This paper addresses the scheduling and inventory management of a straight pipeline system connecting a single refinery to multiple distribution centers. By increasing the number of batches and time periods, maintaining the model resolution by using linear programming-based methods and commercial solvers would be very time-consuming. In this paper, we make an attempt to utilize the problem structure and develop a decomposition-based algorithm capable of finding near-optimal solutions for large instances in a reasonable time. The algorithm starts with a relaxed version of the model and adds a family of cuts on the fly, so that a near-optimal solution is obtained within a few iterations. The idea behind the cut generation is based on the knowledge of the underlying problem structure. Computational experiments on a real-world data case and some randomly generated instances confirm the efficiency of the proposed algorithm in terms of the solution quality and time.