Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-23T12:41:09.278Z Has data issue: false hasContentIssue false
  • English
  • Français

A TWO-ECHELON SPARE PARTS NETWORK WITH LATERAL AND EMERGENCY SHIPMENTS: A PRODUCT-FORM APPROXIMATION

Published online by Cambridge University Press:  14 September 2017

Richard J. Boucherie ,
Geert-Jan van Houtum ,
Judith Timmer Open the ORCID record for Judith Timmer [Opens in a new window]  and
Jan-Kees van Ommeren
Richard J. Boucherie
Affiliation:
Stochastic Operations Research, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands E-mail: r.j.boucherie@utwente.nl
Geert-Jan van Houtum
Affiliation:
School of Industrial Engineering, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands E-mail: g.j.v.houtum@tue.nl
Judith Timmer
Affiliation:
Stochastic Operations Research, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands E-mail: j.b.timmer@utwente.nl
Jan-Kees van Ommeren
Affiliation:
Stochastic Operations Research, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands E-mail: j.c.w.vanommeren@utwente.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high downtime costs. The inventory system consists of multiple local warehouses, a central warehouse, and a central repair facility. When a part at a customer fails, if possible his request for a ready-for-use part is fulfilled by his local warehouse. Also, the failed part is sent to the central repair facility for repair. If the local warehouse is out of stock, then, via an emergency shipment, a ready-for-use part is sent from the central warehouse if it has a part in stock. Otherwise, it is sent via a lateral transshipment from another local warehouse, or via an emergency shipment from the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a basestock policy for the inventory control.

Our inventory system is too complex to solve for a steady-state distribution in closed form. We approximate it by a network of Erlang loss queues with hierarchical jump-over blocking. We show that this network has a product-form steady-state distribution. This enables an efficient heuristic for the optimization of basestock levels, resulting in good approximations of the optimal costs.

Keywords

emergency shipmentsmulti-echelonproduct-form solutionspare parts inventory control
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018 , pp. 536 - 555
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Albin, L. (1982). On Poisson approximations for superposition arrival processes in queues. Management Science 28: 126–137.Google Scholar
2.Alfredsson, P. & Verrijdt, J. (1999). Modeling emergency supply flexibility in a two-echelon inventory system. Management Science 45: 1416–1431.Google Scholar
3.Axsäter, S. (1990). Modelling emergency lateral transshipments in inventory systems. Management Science 36: 1329–1338.Google Scholar
4.Axsäter, S. (1990). Simple solution procedures for a class of two-echelon inventory problems. Operations Research 38: 64–69.Google Scholar
5.Baskett, F., Chandy, K.M., Muntz, R.R., & Palacios, F.G. (1975). Open, closed and mixed networks of queues with different classes of customers. Journal of the ACM 22: 248–260.Google Scholar
6.Basten, R.J.I. & Van Houtum, G.J. (2014). System-oriented inventory models for spare parts. Surveys in Operations Research and Management Science 19: 34–55.Google Scholar
7.Bijvank, M. & Vis, I.F.A. (2011). Lost-sales inventory theory: A review. European Journal of Operational Research 215(1): 1–13.Google Scholar
8.Boucherie, R.J. (1996). Batch routing queueing networks with jump-over blocking. Probability in the Engineering and Informational Sciences 10: 287–297.Google Scholar
9.Boucherie, R.J. & Mandjes, M. (1998). Estimation of performance measures for product form cellular mobile communications networks. Telecommunication Systems 10: 321–354.Google Scholar
10.Boucherie, R.J. & Van Dijk, N.M. (eds.) (2011). Queueuing networks: a fundamental Approach. International Series in Operations Research & Management Science 154. New York: Springer.Google Scholar
11.Caggiano, K.E., Jackson, P.L., Muckstadt, J.A., & Rappold, J.A. (2007). Optimizing service parts inventory in a multi-echelon, multi-item supply chain with time-based customer service level agreements. Operations Research 55(2): 303–318.Google Scholar
12.Caggiano, K.E., Jackson, P.L., Muckstadt, J.A., & Rappold, J.A. (2009). Efficient computation of time-based customer service levels in a multi-item, multi-echelon supply chain: A practical approach for inventory optimization. European Journal of Operational Research 199(3): 744–749.Google Scholar
13.Grahovac, J. & Chakravarty, A. (2001). Sharing and lateral transshipments of inventory in a supply chain with expensive low-demand items. Management Science 47: 579–594.Google Scholar
14.Graves, S.C. (1985). A multi-echelon inventory model for a repairable item with one-for-one replenishment. Management Science 31: 1247–1256.Google Scholar
15.Hausman, W.H. & Erkip, N.K. (1994). Multi-echelon vs. single-echelon inventory control policies for low demand items. Management Science 40: 597–602.Google Scholar
16.Hordijk, A. & Schassberger, R. (1982). Weak convergence for generalized semi-Markov processes. Stochastic Processes and their Applications 12: 271–291.Google Scholar
17.Kruse, K.C. (1984). tAn exact N echelon inventory model: The simple Simon method, U.S. Army Research Office, Technical Report TR 79-2.Google Scholar
18.Lee, H.L. (1987). A multi-echelon inventory model for repairable items with emergency lateral transshipments. Management Science 33: 1302–1316.Google Scholar
19.Muckstadt, J.A. (1973). A Model for a multi-item, multi-echelon, multi-indenture inventory system. Management Science 20: 472–481.Google Scholar
20.Muckstadt, J.A. & Thomas, L.J. (1980). Are multi-echelon inventory methods worth implementing in systems with low-demand-rate items? Management Science 26: 483–494.Google Scholar
21.Özkan, E., Van Houtum, G.J., & Serin, Y. (2015). A new approximate evaluation method for two-echelon inventory systems with emergency shipments. Annals of Operations Research 224: 147–169.Google Scholar
22.Paterson, C., Kiesmüller, G., Teunter, R., & Glazebrook, K. (2011). Inventory models with lateral transshipments: A review. European Journal of Operational Research 210(2): 125–136.Google Scholar
23.Rustenburg, J.W., Van Houtum, G.J., & Zijm, W.H.M. (2003). Exact and approximate analysis of multi-echelon, multi-indenture spare parts systems with commonality. In Shantikumar, J.G., Yao, D.D., & Zijm, W.H.M. (eds.), Stochastic modeling and optimization of manufacturing systems and supply chains. Boston: Kluwer, chapter 7.Google Scholar
24.Sherbrooke, C.C. (1968). METRIC: A multi-echelon technique for recoverable item control. Operations Research 16: 122–141.Google Scholar
25.Sherbrooke, C.C. (1986). VARI-METRIC: Improved approximations for multi-indenture, multi-echelon availability models. Operations Research 34: 311–319.Google Scholar
26.Sherbrooke, C.C. (1992). Multi-echelon inventory systems with lateral supply. Naval Research Logistics 39: 29–40.Google Scholar
27.Selçuk, B. (2013). An adaptive base stock policy for repairable item inventory control. International Journal of Production Economics 143: 304–315.Google Scholar
28.Simon, R.M. (1971). Stationary properties of a two-echelon inventory model for low demand items. Operations Research 19: 761–773.Google Scholar
29.Slay, F.M. (1984). VARI-METRIC: An approach to modeling multi-echelon resupply when the demand process is Poisson with a Gamma prior. Logistics Management Institute, Washington, DC, Report AF301-3.Google Scholar
30.Van Dijk, N.M. (1993). Queueing networks and product forms: a system's approach. New York: Wiley.Google Scholar
31.Wong, H., Kranenburg, A.A., Van Houtum, G.J., & Cattrysse, D. (2007). Efficient heuristics for two-echelon spare parts inventory systems with an aggregate mean waiting time constraint per local warehouse. OR Spectrum 29: 699–722.Google Scholar
32.Wong, H., Van Oudheusden, D., & Cattrysse, D. (2007). Two-echelon multi-item spare parts systems with emergency supply flexibility and waiting time constraints. IIE Transactions 39(11): 1045–1057.Google Scholar