### Abstract

An important and often researched area of management science is mathematical modeling of a supply chain. Competitive situations can occur in supply chains owing to the involvement of multiple decision makers (players) that independently decide their behaviors. To investigate competitive supply chain networks, a supply chain network equilibrium (SCNE) model was proposed. Recently, particular attention has been paid to risk management of a supply chain. In equilibrium models, it is vital to consider players' decisions and interdependence relations. Thus, we consider competitive supply chain networks with uncertainties in the other players' strategies. In the proposed model, each player cannot know exactly the other players' strategies, and they decide their strategy using the minimax principle (that is, assuming the worst case). We call it the robust SCNE model. We formulate the robust SCNE model as a variational inequality problem (VIP) in which the set associated with the VIP is constructed by second-order cone constraints. We show the existence and uniqueness of the equilibrium under mild assumptions. In addition, we give, in a special case, some relations between players' strategies in the equilibrium and magnitudes of uncertainties. Finally, some numerical results are provided.

Original language | English |
---|---|

Pages (from-to) | 1196-1212 |

Number of pages | 17 |

Journal | Transportation Science |

Volume | 53 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Fingerprint

### Keywords

- Existence
- Robust optimization
- Supply chain network equilibrium model
- Transportation
- Uniqueness
- Variational inequality problem

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Transportation

### Cite this

*Transportation Science*,

*53*(4), 1196-1212. https://doi.org/10.1287/trsc.2018.0843

**Robust supply chain network equilibrium model.** / Hirano, Tatsuya; Narushima, Yasushi.

Research output: Contribution to journal › Article

*Transportation Science*, vol. 53, no. 4, pp. 1196-1212. https://doi.org/10.1287/trsc.2018.0843

}

TY - JOUR

T1 - Robust supply chain network equilibrium model

AU - Hirano, Tatsuya

AU - Narushima, Yasushi

PY - 2019/1/1

Y1 - 2019/1/1

N2 - An important and often researched area of management science is mathematical modeling of a supply chain. Competitive situations can occur in supply chains owing to the involvement of multiple decision makers (players) that independently decide their behaviors. To investigate competitive supply chain networks, a supply chain network equilibrium (SCNE) model was proposed. Recently, particular attention has been paid to risk management of a supply chain. In equilibrium models, it is vital to consider players' decisions and interdependence relations. Thus, we consider competitive supply chain networks with uncertainties in the other players' strategies. In the proposed model, each player cannot know exactly the other players' strategies, and they decide their strategy using the minimax principle (that is, assuming the worst case). We call it the robust SCNE model. We formulate the robust SCNE model as a variational inequality problem (VIP) in which the set associated with the VIP is constructed by second-order cone constraints. We show the existence and uniqueness of the equilibrium under mild assumptions. In addition, we give, in a special case, some relations between players' strategies in the equilibrium and magnitudes of uncertainties. Finally, some numerical results are provided.

AB - An important and often researched area of management science is mathematical modeling of a supply chain. Competitive situations can occur in supply chains owing to the involvement of multiple decision makers (players) that independently decide their behaviors. To investigate competitive supply chain networks, a supply chain network equilibrium (SCNE) model was proposed. Recently, particular attention has been paid to risk management of a supply chain. In equilibrium models, it is vital to consider players' decisions and interdependence relations. Thus, we consider competitive supply chain networks with uncertainties in the other players' strategies. In the proposed model, each player cannot know exactly the other players' strategies, and they decide their strategy using the minimax principle (that is, assuming the worst case). We call it the robust SCNE model. We formulate the robust SCNE model as a variational inequality problem (VIP) in which the set associated with the VIP is constructed by second-order cone constraints. We show the existence and uniqueness of the equilibrium under mild assumptions. In addition, we give, in a special case, some relations between players' strategies in the equilibrium and magnitudes of uncertainties. Finally, some numerical results are provided.

KW - Existence

KW - Robust optimization

KW - Supply chain network equilibrium model

KW - Transportation

KW - Uniqueness

KW - Variational inequality problem

UR - http://www.scopus.com/inward/record.url?scp=85071873720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071873720&partnerID=8YFLogxK

U2 - 10.1287/trsc.2018.0843

DO - 10.1287/trsc.2018.0843

M3 - Article

AN - SCOPUS:85071873720

VL - 53

SP - 1196

EP - 1212

JO - Transportation Science

JF - Transportation Science

SN - 0041-1655

IS - 4

ER -