We consider a two-level distribution inventory system with a number of identical retailers at the lower echelon and a single supplier at the upper echelon. The replenishment policy is continuous review policy (R, Q) at all installations. We assume independent Poisson demands with stochastic lead time for the retailers and a constant transportation time for replenishing supplier orders from an external warehouse. Unsatisfied demands are assumed to be lost in the retailers and unsatisfied retailer orders are backordered in the supplier. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations, and the related accuracy is assessed through simulation. We present numerical examples for the gamma distributed lead time for the retailers orders at the supplier.
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Albin S (1982) On Poisson approximation for superposition arrival processes in queues. Manag Sci 28:126–137
Andersson J, Melchiors P (2001) A two echelon inventory model with lost sales. Int J Prod Econ 69:307–315
Axsäter S (1990) Simple solution procedures for a class of two echelon inventory problems. Oper Res 38:64–69
Axsäter S (1993) Exact and approximate evaluation of batch ordering policies for two-level inventory systems. Oper Res 41:777–785
Axsäter S (1998) Evaluation of installation stock based (R, Q) policies for two-level inventory systems with Poisson demand. Oper Res 46:135–145
Axsäter S (2003) Approximate optimization of a two level distribution inventory system. Int J Prod Econ 81–82:545–553
Axsäter S (2005) A simple decision rule for decentralized two-echelon inventory control. Int J Prod Econ 93–94:53–59
Deuermeyer B, Schwarz LB (1981) A model for the analysis of system service level in warehouse/retailer distribution system: the identical retailer case. In: Schwarz L (ed) Multilevel production/inventory control systems (TIMS studies in management science 16). Elsevier, New York, chapter 13
Graves SC (1985) A multi-echelon inventory model for a repairable item with one for one replenishment. Manag Sci 31:1247–1256
Hadley G, Whitin TM (1963) Analysis of inventory systems. Prentice-Hall, Englewood Cliffs
Hill RM, Seifbarghy M, Smith DK (2007) A two-echelon inventory model with lost sales. Eur J Oper Res 181:753–766
Lee HL, Moinzadeh K (1987) Operating characteristics of a two-echelon inventory system for repairable and consumable items under batch ordering and shipment policy. Nav Res Logist 34:365–380
Moinzadeh K, Lee HL (1986) Batch size and stocking levels in multi-echelon repairable systems. Manag Sci 32: 1567–1581
Muckstadt JA (1977) Analysis of a two-echelon inventory system in which all locations follow continuous review(s,S) policy. Technical report no. 337, School of Operations Research, vol 16, pp 122–141
Olsson RJ, Hill RM (2007) A two-echelon base stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon. Eur J Oper Res 177:310–324
Sherbrooke CC (1968) METRIC: a multi-echelon technique for recoverable item control. Oper Res 16:122–141
Johansen SG, Throstenson A (1993) Optimal and approximate (Q, r) inventory policies with lost sales and gamma distributed lead times. Int J Prod Econ 30–31:179–194
Svoronos AP, Zipkin P (1988) Estimating the performance of multi-level inventory systems. Oper Res 36:57–72
Wee HM, Yang PC (2004) The optimal and heuristic solutions of a distribution network. Eur J Oper Res 158:626–632
Wee HM, Jong JF, Jiang JC (2007) A note on a single-vendor and multiple-buyers production-inventory policy for a deteriorating item. Eur J Oper Res 180:1130–1134
Yang PC, Wee HM (2002) A single-vendor and multiple-buyers production inventory policy for a deteriorating item. Eur J Oper Res 143:570–581
Zipkin PH (1986) Models for design and control of stochastic, multi item batch production systems. Oper Res 34:91–104
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Thangam, A., Uthayakumar, R. A two-level distribution inventory system with stochastic lead time at the lower echelon. Int J Adv Manuf Technol 41, 1208 (2009). https://doi.org/10.1007/s00170-008-1567-5
- Stochastic lead time
- Poisson demand
- Continuous review policy