## Abstract

The supply chain network equilibrium problem with capacity constraints (SCNE-C) is an extension of the supply chain network equilibrium problem (SCNE), which also takes into account capacity constraints which refer to the maximum production capacity for a manufacturer or the maximum storage/display space for a retailer. Due to inherent link interactions in the demand functions and cost functions, the SCNE-C problem is formulated as a mathematical model using the variational inequality (VI) approach. This VI model is characterised by the so-called Wardrop second principle (in terms of the 'generalised' route cost). To solve the model, a path-based four-loop nested diagonalisation method, along with a supernetwork representation, is proposed and demonstrated with a few numerical examples. The obtained results fully comply with the Wardrop second principle at both retailer sector and demand markets and can provide useful route information of the product. In addition, the stricter the capacity constraints imposed, the lower the quantity demanded will be, and provided at a higher product price. The concepts developed in this paper can be extended into many other spatial price equilibrium problems.

Original language | English |
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Pages (from-to) | 605-621 |

Number of pages | 17 |

Journal | Papers in Regional Science |

Volume | 87 |

Issue number | 4 |

DOIs | |

State | Published - 2008 |

## Keywords

- Capacity constraint
- Gradient projection algorithm
- Supply chain network equilibrium
- Variational inequality approach