Transportation planning (TP) is a well-known basic network model that can be generally defined as a problem to minimize a total delivery cost. However the concept of inventory is not included in a traditional TP model. These restrictions on this model profoundly affect the use of the TP model in the real world. In this paper, we formulate the two-stage transportation problem with inventory and exclusionary side constraints (esc-2ITP). In this model, one 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. In order to solve the problem, we propose an effective genetic algorithms (GA) method called the Boltzmann random key-based GA (Brk-GA).