Over the past decade, flowsheet optimization has become an important tool for process design. However, for flowsheet optimization the most time consuming step is devoted to the evaluation of the first derivatives, especially for modular process simulators. To overcome this problem, the ProSim simulator has been modified in order to generate exact gradient information automatically. Based on the modular input-output sensitivities and a chain-ruling procedure, this strategy allows significant time savings during the optimization. Several optimization methods are implemented (a Reduced Gradient and two Successive Quadratic Programming strategies) and their results are compared in combination with the analytical derivatives. Furthermore, it is often useful to assess the sensitivity of the optimum flowsheet to design parameters (e.g. feed flowrates, constants in kinetic and transport equations) that may be subject to variation and uncertainty. With the calculation of exact derivatives, post-optimality analyses, which were considered too expensive before, can now be implemented with very inexpensive computational costs. The optimal flowsheet sensitivity analysis thus allows us to estimate easily the changes in the optimal process under parametric variations and other process uncertainties.