Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 325274, 9 pages
http://dx.doi.org/10.1155/2013/325274
Research Article

LQ Optimal Sliding Mode Control of Periodic Review Perishable Inventories with Transportation Losses

Institute of Automatic Control, Technical University of Lodz, 18/22 Bohdana Stefanowskiego Street, 90-924 Lodz, Poland

Received 30 July 2013; Accepted 16 September 2013

Academic Editor: Xudong Zhao

Copyright © 2013 Piotr Leśniewski and Andrzej Bartoszewicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. M. Beamon, “Supply chain design and analysis: models and methods,” International Journal of Production Economics, vol. 55, no. 3, pp. 281–294, 1998. View at Google Scholar · View at Scopus
  2. H. Sarimveis, P. Patrinos, C. D. Tarantilis, and C. T. Kiranoudis, “Dynamic modeling and control of supply chain systems: a review,” Computers and Operations Research, vol. 35, no. 11, pp. 3530–3561, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. C. E. Riddalls, S. Bennett, and N. S. Tipi, “Modelling the dynamics of supply chains,” International Journal of Systems Science, vol. 31, no. 8, pp. 969–976, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. I. Karaesmen, A. Scheller-Wolf, and B. Deniz, “Managing perishable and aging inventories: review and future research directions,” in Handbook of Production Planning, K. Kempf, P. Keskinocak, and R. Uzsoy, Eds., Kluwer, Dordrecht, The Netherlands, 2008. View at Google Scholar
  5. M. Boccadoro, F. Martinelli, and P. Valigi, “Supply chain management by H-infinity control,” IEEE Transactions on Automation Science and Engineering, vol. 5, no. 4, pp. 703–707, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. K. Hoberg, J. R. Bradley, and U. W. Thonemann, “Analyzing the effect of the inventory policy on order and inventory variability with linear control theory,” European Journal of Operational Research, vol. 176, no. 3, pp. 1620–1642, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Subramanian, Integration of control theory and scheduling methods for supply chain management [Ph.D. thesis], University of Wisconsin, Madison, Wis, USA, 2013.
  8. H. A. Simon, “On the application of servomechanism theory in the study of production control,” Econometrica, vol. 20, no. 2, pp. 247–268, 1952. View at Google Scholar
  9. H. J. Vassian, Application of Discrete Variable Servo Theory to Inventory Control, Arthur D. Little, Cambridge, Mass, USA, 1954.
  10. D. R. Towill, “Dynamic analysis of an inventory and order based production control system,” International Journal of Production Research, vol. 20, no. 6, pp. 671–687, 1982. View at Google Scholar · View at Scopus
  11. J. Forrester, “Industrial dynamics, a major breakthrough for decision makers,” Harvard Business Review, vol. 36, no. 4, pp. 37–66, 1958. View at Google Scholar
  12. J. Forrester, Industrial Dynamics, MIT Press, Cambridge, Mass, USA, 1961.
  13. J. Dejonckheere, S. M. Disney, M. R. Lambrecht, and D. R. Towill, “The impact of information enrichment on the Bullwhip effect in supply chains: a control engineering perspective,” European Journal of Operational Research, vol. 153, no. 3, pp. 727–750, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. S. M. Disney and D. R. Towill, “On the bullwhip and inventory variance produced by an ordering policy,” Omega, vol. 31, no. 3, pp. 157–167, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. S. M. Disney and D. R. Towill, “A methodology for benchmarking replenishment-induced bullwhip,” Supply Chain Management, vol. 11, no. 2, pp. 160–168, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. G. Gaalman and S. M. Disney, “State space investigation of the bullwhip problem with ARMA(1,1) demand processes,” International Journal of Production Economics, vol. 104, no. 2, pp. 327–339, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. C. S. Lalwani, S. M. Disney, and D. R. Towill, “Controllable, observable and stable state space representations of a generalized order-up-to policy,” International Journal of Production Economics, vol. 101, no. 1, pp. 172–184, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Potter, D. Towill, T. Böhme, and S. Disney, “The influence of multi-product production strategy on factory induced bullwhip,” International Journal of Production Research, vol. 47, no. 20, pp. 5739–5759, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Zhou, S. Disney, and D. R. Towill, “A pragmatic approach to the design of bullwhip controllers,” International Journal of Production Economics, vol. 128, no. 2, pp. 556–568, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. G. Gaalman, “Bullwhip reduction for ARMA demand: the proportional order-up-to policy versus the full-state-feedback policy,” Automatica, vol. 42, no. 8, pp. 1283–1290, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. E. Aggelogiannaki, P. Doganis, and H. Sarimveis, “An adaptive model predictive control configuration for production-inventory systems,” International Journal of Production Economics, vol. 114, no. 1, pp. 165–178, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. X. Li and T. E. Marlin, “Robust supply chain performance via Model Predictive Control,” Computers and Chemical Engineering, vol. 33, no. 12, pp. 2134–2143, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. W. Wang, D. E. Rivera, and K. G. Kempf, “Model predictive control strategies for supply chain management in semiconductor manufacturing,” International Journal of Production Economics, vol. 107, no. 1, pp. 56–77, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. M. W. Braun, D. E. Rivera, M. E. Flores, W. M. Carlyle, and K. G. Kempf, “A Model Predictive Control framework for robust management of multi-product, multi-echelon demand networks,” Annual Reviews in Control, vol. 27, pp. 229–245, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. E. K. Boukas, P. Shi, and R. K. Agarwal, “An application of robust control technique to manufacturing systems with uncertain processing time,” Optimal Control Applications and Methods, vol. 21, no. 6, pp. 257–268, 2000. View at Publisher · View at Google Scholar · View at Scopus
  26. E. Aggelogiannaki and H. Sarimveis, “Design of a novel adaptive inventory control system based on the online identification of lead time,” International Journal of Production Economics, vol. 114, no. 2, pp. 781–792, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. C. E. Riddalls and S. Bennett, “The stability of supply chains,” International Journal of Production Research, vol. 40, no. 2, pp. 459–475, 2002. View at Publisher · View at Google Scholar · View at Scopus
  28. R. Sipahi and I. I. Delice, “Stability of inventory dynamics in supply chains with three delays,” International Journal of Production Economics, vol. 123, no. 1, pp. 107–117, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. R. D. H. Warburton, S. M. Disney, D. R. Towill, and J. P. E. Hodgson, “Further insights into the stability of supply chains,” International Journal of Production Research, vol. 42, no. 3, pp. 639–648, 2004. View at Publisher · View at Google Scholar · View at Scopus
  30. I. Delice, Stability analysis of multiple time-delay systems with applications to supply chain management [Ph.D. thesis], Northeastern University, 2011.
  31. Y. Feng, S. Chen, A. Kumar, and B. Lin, “Solving single-product economic lot-sizing problem with non-increasing setup cost, constant capacity and convex inventory cost in O(N log N) time,” Computers and Operations Research, vol. 38, no. 4, pp. 717–722, 2011. View at Publisher · View at Google Scholar · View at Scopus
  32. S. H. R. Pasandideh, S. T. A. Niaki, and A. R. Nia, “A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model,” Expert Systems with Applications, vol. 38, no. 3, pp. 2708–2716, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. S.-C. Liu and J.-R. Chen, “A heuristic method for the inventory routing and pricing problem in a supply chain,” Expert Systems with Applications, vol. 38, no. 3, pp. 1447–1456, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. P. Köchel and U. Nieländer, “Simulation-based optimisation of multi-echelon inventory systems,” International Journal of Production Economics, vol. 93-94, pp. 505–513, 2005. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Tal and T. Arponen, “An EOQ model for items with a fixed shelf-life and a declining demand rate based on time-to-expiry technical note,” Asia-Pacific Journal of Operational Research, vol. 26, no. 6, pp. 759–767, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. P. Ignaciuk and A. Bartoszewicz, “Linear-quadratic optimal control strategy for periodic-review inventory systems,” Automatica, vol. 46, no. 12, pp. 1982–1993, 2010. View at Publisher · View at Google Scholar · View at Scopus
  37. P. Ignaciuk and A. Bartoszewicz, “LQ optimal sliding mode supply policy for periodic review inventory systems,” IEEE Transactions on Automatic Control, vol. 55, no. 1, pp. 269–274, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. P. Ignaciuk and A. Bartoszewicz, “Linear-quadratic optimal control of periodic-review perishable inventory systems,” IEEE Transactions on Control Systems Technology, vol. 20, no. 5, pp. 1400–1407, 2012. View at Google Scholar
  39. P. Ignaciuk and A. Bartoszewicz, “LQ optimal sliding-mode supply policy for periodic-review perishable inventory systems,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1561–1582, 2012. View at Publisher · View at Google Scholar · View at Scopus
  40. V. Utkin and S. V. Drakunow, “On discrete-time sliding mode control,” IFAC Conference on Nonlinear Control, pp. 484–489, 1989. View at Google Scholar
  41. K. Furuta, “Sliding mode control of a discrete system,” Systems and Control Letters, vol. 14, no. 2, pp. 145–152, 1990. View at Google Scholar · View at Scopus
  42. W. Gao, Y. Wang, and A. Homaifa, “Discrete-time variable structure control systems,” IEEE Transactions on Industrial Electronics, vol. 42, no. 2, pp. 117–122, 1995. View at Publisher · View at Google Scholar · View at Scopus
  43. A. Bartoszewicz, “Remarks on ‘Discrete-time variable structure control systems’,” IEEE Transactions on Industrial Electronics, vol. 43, no. 1, pp. 235–238, 1996. View at Google Scholar · View at Scopus
  44. G. Golo and C. Milosavljević, “Robust discrete-time chattering free sliding mode control,” Systems and Control Letters, vol. 41, no. 1, pp. 19–28, 2000. View at Google Scholar · View at Scopus
  45. B. Bandyopadhyay and S. Janardhanan, “Discrete-time sliding mode control: a multirate output feedback approach,” Lecture Notes in Control and Information Sciences, vol. 323, pp. 1–151, 2005. View at Google Scholar · View at Scopus
  46. C. Milosavljević, B. Peruničić-Draženović, B. Veselić, and D. Mitić, “Sampled data quasi-sliding mode control strategies,” IEEE International Conference on Industrial Technology, pp. 2640–2645, 2006. View at Google Scholar
  47. S. Janardhanan and B. Bandyopadhyay, “Multirate output feedback based robust quasi-sliding mode control of discrete-time systems,” IEEE Transactions on Automatic Control, vol. 52, no. 3, pp. 499–503, 2007. View at Publisher · View at Google Scholar · View at Scopus
  48. S. J. Mija and S. Thomas, “Reaching law based sliding mode control for discrete MIMO systems,” in Proceedings of the 11th International Conference on Control, Automation, Robotics and Vision (ICARCV '10), pp. 1291–1296, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  49. M. L. Corradini, V. Fossi, A. Giantomassi, G. Ippoliti, S. Longhi, and G. Orlando, “Discrete time sliding mode control of robotic manipulators: Development and experimental validation,” Control Engineering Practice, vol. 20, no. 20, pp. 816–822, 2012. View at Publisher · View at Google Scholar · View at Scopus
  50. X. Yu, B. Wang, and X. Li, “Computer-controlled variable structure systems: the state-of-the-art,” IEEE Transactions on Industrial Informatics, vol. 8, no. 2, pp. 197–205, 2012. View at Publisher · View at Google Scholar · View at Scopus
  51. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, Wiley-Interscience, New York, NY, USA, 1972.