A comparison of two reference point methods in multiple objective mathematical programming

When making decisions with multiple criteria, a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria. In multiple objective mathematical programming, solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions. These reference point solution methods commonly use a scalarizing function that reaches down from the ideal solution, in a direction specified by the aspiration point. Conversely, a similar scalarizing function can push out from the nadir point toward a specified aspiration point. In this paper we explore the structure of these two reference point approaches, examine the discrepancy between resulting solutions and consider the effect of problem framing on decision maker behaviour.