A new decomposition algorithm for a liquefied natural gas inventory routing problem

We consider an inventory routing problem (IRP) in the liquefied natural gas (LNG) supply chain, called the LNG-IRP. Here, an actor is responsible for the LNG production and inventory management at the liquefaction plants, the routing and scheduling of a heterogeneous fleet of LNG ships, as well as the inventories and sales at the regasification terminals. Furthermore, all ports have a limited number of berths available for loading and unloading. The LNG-IRP is more complicated than many other maritime inventory routing problems because a constant rate of the cargo evaporates in the tanks each day and is used as fuel during transportation. In addition, a variable number of tanks are unloaded at the regasification terminals. We introduce a new path flow formulation for this problem arising from a novel decomposition scheme based on parts of a ship schedule, called duties. A ship schedule for the entire planning horizon can be divided into duties consisting of a visit to a liquefaction plant, then one or two visits to a regasification terminal before ending in a liquefaction plant. The solution method suggested is based on a priori generation of duties, and the formulation is strengthened by valid inequalities. The same problem was previously solved by a branch-price-and-cut algorithm for a schedule-based formulation. Computational results show that the new formulation provides tighter bounds than the previous schedule-based formulation. Furthermore, on a set of 27 benchmark instances, the proposed algorithm clearly outperforms the previous branch-price-and-cut algorithm both with regard to computational time and the number of problems solved within a 10-h time limit.