Meta-heuristic Algorithms for an Integrated Production-Distribution Planning Problem in a Multi-Objective Supply Chain

Document Type : Original Manuscript


1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Industrial Management Allameh Tabatabaei University, Tehran, Iran


In today's globalization, an effective integration of production and distribution plans into a unified framework is crucial for attaining competitive advantage. This paper addresses an integrated multi-product and multi-time period production/distribution planning problem for a two-echelon supply chain subject to the real-world variables and constraints. It is assumed that all transportations are outsourced to third-party logistics providers and all-unit quantity discounts in transportation costs are taken into consideration. The problem has been formulated as a multi-objective mixed-integer linear programming model which attempts to simultaneously minimize total delivery time and total transportation costs. Due to the complexity of the considered problem, genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are developed within the LP-metric method and desirability function framework for solving the real-sized problems in reasonable computational time. As the performance of meta-heuristic algorithms is significantly influenced by calibrating their parameters, Taguchi methodology has been used to tune the parameters of the developed algorithms. Finally, the efficiency and applicability of the proposed model and solution methodologies are demonstrated through several problems in different sizes