Generalized spare ordering policies with allowable inventory time

In this paper, a generalized ordering policy of a one-unit system with age-dependent minimal repair and random lead time is considered. We treat the general order-replacement model with two decision variables: ordering time and allowable inventory time. The allowable inventory period is measured from the time instant that the ordered spare is delivered. By introducing costs due to ordering, repairs, shortage, and holding, we derive the expected cost per unit time in the long run as a criterion of optimality, and seek the optimum policy by minimizing that cost. And we can prove under some mild conditions that there exists a finite and unique optimum policy. Various special cases are discussed.

[1]  Shunji Osaki,et al.  Ordering policies with two types of lead times , 1977 .

[2]  Toshio Nakagawa.  A SUMMARY OF PERIODIC REPLACEMENT WITH MINIMAL REPAIR AT FAILURE , 1981 .

[3]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[4]  Shigeru Yamada,et al.  A Summary of Optimal Ordering Policies , 1981, IEEE Transactions on Reliability.

[5]  Richard M. Simon,et al.  Technical Note - Comments on a Paper by S. G. Allen and D. A. D'Esopo: "An Ordering Policy for Repairable Stock Items" , 1971, Oper. Res..

[6]  Suunji Osaki.  An ordering policy with lead time , 1977 .

[7]  Philip J. Boland.  Periodic replacement when minimal repair costs vary with time , 1982 .

[8]  Frank Proschan,et al.  Periodic Replacement with Increasing Minimal Repair Costs at Failure , 1982, Oper. Res..

[9]  Charles H. Falkner.  Jointly Optimal Deterministic Inventory and Replacement Policies , 1970 .

[10]  R. Barlow,et al.  Optimum Preventive Maintenance Policies , 1960 .

[11]  Alvin D. Wiggins.  A Minimum Cost Model of Spare Parts Inventory Control , 1967 .

[12]  Shey-Huei Sheu.  A general ordering policy with number‐dependentminimal repair and random lead time , 1999, Ann. Oper. Res..

[13]  C. Tilquin,et al.  The Age Replacement Problem with Minimal Repair and Random Repair Costs , 1979, Oper. Res..

[14]  Frank Beichelt,et al.  A unifying treatment of replacement policies with minimal repair , 1993 .

[15]  Shey-Huei Sheu.  A Generalized Block Replacement Policy with Minimal Repair and General Random Repair Costs for a Multi-unit System , 1991 .

[16]  Daoud Ait Kadi,et al.  Optimal block replacement policies with multiple choice at failure , 1988 .

[17]  Kyung S. Park,et al.  Ordering Policies under Minimal Repair , 1986, IEEE Transactions on Reliability.

[18]  Masashi Kowada,et al.  Analysis of a system with minimal repair and its application to replacement policy , 1983 .

[19]  Henry W. Block,et al.  A general age replacement model with minimal repair , 1988, Naval Research Logistics (NRL).

[20]  Kyung S. Park,et al.  Generalized spare ordering policies with random lead time , 1986 .

[21]  Stephen G. Allen,et al.  An Ordering Policy for Repairable Stock Items , 1968, Oper. Res..

[22]  Shey-Huei Sheu,et al.  Optimal age-replacement policy with age-dependent minimal-repair and random-leadtime , 2001, IEEE Trans. Reliab..

[23]  Shunji Osaki,et al.  A Note on Ordering Policy , 1978, IEEE Transactions on Reliability.

[24]  L. Thomas,et al.  An optimal ordering policy for a spare unit with lead time , 1978 .

[25]  T. H. Savits.  Some multivariate distributions derived from a non-fatal shock model , 1988 .

[26]  T. Nakagawa,et al.  Extended optimal replacement model with random minimal repair costs , 1995 .

[27]  S. G. Allen,et al.  Letter to the Editor - An Ordering Policy for Stock Items when Delivery Can be Expedited , 1967, Oper. Res..

[28]  Shey-Huei Sheu,et al.  Generalized ordering policies with general random minimal repair costs and random lead times , 1994 .

[29]  Shey-Huei Sheu,et al.  Optimal age-replacement policy of a system subject to shocks with random lead-time , 2004, Eur. J. Oper. Res..