An integrated production-distribution planning with a routing problem and transportation cost discount in a supply chain

The motivation behind this research refers to the significant role of integration of production-distribution plans in effective performance of supply chain networks under fierce competition of today’s global marketplace. In this regard, this paper aims to deal with an integrated production-distribution planning problem in deterministic, multi-product and multi-echelon supply chain network. The bi-objective mixed-integer linear programming model is constructed to minimize not only the total transportation costs but also the total delivery time of supply chain, subject to satisfying retailer demands and capacity constraints where quantity discount on transportation costs, fixed cost associated with transportation vehicles usage and routing decisions have been included in the model.,As the proposed mathematical model is NP-hard and that finding an optimum solution in polynomial time is not reasonable, two multi-objective meta-heuristic algorithms, namely, non-dominated sorting genetic algorithm II (NSGAII) and multi-objective imperialist competitive algorithm (MOICA) are designed to obtain near optimal solutions for real-sized problems in reasonable computational times. The Taguchi method is then used to adjust the parameters of the developed algorithms. Finally, the applicability of the proposed model and the performance of the solution methodologies in comparison with each other are demonstrated for a set of randomly generated problem instances.,The practicality and applicability of the proposed model and the efficiency and efficacy of the developed solution methodologies were illustrated through a set of randomly generated real-sized problem instances. Result. In terms of two measures, the objective function value and the computational time were required to get solutions.,The main contribution of the present work was addressing an integrated production-distribution planning problem in a broader view, by proposing a closer to reality mathematical formulation which considers some real-world constraints simultaneously and accompanied by efficient multi-objective meta-heuristic algorithms to provide effective solutions for practical problem sizes.