Advertisement

Journal of Scheduling

, Volume 15, Issue 2, pp 201–216 | Cite as

Dynamic supply chain scheduling

  • D. IvanovEmail author
  • B. Sokolov
Article

Abstract

Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of dynamics, uncertainty, and adaptivity. Both supply chain schedule generation and execution control are represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. Hence, the problems and models of planning, scheduling, and adaptation can be consistently integrated on a unified mathematical axiomatic of modern control theory. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes. The application of optimal control for supply chain scheduling becomes possible by formulating the scheduling model as a linear non-stationary finite-dimensional controlled differential system with the convex area of admissible control and a reconfigurable structure. For this model class, theorems of optimal control existence can be used regarding supply chain scheduling. The essential structural property of this model are the linear right parts of differential equations. This allows applying methods of discrete optimization for optimal control calculation. The calculation procedure is based on applying Pontryagin’s maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. The gained insights contribute to supply chain scheduling theory, providing advanced insights into dynamics of the whole supply chains (and not any dyadic relations in them) and transition from a partial “one-way” schedule optimization to the feedback loop-based dynamic and adaptive supply chain planning and scheduling.

Keywords

Supply chain Scheduling Dynamics Adaptation Optimal program control Maximum principle Operations research Mathematical programming 

Abbreviations

SC

Supply Chain

OPC

Optimal Program Control

OR

Operations Research

MP

Mathematical Programming

CT

Control Theory

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agnetis, A., Hall, N. G., & Pacciarelli, D. (2006). Supply chain scheduling: Sequence coordination. Discrete Applied Mathematics, 154, 2044–2063. CrossRefGoogle Scholar
  2. Aytug, H., Lawley, M. A., McKay, K., Mohan, S., & Uzsoy, R. (2005). Executing production schedules in the face of uncertainties: a review and some future directions. European Journal of Operational Research, 161(1), 86–100. CrossRefGoogle Scholar
  3. Bryson, A. E., & Ho, Y.-C. (1975). Applied optimal control. Washington: Hemisphere. Google Scholar
  4. Chandra, C., & Grabis, J. (2007). Supply chain configuration. New York: Springer. Google Scholar
  5. Chauhan, S. S., Gordon, V., & Proth, J.-M. (2007). Scheduling in supply chain environment. European Journal of Operational Research, 183(3), 961–970. CrossRefGoogle Scholar
  6. Chen, Z. L., & Pundoor, G. (2006). Order assignment and scheduling in a supply chain. Operations Research, 54(3), 555–572. CrossRefGoogle Scholar
  7. Chernousko, F. L., & Zak, V. L. (1985). On differential games of evasion from many pursuers. Journal of Optimal Theory Applications, 46(4), 461–470. CrossRefGoogle Scholar
  8. Daganzo, C. F. (2004). On the stability of supply chains. Operations Research, 52(6), 909–921. CrossRefGoogle Scholar
  9. Disney, S. M., Towill, D. R., & Warburton, R. D. H. (2006). On the equivalence of control theoretic, differential, and difference equation approaches to modeling supply chains. International Journal of Production Economics, 101, 194–208. CrossRefGoogle Scholar
  10. Dolgui, A., & Proth, J. M. (2010). Supply chains engineering: useful methods and techniques. Berlin: Springer. Google Scholar
  11. Dorfman, R. (1969). An economic interpretation of optimal control theory. American Economic Review, 59, 817–831. Google Scholar
  12. Fang, J., & Xi, Y. (1997). A rolling horizon job shop rescheduling strategy in the dynamic environment. The International Journal of Advanced Manufacturing Technology, 13, 227–232. CrossRefGoogle Scholar
  13. Feichtinger, G., & Hartl, R. (1985). Optimal pricing and production in an inventory model. European Journal of Operational Research, 19, 45–56. CrossRefGoogle Scholar
  14. Fleming, W. H., & Rishel, R. W. (1975). Deterministic and stochastic optimal control. Berlin: Springer. Google Scholar
  15. Gaimon, C. (1988). Simultaneous and dynamic price, production, inventory and capacity decisions. European Journal of Operational Research, 35, 426–441. CrossRefGoogle Scholar
  16. Gershwin, S. B. (1994). Manufacturing systems engineering. Englewood Cliffs: PTR Prentice-Hall. Google Scholar
  17. Gubarev, V. A., Zakharov, V. V., & Kovalenko, A. N. (1988). Introduction to systems analysis. Leningrad: LGU. Google Scholar
  18. Hwang, C. L., Fan, L. T., Tillman, F. A., & Sharma, R. (1969). Optimal production planning and inventory control. International Journal of Production Research, 8(1), 75–83. CrossRefGoogle Scholar
  19. Ivanov, D. (2009). DIMA—a research methodology for comprehensive multi-disciplinary modelling of production and logistics networks. International Journal of Production Research, 47(5), 1133–1155. CrossRefGoogle Scholar
  20. Ivanov, D. (2010). Adaptive aligning of planning decisions on supply chain strategy, design, tactics, and operations. International Journal of Production Research, 48(13), 3999–4017. CrossRefGoogle Scholar
  21. Ivanov, D., & Sokolov, B. (2010). Adaptive supply chain management. Berlin: Springer. CrossRefGoogle Scholar
  22. Ivanov, D., Arkhipov, A., & Sokolov, B. (2007). Intelligent planning and control of manufacturing supply chains in virtual enterprises. International Journal of Manufacturing Technology and Management, 11(2), 209–227. CrossRefGoogle Scholar
  23. Ivanov, D., Sokolov, B., & Kaeschel, J. (2010). A multi-structural framework for adaptive supply chain planning and operations with structure dynamics considerations. European Journal of Operational Research, 200(2), 409–420. CrossRefGoogle Scholar
  24. Kalinin, V. N., & Sokolov, B. V. (1985). Optimal planning of the process of interaction of moving operating objects. International Journal of Difference Equations, 21(5), 502–506. Google Scholar
  25. Kalinin, V. N., & Sokolov, B. V. (1987). A dynamic model and an optimal scheduling algorithm for activities with bans of interrupts. Automation and Remote Control, 48(1–2), 88–94. Google Scholar
  26. Khmelnitsky, E., Kogan, K., & Maimom, O. (1997). Maximum principle-based methods for production scheduling with partially sequence-dependent setups. International Journal of Production Research, 35(10), 2701–2712. CrossRefGoogle Scholar
  27. Kimemia, J. G., & Gershwin, T. I. (1983). An algorithm for the computer control of a flexible manufacturing system. IIE Transactions, 15, 353–362. CrossRefGoogle Scholar
  28. Kogan, K., & Khmelnitsky, E. (2000). Scheduling: control-based theory and polynomial-time algorithms. Dordrecht: Kluwer Academic. Google Scholar
  29. Kreipl, S., & Pinedo, M. (2004). Planning and scheduling in supply chains: an overview of issues in practice. Production and Operations Management, 13(1), 77–92. CrossRefGoogle Scholar
  30. Kuehnle, H. (2008). A system of models contribution to production network (PN) theory. Journal of Intelligent Manufacturing, 18(5), 543–551. CrossRefGoogle Scholar
  31. Lalwani, C. S., Disney, S., & Towill, D. R. (2006). Controllable, observable and stable state space representations of a generalized order-up-to policy. International Journal of Production Economics, 101, 172–184. CrossRefGoogle Scholar
  32. Lee, E. B., & Markus, L. (1967). Foundations of optimal control theory. New York: Wiley. Google Scholar
  33. Lloret, J., Garcia-Sabater, J. P., & Marin-Garcia, J. A. (2009). Cooperative supply chain re-scheduling: the case of an engine supply chain. In Cooperative design, visualization, and engineering (pp. 376–383). Berlin/Heidelberg: Springer. CrossRefGoogle Scholar
  34. Mulani, N. P., & Lee, H. L. (2002). New business models for supply chain excellence. In N. Mulani (Ed.), Achieving supply chain excellence through technology. (Vol. 4). San Francisco: Montgomery Research. Google Scholar
  35. Moiseev, N. N. (1974). Element of the optimal systems theory. Moscow: Nauka (in Russian). Google Scholar
  36. Moon, C., Lee, Y. H., Jeong, C. S., & Yun, Y. S. (2008). Integrated process planning and scheduling in a supply chain. Computers & Industrial Engineering, 54(4), 1048–1061. CrossRefGoogle Scholar
  37. Okhtilev, M., Sokolov, B., & Yusupov, R. (2006). Intelligent technologies of complex systems monitoring and structure dynamics control. Moscow: Nauka (in Russian). Google Scholar
  38. Pinedo, M. (2008). Scheduling: theory, algorithms, and systems. New York: Springer. Google Scholar
  39. Pfund, M. E., Balasubramanian, H., Fowler, J. W., Mason, J. S., & Rose, O. (2008). A multi-criteria approach for scheduling semiconductor wafer fabrication facilities. Journal of Scheduling, 11(1), 29–47. CrossRefGoogle Scholar
  40. Poirier, C. C. (2003). Using models to improve the supply chain. London: Routledge. CrossRefGoogle Scholar
  41. Pontryagin, L. S., Boltyanskiy, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1964). The mathematical theory of optimal processes. Pergamon Press: Oxford. Google Scholar
  42. Pontryagin, L. S., Boltyanskiy, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1983). The mathematical theory of optimal processes. Moscow: Nauka (in Russian). Google Scholar
  43. Potts, C. N., & Whitehead, J. D. (2007). Heuristics for a coupled-operation scheduling problem. Journal of the Operational Research Society, 58, 1375–1388. CrossRefGoogle Scholar
  44. Proth, J. M. (2006). Scheduling: new trends in industrial environment. In A. Dolgui et al. (Eds.), Information control problems in manufacturing (pp. 41–47). Amsterdam: Elsevier. CrossRefGoogle Scholar
  45. Puigjaner, L., & Lainez, J. M. (2008). Capturing dynamics in integrated supply chain management. Computers and Chemical Engineering, 32, 2582–2605. CrossRefGoogle Scholar
  46. Sarker, R., Bhaba, R., & Diponegoro, A. (2009). Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers. European Journal of Operation Research, 194(3), 753–773. CrossRefGoogle Scholar
  47. Sethi, S. P., & Thompson, G. L. (2006). Optimal control theory: applications to management science and economics (2nd ed.). Berlin: Springer. Google Scholar
  48. Shao, X., Li, X., Gao, L., & Zhang, C. (2009). Integration of process planning and scheduling. A modified genetic algorithm-based approach. Computers in Industry, 36(6), 2082–2096. Google Scholar
  49. Simchi-Levi, D., Wu, S. D., & Zuo-Yun, S. (2004). Handbook of quantitative supply chain analysis. New York: Springer. Google Scholar
  50. Skurikhin, V. I., Zabrodsky, V. A., & Kopeychenko, Y. V. (1989). Adaptive control systems in machinery industry. Moscow: Mashinostroenie (in Russian). Google Scholar
  51. Sokolov, B., & Yusupov, R. (2004). Conceptual foundations of quality estimation and analysis for models and multi-model systems. Journal of Computer and Systems Science International, 6, 5–16. Google Scholar
  52. Son, Y.-J., & Venkateswaran, J. (2007). Hierarchical supply chain planning architecture for integrated analysis of stability and performance. International Journal of Simulation and Process Modelling, 3(3), 153–169. CrossRefGoogle Scholar
  53. Tabak, D., & Kuo, B. C. (1971). Optimal control by mathematical programming. New York: Prentice Hall. Google Scholar
  54. Van de Vonder, S., Demeulemeester, E., & Herroelen, W. (2007). A classification of predictive-reactive project scheduling procedures. Journal of Scheduling, 10(3), 195–207. CrossRefGoogle Scholar
  55. Van Houtum, G. Y., Scheller-Wolf, A., & Yi, Y. (2007). Optimal control of serial inventory systems with fixed replenishment intervals. Operations Research, 55(4), 674–687. CrossRefGoogle Scholar
  56. Vieira, G. E., Herrmann, J. W., & Lin, E. (2003). Rescheduling manufacturing systems: a framework of strategies, policies, and methods. Journal of Scheduling, 6(1), 35–58. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Faculty of Economics and Business Administration, Department of Production Economics and Industrial OrganizationChemnitz University of TechnologyChemnitzGermany
  2. 2.Saint Petersburg Institute for Informatics and Automation of the Russian Academy of ScienceSaint-PetersburgRussia

Personalised recommendations