In multiattribute decision theory, the distinction is made between dominated and undominated solutions. A solution is undominated if there is no solution that dominates it. Undominated solutions are on the boundary of the solution space and are also called Pareto efficient solutions. The theory of multiattribute decision making is primarily interested in how to move from inefficient solutions to efficient solutions, in sub-optimization. Managers search scenarios using computers in an interactive mode.
Spreadsheets are one of the most popular tools to manage scenarios.
WHAT-IF diagrams and ratios are commonly used to facilitate traveling in the solution space. The most powerful mathematical tool for trade-up is calculus, by evaluating ordinary and partial differential quotients. These predict the slopes of changes in values, when parameters or decision variables are changed slightly. The method of steepest descent is the basis of most search techniques. Tornado diagrams are popular graphical tools in decision analysis, but could be used in practically any field of decision sciences.