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Transient behavior of large Markovian multiechelon repairable item inventory systems using a truncated state space approach. (English) Zbl 0617.90018

The authors discuss the transient behavior of repairable item systems. They use a randomisation algorithm of Markov processes and truncate the state-space for computational purposes.
Reviewer: H.Neffke

MSC:

90B05 Inventory, storage, reservoirs
60J25 Continuous-time Markov processes on general state spaces
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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[1] Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, NJ, 1975. · Zbl 0341.60019
[2] Grassmann, Computers and Operations Research 4 pp 47– (1977)
[3] personal communication, 1984.
[4] Gross, Operations Research 32 pp 343– (1984)
[5] Gross, Naval Research Logistics Quarterly 31 pp 347– (1984)
[6] , and , ”Simulation Methodologies for Transient Markov Processes: A Comparative Study Based on Multi-echelon Repairable Item Inventory Systems,” Proceedings of the 1984 Summer Computer Simulation Conference, Ed., The Society for Computer Simulation, La Jolla, California, 1984. pp. 37–43.
[7] and , Stochastic Models in Operations Research, Volume 1. McGraw-Hill, New York, 1982.
[8] , ”Models and Techniques for Recoverable Item Stockage When Demand and the Repair Process are Nonstationary–Part I: Performance Measurement,” Rand Report No. N-1482-AF, Santa Monica, CA, 1980.
[9] ”Dyna-METRIC: Dynamic Multi-Echelon Technique for Recoverable Item Control,” Rand Report No. WD-911-AF, Santa Monica, CA, 1981.
[10] Markov Chain Models–Rarity and Exponentiality, Springer Verlag, New York, 1979. · Zbl 0411.60068 · doi:10.1007/978-1-4612-6200-8
[11] and , ”Randomization Procedures in the Computation of Cumulative Time Distributions over Discrete State Markov Processes,” Bell Laboratories Report, Holmdel, NJ, 1980.
[12] ”Reliability Calculation Using Randomization for Markovian Fault-Tolerant Computing Systems,” 13th Annual International Symposium on Fault-Tolerant Computing, Digest of Papers, IEEE Computer Society Press, Washington, DC, 1983, pp. 284–289.
[13] Muckstadt, Management Science 20 pp 472– (1973)
[14] Introduction to Probability Models, 2nd ed. Academic, New York, 1980.
[15] Sherbrooke, Operations Research 16 pp 122– (1968)
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