Planejamento das viagens de navios com vários porões para transporte de blocos de granito considerando a arrumação com rotação em três dimensões em cada porão e o equilíbrio dos navios nos sentidos proa-popa e bombordo-boreste

Abstract

Brazil is among the largest producers in the world market of ornamental stones, and Espírito Santo is responsible for more than 60% of the national production. More specifically, the Port of Vitoria is the one that stands out most in the export of granite blocks and the like. The granite blocks have different sizes and are transported in the holds of general cargo ships, but transport costs are high. For this reason, it is extremely important to plan the ships’ trips and the arrangement of the loads, in order to reduce these costs. Aiming to assist in this planning, a mathematical model for the integrated problem of ship routing and three-dimensional arrangement of blocks in holds is proposed, considering the availability of different ships, multiple trips, time windows, orthogonal rotation of blocks in three dimensions (3D rotation), unloading sequence and the balance of ships in loading. The model seeks to minimize the costs of ships to be chartered and the distance to sail in the planning horizon. In addition, it minimizes total travel time and unbalanced load distribution in the bow-stern and portstarboard directions. The model was tested with CPLEX solver. In the tests, an exporter that charters ships under Time Charter contracts to export granite blocks from the Port of Vitoria was considered, and the model proved to be capable of representing the transportation planning problem in question. The results obtained showed that 3D rotation in cargo arrangement can save a trip or even a ship. By minimizing the imbalance in cargo distribution, completely balanced arrangements were obtained that avoid maneuvers with water ballast to maintain the balance of ships in the loading port.