OMER OZTURKOGLUOzturkoglu, Omer2025-10-222017[1] Mohring R. and Rademacher F. An Introduction to Stochastic Scheduling Problems . In: Neumann K. and Pallaschke D. (Eds.) Contributions to Operations Research Springer Berlin (1985).[2] Righter R. Stochastic Scheduling . In: Skaked M. and Shanthikumar G. (Eds.) Academic Press San Diego CA (1994).[3] Pinedo M. Scheduling Theory Algorithms and Systems . Prentice-Hall Englewood Cliffs NJ (1995).[4] Boudreau J. Hopp W. McClain J. and Thomas L. On the Interface Between Operations and Human Resources Management . Manufacturing and Service Operations Management 5(3) 179–202 (2003).[5] Gupta J. and Gupta S. Single Facility Scheduling with Nonlinear Processing Times . Computers and Industrial Engineering 14 387–393 (1988).[6] Gupta S. Kunnathur A. and Dandapani K. Optimal Repayment Policies for Multiple Loans . OMEGA 15(4) 323–330 (1987).[7] Tanaev V. Gordon V. and Shafransky Y. Scheduling Theory Single-stage Systems . Kluwer Dordrecht (1994).[8] Browne S. and Yechiali U. Scheduling Deteriorating Jobs on a Single Processor . Operations Research 38 495–498 (1990).[9] Gawiejnowicz S. and Pankowska L. Scheduling Jobs with Varying Processing Times . Information Processing Letters 54(3) 175–178 (1995).[10] Kunnathur A. and Gupta S. Minimizing the Makespan with Late Start Penalties Added to Processing Times in a Single Facility Scheduling Problem . European Journal of Operational Research 47(1) 56– 64 (1990).[11] Mosheiov G. Scheduling Jobs With StepDeterioration , Minimizing Makespan on a Single and Multi-Machine . Computers and Industrial Engineering 28(4) 869–879 (1995)[12] Ozturkoglu Y. and Bulfin R. L. A Unique Integer Mathematical Model for Scheduling Deteriorating Jobs with Rate-Modifying Activities on a Single Machine. The International Journal of Advanced Manufacturing Technology 57(5-8) 753–762 (2011).[13] Alidaee B. and Womer N. Scheduling with Time Dependent Processing Times: Review and Extensions. Journal of the Operational Research Society 50(7) 711–721 (1999).[14] Cheng T. Ding Q. and Lin B. A Concise Survey of Scheduling with Time-Dependent Processing Times . European Journal of Operational Research 152 1–13 (2004).[15] Lodree E. Geiger C. and Jiang X. Taxonomy for Integrating Scheduling Theory and Human Factors: Review and Research Opportunities . International Journal of Industrial Ergonomics 39 39–51 (2009).[16] Chen Z. Parallel Machine Scheduling with Time Dependent Processing Times . Discrete Applied Mathematics 70 81–93 (1996).[17] Mosheiov G. Multi-machine Scheduling with Linear Deterioration. Infor 36 205–214 (1998).[18] Kang L. and Ng C. A Note on a Fully PolynomialTime Approximation Scheme for Parallel-Machine Scheduling with Deteriorating Jobs . International Journal of Production Economics 109 180–184 (2007).[19] Ji M. and Cheng T. Parallel-Machine Scheduling with Simple Linear Deterioration to Minimize Total Completion Time . European Journal of Operational Research 188 341–347 (2008).[20] Ji M. and Cheng T. Parallel-Machine Scheduling of Simple Linear Deteriorating Jobs . Theoretical Computer Science 410 3761–3768 (2009).[21] Lee C.-Y. and Leon V. Machine Scheduling with Rate-Modifying Activity . European Journal of Operational Research 128 493–513 (2001).[22] Lee C.-Y. and Lin C.-S. Single Machine Scheduling with Maintenance and Repair Rate-Modifying Activities . European Journal of Operational Research 135 495–513 (2001).[23] Mosheiov G. and Sidney J. New Results on Sequencing with Rate Modification . Information Systems and Operational Research 41(2) 155–163 (2003).[24] Ozturkoglu Y. A Bi-Criteria Single Machine Scheduling with Rate-Modifying-Activity. Gazi University Journal of Science 26(1) 97–106 (2013).[25] Kim B. S. and Ozturkoglu Y. Scheduling a Single Machine With Multiple Preventive Maintenance Activities And Position-Based Deteriorations Using Genetic Algorithms. The International Journal of Advanced Manufacturing Technology 67(5-8) 1127– 1137 (2013).[26] Ozturkoglu Y. An Efficient Time Algorithm for Makespan Objectives. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 5(2) 75-80 (2015).[27] Lee W.-C. and Wu C.-C. Multi-Machine Scheduling with Deteriorating Jobs and Scheduled Maintenance . Applied Mathematical Modeling 32 362–373 (2008).[28] Dalfard V. M. and Mohammadi G. Two MetaHeuristic Algorithms for Solving Multi-Objective Flexible Job-Shop Scheduling with Parallel Machine and Maintenance Constraints. Computers & Mathematics with Applications 64(6) 2111–2117 (2012).[29] Cheng B. Wang Q. Yang S. and Hu X. An Improved Ant Colony Optimization for Scheduling Identical Parallel Batching Machines With Arbitrary Job Sizes. Applied Soft Computing 13(2):765–772 (2013).[30] Wang J.-B. and Wei C.-M. Parallel Machine Scheduling With a Deteriorating Maintenance Activity And Total Absolute Differences Penalties. Applied Mathematics and Computation 217(20) 8093–8099 (2011).[31] Wang J.-J. Wang J.-B. and Liu F. Parallel Machines Scheduling With a Deteriorating Maintenance Activity. Journal of the Operational Research Society 62(10) 1898–1902 (2011).[32] Yang D.-L. and Yang S.-J. Unrelated ParallelMachine Scheduling Problems with Multiple RateModifying Activities. Information Sciences 235 280– 286 (2013).[33] Yang D.-L. Cheng T. and Yang S.-J. ParallelMachine Scheduling With Controllable Processing Times and Rate-Modifying Activities to Minimise Total Cost Involving Total Completion Time and Job Compressions. International Journal of Production Research 52(4) 1133–1141 (2014).[34] Dorigo M. Maniezzo V. and Colorni A. Positive Feedback as a Search Strategy . Technical Report 91-016 Dip. ElettronicaPolitecnico di Milano Italy (1991).[35] Sankar S. Ponnambalam S. Rathinavel V. and Visveshvaren M. Scheduling in Parallel Machine Shop: An Ant Colony Optimization Approach . Industrial Technology ICIT IEEE Industrial Conference pages 276–280 (2005).[36] Tkindt V. Monmarche N. Tercinet F. and Laugt D. An Ant Colony Optimization Algorithm to Solve a 2-Machine Bicriteria Flowshop Scheduling Problem . European Journal of Operational Research 142 250– 257 (2002).[37] Alaykiran K. Engin O. and Doyen A. Using Ant Colony Optimization to Solve Hybrid Flowshop Scheduling Problems . International Journal of Advanced Manufacturing Technology 35 541–550 (2007).38] Arnaout J.-P. Musa R. and Rabadi G. Ant Colony Optimization Algorithm to Parallel Machine Scheduling Problem with Setups . 4th IEEE Conference on Automation Science Engineering Washington DC USA pages 578–582 (2008).[39] Arnaout J.P. and Rabadi G. and Musa R. A TwoStage Ant Colony Optimization Algorithm to Minimize the Makespan on Unrelated Parallel Machines with Sequence-Dependent Setup Times . Journal of Intelligent Manufacturing 21(6) 693-701 (2010).[40] Rossi A. and Boschi E. A Hybrid Heuristic to Solve the Parallel Machines Job-shop Scheuling Problem . Advances in Engineering Software 40 118–127 (2009).[41] Behnamian J. Zandieh M. and Ghomi S. Parallel-Machine Scheduling Problems with SequenceDependent Setup Times using an ACO SA and VNS Hybrid Algorithm . Experts Systems with Applications 36 9637–9644 (2009).[42] Kirkpatrick S. Gelatt C. and Vecchi M. Optimization by Simulated Annealing . Science 220 671–680 (1983).[43] Koulamas C. Decomposition and Hybrid Simulated Annealing Heuristics for the Parallel-Machine Total Tardiness Problem . Naval Research Logistics 44 105–125 (1997).[44] Park M.-W. and Kim Y.-D. Search Heuristics for a Parallel Machine Scheduling Problem with Ready Times and Due Dates . Computers and Industrial Engineering 33(3-4) 793–796 (1997).[45] J´ozefowska J. Mika M. R´o˙zycki R. and Walig´ora G. Local Search Metaheuristics for DiscreteContinuous Scheduling Problems . European Journal of Operational Research 107 354–370 (1998).[46] Hindi K. and Mhlanga S. Scheduling Linearly Deteriorating Jobs on Parallel Machines: A Simulated Annealing Approach . Production Planning and Control 12(1) 76–80 (2001).[47] Kim D.-W. Kim K.-H. Jang W. and Chen F. Unrelated Parallel Machine Scheduling with Setup Times Using Simulated Annealing . Robotics and Computer Integrated Manufacturing 18(3-4) 223–231 (2002).2146-09572146-5703https://gcris.yasar.edu.tr/handle/123456789/11019https://search.trdizin.gov.tr/en/yayin/detay/240475This study focuses on identical parallel machine scheduling of jobs with deteriorating processing times and rate-modifying activities. We consider nonlinearly increasing processing times of jobs based on their position assignment. Rate modifying activities (RMAs) are also considered to recover the increase in processing times of jobs due to deterioration. We also propose heuristics algorithms that rely on ant colony optimization and simulated annealing algorithms to solve the problem with multiple RMAs in a reasonable amount of time. Finally we show that ant colony optimization algorithm generates close optimal solutions and superior results than simulated annealing algorithm.İngilizceinfo:eu-repo/semantics/openAccessMatematik-Bilgisayar Bilimleri- Teori ve MetotlarBilgisayar Bilimleri, Teori Ve MetotlarMatematikIdentical parallel machine scheduling with nonlinear deterioration and multiple rate modifying activitiesArticle