Adaptive Control of a Production-Inventory Model with Uncertain Deterioration Rate
Fawzy Bukhari
DOI: 10.4236/am.2011.29162   PDF    HTML     4,850 Downloads   9,129 Views   Citations


This paper studied a continuous-time model of a production maintenance system in which a manufacturing firm produces a single product selling some and stocking the remaining. The problem of adaptive control of a production-maintenance system with unknown deterioration has been presented. Using Liapunov technique, the production rate and updating rule of deterioration rate are derived as non-linear functions of inventory level perturbation. Numerical analysis for the system has been presented for a set of parameter values and demand rate.

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Bukhari, F. (2011) Adaptive Control of a Production-Inventory Model with Uncertain Deterioration Rate. Applied Mathematics, 2, 1170-1174. doi: 10.4236/am.2011.29162.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Sethi and G. Thompson, “Optimal Control Theory: Applications to Management Science and Economics,” 2nd Edition, Kluwer Academic Publishers, Dordrecht, 2000.
[2] I. Dobos, “Optimal Production-Inventory Strategies for a HMMS-type Reverse Logistics System,” International Journal of Production Economics, Vol. 81-82, 2003, pp. 351-360. doi:10.1016/S0925-5273(02)00277-3
[3] S. Nahmias, “Perishable Inventory Theory: A Review,” Operations Research, Vol. 30, No. 3, 1982, pp. 680-708. doi:10.1287/opre.30.4.680
[4] B. Porter and F. Taylor, “Modal Control of Production-Inventory Systems,” International Journal of Systems Science, Vol. 3, No. 3, 1972, pp. 325-331. doi:10.1080/00207727208920270
[5] F. Raafat, “Survey of Literature on Continuously Deteriorating Inventory Models,” Journal of the Operational Research Society, Vol. 42, 1991, pp. 27-37. doi:10.2307/2582993
[6] E. Khemlnitsky and Y. Gerchak, “Optimal Control Approach to Production Systems with Inventory Level Dependent Demand,” IIE Transactions on Automatic Control, Vol. 47, No. 3, 2002, pp. 289-292. doi:10.1109/9.983360
[7] W. Caldwell, “Control System with Automatic Response Adjustment,” US Patent No. 2,517,081., Filed 25, 1950.
[8] J. Aseltine, A. R. Mancini and C. W. Sartune, “A Survey of Adaptive Control Systems,” IRE Transactions on Automatic Control, Vol. 3, No. 6, 1958, pp. 102-108. doi:10.1109/TAC.1958.1105168
[9] I. D. Landau, “Adaptive Control: The Model Reference Approach,” Marcel Dekker, New York, 1979.
[10] K. S. Narendra and A. M. Annaswamy, “Stable Adaptive Systems,” Prentice-Hall, Englewood Cliffs, 1989.
[11] A. El-Gohary and A. Al-Ruzaiza, “Chaos and Adaptive Control in Two Prey, One Predator System with Nonlinear Feedback,” Chaos, Solitons and Fractals, Vol. 34, 2007, pp. 443-453. doi:10.1016/j.chaos.2006.03.101
[12] A. El-Gohary and R. Yassen, “Adaptive Control and Synchronization of a Coupled Dynamo System with Uncertain Parameters,” Chaos, Solitons and Fractals, Vol. 29, 2006, pp. 1085-1094.doi:10.1016/j.chaos.2005.08.215
[13] L. Tadj, A. Sarhan and A. El-Gohary, “Optimal Control of an Inventory System with Ameliorating and Deteriorating Items,” Journal of Applied Sciences, Vol. 10, 2008, pp. 243-255.
[14] A. Foul, L. Tadj and R. Hedjar, “Adaptive Control of Inventory Systems with Unknown Deterioration Rate,” Journal of King Saud University-Science, In Press, 2011, doi:10.1016/j.jksus.2011.02.001

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