Some Thoughts on MCDM: Myths and Ideas
Decision making is a most important function and process of management. It is one of the most pervasive problems of management and a pervasive problem in general. Multiple criteria decision making is an approach to decision making. It is the making of decisions taking into consideration multiple conflicting objectives. How do we make decisions? What is involved? There are many simple paradigms, and until recently about all that could be said was that you should list the alternatives, score them on certain dimensions, and then somehow aggregate the scores, and choose an alternative. Unfortunately, many excellent decision makers simply choose an alternative, based on instinct, intuition, or feel. Then they go on. Though that is fine in many cases; in some cases it is not. In this paper I consider some myths of decision making. I then propose some steps that we, as decision analysts and scientists, should consider taking to try to sensitize decision makers to thinking more about their decisions and making better decisions.
Optimum Multivariate Stratified Sampling Designs with Travel Cost: A Multiobjective Integer Nonlinear Programming Approach
The problem of optimum allocation in stratified sampling and its solution is well known in sampling literature for univariate populations (see Cochran, 1977; Sukhatme et al., 1984). In multivariate populations where more than one characteristics are to be studied on every selected unit of the population the problem of finding an optimum allocation becomes more complex due to conflicting behaviour of characteristics. Various authors such as Dalenius (1953, 1957), Ghosh (1958), Yates (1960), Aoyama (1963), Gren (1964, 1966), Folks and Antle (1965), Hartley (1965), Kokan and Khan (1967), Chatterjee (1972), Ahsan and Khan (1977, 1982), Chromy (1987), Wywial (1988), Bethel (1989), Kreienbrock (1993), Jahan et al. (1994), Khan et al. (1997), Khan et al. (2003), Ahsan et al. (2005), Díaz-García and Ulloa (2006, 2008), Ahsan et al. (2009) etc. used different compromise criteria to work out a compromise allocation that is optimum for all characteristics in some sense. Almost all the previous authors used some function of the sampling variances of the estimators of various characteristics to be measured as an objective that is to be minimized for a fixed cost given as a linear function of sample allocations. Because the variances are not unit free it is more logical to consider the minimization of some function of squared coefficient of variations as an objective. Previously this concept was used by Kozok (2006). Furthermore, investigators have to approach the sampled units in order to get the observations. This involves some travel cost. Usually this cost is neglected while constructing a cost function. This travel cost may be significant in some surveys. For example if the strata consist of some geographically difficult-to-approach areas. The authors problem of optimum allocation in multivariate stratified sampling is discussed with an objective to minimize simultaneously the coefficients of variation of the estimators of various characteristics under a cost constraint that includes the measurement as well as travel cost. The formulated problem of obtaining an optimum compromise allocation turns out to be a multiobjective all-integer nonlinear programming problem. Three different approaches are considered: the value function approach, ∈ –constraint method, and Distance–based method, to obtain compromise allocations. The cost function considered also includes the travel cost within stratum to reach the selected units. Additional restrictions are placed on the sample sizes to avoid oversampling and ensure the availability of the estimates of the strata variances. Numerical examples are also presented to illustrate the computational details of the proposed methods.
An exposition of the AHP in reply to the paper “remarks on the analytic hierarchy process”
It is a fact that people make decisions and have been making decisions for a very long time. Contrary to what some of us who are interested in decision-making may like to believe, most people do not take seriously the existence of theories which purport to set their thinking and feeling right. They claim to know their own value system and what they want. They may wonder how anyone else can know well enough to tell them how best to organize their thinking in order to make better choices. Yet, research has shown that complex decisions are beyond the capacity of the brain to synthesize intuitively and efficiently. Since decision making is a natural characteristic of people, how do we describe what they do so that an ordinary mortal can understand what we are saying? We do not wish to legislate the method with which people should make decisions, but only to describe it even when it is prescribed by some method. In the process, we may learn things that can help people make better decisions. How? The Analytic Hierarchy Process (AHP) (Forman et al., Harker 1986, Harker and Vargas 1987, Saaty 1986, 1988a, b, Saaty and Vargas 1987, Xu 1988, Golden et al. 1989, Saaty and Alexander 1989) is a theory of measurement. When applied in decision making it assists one to describe the general decision operation by decomposing a complex problem into a multi-level hierarchic structure of objectives, criteria, subcriteria and alternatives. The AHP provides a fundamental scale of relative magnitudes expressed in dominance units to represent judgments in the form of paired comparisons. A ratio scale of relative magnitudes expressed in priority units is then derived from each set of comparisons. An overall rcatio scale of priorities is then synthesized to obtain a ranking of the alternatives. From its axioms to its procedures, the AHP has turned out to be historically and theoretically a different and independent theory of decision making from utility theory. Much as a dialogue evolved in mathematics around the consistency of different geometries and around absolute and relative space and time in physics, both to dispel absolute notions, those who believe that only utility theory can tell us the absolute truth about man's decision-making might take a close look at the AHP. It has found varied and serious applications. It also has a particular way of generating ratio scales and dealing with inconsistency in judgment that have contributed to its effectiveness in resource allocation and in the setting of priorities by a group of decision makers. Utility theory is a normative process. The AHP as a descriptive theory encompasses procedures leading to outcomes as would be ranked by a normative theory. But it must go beyond to deal with outcomes not accounted for by the demanding assumptions of a normative theory. We must briefly describe the AHP to enable the reader to see that a practicable theory based on ratio scales need not dilute itself to satisfy expectations of people who derive their understanding from a theory based on interval scales. This is particularly true if the rival theory, in aspiring for generality, also makes unrealistic assumptions, for example about the transitivity and consistency of preferences and the difficult use of lotteries,