Nowadays, oil refineries are facing a challenging task to optimize their production levels and increase their incomes. The objective of refinery optimization is to determine the best production levels that can maximize profit and minimize operating costs with respect to operational and environmental constraints. The existence of uncertainty or variations in some parameters such as the prices of raw materials and products can seriously affect the optimization results and lead to inefficient operation. Many techniques of stochastic programming were proposed to handle the effect of variations in process parameters in order to determine a robust operation conditions; however, applications of postoptimality analysis have received less attention, especially in the refinery industry. In this work, postoptimality analysis is used to study the effect of such variations on the optimal solution of refinery process that is simplified and formulated as a LP model. We used a modified method of postoptimality analysis that jointly use sensitivity relations and stability region calculations to provide the decision maker in the refinery with valuable and easy-to-use information that helps in handling the effect of variation in process parameters. The results of this study can help the decision maker to identify sensitive parameters that need accurate estimate or intensive monitoring; and compute their stability limits, allowable variation ranges, within which the operation remains optimum. Independent and simultaneous variations in the products prices or in the capacities of process units are considered in this study; and it is shown how the refinery profit can be increased up to 4.2% by utilizing sensitivity and stability results.