On optimal replacement policy

Raimi Ajibola Kasumu; Antonín Lešanovský

Aplikace matematiky (1983)

  • Volume: 28, Issue: 5, page 317-329
  • ISSN: 0862-7940

Abstract

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A system with a single activated unit which can be in k + 1 states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time. It requests to investigate not more than log 2 k time-stationary replacement strategies.

How to cite

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Kasumu, Raimi Ajibola, and Lešanovský, Antonín. "On optimal replacement policy." Aplikace matematiky 28.5 (1983): 317-329. <http://eudml.org/doc/15311>.

@article{Kasumu1983,
abstract = {A system with a single activated unit which can be in $k+1$ states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time. It requests to investigate not more than $\text\{log\}_2$$k$ time-stationary replacement strategies.},
author = {Kasumu, Raimi Ajibola, Lešanovský, Antonín},
journal = {Aplikace matematiky},
keywords = {replacement strategy maximizing the average income; time-stationary replacement strategies; replacement strategy maximizing the average income; time-stationary replacement strategies},
language = {eng},
number = {5},
pages = {317-329},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On optimal replacement policy},
url = {http://eudml.org/doc/15311},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Kasumu, Raimi Ajibola
AU - Lešanovský, Antonín
TI - On optimal replacement policy
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 5
SP - 317
EP - 329
AB - A system with a single activated unit which can be in $k+1$ states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time. It requests to investigate not more than $\text{log}_2$$k$ time-stationary replacement strategies.
LA - eng
KW - replacement strategy maximizing the average income; time-stationary replacement strategies; replacement strategy maximizing the average income; time-stationary replacement strategies
UR - http://eudml.org/doc/15311
ER -

References

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  1. C. Derman, On optimal replacement rules when changes of state are markovian, in: Mathematical optimization techniques (R. Bellman ed.) Project Rand Report, April 1963. (1963) Zbl0173.46702
  2. C. Derman, Finite State Markovian Decision Processes, Mathematics in Science and Engineering, vol. 67, Academic Press, New York and London (1970). (1970) Zbl0262.90001MR0267686
  3. R. A. Kasumu, On optimal replacement policy, (1980) - unpublished. (1980) 
  4. P. Kolesar, 10.1287/mnsc.12.9.694, Manag. Sci., vol. 12, No. 9, May (1966), 694-706. (1966) Zbl0204.20002MR0195592DOI10.1287/mnsc.12.9.694
  5. A. Lešanovský, On dependences of the expected income of a system on its initial state, to appear in IEEE Transactions on Reliability. 
  6. A. Lešanovský, On optimal replacement policy II, to appear in Proceedings of the Third Pannonian Symposium on Mathematical Statistics, Visegrád (1982). (1982) MR0759011
  7. A. Lešanovský, Some remarks on the paper by P. Kolesar "Minimum cost replacement under markovian deterioration", to appear in Management Science. 
  8. A. Lešanovský, Comparison of two replacement policies, to appear in Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf (1983). (1983) MR0855381
  9. D. B. Rosenfield, Deteriorating Markov processes under uncertainty, Technical report No. 162, May (1974), Dept. of operations research and Dept. of statistics Stanford University, Stanford, California. (1974) 
  10. S. Ross, 10.1214/aoms/1177698041, Ann. Math. Stat. 39 (1968), 2118 to 2122. (1968) Zbl0179.24704MR0242313DOI10.1214/aoms/1177698041

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