Existence of Equilibria in a Decentralized Two-level Supply Chain

Dolores Romero Morales, Dries Vermeulen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.
Our main motivation to study this problem of co-dependency comes from the field of supply chain planning. A set of buyers is faced with external demand over a planning horizon, and to satisfy this demand they request inputs from a set of suppliers. Both suppliers and buyers face production capacities and they plan their own production in a decentralized manner. A well-known coordination scheme for this setting is the upstream approach where the plan of the buyers is used to decide the request to the suppliers. We show the existence of equilibria for a (shared) inventory cost minimization version of this coordination scheme in which a distribution center manages the inventory of the inputs. However, we illustrate with an example that the centralized solution is not, in general, an equilibrium, suggesting that regulation may be needed.
In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.
Our main motivation to study this problem of co-dependency comes from the field of supply chain planning. A set of buyers is faced with external demand over a planning horizon, and to satisfy this demand they request inputs from a set of suppliers. Both suppliers and buyers face production capacities and they plan their own production in a decentralized manner. A well-known coordination scheme for this setting is the upstream approach where the plan of the buyers is used to decide the request to the suppliers. We show the existence of equilibria for a (shared) inventory cost minimization version of this coordination scheme in which a distribution center manages the inventory of the inputs. However, we illustrate with an example that the centralized solution is not, in general, an equilibrium, suggesting that regulation may be needed.
LanguageEnglish
JournalEuropean Journal of Operational Research
Volume197
Issue number2
Pages642–658
ISSN0377-2217
DOIs
StatePublished - 2009
Externally publishedYes

Keywords

    Cite this

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    Existence of Equilibria in a Decentralized Two-level Supply Chain. / Morales, Dolores Romero; Vermeulen, Dries.

    In: European Journal of Operational Research, Vol. 197, No. 2, 2009, p. 642–658.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Existence of Equilibria in a Decentralized Two-level Supply Chain

    AU - Morales,Dolores Romero

    AU - Vermeulen,Dries

    PY - 2009

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    N2 - In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.Our main motivation to study this problem of co-dependency comes from the field of supply chain planning. A set of buyers is faced with external demand over a planning horizon, and to satisfy this demand they request inputs from a set of suppliers. Both suppliers and buyers face production capacities and they plan their own production in a decentralized manner. A well-known coordination scheme for this setting is the upstream approach where the plan of the buyers is used to decide the request to the suppliers. We show the existence of equilibria for a (shared) inventory cost minimization version of this coordination scheme in which a distribution center manages the inventory of the inputs. However, we illustrate with an example that the centralized solution is not, in general, an equilibrium, suggesting that regulation may be needed.

    AB - In this paper, we analyze equilibria in competitive environments under constraints across players’ strategies. This means that the action taken by one player limits the possible choices of the other players. In this context, the usual approach to show existence of equilibrium, Kakutani’s fixed point theorem, cannot be applied directly. In particular, best replies against a given strategy profile may not be feasible. We devise a new fixed point correspondence to deal with the feasibility issue.Our main motivation to study this problem of co-dependency comes from the field of supply chain planning. A set of buyers is faced with external demand over a planning horizon, and to satisfy this demand they request inputs from a set of suppliers. Both suppliers and buyers face production capacities and they plan their own production in a decentralized manner. A well-known coordination scheme for this setting is the upstream approach where the plan of the buyers is used to decide the request to the suppliers. We show the existence of equilibria for a (shared) inventory cost minimization version of this coordination scheme in which a distribution center manages the inventory of the inputs. However, we illustrate with an example that the centralized solution is not, in general, an equilibrium, suggesting that regulation may be needed.

    KW - Supply chain coordination

    KW - Decentralization

    KW - Upstream planning

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