Abstract A system of classifying about two dozen major methods for mathematical programming with multiple objectives, or multiple objective decision making (MODM) is presented. The classification has been based upon four categories of the preference information given to the analyst by a decision maker: (1) a priori , (2) progressive, (3) a posteriori and (4) no articulation of the preference information. A method or two from each category is illustrated by approaching a simple common numerical example in detail for the comparison and tutorial purpose. Consideration in selecting criteria for comparative evaluation of the methods and availability of computer codes for some methods are discussed.