Many multinational chemical companies (MNCs) manage the inventories of several raw materials at their worldwide sites. Maritime transportation plays a key role in this chemical logistics. In this paper, we address an inventory service problem in which a chemical MNC uses a fleet of multi-parcel ships with dedicated compartments to move multiple chemicals continually among its internal and external production and consumption sites. The objective is to ensure continuity of operation at all sites by maintaining adequate inventory levels of all raw materials. We develop a novel multi-grid continuous-time mixed-integer linear programming (MILP) formulation based (Susarla, Li, & Karimi, 2010) for this chemical logistics problem. Our model allows limited jetties at each site, non-zero transfer times, variable load/unload quantities, transfer task sequencing, etc. In contrast to the literature, it needs no separate estimates for arrivals at each site. Several examples are solved to illustrate the efficiency of our proposed formulation.