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 journalJournal articleResearchpeer-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.
Original languageEnglish
JournalManagement Science
Volume51
Issue number11
Pages (from-to)1706-1719
ISSN0025-1909
DOIs
Publication statusPublished - 2005
Externally publishedYes

Cite this

van Hoesel, Stan ; Romeijn, H. Edwin ; Romero Morales, Dolores ; 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.
@article{259c67dc5ae14759a06c155b89207817,
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 {Romero Morales}, Dolores and Wagelmans, {Albert P. M.}",
year = "2005",
doi = "10.1287/mnsc.1050.0378",
language = "English",
volume = "51",
pages = "1706--1719",
journal = "Management Science",
issn = "0025-1909",
publisher = "Institute for Operations Research and the Management Sciences",
number = "11",

}

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

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

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

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

AU - van Hoesel, Stan

AU - Romeijn, H. Edwin

AU - Romero Morales, Dolores

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

U2 - 10.1287/mnsc.1050.0378

DO - 10.1287/mnsc.1050.0378

M3 - Journal article

VL - 51

SP - 1706

EP - 1719

JO - Management Science

JF - Management Science

SN - 0025-1909

IS - 11

ER -