We propose a global optimization algorithm for mixed-integer nonlinear programming (MINLP) problems arising from oil refinery planning. It relies on tight mixed-integer linear programming (MILP) relaxations that discretize the bilinear terms dynamically using either piecewise McCormick (PMCR) or normalized multiparametric disaggregation (NMDT). Tight relaxations help finding a feasible solution of the original problem via a local nonlinear solver, with the novelty being the generation of multiple starting points from CPLEXs solution pool and the parallel execution. We show that optimality-based bound tightening (OBBT) is essential for large-scale problems, even though it is computationally expensive. To reduce execution times, OBBT is implemented in parallel. The results for a refinery case study, featuring units with alternative operating modes, intermediate storage tanks, and single- and multiple-period supply and demand scenarios, show that the algorithms performance is comparable to commercial solvers BARON and ANTIGONE.