This research deals with chemical transport Problems involving maritime pick up from and delivery to storage tanks that are continuously filled and drained. More specifically, we developed decision technology to determine the efficient use of multi compartment bulk ships to transport chemical products while ensuring continuous production with no stock-outs, so that the inventory level of chemical products in storage tanks are maintained between prescribed upper and lower stock levels during the planning horizon. Due to the nature of the products, it is impossible to carry more than two products without these being separated into dedicated compartments of the ships. We need to decide how much of each product to carry, on which ship, subject to the conditions that all harbors must have sufficient product to meet demand, and the stock levels of the products cannot exceed the inventory capacity of that harbor. We have formulated this ship-routing problem as a combined multi-ship pickup-delivery problem with inventory constraints. The original problem is a large-scale non-convex mixed-integer programming problem. All non-convexities involved weighted sums of products of two variables, one of which is binary and the other is continuous but bounded. We have shown that the structure gives rise to an equivalent large-scale linear mixed-integer programming problem (MILP). We studied the underlying structure of the MILP and developed a solution strategy by Lagrangian relaxation method for this large scale MILP with special structure. We also devised heuristic methods that are fast and find a good solution and conducted numerical studies that show how good does the heuristic solution compared to the dual bounds.