Abstract
General spare parts networks, in which items are both repaired and stocked for future use have received considerable attention since the pathbreaking work of Sherbrooke [20] in 1968. In this chapter, we present both an exact and, under somewhat relaxed assumptions, a fast approximate evaluation method of fairly general multi-echelon, multi-indenture spare parts networks that serve to support the operation of technologically highly involved field systems. These evaluation methods provide the basis for a procedure to optimize the availability of these systems, given limited spare parts budgets. In this introductory section, we first describe the general structure of the networks we wish to study, and we motivate their importance. Next, we discuss some key references and finally summarize the main contributions of the current chapter.
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References
Adan, I.J.B.F., Van Eenige, M.J.A. and Resing, J.A.C., Fitting Discrete Distributions on the First Two Moments, Probability in the Engineering and Informational Sciences, 9 (1996), 623–632.
Albright, S.C., An Approximation to the Stationary Distribution of a Multi-Echelon Repairable Item Inventory System with Finite Sources and Repair Channels. Naval Research Logistics, 36 (1989), 179–195.
Avsar Z.M. and Zijm, W.H.M., Capacitated Two-Echelon Inventory Models for Repairable Item Systems, in: Analysis and Modeling of Manufacturing Systems, S. Gershwin et al. (eds.), Kluwer, Boston, 2002.
Axsäter, S., Simple Solution Procedures for a Class of Two-Echelon Inventory Problems, Operations Research, 38 (1990), 64–69.
Axsäter, S., Exact Analysis of Continuous Review (R,Q) Policies in Two-Echelon Inventory Systems with Compound Poisson Demand, Operations Research, 48 (2000), 686–696.
Buzacott, J.A., Price S.M. and Shantikumar, J.G., Service Levels in Multi-Stage MRP and Base Stock Controlled Production Systems, in: New directions for Operations Research in Manufacturing, G. Fandel, Th. Gulledge and A. Jones (eds.), Springer, Berlin, 1992.
Caggiano, K.E., Jackson, P.L., Mockstadt, J.A. and Rappold, J.A. A Multi-Echelon, Multi-Item Inventory Model for Service Parts Management with Generalized Service Level Constraints, Working paper, School of Business, University of Wisconsin, 2001.
Diaz, A. and Fu, M.C., Models for Multi-Echelon Repairable Item Inventory Systems with Limited Repair Capacity, European Journal of Operational Research, 97 (1997), 480–492.
Feeney, G.J. and Sherbrooke, C.C., The (s — 1, s) Inventory Policy under Compound Poisson Demand, Management Science, 12 (1966), 391–411.
Graves, S.C., A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment, Management Science, 31 (1985), 1247–1256.
Gross, D. Miller, D.R. and Soland, R.M., A Closed Queuing Network Model for Multi-Echelon Repairable Item Provisioning, IIE Transactions, 15 (1983), 344–352.
Guide Jr., V.D.R. and Srivastava, R., Repairable Inventory Theory: Models and Applications, European Journal of Operational Research, 102 (1997), 1–20.
Kruse, K.C., An Exact N Echelon Inventory Model: The Simple Simon Method, U.S. Army Research Office, Technical Report TR 79-2, 1984.
Muckstadt, J., A Model for a Multi-Item, Multi-Echelon, Multi-Indenture Inventory System, Management Science, 20 (1973), 472–481.
Palm, C., Analysis of the Erlang Traffic Formula for Busy-Signal Arrangements, Ericsson Technics, 4 (1938), 204–212.
Rustenburg, W.D., A System Approach to Budget-Constrained Spare Parts Management, Ph.D. Thesis, Eindhoven University of Technology, 2000.
Rustenburg, W.D., Van Houtum, G.J. and Zijm, W.H.M., Spare Parts Management for Technical Systems: Resupply under Limited Budgets, IIE Transactions, 32 (2000), 1013–1026.
Rustenburg, W.D., Van Houtum, G.J. and Zijm, W.H.M., Spare Parts Management at Complex Technology-Based Organizations: An Agenda For Research, International Journal of Production Economics, 71 (2001), 177–193.
Shanker, K., Exact Analysis of a Two-Echelon Inventory System for Recoverable Items under Batch Inspection Policy, Naval Research Logistics Quarterly, 28 (1981), 579–601.
Sherbrooke, C.C., METRIC: A Multi-Echelon Technique for Recoverable Item Control, Operations Research, 16 (1968), 122–141.
Sherbrooke, C.C., An Evaluator of Operational Ready Aircraft in a Multilevel Supply System, Operations Research, 19 (1971), 618–635.
Sherbrooke, C.C., VARI-METRIC: Improved Approximations for Multi-Indenture, Multi-Echelon Availability Models, Operations Research, 34 (1986), 311–319.
Sherbrooke, C.C., Optimal Inventory Modeling of Systems: Multi-Echelon Techniques, Wiley, New York, 1992.
Simon, R.M., Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items, Operations Research, 19 (1971), 761–773.
Slay, F.M., VARI-METRIC: An Approach to Modeling Multi-Echelon Resupply When the Demand Process is Poisson with a Gamma Prior, Report AF301-3, Logistics Management Institute, Washington D.C., 1984.
Sleptchenko, A., Integral Inventory Control in Service Networks with Capacity Constraints, Ph.D. Thesis, University of Twente, 2002.
Sleptchenko, A., Van der Heijden, M.C. and Van Harten, A., Effects of Finite Repair Capacity in Multi-Echelon, Multi-Indenture Service Part Supply Systems, International Journal of Production Economics, 79 (2002), 209–230.
Sleptchenko, A., Van Harten, A. and Van der Heijden, M.C., Analyzing Multi-Class, Multi-Server Queueing Systems with Preemptive Priorities, Working Paper, University of Twente, 2002. Submitted for publication.
Song, J.S. and Yao, D.D., Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times, Operations Research, 50 (2002), 889–903.
Van Houtum, G.J. and Zijm, W.H.M., Incomplete Convolutions in Production and Inventory Models, OR Spektrum, 19 (1997), 97–107.
Van Houtum, G.J. and Zijm, W.H.M., On the Relation between Cost and Service Models for General Inventory Systems, Statistica Neerlandica, 54 (2000), 127–147.
Zijm, W.H.M. and Avsar, Z.M., Capacitated Two-Indenture Models for Repairable Item Systems, International Journal of Production Economics, 81–82 (2003), 573–588.
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Rustenburg, J.W., van Houtum, GJ., Zijm, W.H.M. (2003). Exact and Approximate Analysis of Multi-Echelon, Multi-Indenture Spare Parts Systems with Commonality. In: Shanthikumar, J.G., Yao, D.D., Zijm, W.H.M. (eds) Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chains. International Series in Operations Research & Management Science, vol 63. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0373-6_7
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DOI: https://doi.org/10.1007/978-1-4615-0373-6_7
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