• transportation planning;
  • inventory;
  • random key-based encoding;
  • Boltzmann scaling selection


Logistics network design is one of the most important phases in supply chain management (SCM). Transportation planning (TP) is a well-known basic network model that can be generally defined as a problem to minimize the total delivery cost. But for some real-world applications, the TP model is often extended to satisfy other additional constraints or is performed in several stages. In addition, the concept of inventory is not included in a traditional TP model. Moreover, time concepts, such as carrying costs in a certain period, are not treated. Even if it is a plant that belongs to the same company, delivery methods may be different for each product. These restrictions on this model profoundly affect the use of the TP model in the real world. In this paper, we formulate a two-stage transportation problem with inventory and exclusionary side constraints. In this model, 1 year is divided into several terms and the annual demands of delivery centers are satisfied for each term. This model includes the additional constraint in which simultaneous shipments between some plants are prohibited. To solve the problem, we propose an effective genetic algorithm (GA) method called the Boltzmann random key-based GA (Brk-GA). One characteristic of this method is that it features new selection processing through Boltzmann scaling and the local search techniques. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.