo, I. F. J. Varela and P. Bourgine, Distributed Optimization by Ant Colonies, Proceedings of the first European Conference on Artificial Life, Pairs, 1991. |
[18] |
A. Colorni, M. Dorigo, V. Maniezzo and M. Trubian, Ant system for job-shop scheduling, Belgian Journal of Operations Research, 34 (1994), 39-53. |
[19] |
M. Dorigo, Di Caro G and L. M. Gambardella, Ant algorithms for discrete optimization, Artificial Life, 5 (1999), 137-172.
doi: 10.1162/106454699568728. |
[20] |
M. Dorigo and L. M. Gambardella, Ant colony system: A cooperative learning approach to travel salesman problem, IEEE Trans Evol Computing, 1 (1997), 53-66.
doi: 10.1109/4235.585892. |
[21] |
M. L. Fisher, A dual algorithm for the one-machine scheduling problem, Math Programming, 11 (1976/77), 229-251.
doi: 10.1007/BF01580393. |
[22] |
R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and heuristic in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics, 5 (1979), 287-326.
doi: 10.1016/S0167-5060(08)70356-X. |
[23] |
A. Janiak, T. Krysiak and R. Trela, Scheduling problems with learning and aging effects: A survey, Decision Making in Manufacturing and Services, 5 (2011), 19-36. |
[24] |
S. Kirkpatrick, C. Gelatt and M. Vecchi, Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[25] |
A. S. Kunnathur and S. K. Gupta, Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem, European Journal of Operation Research, 47 (1990), 56-64.
doi: 10.1016/0377-2217(90)90089-T. |
[26] |
K. Lee, B. C. Choi, J. Y. T. Leung and M. L. Pinedo, Approximation algorithms for multi-agent scheduling to minimize total weighted completion time, Information Processing Letters, 109 (2009), 913-917.
doi: 10.1016/j.ipl.2009.04.018. |
[27] |
J. Lenstra, A. H. G. Rinnooy Kan and P. Brucker, Complexity of Machine Scheduling Problems, Annals of Discrete Mathematics, 1 (1977), 343-362. |
[28] |
M. Lai and X. Tong, A metaheuristic method for vehicle routing problem based on improved ant colony optimization and Tabu search, Journal of Industrial and Management Optimization, 8 (2012), 469-484.
doi: 10.3934/jimo.2012.8.469. |
[29] |
P. Liu and L. Tang, Two-agent scheduling with linear deteriorating jobs on a single machine, Lecture Notes in Computer Science, 5092 (2008), 642-650. |
[30] |
P. Liu, X. Y. Zhou and L. X. Tang, Two-agent single-machine scheduling with position-dependent processing times, International Journal of Advanced Manufacturing Technology, 48 (2010), 325-331.
doi: 10.1007/s00170-009-2259-5. |
[31] |
D. C. Li and P. H. Hsu, Solving a two-agent single-machine scheduling problem considering learning effect, Computers & Operations Research, 39 (2012), 1644-1651.
doi: 10.1016/j.cor.2011.09.018. |
[32] |
W. Luo, L. Chen and G. Zhang, Approximation schemes for two-machine flow shop scheduling with two agents, Journal of Combinatorial Optimization, 24 (2012), 229-239.
doi: 10.1007/s10878-011-9378-2. |
[33] |
W. Luo and L. Chen, Approximation schemes for scheduling a maintenance and linear deteriorating jobs, Journal of Industrial and Management Optimization, 8 (2012), 271-283.
doi: 10.3934/jimo.2012.8.271. |
[34] |
E. Mokotoff, Algorithms for bicriteria minimization in the permutation flow shop scheduling problem, Journal of Industrial and Management Optimization, 7 (2011), 253-282.
doi: 10.3934/jimo.2011.7.253. |
[35] |
G. Mosheiov, $V$-shaped policies for scheduling deteriorating jobs, Operations Research, 39 (1991), 979-991.
doi: 10.1287/opre.39.6.979. |
[36] |
G. Mosheiov, Scheduling jobs under simple linear deterioration, Computers & Operations Research, 21 (1994), 653-659.
doi: 10.1016/0305-0548(94)90080-9. |
[37] |
B. Mor and G. Mosheiov, Scheduling problems with two competing agents to minimize minmax and minsum earliness measures, European Journal of Operational Research, 206 (2010), 540-546.
doi: 10.1016/j.ejor.2010.03.003. |
[38] |
C. T. Ng, T. C. E. Cheng and J. J. Yuan, A note on the complexity of the problem of two-agent scheduling on a single machine, Journal of Combinatorial Optimization, 12 (2006), 387-394.
doi: 10.1007/s10878-006-9001-0. |
[39] |
Q. Q. Nong, T. C. E. Cheng and C. T. Ng, Two-agent scheduling to minimize the total cost, European Journal of Operational Research, 215 (2011), 39-44.
doi: 10.1016/j.ejor.2011.05.041. |
[40] |
J. B. Wang and T. C. E. Cheng, Scheduling problems with the effects of deterioration and learning, Asia-Pacific Journal of Operational Research, 24 (2007), 245-261.
doi: 10.1142/S021759590700122X. |
[41] |
J. B. Wang and Q. Guo, A due-date assignment problem with learning effect and deteriorating jobs, Applied Mathematical Modelling, 34 (2010), 309-313.
doi: 10.1016/j.apm.2009.04.020. |
[42] |
J. B. Wang, L. H. Sun and L. Y. Sun, Single-machine total completion time scheduling with a time-dependent deterioration, Applied Mathematical Modelling, 35 (2011), 1506-1511.
doi: 10.1016/j.apm.2010.09.028. |
[43] |
G. Wan, R. S. Vakati, J. Y. T. Leung and M. Pinedo, Scheduling two agents with controllable processing times, European Journal of Operational Research, 205 (2010), 528-539.
doi: 10.1016/j.ejor.2010.01.005. |
[44] |
W. H. Wu, S. R. Cheng, C. C. Wu and Y. Yin, Ant colony algorithms for a two-agent scheduling with sum-of processing times-based learning and deteriorating considerations, Journal of Intelligent Manufacturing, 23 (2012), 1985-1993.
doi: 10.1007/s10845-011-0525-5. |
[45] |
C. C. Wu, S. K. Huang and W. C. Lee, Two-agent scheduling with learning consideration, Computers & Industrial Engineering, 61 (2011), 1324-1335.
doi: 10.1016/j.cie.2011.08.007. |
[46] |
D. L. Yang and W. H. Kuo, Single-machine scheduling with both deterioration and learning effects, Annals of Operations Research, 172 (2009), 315-327.
doi: 10.1007/s10479-009-0615-3. |
[47] |
D. L. Yang and W. H. Kuo, Scheduling with deteriorating jobs and learning effects, Applied Mathematics and Computation, 218 (2011), 2069-2073.
doi: 10.1016/j.amc.2011.07.023. |
[48] |
S. H. Yang and J. B. Wang, Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration, Applied Mathematics and Computation, 217 (2011), 4819-4826.
doi: 10.1016/j.amc.2010.11.037. |
[49] |
S. H. Yang and D. L. Yang, Minimizing the total completion time in single-machine scheduling with aging/deteriorating effects and deteriorating maintenance activities, Computers and Mathematics with Applications, 60 (2010), 2161-2169.
doi: 10.1016/j.camwa.2010.08.003. |
[50] |
Y. Yin and D. Xu, Some single-machine scheduling problems with general effects of learning and deterioration, Computers and Mathematics with Applications, 61 (2011), 100-108.
doi: 10.1016/j.camwa.2010.10.036. |
[51] |
Y. Yin, S. R. Cheng and C. C. Wu, Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties, Information Sciences, 189 (2012), 282-292.
doi: 10.1016/j.ins.2011.11.035. |
[52] |
Y. Yin, S. R. Cheng, T. C. E. Cheng, W. H. Wu and C. C. Wu, Two-agent single-machine scheduling with release times and deadlines, International Journal of Shipping and Transport Logistics, 5 (2013), 75-94.
doi: 10.1504/IJSTL.2013.050590. |
[53] |
Y. Yin, T. C. E. Cheng, J. Xu, S. R. Cheng and C. C. Wu, Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration, Journal of Industrial and Management Optimization, 9 (2013), 323-339.
doi: 10.3934/jimo.2013.9.323. |
[54] |
C. L. Zhao, Q. L. Zhang and H. Y. Tang, Scheduling problems under linear deterioration, Acta Automatica Sinica, 29 (2003), 531-535. |
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