Scheduling problems with position dependent job processing times: computational complexity results

In this paper, we analyse single machine scheduling problems with learning and aging effects to minimize one of the following objectives: the makespan with release dates, the maximum lateness and the number of late jobs. The phenomena of learning and aging are modeled by job processing times described by non-increasing (learning) or non-decreasing (aging) functions dependent on the number of previously processed jobs, i.e., a job position in a sequence. We prove that the considered problems are strongly NP-hard even if job processing times are described by simple linear functions dependent on a number of processed jobs. Additionally, we show a property of equivalence between problems with learning and aging models. We also prove that if the function describing decrease/increase of a job processing time is the same for each job then the problems with the considered objectives are polynomially solvable even if the function is arbitrary. Therefore, we determine the boundary between polynomially solvable and strongly NP-hard cases.

[1]  Shimon Whiteson,et al.  Adaptive job routing and scheduling , 2004, Eng. Appl. Artif. Intell..

[2]  Wen-Chiung Lee,et al.  Scheduling problems with general effects of deterioration and learning , 2011, Inf. Sci..

[3]  Dirk Biskup,et al.  Single-machine scheduling with learning considerations , 1999, Eur. J. Oper. Res..

[4]  Harold Kerzner,et al.  SUMMER 2011 TEXTBOOKS EM 536 Project Management Project Management: A System Approach to Planning, Scheduling, and Controlling , 2011 .

[5]  Adam Janiak,et al.  Scheduling jobs with position-dependent processing times , 2004, J. Oper. Res. Soc..

[6]  Maurice Bonney,et al.  The economic manufacture/order quantity (EMQ/EOQ) and the learning curve: Past, present, and future , 1999 .

[7]  Dvir Shabtay,et al.  The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times , 2008, Ann. Oper. Res..

[8]  G. Kent Webb.  Integrated circuit (IC) pricing , 1994 .

[9]  Dr-Ing. N.V. Mandich,et al.  Overview of surface preparation of metals prior to finishing: Part 2 , 2003 .

[10]  Radoslaw Rudek,et al.  A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models , 2011, Comput. Math. Appl..

[11]  Mark Stanford,et al.  Investigation into the Relationship between Tool-Wear and Cutting Environments when Turning En32 Steel , 2004 .

[12]  Joseph Y.-T. Leung,et al.  Scheduling orders on either dedicated or flexible machines in parallel to minimize total weighted completion time , 2008, Ann. Oper. Res..

[13]  John C. Fisk,et al.  Production Lot Sizing Under A Learning Effect , 1982 .

[14]  T.C.E. Cheng,et al.  Single-machine scheduling with deteriorating functions for job processing times , 2010 .

[15]  Gur Mosheiov,et al.  Parallel machine scheduling with a learning effect , 2001, J. Oper. Res. Soc..

[16]  Guoqing Wang,et al.  Single Machine Scheduling with Learning Effect Considerations , 2000, Ann. Oper. Res..

[17]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[18]  T. C. Edwin Cheng,et al.  Single-machine due-window assignment and scheduling with job-dependent aging effects and deteriorating maintenance , 2010, Comput. Oper. Res..

[19]  Guochun Tang,et al.  Single-machine scheduling problems with time and position dependent processing times , 2011, Ann. Oper. Res..

[20]  Peter Roberts,et al.  A Theory of the Learning Process , 1983 .

[21]  L. B. J. M. Sturm.  A Simple Optimality Proof of Moore's Sequencing Algorithm , 1970 .

[22]  Bertrand M. T. Lin,et al.  A concise survey of scheduling with time-dependent processing times , 2004, Eur. J. Oper. Res..

[23]  T.C.E. Cheng,et al.  AN ECONOMIC PRODUCTION QUANTITY MODEL WITH LEARNING AND FORGETTING CONSIDERATIONS , 1994 .

[24]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[25]  T. Eren,et al.  SINGLE MACHINE SCHEDULING PROBLEMS WITH TIME-DEPENDENT LEARNING EFFECTS , 2013 .

[26]  Ahmed Riahi-Belkaoui.  The learning curve : a management accounting tool , 1986 .

[27]  Adam Janiak,et al.  Scheduling jobs under an aging effect , 2010, J. Oper. Res. Soc..

[28]  Dar-Li Yang,et al.  Some scheduling problems with deteriorating jobs and learning effects , 2010, Comput. Ind. Eng..

[29]  Dar-Li Yang,et al.  Minimizing the makespan in a single-machine scheduling problem with the cyclic process of an aging effect , 2008, J. Oper. Res. Soc..

[30]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

[31]  Zuren Feng,et al.  A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates , 2010, Ann. Oper. Res..

[32]  Kim B. Clark,et al.  Behind the learning curve: a sketch of the learning process , 1991 .

[33]  Stanislaw Gawiejnowicz,et al.  Time-Dependent Scheduling , 2008, Monographs in Theoretical Computer Science. An EATCS Series.

[34]  Louis E. Yelle.  THE LEARNING CURVE: HISTORICAL REVIEW AND COMPREHENSIVE SURVEY , 1979 .

[35]  E. C. Keachie,et al.  Effects of Learning on Optimal Lot Size , 1966 .

[36]  Wen-Chiung Lee,et al.  Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations , 2007, Comput. Ind. Eng..

[37]  Stanislaw Gawiejnowicz,et al.  A Note on Scheduling on a Single Processor with Speed Dependent on a Number of Executed Jobs , 1996, Inf. Process. Lett..

[38]  S. Eilon.  ON A MECHANISTIC APPROACH TO FATIGUE AND REST PERIODS , 1964 .

[39]  Wen-Chiung Lee,et al.  A single-machine learning effect scheduling problem with release times , 2010 .

[40]  T. P. Wright,et al.  Factors affecting the cost of airplanes , 1936 .

[41]  A. Dababneh,et al.  Impact of added rest breaks on the productivity and well being of workers , 2001, Ergonomics.

[42]  T. K. Lien,et al.  Hybrid Automatic-manual Assembly Systems , 2001 .

[43]  Rui Zhang,et al.  Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries , 2011, Ann. Oper. Res..

[44]  Ji-Bo Wang,et al.  Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects , 2011, Ann. Oper. Res..

[45]  Dirk Biskup,et al.  A state-of-the-art review on scheduling with learning effects , 2008, Eur. J. Oper. Res..

[46]  Bart De Schutter,et al.  A Comprehensive Survey of Multiagent Reinforcement Learning , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[47]  Suh-Jenq Yang,et al.  Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities , 2010 .

[48]  Dar-Li Yang,et al.  Single-machine scheduling with both deterioration and learning effects , 2009, Ann. Oper. Res..

[49]  Adam Janiak,et al.  A note on the learning effect in multi-agent optimization , 2011, Expert Syst. Appl..

[50]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .