Abstract
In this paper, we consider single-machine scheduling problem with controllable processing times and learning effect, i.e., processing times of jobs are controllable variables with linear costs and also are defined as functions of positions in a schedule. We concentrate on two goals separately, namely minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total compression cost and minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total compression cost. The problem is modeled as an assignment problem and thus can be solved with the well-known algorithms.
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References
Badiru AB (1992) Computational survey of univariate and multivariate learning curve models. IEEE Trans Eng Manage 39:176–188
Biskup D (2008) A state-of-the-art review on scheduling with learning effects. Eur J Oper Res 188:315–329
Wang J-B, Ng CT, Cheng TCE, Liu LL (2008) Single-machine scheduling with a time-dependent learning effect. Int J Prod Econ 111:802–811
Mosheiov G (2008) Minimizing total absolute deviation of job completion times: extensions to position-dependent processing times and parallel identical machines. J Oper Res Soc 59:1422–1424
Toksar MD, Guner E (2008) Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach. Int J Adv Manuf Technol 38:801–808
Wang J-B (2010) Single-machine scheduling with a sum-of-actual-processing-time based learning effect. J Oper Res Soc 61:172–177
Wang J-B, Jiang Y, Wang G (2009) Single-machine scheduling with past-sequence-dependent setup times and effects of deterioration and learning. Int J Adv Manuf Technol 41:1221–1226
Wang J-B, Wang D, Wang L-Y, Lin L, Yin N, Wang W-W (2009) Single machine scheduling with exponential time-dependent learning effect and past-sequence-dependent setup times. Comput Math Appl 57:9–16
Wang J-B (2008) Single-machine scheduling with general learning functions. Comput Math Appl 56:1941–1947
Wang J-B (2008) Single machine scheduling with past-sequence-dependent setup times and time-dependent learning effect. Comput Ind Eng 55(3):584–591
Wang J-B (2009) Single machine scheduling with a time-dependent learning effect and deteriorating jobs. J Oper Res Soc 60:583–586
Wang J-B, Liu L-L (2009) Two-machine flow shop problem with effects of deterioration and learning. Comput Ind Eng 57:1114–1121
Wang L-Y, Wang J-B, Wang D, Yin N, Huang X, Feng E-M (2009) Single-machine scheduling with a sum-of-processing-time based learning effect and deteriorating jobs. Int J Adv Manuf Technol 45:336–340
Eren T, Guner E (2009) A bicriteria parallel machine scheduling with a learning effect. Int J Adv Manuf Technol 40:1202–1205
Toksari MD, Guner E (2009) Scheduling problems with the nonlinear effects of learning and deterioration. Int J Adv Manuf Technol 45:801–807
Wang J-B, Huang X, Wang X-Y, Yin N, Wang L-Y (2009). Learning effect and deteriorating jobs in the single machine scheduling problems. Appl Math Model 33:3848–3853
Wang J-B, Guo Q (2010) A due-date assignment problem with learning effect and deteriorating jobs. Appl Math Model 34:309–313
Wang J-B, Wang D, Zhang G-D (2010) Single-machine scheduling problems with both deteriorating jobs and learning effects. Appl Math Model 34:2831–2839
Yin N, Wang J-B, Wang D, Wang L-Y, Wang X-Y (2010) Deteriorating jobs and Learning effects on a single-machine scheduling with past-sequence-dependent setup times. Int J Adv Manuf Technol 46:707–714
Wang L-Y, Wang J-B, Gao W-J, Huang X, Feng E-M (2010) Two single-machine scheduling problems with the effects of deterioration and learning. Int J Adv Manuf Technol 46:715–720
Wang X-R, Wang J-B (2010) Scheduling with past-sequence-dependent setup times and learning effects on a single machine. Int J Adv Manuf Technol 48:739–746
Wang J-B, Sun L-H, Sun L-Y (2010) Single machine scheduling with a learning effect and discounted costs. Int J Adv Manuf Technol 49:1141–1149
Yin Y, Xu D, Wang J (2010) Some single-machine scheduling problems with past-sequence-dependent setup times and a general learning effect. Int J Adv Manuf Technol 48:1123–1132
Wang J-B, Sun L, Sun L (2010) Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect. Appl Math Model 34:2813–2819
Wang J-B, Wang D, Zhang G-D (2010) Single-machine scheduling with learning functions. Appl Math Comput 216:1280–1286
Wang J-B, Wang M-Z (2010) A revision of machine scheduling problems with a general learning effect. Math Comput Model. doi:10.1016/j.mcm.2010.08.020
Wang J-B, Sun L-H, Sun L-Y (2010) Scheduling jobs with an exponential sum-of-actual-processing-time based learning effect. Comput Math Appl. doi:10.1016/j.camwa.2010.09.005
Wang J-B, Li J-X (2010) Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects. Appl Math Model. doi:10.1016/j.apm.2010.09.017
Nowicki E, Zdrzalka S (1990) A survey of results for sequencing problems with controllable processing times. Discrete Appl Math 26:271–287
Zdrzalka S (1991) Scheduling jobs on a single machine with release dates, delivery times and controllable processing times: worst-case analysis. Oper Res Lett 10:519–524
Panwalkar SS, Rajagopalan R (1992) Single machine sequencing with controllable processing times. Eur J Oper Res 59:298–302
Alidaee B, Ahmadian A (1993) Two parallel machine sequencing problems involving controllable job processing times. Eur J Oper Res 70: 335–341
Cheng TCE, Janiak A (1994) Resource optimal control in some single machine scheduling problems. IEEE Trans Automat Contr 39:1243–1246
Cheng TCE, Oǧuz C, Qi XD (1996) Due-date assignment and single machine scheduling with compressible processing times. Int J Prod Econ 43:29–35
Alidaee B, Kochenberger G (1996) A framework for machine scheduling problems with controllable processing times. Prod Oper Manag 5(4):391–405
Biskup D, Cheng TCE (1999) Single machine scheduling with controllable processing times and earliness, tardiness and completion time penalties. Eng Optim 31:329–336
Biskup D, Jahnke H (2001) Common due date assignment for scheduling on a single machine with jointly reducible processing times. Int J Prod Econ 69:317–322
Hoogeveen H, Woeginger GJ (2002) Some comments on sequencing with controllable processing times. Computing 68:181–192
Ng CT, Cheng TCE, Kovalyov MY, Lam SS (2003) Single machine scheduling with a variable common due date and resource-dependent processing times. Comput Oper Res 30:1173–1185
Shabtay D, Kaspi M (2004) Minimizing the total weighted flow time in a single machine with controllable processing times. Comput Oper Res 31:2279–2289
Ng CT, Cheng TCE, Kovalyov MY (2004) Single machine batch scheduling with jointly compressible setup and processing times. Eur J Oper Res 153:211–219
Wang J-B (2006) Single machine scheduling with common due date and controllable processing times. Appl Math Comput 174(2):1245–1254
Wang J-B (2006) Single machine common flow allowance scheduling with controllable processing times. J Appl Math Comput 21:249–257
Wang J-B, Xia Z-Q (2007) Single machine scheduling problems with controllable processing times and total absolute differences penalties. Eur J Oper Res 177:638–645
Tseng C-T, Liao C-T, Huang K-L (2009) Minimizing total tardiness on a single machine with controllable processing times. Comput Oper Res 36:1852–1858
Biskup D (1999) Single-machine scheduling with learning considerations. Eur J Oper Res 115:173–178
Kanet JJ (1981) Minimizing variation of flow time in single machine systems. Manage Sci 27(12):1453–1459
Bagchi UB (1989) Simultaneous minimization of mean and variation of flow-time and waiting time in single machine systems. Oper Res 37:118–125
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Yin, N., Wang, XY. Single-machine scheduling with controllable processing times and learning effect. Int J Adv Manuf Technol 54, 743–748 (2011). https://doi.org/10.1007/s00170-010-2973-z
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DOI: https://doi.org/10.1007/s00170-010-2973-z