Optimization Methods for a Stakeholder Society pp 125-138 | Cite as

# Multifarious Comparisons for Objectives and Attributes

## Abstract

The previous chapter concluded that multifarious comparisons of alternatives are preferred above binary ones. For multifarious comparison, this chapter moves from some theoretically self-evident approaches to situations in which the alternatives seem to be incomparable. Indeed, an a priori priority between the objectives gives the impression that the problem is easily solved. This seems also the case, if some alternatives are dropped out, due to not satisfying some minimum or maximum requirements. In addition, domination of one alternative over all the others would easily solve the problem. The problem remains if a ranking turns out to be impossible with incomparably looking alternatives.

### Keywords

Manifold Sine Payback## Preview

Unable to display preview. Download preview PDF.

### Notes Part 3 Chapter 3

- 1.J.C. Holmes,
*An Ordinal Method of Evaluation*, Urban Studies, Vol. 9,N^{o}1,1972,179–191.Google Scholar - 2.D. Giokas, M. Vassiloglou,
*A goal programming model for bank assets and liabilities management*, European Journal of Operational Research, vol. 50, N^{o}l, 1991, 48–60.CrossRefGoogle Scholar - 3.R.E. Steuer,
*Multiple Criteria Optimization: Theory, Computation and Application*, Krieger, Malabar (Fla., U.S.), 1989, 292, develops a similar approach and calls it “preemptive goal programming”.Google Scholar - 4.The full details of the model with simulations not only for one country but also for the economic integration of several countries are given in: W.K. Brauers,
*Input-Output Analysis and International Economic Integration*(in Dutch with English Summary), Standaard Uitg., Antwerpen-Utrecht, 1968. W.K. Brauers,*Prévisions économiques à l’aide de la méthode entrées-sorties*, Economica, Paris, 1995.Google Scholar - 5.We represented lower bounds and upper limits by scalars, but these constraints could also be linear functions. In fact in the example of Chapter 2.4 and in Figure 3.2 the constraints are linear functions. Even nonlinear constraints are acceptable. The underlying idea we developed for the linear constraints still apply for the nonlinear ones. For nonlinear constraints, see: L.E. Edlefsen,
*The Comparative Statics of Hedonic Price Functions and other Nonlinear Constraints*, Econometrica, vol.49, 1981, 1501–1520.CrossRefGoogle Scholar - 6.A.P. Wierzbicki, M. Makowski,
*Multi-Objective Optimization in Negotiation Support*, WP-92-007, IASA Laxenburg (A), 1992., 4.Google Scholar - 7.As an example, see: W. K Brauers,
*Multiple Criteria Decision Making in Industrial Project Management*, Engineering Costs and Production Economics, Vol.20, 1990,.231–240.CrossRefGoogle Scholar - 8.R.E. Steuer,
*op.cit.*, 1989,147.Google Scholar - 9.Is domination absolute? Weitzman seems to deny it (M.L. Weitzman,
*Optimal search for the Best Alternative*, Econometrica, vol.47,3, May 1979, 641–654). There could be a problem of search known as*Pandora’s Box*. Weitzman shows an application of*Research and Development*. Two new technologies are considered: alpha and omega. Alpha dominates strongly omega. Alpha has lower research cost, shorter development lag, higher expected return, greater minimum return and less variance than omega. Nevertheless Weitzman proves that it is better to develop omega first. The example is completely theoretical. The final return is only known when the products are on the market. The problem is not sequential: try omega first and by failure, try alpha. The problem was just to make a choice on the basis of expectations. The expectations for alpha were: a 0.5 probability of a return of 100 and 0.5 of 55. It is not excluded that the final return of alpha is, for example, 80, but probably never 240. The expectations of omega were of another kind: 0.2 for 240 and 0.8 for zero.CrossRefGoogle Scholar - 10.H.H. Gossen, Entwicklung der Gesetze des menschlichen Verkehrs und der daraus flieszenden Regeln für menschliches Handeln, 1853, 3. Auflage, Prager, Berlin, 1927,6.Google Scholar
- 11.V. Pareto,
*Manuale di Economia Politica*, 1906, translation revised by Pareto himself::*Manuel d’économie politique*, second ed.. Paris, 1927.Google Scholar - 12.H. Gossen,,
*The Laws of Human Relations and the Rules of Human Action Derived Therefrom*, 1853, translated by R.C.Blitz, The MIT Press, Cambridge (Mass), 1983, 9. Edition in German of 1927,6.Google Scholar - 13.W. Vickrey,
*Microstatics*, Harcourt and Brace, New York — Chicago, 1964.Google Scholar - 14.G. Stigler,
*Notes on the history of the Giffen Paradox*, Journal of Political Economy, 152–155, April 1947.Google Scholar - 15.H. Minkowsky,
*Geometrie der Zahlen*, Teubner, Leipzig, 1896, 35. D. Hilbert,*Gesammelte Abhandlungen von Hermann Minkowski, 1911*, Teubner, Leipzig, reprinted by Chelsea publishing company, New York, 1967, XI and Vol.II, 103. A.V. Pogorelov,*The Minkowski Multidimensional Problem*, John Wiley, New York, 1978, 9.Google Scholar - 16.For this point, see: W.W. Leontief,
*The Use of Indifference Curves in the Analysis of Foreign Trade*, Quarterly Journal of Economics, 1933, 493–503Google Scholar - 17.W.W. Leontief,
*op. cit.*More developed in: C.P. Kindleberger,*International Economics*, first edition, Irwin Inc. Homewood (Ill.), 1953,102–103.Google Scholar