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Learning effect is a phenomenon in industrial processes that a machine (plant, worker, etc) can improve its productivity continuously with time, that is the actual processing time of a job decreases after the machine (plant, worker, etc) processes other jobs and gains some experiences. We study single machine scheduling problems with sum-of-processing-time based and job-dependent learning effect. The objectives are to minimize the maximum lateness, the number of tardy jobs, and total weighted completion time. By performing reductions from equal cardinality partition problem, we prove that these problems under investigation are all NP-hard. Two special cases that can be solved in polynomial time are also presented.
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References
Adler PS, Clark KB (1991) Behind the learning curve: A sketch of the learning process. Management Science 37(3):267–281
Bachman A, Janiak A (2004) Scheduling jobs with position dependent processing time. Journal of the Operational Research Society 55(3):257–264
Badiru AB (1992) Computational survey of univariate and multivariate learning curve models. IEEE Transactions on Engineering Management 39(2):173–178
Biskup D (1999) Single-machine scheduling with learning considerations. European Journal of Operational Research 115(1):173–178
Biskup D (2008) A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research 188(2):315–329
Cheng M, Tadikamalla PR, Shang J, Zhang B (2015) Single machine scheduling problems with exponentially time-dependent learning effects. Journal of Manufacturing Systems 34:60–65
Cheng TCE, Ding Q, Lin BMT (2004) A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research 152(1):1–13
Cheng TCE, Wang G (2000) Single machine scheduling with learning effect considerations. Annals of Operations Research 98(1):273–290
Cochran EB (1960) New concepts of the learning curve. The Journal of Industrial Engineering 11(4):317–327
Garey MR, Johnson DS (1979) Computers and Intractability A Guid to the Theory of NP-Completeness. W.H.Freeman, San Francisco
Gawiejnowicz S (2008) Time-dependent Scheduling. Springer, Berlin
Gawiejnowicz S, Lin BMT (2010) Scheduling time-dependent jobs under mixed deterioration. Applied Mathematics and Computation 216(2):438–447
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals Discrete Mathematics 5:287–326
Janiak A, Janiak WA, Krysiak T, Kwiatkowski T (2015) A survey on scheduling problems with due windows. European Journal of Operational Research 242(2):347–357
Janiak A and Rudek R (2009). Experience-based approach to scheduling problems with the learning effect. IEEE Transactions on Systems. Man and Cybernetics, Part A 39(2): 344–357.
Ji M, Yao D, Yang Q, Cheng TCE (2015) Machine scheduling with DeJongs learning effect. Computers & Industrial Engineering 80:195–200
Koulamas C, Kyparisis GJ (2007) Single-machine and two-machine folowshop scheduling with general learning function. European Journal of Operational Research 178(2):402–407
Kuo W-H, Yang D-L (2006) Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect. European Journal of Operational Research 174(2):1184–1190
Lu Y-Y, Wang J-J, Huang X (2015) Scheduling jobs with position and sum-of-processing-time based processing times. Applied Mathe matical Modelling 39(14):4013–4021
Mosheiov G, Sidney JB (2003) Scheduling with general job dependent learning curves. European Journal of Operational Research 147(3):665–670
Mosheiov G, Sidney JB (2005) Note on scheduling with general learning curves to minimize the number of tardy jobs. Journal of the Operational Research Society 56(1):110–112
Rudek R (2011) Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect. Computers & Industrial Engineering 61(1):20–31
Rudek R (2014) Computational complexity of the single processor makespan minimization problem with release dates and job dependent learning. Journal of the Operational Research Society 65(8):1170–1176
Wang J-B, Li J-X (2011) Single-machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effect. Applied Mathematical Modelling 35(3):1388–1395
Wang J-B, Ng CT, Chen TCE, Liu LL (2008) Single-machine scheduling with a time-dependent learning effect. International Journal of Production Economics 111(2):802–811
Wang L-Y, Wang J-J, Wang J-B, Feng E-M (2011) Scheduling jobs with general learning functions. Journal of Systems Science and Systems Engineering 20(1):119–125
Wright TP (1936) Factors affecting the cost of airplanes. Journal of Aeronautical Sciences 3(4):122–128
Wu C-H, Lai P-J, Lee W-C (2015) A note on single-machine scheduling with sum-of-processing-time-based learning and forgetting effects. Applied Mathematical Modelling 39(2):415–424
Yang D-L, Kuo W-H (2007) Single-machine scheduling with an actual time-dependent learning effect. Journal of the Operational Research Society 58(10):1348–1353
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This work was supported in part by projects of National Natural Science Foundation of China (No. 71171058 and No. 11371103). We are grateful to the anonymous referees for their valuable comments on an earlier version of this paper.
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Jiang, Z., Chen, F. & Zhang, X. Single-machine scheduling with times-based and job-dependent learning effect. J Oper Res Soc 68, 809–815 (2017). https://doi.org/10.1057/jors.2016.40
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DOI: https://doi.org/10.1057/jors.2016.40