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Optimal allocation of unreliable components for maximizing expected profit over time

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  • Claude G. Henin

Abstract

In the present paper, we solve the following problem: Determine the optimum redundancy level to maximize the expected profit of a system bringing constant returns over a time period T; i. e., maximize the expression \documentclass{article}\pagestyle{empty}\begin{document}$ P\int_0^T {Rdt - C} $\end{document}, where P is the return of the system per unit of time, R the reliability of this system, C its cost, and T the period for which the system is supposed to work We present theoretical results so as to permit the application of a branch and bound algorithm to solve the problem. We also define the notion of consistency, thereby determining the distinction of two cases and the simplification of the algorithm for one of them.

Suggested Citation

  • Claude G. Henin, 1973. "Optimal allocation of unreliable components for maximizing expected profit over time," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(3), pages 395-403, September.
    • Handle: RePEc:wly:navlog:v:20:y:1973:i:3:p:395-403
    DOI: 10.1002/nav.3800200304
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    Cited by:

    1. Prigogine, Ilya & Petrosky, Tomio Y., 1988. "An alternative to quantum theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(3), pages 461-486.
    2. Petrosky, T. & Prigogine, I., 1991. "Alternative formulation of classical and quantum dynamics for non-integrable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 146-209.
    3. Armentia, M.Díaz & Veguillas, J. & Palomares, F., 1984. "On generalized Waldmann-Snider equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 447-466.
    4. Antoniou, Ioannis E. & Prigogine, Ilya, 1993. "Intrinsic irreversibility and integrability of dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 192(3), pages 443-464.
    5. Veguillas, J. & Díaz, M.A. & Palomares, F., 1984. "On generalized Waldmann-Snider equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 463-480.
    6. Henin, F. & Mayné, F., 1981. "Physical description of decay processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(2), pages 281-304.
    7. Škarka, V. & George, C., 1984. "A generalization of the van Kampen-Case treatment of the Vlasov equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(3), pages 473-489.
    8. Antoniou, I. & Suchanecki, Z. & Laura, R. & Tasaki, S., 1997. "Intrinsic irreversibility of quantum systems with diagonal singularity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 737-772.

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