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**Multi-site production planning integrating procurement and distribution plans in multi-echelon supply chains: an interactive fuzzy goal programming approach.**
*(English)*
Zbl 1198.90150

Summary: Motivated by a real case of an automobile company, this study proposes a multi-objective, multi-site production planning model integrating procurement and distribution plans in a multi-echelon supply chain network with multiple suppliers, multiple manufacturing plants and multiple distribution centres. The model incorporates four important conflicting objectives simultaneously: minimisation of the total cost of logistics, maximisation of the total value of purchasing, minimisation of defective items and minimisation of late deliveries subject to some realistic constraints. Due to the imprecise/fuzzy nature of the objectives’ aspiration levels and some critical data, an interactive fuzzy goal programming formulation is first developed. Then, a novel fuzzy approach is proposed to convert the FGP model into an auxiliary crisp formulation to find an efficient compromise solution. The proposed model and solution method are validated through some numerical tests. Computational results indicate the practicality and tractability of the proposed model and also the superiority of the proposed auxiliary crisp formulation in contrast to the current alternative fuzzy approaches.

### MSC:

90B30 | Production models |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C29 | Multi-objective and goal programming |