Optimal and Heuristic Echelon (r,nQ,T) policies in serial inventory systems with fixed costs
Abstract
This paper studies a periodic-review, serial inventory system in which echelon (r,nQ,T)
policies are implemented. Under such a policy, each stage reviews its inventory in
every T period and orders according to an echelon (r,nQ,T) policy. Two types of fixed
costs are considered: one is associated with each order batch Q, and the other is
incurred for each inventory review. The objective is to find the policy parameters
such that the average total cost per period is minimized. This paper provides a method
for obtaining heuristic and optimal policy parameters. The heuristic is based on minimizing
lower and upper bounds on the total cost function. These total cost bounds, which
are separable functions of the policy parameters, are obtained in two steps: First,
we decompose the total cost into costs associated with each stage, which include a
penalty cost for holding inadequate stock. Second, we construct lower and upper bounds
for the penalty cost by regulating downstream policy parameters. To find the optimal
solution, we further construct cost bounds for each echelon (a subsystem that includes
a stage and all of its downstream stages) by regulating holding and backorder cost
parameters. The echelon lower-bound cost functions, as well as the stage cost bounds,
generate bounds for the optimal solution. In a numerical study, we find that the heuristic
is near optimal when the ratio of the fixed cost to the holding cost at the most downstream
stage is large. We also find that changing the optimal batch sizes may not affect
the optimal reorder intervals or, equivalently, the delivery schedules under some
conditions. © 2010 INFORMS.
Type
Journal articlePermalink
https://hdl.handle.net/10161/4433Published Version (Please cite this version)
10.1287/opre.1090.0734Publication Info
Shang, KH; & Zhou, SX (2010). Optimal and Heuristic Echelon (r,nQ,T) policies in serial inventory systems with fixed
costs. Operations Research, 58(2). pp. 414-427. 10.1287/opre.1090.0734. Retrieved from https://hdl.handle.net/10161/4433.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
Kevin H. Shang
Joseph J. Ruvane, Jr. Distinguished Professor
Kevin Shang is the Joseph J. Ruvane, Jr. Distinguished Professor of Operations Management
at the Fuqua School of Business, Duke University. Professor Shang received his M.B.A.
from University of California, Riverside in 1998 and Ph.D. from University of California,
Irvine in 2002. Professor Shang's expertise is in supply chain management and inventory
control. His research mainly focuses on developing simple and effective inventory
policies for supply chain systems.

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