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Lower Bounds and Heuristics for Supply Chain stoch Allocation

Marklund, Johan LU and Rosling, Kaj LU (2012) In Operations Research 60(1). p.92-105
Abstract (Swedish)
Abstract in Undetermined

Assume that in periods with stochastic demand remain until the next replenishment arrives at a central warehouse. How should the available inventory be allocated among N retailers? This paper presents a new policy and a new lower bound for the expected cost of this problem. The lower bound becomes tight as N -> infinity. The infinite horizon problem then decomposes into N independent m-period problems with optimal retailer ship-up-to levels that decrease over the in periods, and the warehouse is optimally replenished by an order-up-to level that renders zero (local) warehouse safety stock at the end of each replenishment cycle. Based on the lower bound solution, we suggest a heuristic for finite... (More)
Abstract in Undetermined

Assume that in periods with stochastic demand remain until the next replenishment arrives at a central warehouse. How should the available inventory be allocated among N retailers? This paper presents a new policy and a new lower bound for the expected cost of this problem. The lower bound becomes tight as N -> infinity. The infinite horizon problem then decomposes into N independent m-period problems with optimal retailer ship-up-to levels that decrease over the in periods, and the warehouse is optimally replenished by an order-up-to level that renders zero (local) warehouse safety stock at the end of each replenishment cycle. Based on the lower bound solution, we suggest a heuristic for finite N. In a numerical study it outperforms the heuristic by Jackson [Jackson, P. L. 1988. Stock allocation in a two-echelon distribution system or what to do until your ship comes in. Management Sci. 34(7) 880-895], and the new lower bound improves on Clark and Scarf's [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci. 6(4) 475-490] bound when N is not too small. Moreover, the warehouse zero-safety-stock heuristic is comparable to Clark and Scarf's warehouse policy for lead times that are not too long. The suggested approach is quite general and may be applied to other logistical problems. In the present application it retains some of the risk-pooling benefits of holding central warehouse stock. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Operations Research
volume
60
issue
1
pages
92 - 105
publisher
Inst Operations Research Management Sciences
external identifiers
  • wos:000302113900008
  • scopus:84859569075
ISSN
0030-364X
DOI
10.1287/opre.1110.1009
language
English
LU publication?
yes
id
711b0a15-33bf-4c6e-a0a4-b51fe7aa2118 (old id 2019121)
date added to LUP
2011-07-05 11:22:52
date last changed
2017-03-26 03:23:18
@article{711b0a15-33bf-4c6e-a0a4-b51fe7aa2118,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
Assume that in periods with stochastic demand remain until the next replenishment arrives at a central warehouse. How should the available inventory be allocated among N retailers? This paper presents a new policy and a new lower bound for the expected cost of this problem. The lower bound becomes tight as N -&gt; infinity. The infinite horizon problem then decomposes into N independent m-period problems with optimal retailer ship-up-to levels that decrease over the in periods, and the warehouse is optimally replenished by an order-up-to level that renders zero (local) warehouse safety stock at the end of each replenishment cycle. Based on the lower bound solution, we suggest a heuristic for finite N. In a numerical study it outperforms the heuristic by Jackson [Jackson, P. L. 1988. Stock allocation in a two-echelon distribution system or what to do until your ship comes in. Management Sci. 34(7) 880-895], and the new lower bound improves on Clark and Scarf's [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci. 6(4) 475-490] bound when N is not too small. Moreover, the warehouse zero-safety-stock heuristic is comparable to Clark and Scarf's warehouse policy for lead times that are not too long. The suggested approach is quite general and may be applied to other logistical problems. In the present application it retains some of the risk-pooling benefits of holding central warehouse stock.},
  author       = {Marklund, Johan and Rosling, Kaj},
  issn         = {0030-364X},
  language     = {eng},
  number       = {1},
  pages        = {92--105},
  publisher    = {Inst Operations Research Management Sciences},
  series       = {Operations Research},
  title        = {Lower Bounds and Heuristics for Supply Chain stoch Allocation},
  url          = {http://dx.doi.org/10.1287/opre.1110.1009},
  volume       = {60},
  year         = {2012},
}