Integrated Lot Sizing in Serial Supply Chains with Production Capacities

Stan van Hoesel; H. Edwin Romeijn; Dolores Romero Morales; Albert P. M. Wagelmans

doi:10.1287/mnsc.1050.0378

Integrated Lot Sizing in Serial Supply Chains with Production Capacities

Stan van Hoesel, H. Edwin Romeijn, Dolores Romero Morales, Albert P. M. Wagelmans

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated in the presence of production capacities and concave cost functions. The model we study generalizes the uncapacitated serial single-item multilevel economic lot-sizing model by adding stationary production capacities at the manufacturer level. We present algorithms with a running time that is polynomial in the planning horizon when all cost functions are concave. In addition, we consider different transportation and inventory holding cost structures that yield improved running times: inventory holding cost functions that are linear and transportation cost functions that are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. While the running times of the algorithms are exponential in the number of levels in the supply chain in the general concave cost case, the running times are remarkably insensitive to the number of levels for the other two cost structures.

Language	English
Journal	Management Science
Volume	51
Issue number	11
Pages	1706-1719
ISSN	0025-1909
DOIs	10.1287/mnsc.1050.0378
State	Published - 2005
Externally published	Yes

Keywords

Cite this

van Hoesel, S., Romeijn, H. E., Morales, D. R., & Wagelmans, A. P. M. (2005). Integrated Lot Sizing in Serial Supply Chains with Production Capacities. Management Science, 51(11), 1706-1719. DOI: 10.1287/mnsc.1050.0378

van Hoesel, Stan ; Romeijn, H. Edwin ; Morales, Dolores Romero ; Wagelmans, Albert P. M./ Integrated Lot Sizing in Serial Supply Chains with Production Capacities. In: Management Science. 2005 ; Vol. 51, No. 11. pp. 1706-1719

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title = "Integrated Lot Sizing in Serial Supply Chains with Production Capacities",

abstract = "We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated in the presence of production capacities and concave cost functions. The model we study generalizes the uncapacitated serial single-item multilevel economic lot-sizing model by adding stationary production capacities at the manufacturer level. We present algorithms with a running time that is polynomial in the planning horizon when all cost functions are concave. In addition, we consider different transportation and inventory holding cost structures that yield improved running times: inventory holding cost functions that are linear and transportation cost functions that are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. While the running times of the algorithms are exponential in the number of levels in the supply chain in the general concave cost case, the running times are remarkably insensitive to the number of levels for the other two cost structures.",

keywords = "Lot sizing, Integration of production planning and transportation, Dynamic programming, Polynomial time algorithms",

author = "{van Hoesel}, Stan and Romeijn, {H. Edwin} and Morales, {Dolores Romero} and Wagelmans, {Albert P. M.}",

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van Hoesel, S, Romeijn, HE, Morales, DR & Wagelmans, APM 2005, 'Integrated Lot Sizing in Serial Supply Chains with Production Capacities' Management Science, vol. 51, no. 11, pp. 1706-1719. DOI: 10.1287/mnsc.1050.0378

Integrated Lot Sizing in Serial Supply Chains with Production Capacities. / van Hoesel, Stan; Romeijn, H. Edwin; Morales, Dolores Romero; Wagelmans, Albert P. M.

In: Management Science, Vol. 51, No. 11, 2005, p. 1706-1719.

Research output: Contribution to journal › Journal article › Research › peer-review

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T1 - Integrated Lot Sizing in Serial Supply Chains with Production Capacities

AU - van Hoesel,Stan

AU - Romeijn,H. Edwin

AU - Morales,Dolores Romero

AU - Wagelmans,Albert P. M.

PY - 2005

Y1 - 2005

N2 - We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated in the presence of production capacities and concave cost functions. The model we study generalizes the uncapacitated serial single-item multilevel economic lot-sizing model by adding stationary production capacities at the manufacturer level. We present algorithms with a running time that is polynomial in the planning horizon when all cost functions are concave. In addition, we consider different transportation and inventory holding cost structures that yield improved running times: inventory holding cost functions that are linear and transportation cost functions that are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. While the running times of the algorithms are exponential in the number of levels in the supply chain in the general concave cost case, the running times are remarkably insensitive to the number of levels for the other two cost structures.

AB - We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated in the presence of production capacities and concave cost functions. The model we study generalizes the uncapacitated serial single-item multilevel economic lot-sizing model by adding stationary production capacities at the manufacturer level. We present algorithms with a running time that is polynomial in the planning horizon when all cost functions are concave. In addition, we consider different transportation and inventory holding cost structures that yield improved running times: inventory holding cost functions that are linear and transportation cost functions that are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. While the running times of the algorithms are exponential in the number of levels in the supply chain in the general concave cost case, the running times are remarkably insensitive to the number of levels for the other two cost structures.

KW - Lot sizing

KW - Integration of production planning and transportation

KW - Dynamic programming

KW - Polynomial time algorithms

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