A bi-objective location inventory model for three-layer supply chain network design considering capacity planning

This paper aims at bi‐objective optimisation of single product for three‐layer supply chain network consisting of a factory, distribution centres (DCs) and customers including the impact of inventory management system. The key design decisions are: the location of DCs and their capacity, production capacity of the factory, product quantity to be transported from factory to each DC, product quantity to be transported from each DC to each customer, and order quantity at DCs, so as to minimise the sum of the production cost, location cost, transportation cost, ordering cost, inventory holding cost, and lost sales. The problem is formulated as a mixed‐integer nonlinear programming (MINLP) model and solved using GAMS solver and proposed meta‐heuristic algorithm. The ϵ‐constraint method is used as solution approach to tackle the multi‐objective problem when using GAMS. Because of NP‐hardness of the problem, a hybrid meta‐heuristic algorithm based on genetic algorithm is proposed to solve large scale problems. Computational experiments demonstrate the effectiveness of the proposed model and algorithm in designing large supply chain networks.