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.
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.
LanguageEnglish
JournalManagement Science
Volume51
Issue number11
Pages1706-1719
ISSN0025-1909
DOIs
StatePublished - 2005
Externally publishedYes

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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    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 journalJournal articleResearchpeer-review

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    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.

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    KW - Integration of production planning and transportation

    KW - Dynamic programming

    KW - Polynomial time algorithms

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    van Hoesel S, Romeijn HE, Morales DR, Wagelmans APM. Integrated Lot Sizing in Serial Supply Chains with Production Capacities. Management Science. 2005;51(11):1706-1719. Available from, DOI: 10.1287/mnsc.1050.0378