# American Institute of Mathematical Sciences

April  2016, 12(2): 757-770. doi: 10.3934/jimo.2016.12.757

## The coordination of single-machine scheduling with availability constraints and delivery

 1 Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai 200237, China

Received  August 2014 Revised  March 2015 Published  June 2015

Single-machine scheduling problems with production and delivery are studied in this paper. There is only one delivery vehicle with capacity $z$. Jobs are not allowed to resume. The $P \rightarrow D$ system and $D \rightarrow P$ system are considered, respectively. For the machine with an availability constraint, we present two $4/3$-approximation algorithms and show that the bounds are tight. For the machine with periodic availability constraints, we provide two polynomial time approximation algorithms which are the best possible.
Citation: Ganggang Li, Xiwen Lu, Peihai Liu. The coordination of single-machine scheduling with availability constraints and delivery. Journal of Industrial and Management Optimization, 2016, 12 (2) : 757-770. doi: 10.3934/jimo.2016.12.757
##### References:
 [1] Y. C. Chang and C. Y. Lee, Machine scheduling with job delivery coordination, European Journal of Operational Research, 158 (2004), 470-487. doi: 10.1016/S0377-2217(03)00364-3. [2] N. G. Hall and C. N. Potts, Supply chain scheduling: Batching and delivery, Operations Research, 51 (2003), 566-584. doi: 10.1287/opre.51.4.566.16106. [3] M. Ji, Y. He and T. C. E. Cheng, Single-machine scheduling with periodic maintenance to minimize makespan, Computers & Operations Research, 34 (2007), 1764-1770. doi: 10.1016/j.cor.2005.05.034. [4] C. Y. Lee, Machine scheduling with an availability constraint, Journal of Global Optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681. [5] C. Y. Lee and Z. L. Chen, Machine scheduling with transportation considerations, Journal of Scheduling, 4 (2001), 3-24. doi: 10.1002/1099-1425(200101/02)4:1<3::AID-JOS57>3.0.CO;2-D. [6] C. Y. Lee, L. Lei and M. Pinedo, Current trends in deterministic scheduling, Annals of Operations Research, 70 (1997), 1-41. doi: 10.1023/A:1018909801944. [7] C. L. Li and J. W. Ou, Machine scheduling with pickup and delivery, Naval Research Logistics, 52 (2005), 617-630. doi: 10.1002/nav.20101. [8] C. L. Li, G. Vairaktarakis and C. Y. Lee, Machine scheduling with deliveries to multiple customer locations, European Journal of Operational Research, 164 (2005), 39-51. doi: 10.1016/j.ejor.2003.11.022. [9] G. Schmidt, Scheduling with limited machine availability, European Journal of Operational Research, 121 (2000), 1-15. doi: 10.1016/S0377-2217(98)00367-1. [10] L. X. Tang, J. Guan and G. F. Hu, Steelmaking and refining coordinated scheduling problem with waiting time and transportation consideration, Computers & Industrial Engineering, 58 (2010), 239-248. doi: 10.1016/j.cie.2009.07.014. [11] D. J. Thomas and P. M. Griffin, Coordinated supply chain management, European Journal of Operational Research, 94 (1996), 1-15. doi: 10.1016/0377-2217(96)00098-7. [12] L. Y. Wang and Z. H. Liu, Heuristics for parallel machine scheduling with batch delivery consideration, Journal of Industrial and Management Optimization, 10 (2014), 259-273. doi: 10.3934/jimo.2014.10.259. [13] X. L. Wang and T. C. E. Cheng, Machine scheduling with an availability constraint and job delivery coordination, Naval Research Logistics, 54 (2007), 11-20. doi: 10.1002/nav.20175.

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##### References:
 [1] Y. C. Chang and C. Y. Lee, Machine scheduling with job delivery coordination, European Journal of Operational Research, 158 (2004), 470-487. doi: 10.1016/S0377-2217(03)00364-3. [2] N. G. Hall and C. N. Potts, Supply chain scheduling: Batching and delivery, Operations Research, 51 (2003), 566-584. doi: 10.1287/opre.51.4.566.16106. [3] M. Ji, Y. He and T. C. E. Cheng, Single-machine scheduling with periodic maintenance to minimize makespan, Computers & Operations Research, 34 (2007), 1764-1770. doi: 10.1016/j.cor.2005.05.034. [4] C. Y. Lee, Machine scheduling with an availability constraint, Journal of Global Optimization, 9 (1996), 395-416. doi: 10.1007/BF00121681. [5] C. Y. Lee and Z. L. Chen, Machine scheduling with transportation considerations, Journal of Scheduling, 4 (2001), 3-24. doi: 10.1002/1099-1425(200101/02)4:1<3::AID-JOS57>3.0.CO;2-D. [6] C. Y. Lee, L. Lei and M. Pinedo, Current trends in deterministic scheduling, Annals of Operations Research, 70 (1997), 1-41. doi: 10.1023/A:1018909801944. [7] C. L. Li and J. W. Ou, Machine scheduling with pickup and delivery, Naval Research Logistics, 52 (2005), 617-630. doi: 10.1002/nav.20101. [8] C. L. Li, G. Vairaktarakis and C. Y. Lee, Machine scheduling with deliveries to multiple customer locations, European Journal of Operational Research, 164 (2005), 39-51. doi: 10.1016/j.ejor.2003.11.022. [9] G. Schmidt, Scheduling with limited machine availability, European Journal of Operational Research, 121 (2000), 1-15. doi: 10.1016/S0377-2217(98)00367-1. [10] L. X. Tang, J. Guan and G. F. Hu, Steelmaking and refining coordinated scheduling problem with waiting time and transportation consideration, Computers & Industrial Engineering, 58 (2010), 239-248. doi: 10.1016/j.cie.2009.07.014. [11] D. J. Thomas and P. M. Griffin, Coordinated supply chain management, European Journal of Operational Research, 94 (1996), 1-15. doi: 10.1016/0377-2217(96)00098-7. [12] L. Y. Wang and Z. H. Liu, Heuristics for parallel machine scheduling with batch delivery consideration, Journal of Industrial and Management Optimization, 10 (2014), 259-273. doi: 10.3934/jimo.2014.10.259. [13] X. L. Wang and T. C. E. Cheng, Machine scheduling with an availability constraint and job delivery coordination, Naval Research Logistics, 54 (2007), 11-20. doi: 10.1002/nav.20175.
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