This article is an update of an article five of us published in 1992. The areas of Multiple Criteria Decision Making (MCDM) and Multiattribute Utility Theory (MAUT) continue to be active areas of management science research and application. This paper extends the history of these areas and discusses topics we believe to be important for the future of these fields.

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Management science and decision science have grown exponentially since midcentury. Two closely-related fields central to this growth are multiple criteria decision making (MCDM) and multiattribute utility theory (MAUT). This paper comments on the history of MCDM and MAUT and discusses topics we believe are important in their continued development and usefulness to management science over the next decade. Our aim is to identify exciting directions and promising areas for future research.decision making, multiattribute, multiple criteria

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We present a framework for inverse optimization in a Markowitz portfolio model that is extended to include a third criterion. The third criterion causes the traditional nondominated frontier to become a surface. Until recently, it had not been possible to compute such a surface. But by using a new method that is able to generate the nondominated surfaces of tri-criterion portfolio selection problems, we are able to compute via inverse optimization the implied risk tolerances of given funds that pursue an additional objective beyond risk and return. In applying this capability to a broad sample of conventional and socially responsible (SR) mutual funds, we find that after the screening process there appears to be no significant difference between how assets are allocated in socially responsible and conventional mutual funds, which is likely to be different from what most SR investors would expect.

In standard portfolio theory, an investor is typically taken as having one stochastic objective, to maximize the random variable of portfolio return. But in this paper, we focus on investors whose purpose is to build, more broadly, a "suitable portfolio" taking additional concerns into account. Such investors would have additional stochastic and deterministic objectives that might include liquidity, dividends, number of securities in a portfolio, social responsibility, and so forth. To accommodate such investors, we develop a multiple criteria portfolio selection formulation, corroborate its appropriateness by examining the sensitivity of the nondominated frontier to various factors, and observe the conversion of the nondominated frontier to a nondominated surface. Furthermore, multiple criteria enable us to provide an explanation as to why the "market portfolio," so often found deep below the nondominated frontier, is roughly where one would expect it to be with multiple criteria. After commenting on solvability issues, the paper concludes with the idea that what is the "modern portfolio theory" of today might well be interpreted as a projection onto two-space of a real multiple criteria portfolio selection problem from higher dimensional space.

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