Optimization technique by genetic algorithms for international logistics

In recent years, sea and air transport has become a big trend. Getting an optimal solution with minimum costs (freight cost, warehouse cost) under certain constraints (delivery due date etc.) must be sought. Formerly, we made a mathematical formulation of the fundamental case (a single supply site and a single demand site with multiple delivery dates/different delivery quantities) and next we expanded the objective function from considering transportation costs to considering transportation costs and warehouse stock fees. Under certain constraints, a minimum cost was pursued. In this paper, the objective function is expanded to the scheme which considers a reduced cost for the volume of lots. Here, a reduced cost by the discount of volume is also taken into account when multiple lots are transported using the same type of transport. A new selection method, "Multi-step tournament selection method" which is suitable for this problem is devised and utilized in this paper. Numerical examples are examined for the cases in which the discount of volume is considered. Theoretical optimal solution is derived by using genetic algorithm. An application of genetic algorithm to International Logistics is executed before by us. In this paper, the further expansion of constraints is executed and fruitful result is obtained, which contributes to the real management of International Logistics for the better decision making.