This paper addresses the problem of inventory management of a refinery that imports several types of crude oil which are delivered by different vessels. This problem involves optimal operation of crude oil unloading, its transfer from storage tanks to charging tanks, and the charging schedule for each crude oil distillation unit. A mixed-integer optimization model is developed which relies on time discretization. The problem involves bilinear equations due to mixing operations. However, the linearity in the form of a mixed-integer linear program (MILP) is maintained by replacing bilinear terms with individual component flows. The LP-based branch and bound method is applied to solve the model, and several techniques, such as priority branching and bounding, and special ordered sets are implemented to reduce the computation time. This formulation and solution method was applied to an industrial-size problem involving 3 vessels, 6 storage tanks, 4 charging tanks, and 3 crude oil distillation units over 15 time intervals. The MILP model contained 105 binary variables, 991 continuous variables, and 2154 constraints and was effectively solved with the proposed solution approach.