A model for the investigation of cost variances: the fuzzy set theory approach

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Virginia Polytechnic Institute and State University

Available cost-variance investigation models are reviewed and evaluated in Chapter Three of this study. As shown in the chapter, some models suffer from ignoring the costs and benefits of the investigation. Other models, although meeting the cost-benefit test, fail to capture the essence of the real-world problem. For example, they fail to handle the imprecision (fuzziness) surrounding the investigation decision. They are also based on the unrealistic assumptions of (1) a two-state system, and (2) constant level of accuracy and precision. In addition, the models suffer from the lack of applicability. They require precise numerical inputs to the analysis that are difficult, if not impossible, to attain.

This dissertation provides a new cost-variance investigation model that may overcome some of these problems. The new model utilizes the calculus of fuzzy set theory which was introduced by Zadeh in 1965 as a means for dealing with fuzziness. The theory is also intended to reduce the need for precise measures that are difficult to obtain. Consequently, the theory seems to be well suited for handling the investigation problem. (Chapter Two provides a summary of the theory and its applications in the decision making area.)

The new model is presented in Chapter Four and extended in Chapter Five. The performance is assumed to be described by·a transformation function,

St+1 = f(St,Dt),

where St, Dt, and St+1 represent the sets of the input states, available decisions, and output states, respectively. The transformation function can be deterministic, stochastic, or fuzzy.

Methods are suggested to obtain the optimal decision for the three cases of transformation functions. These methods are based on formulating a fuzzy optimal decision set

DO = {uDO(dj)dj},

where uDO(dj) represents the compatibility (i.e., relative merit) of decision dj with the optimal decision set. The optimal decision is the decision having the highest compatibility with the fuzzy optimal decision set.

In addition to allowing for different transformation functions, the new model allows for varying degrees of out-of-controllness. The model also provides for the fuzziness (imprecision) surrounding (1) the states of performance, (2) the net benefits from the investigation, and (3) the probabilities. This is done by employing the basic concept in fuzzy set theory, namely, the membership function concept.

The new model was examined (in Chapter Six) for feasibility. First, the model was computerized. Then, it was applied to an actual investigation problem encountered by a manufacturing company. As the application may indicate, the new model can be applied to real-world situations.