Abstract
Operation scheduling for a class of production systems with “instantly consumed” products is very important. It is challenging to satisfy the real time system demand and to consider the realizability of the production schedules. This paper formulates a new model for optimization based production scheduling problems with integral constraints. Based on the detailed analysis of the production rate constraints, it is proved that this type of optimization problems is equivalent to a smooth nonlinear programming problem. The reachable upper and lower bounds of the production amount in every period can be expressed as functions of two variables, i.e., the production rate at the start and end of that period. It is also proved that the gradients of these functions are monotonic, and their convexity or concavity is guaranteed. When the production cost function is convex, this type of optimization problems is equivalent to a convex programming problem. With the above analysis, a two-stage solution method is developed to solve the production scheduling problems with integral constraints, and in many applications the global optimal solution can be obtained efficiently. With the new model and solution method, the difficulties caused by the constraints on production rate can be overcome and the optimal schedule can be obtained with the real time system demand satisfied. Numerical testing for scheduling of electric power production systems is performed and the testing results are discussed. It is demonstrated that the new model and solution method are effective.
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Talluri T T, Van Ryzin G J. The Theory and Practice of Revenue Management. Heidelberg: Springer, 2004
Bannister C H, Kaye R J. A Rapid method for optimization of linear systems with storage. Operations Research, 1991, 39.(2): 220–232
Chen H, Chu C, Proth J M. An improvement of the Lagrangian relaxation approach for Job Shop Scheduling: A dynamic programming method. IEEE Trans Rob Autom, 1998, 14(5): 786–795
Cohen A I, Sherkat V. Optimization-based methods for operations scheduling. Proc IEEE, 1987, 75(12): 1574–1591
Wang Z H, Chen H X, Hu B S. Scheduling for batch chemical processes using Lagrangian relaxation based approach (in Chinese). Acta Autom Sin, 1998, 24(1): 1–8
Muiser R F H, Evans L B. An approximated method for the production scheduling of industrial batch process with parallel units. Computers Chem Eng, 1989, 13(2): 229–238
Salam M S, Nor K M, Hamdan A R. Hydrothermal scheduling based Lagrangian relaxation approach to hydrothermal coordination. IEEE Trans Power Syst, 1998, 13(1): 226–235
Bard J F. Short-term scheduling of thermal-eglectric enerators using Lagrangian relaxation. Operations Res, 1988, 36(5): 756–766
Zhai Q Z, Guan X H, Guo Y, et al. A new mpethod for roduction scheduling with hybrid dynamic constraints (in Chinese). Acta Autom Sin, 2004, 30(4): 539–546
Sand G, Engell S. Modeling and solving real-time scheduling problems by stochastic integer programming. Comp Chem Eng, 2004, 28: 1087–1103
Guan X, Guo S, Zhai Q. The conditions for obtaining feasible solutions to security-constrained unit commitment problems. IEEE Trans Power Syst, 2005, 20(4): 1746–1756
Fu Y, Shahidehpour M. Fast SCUC for large-scale power systems. IEEE Trans Power Syst, 2007, 22(4): 2144–2151
Silva B, Stursberg O, Krogh B, et al. An assessment of the current status of algorithmic approaches to the verification of hybrid systems. Proceedings of IEEE Conference on Decision and Control, Orlando, Florida, 2001. 2867–2874
Till J, Engell S, Panek S, et al. Applied hybrid system optimization: An empirical investigation of complexity. Control Eng Practice, 2004, 12(10): 1291–1303
Ferreira L A F M, Anderson T, Imparato C F, et al. Short-term resource scheduling in multi-area hydrothermal power systems. Electric Power & Energy Systems, 1989, 11(3): 200–212
Guan X, Gao F, Svoboda A J. Energy delivery capacity and generation scheduling in the deregulated electric power Market. IEEE Trans Power Syst, 2000, 15(4): 1275–1280
Wang C, Shahidehpour S M. Optimal generation scheduling with ramping costs. IEEE Trans Power Syst, 1995, 10(1): 60–67
Yu Y X, Wang D T. Dynamic security risk assessment and optimization of power transmission system. Sci China Ser E-Tech Sci, 2008, 51(6): 713–723
Si B F, Long J C, Gao Z Y. Optimization model and algorithm for mixed traffic of urban road network with flow interference. Sci China Ser E-Tech Sci, 2008, 51(12): 2223–2232
Travers D, Kaye R J. Dynamic dispatch by constructive dynamic programming. IEEE Trans Power Syst, 1998, 13(1): 72–78
Han X S, Gooi H B, Kirschen D S. Dynamic economic dispatch: Feasible and optimal solutions. IEEE Trans Power Syst, 2001, 16(1): 22–28
Arroyo J M, Conejo A J. Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst, 2000, 15(3): 1098–1104
Shrestha G B, Song K, Goel L. Strategic self-dispatch considering ramping costs in deregulated power market. IEEE Trans Power Syst, 2004, 19(3): 1575–1581
Hiriart-Urruty J, Lemarechal C. Fundamentals of Convex Analysis. Heidelberg: Springer, 2001
Bazaraa M S, Sherali H D, Shetty C. M. Nonlinear Programming: Theory and Algorithms. 2nd ed. New York: John Wiely, 1993
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Supported in part by the National Natural Science Foundation of China (Grant Nos. 60736027, 60704033), the National High Technology Research and Development Program of China (863 Program) (Grant No. 2007AA04Z154), 111 International Collaboration Program of China and Program for New Century Talents of Education Ministry of China (Grant No. NCET-08-0432)
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Guan, X., Zhai, Q., Feng, Y. et al. Optimization based scheduling for a class of production systems with integral constraints. Sci. China Ser. E-Technol. Sci. 52, 3533–3544 (2009). https://doi.org/10.1007/s11431-009-0359-y
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DOI: https://doi.org/10.1007/s11431-009-0359-y