Supply chain network (SCN) design is a strategic issue which aims at selecting the best combination of a set of facilities to achieve an efficient and effective management of the supply chain. This paper presents an innovative encoding-decoding procedure embedded within a genetic algorithm (GA) to minimize the total logistic cost resulting from the transportation of goods and the location and opening of the facilities in a single product three-stage supply chain network. The new procedure allows a proper demand allocation procedure to be run which avoids the decoding of unfeasible distribution flows at the stage of the supply chain transporting products from plants to distribution centers. A numerical study on a benchmark of problems demonstrates the statistical outperformance of the proposed approach vs. others currently available in literature in terms of total supply chain logistic cost saving and reduction of the required computation burden to achieve an optimal design.