Abstract
We review the results on scheduling with due date assignment under such conditions on job processing as given precedence constraints, maintenance activity or various scenarios of processing time changing. The due date assignment and scheduling problems arise in production planning when the management is faced with setting realistic due dates for a number of jobs. Most research on scheduling with due date assignment is focused on optimal sequencing of independent jobs. However, it is often found in practice that some products are manufactured in a certain order implied, for example, by technological, marketing or assembly requirements and this can be modeled by imposing precedence constraints on the set of jobs. In classical deterministic scheduling models, the processing conditions, including job processing times, are usually viewed as given constants. In many real-life situations, however, the processing conditions may vary over time, thereby affecting actual durations of jobs. In the models with controllable processing times, the scheduler can speed up job execution times by allocating some additional resources to the jobs. In the models with deterioration or learning, the actual processing time can depend either on the position or on the start time of a job in the schedule. In scheduling with deterioration, the later a job starts, the longer it takes to process, while in scheduling with learning, the actual processing time of a job gets shorter, provided that the job is scheduled later. We consider also scheduling models with optional maintenance activity. In manufacturing processing, production scheduling with preventive maintenance planning is one of the most significant methods in preventing the machinery from failure or wear.
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References
Alidaee, B., & Ahmadian, A. (1993). Two parallel machines sequencing problems involving controllable job processing times. European Journal of Operational Research, 70, 335–341.
Alidaee, B., & Womer, N. K. (1999). Scheduling with time dependent processing times: Review and extensions. The Journal of the Operational Research Society, 50, 711–720.
Baker, K. R., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1983). Preemptive scheduling of a single machine to minimize maximum cost subject to release dates and precedence constraints. Operations Research, 31, 381–386.
Birman, M., & Mosheiov, G. (2004). A note on a due-date assignment on a two-machine flow-shop. Computers & Operations Research, 31, 473–480.
Biskup, D. (1999). Single-machine scheduling with learning considerations. European Journal of Operational Research, 115, 173–178.
Biskup, D. (2008). A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188, 315–329.
Biskup, D., & Cheng, T. C. E. (1999). Single-machine scheduling with controllable processing times and earliness, tardiness and completion time penalties. Engineering Optimization, 31, 329–336.
Biskup, D., & Jahnke, H. (2001). Common due date assignment for scheduling on a single machine with jointly reducible processing times. International Journal of Production Economics, 69, 317–322.
Blazewicz, J., Brauner, N., & Finke, G. (2004). Scheduling with discrete resource constraints. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 23-1–23-18). Boca Raton: CRC Press.
Browne, S., & Yechiali, U. (1990). Scheduling deteriorating jobs on a single processor. Operations Research, 38, 495–498.
Cheng, T. C. E. (1989). Optimal assignment of slack due dates and sequencing in a single-machine shop. Applied Mathematics Letters, 2, 333–335.
Cheng, T. C. E., & Gordon, V. S. (1994). Optimal assignment of due-dates for preemptive single-machine scheduling. Mathematical and Computer Modelling, 20, 33–40.
Cheng, T. C. E., Oguz, C., & Qi, X. D. (1996). Due-date assignment and single machine scheduling with compressible processing times. International Journal of Production Economics, 43, 29–35.
Cheng, T. C. E., Ding, Q., & Lin, B. M. T. (2004a). A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research, 152, 1–13.
Cheng, T. C. E., Kang, L., & Ng, C. T. (2004b). Due-date assignment and single machine scheduling with deteriorating jobs. The Journal of the Operational Research Society, 55, 198–203.
Cheng, T. C. E., Kovalyov, M. Y., & Shakhlevich, N. (2006). Scheduling with controllable release dates and processing times: total completion time minimization. European Journal of Operational Research, 175, 769–781.
Cheng, T. C. E., Kang, L., & Ng, C. T. (2007). Due-date assignment and parallel-machine scheduling with deteriorating jobs. The Journal of the Operational Research Society, 58, 1103–1108.
Gordon, V. S. (1993). A note on optimal assignment of slack due-dates in single-machine scheduling. European Journal of Operational Research, 70, 311–315.
Gordon, V. S., & Strusevich, V. A. (1999). Earliness penalties on a single machine subject to precedence constraints: SLK due date assignment. Computers & Operations Research, 26, 157–177.
Gordon, V. S., & Strusevich, V. A. (2009). Single machine scheduling and due date assignment with positionally dependent processing times. European Journal of Operational Research, 198, 57–62.
Gordon, V. S., & Tanaev, V. S. (1983). On minmax single machine scheduling problems. Izvestiya Akademii Nauk BSSR,Seryâ Fizika-Matematyčnyh Nauk, 3, 3–9. (In Russian) (Transactions of the Academy of Sciences of BSSR, Ser. Phys.-Math. Sci.).
Gordon, V. S., & Tarasevich, A. A. (2009). A note: Common due date assignment for a single machine scheduling with the rate-modifying activity. Computers and Operations Research, 36, 325–328.
Gordon, V., Proth, J. M., & Chu, C. (2002a). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research, 139, 1–25.
Gordon, V., Proth, J. M., & Chu, C. (2002b). Due date assignment and scheduling: SLK, TWK and other due date assignment models. Production Planning and Control, 13, 117–132.
Gordon, V. S., Proth, J.-M., & Strusevich, V. A. (2004). Scheduling with due date assignment. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 21-1–21-22). Boca Raton: CRC Press.
Gordon, V. S., Proth, J.-M., & Strusevich, V. A. (2005). Single machine scheduling and due date assignment under series-parallel precedence constraints. Central European Journal of Operations Research, 13, 15–35.
Gordon, V. S., Potts, C. N., Strusevich, V. A., & Whitehead, J. D. (2008). Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation. Journal of Scheduling, 11, 357–370.
Hall, N. G. (1986). Scheduling problems with generalized due dates. IIE Transactions, 18, 220–222.
Hall, N. G., Sethi, S. P., & Sriskandarajah, C. (1991). On the complexity of generalized due date scheduling problems. European Journal of Operational Research, 51, 100–109.
Janiak, A. (1987). One-machine scheduling with allocating of continuously-divisible resource and with no precedence constraints. Kybernetika, 23(4), 289–293.
Janiak, A., & Kovalyov, M. Y. (1996). Single machine scheduling subject to deadlines and resource dependent processing times. European Journal of Operational Research, 94, 284–291.
Jozefowska, J., & Weglarz, J. (2004). Scheduling with resource constraints – continuous resources. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 24-1–24-15). Boca Raton: CRC Press.
Kaminsky, P., & Hochbaum, D. (2004). Due-date quotation models and algorithms. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 20-1–20-22). Boca Raton: CRC Press.
Kubzin, M. A., & Strusevich, V. A. (2006). Planning machine maintenance in two-machine job scheduling. Operations Research, 54, 789–800.
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (1993). Sequencing and scheduling: algorithms and complexity. In S. C. Graves, A. H. G. Rinnooy Kan, & P. H. Zipkin (Eds.), Logistics of production and inventory: Vol. 4. Handbooks in operations research and management science (pp. 445–522). Amsterdam: North-Holland.
Lee, C.-Y. (2004). Machine scheduling with availability constraints. In J. Y.-T. Leung (Ed.), Handbook of scheduling: algorithms, models and performance analysis (pp. 22-1–20-13). Boca Raton: CRC Press.
Lee, C.-Y., & Chen, Z.-L. (2000). Scheduling jobs and maintenance activities on parallel machines. Naval Research Logistics, 47, 145–165.
Lee, C.-Y., & Leon, V.-J. (2001). Machine scheduling with a rate modifying activity. European Journal of Operational Research, 128, 119–128.
Lee, C.-Y., Lei, L., & Pinedo, M. (1997). Current trends in deterministic scheduling. Annals of Operation Research, 70, 1–41.
Leyvand, Y., Shabtay, D., & Steiner, G. (2010). Optimal delivery time quotation to minimize total tardiness penalties with controllable processing times. IIE Transactions, 42, 221–231.
Liman, S. D., Panwalkar, S. S., & Thongmee, S. (1997). A single machine scheduling problem with common due window and controllable processing times. Annals of Operation Research, 70, 145–154.
Liman, S. D., Panwalkar, S. S., & Thongmee, S. (1998). Common due window size and location determination in a single machine scheduling problem. The Journal of the Operational Research Society, 49, 1007–1010.
Ma, Y., Chu, C., & Zuo, C. (2010). A survey of scheduling with deterministic machine availability constraints. Computers & Industrial Engineering, 58, 199–211.
Min, L., & Cheng, W. (2006). Genetic algorithms for the optimal common due date assignment and the optimal scheduling policy in parallel machine earliness/tardiness scheduling problems. Robotics and Computer-Integrated Manufacturing, 22, 279–287.
Monma, C. L., & Sidney, J. B. (1987). Optimal sequencing via modular decomposition: characterization of sequencing functions. Mathematics of Operations Research, 12, 22–31.
Monma, C. L., Schrijver, A., Todd, M. J., & Wei, V. K. (1990). Convex resource allocation problems on directed acyclic graphs: duality, complexity, special cases and extensions. Mathematics of Operations Research, 15, 736–748.
Mosheiov, G. (2001). Scheduling problems with a learning effect. European Journal of Operational Research, 132, 687–693.
Mosheiov, G., & Oron, D. (2006). Due-date assignment and maintenance activity scheduling problem. Mathematical and Computer Modelling, 44, 1053–1057.
Mosheiov, G., & Sarig, A. (2008). A due-window assignment problem with position-dependent processing times. The Journal of the Operational Research Society, 59, 997–1003.
Mosheiov, G., & Sarig, A. (2009). Scheduling a maintenance activity and due-window assignment on a single machine. Computers and Operations Research, 36, 2541–2545.
Mosheiov, G., & Sidney, J. B. (2003). Scheduling with general job-dependent learning curves. European Journal of Operational Research, 147, 665–670.
Mosheiov, G., & Sidney, J. B. (2009). Scheduling a deteriorating maintenance activity on a single machine. The Journal of the Operational Research Society, 60, 1–6.
Mosheiov, G., & Yovel, U. (2006). Minimizing weighted earliness-tardiness and due-date cost with unit processing-time jobs. European Journal of Operational Research, 172, 528–544.
Muller, J. H., & Spinrad, J. (1989). Incremental modular decomposition: Polynomial algorithms. Journal of the Association for Computing Machinery, 36, 1–19.
Ng, C. T. D., Cheng, T. C. E., Kovalyov, M. Y., & Lam, S. S. (2003). Single machine scheduling with a variable common due date and resource-dependent processing times. Computers and Operations Research, 30, 1173–1185.
Nowicki, E., & Zdrzałka, S. (1990). A survey of results for sequencing problems with controllable processing times. Discrete Applied Mathematics, 26, 271–287.
Panwalkar, S. S., & Rajagopalan, R. (1992). Single-machine sequencing with controllable processing times. European Journal of Operational Research, 59, 298–302.
Panwalkar, S. S., Smith, M. L., & Seidmann, A. (1982). Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research, 30, 391–399.
Schmidt, G. (2000). Scheduling with limited machine availability. European Journal of Operational Research, 121, 1–15.
Shabtay, D., & Steiner, G. (2006). Two due date assignment problems in scheduling a single machine. Operations Research Letters, 34, 683–691.
Shabtay, D., & Steiner, G. (2007a). Optimal due date assignment and resource allocation to minimize the weighted number of tardy jobs on a single machine. Manufacturing & Service Operations Management, 9, 332–350.
Shabtay, D., & Steiner, G. (2007b). A survey of scheduling with controllable processing times. Discrete Applied Mathematics, 155(13), 1643–1666.
Shabtay, D., & Steiner, G. (2008a). The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times. Annals of Operation Research, 159, 25–40.
Shabtay, D., & Steiner, G. (2008b). Optimal due date assignment in multi-machine scheduling environments. Journal of Scheduling, 11, 217–228.
Shakhlevich, N. V., & Strusevich, V. A. (2005). Preemptive scheduling problems with controllable processing times. Journal of Scheduling, 8, 233–253.
Shakhlevich, N. V., & Strusevich, V. A. (2006). Single machine scheduling with controllable release and processing times. Discrete Applied Mathematics, 154, 2178–2199.
Sidney, J. B., & Steiner, G. (1986). Optimal sequencing by modular decomposition: Polynomial algorithms. Operations Research, 34, 606–612.
Vickson, R. G. (1980). Two single machine sequencing problems involving controllable job processing times. AIIE Transactions, 12(3), 258–262.
Yang, S.-J., Yang, D.-L., & Cheng, T. C. E. (2010). Single-machine due-window assignment and scheduling with job-dependent aging effects and deteriorating maintenance. Computers and Operations Research, 37, 1510–1514.
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Valery Gordon passed away in June 2010.
The shorten variant of the paper was presented at the 13th IFAC Symposium on Information Control Problems in Manufacturing, Moscow, Russia, June 3–5, 2009.
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Gordon, V., Strusevich, V. & Dolgui, A. Scheduling with due date assignment under special conditions on job processing. J Sched 15, 447–456 (2012). https://doi.org/10.1007/s10951-011-0240-2
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DOI: https://doi.org/10.1007/s10951-011-0240-2