Competitive facility location on decentralized supply chains.

*(English)*Zbl 1163.90342Summary: This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction-correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction-correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms.

##### MSC:

90B05 | Inventory, storage, reservoirs |

##### Keywords:

supply chain management; network equilibrium; competitive facility location; variational inequalities; mathematical program with equilibrium constraints
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\textit{Q. Meng} et al., Eur. J. Oper. Res. 196, No. 2, 487--499 (2009; Zbl 1163.90342)

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