Solving a New Mathematical Model for Scheduling in Distribution Networks by Multi-Objective Particle Swarm Optimization

In this paper a novel، bi-objective mixed-integer mathematical programming has been proposed for a distribution network problem. One objective function minimizes the total purchasing، transportation and holding costs and the another objective minimizes the total amount of delayed or before time deliveries multiplied by respective durations، named «JIT distribution». Supplying the customer demand، holding and delivering products at warehouse are the most important constraints considered in this model. This model has been designed for a three-echelon distribution network consisting multiple suppliers، wholesalers and retailers to distribute multiple products with a deterministic amount of demand through either direct or indirect channels in a planning horizon. Since real-sized problems of the resulting bi-objective mixed-integer linear programming (MILP) cannot be solved with exact methods، a multi objective particle swarm algorithm (MOPSO) is designed of which، quality in small-sized problems is compared with the solutions obtained by the LINGO software. The computational results show that the proposed MOPSO algorithm finds good solutions in shorter times than LINGO and has acceptable running times in large-scale problems.