The dual simplex method is preferred in situations where the primal feasible region is not maintained, such as during the modification of an optimal solution when constraints are added or changed. It is particularly useful when dealing with large-scale linear programming problems where maintaining primal feasibility is challenging. Additionally, the dual simplex method is beneficial when the dual problem is easier to solve or when the objective function needs to be minimized rather than maximized, as it efficiently handles situations where dual feasibility is maintained while primal feasibility may not be.