The Analysis of Interconnected Decision Areas: A Computational Approach to Finding All Feasible Solutions

Abstract

This paper provides a method for finding the complete set of feasible solutions to a problematic situation, whose structure is that of a network amenable to the analytical approach known as “analysis of interconnected decision areas”, or AIDA. In doing so, the paper not only resolves a long-standing computational problem, but also offers means for examining all solutions in either lists or diagrams, thus empowering decision-makers to make informed judgments as to how to tackle an entire problem or its subsets. The analytical advantage of using a signed graph in AIDA computations is demonstrated, proffering an innovative contribution to the approach. The paper concludes by identifying potentially fruitful avenues of future research as well as interdisciplinary opportunities.

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Notes

  1. 1.

    The term “feasible solution” is one used by Harary et al. (1965), who also use the term “α-combination”. Synonymous terms in the literature include “solution stream” (Hickling 1978: 473), “feasible strategy” (Friend 1992: 160), “compatible set” (Weas and Campbell 2004: 233), and “decision scheme” (Friend and Hickling 2005: 37–38, 67–69, 130–135).

  2. 2.

    Harary et al. (1965) also asked a third question concerning the “cost”, or weight, of each feasible solution. This is a simple matter of appending coefficients to options that constitute a feasible solution, and is, therefore, not addressed in this paper.

  3. 3.

    Since the present paper is concerned solely with the computational problem, all designations in the example of Fig. 1 serve merely as convenient labels. For contextual information concerning the data shown in Fig. 1, readers may follow the indicated reference.

  4. 4.

    Also known as “compatibility matrix” (Friend and Hickling 2005: 35; Hickling 1978: 472), “incompatibility matrix” (Blandford and Hope 1985: 209), and “interaction matrix” (Jones 1970/1992: 311–312).

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Georgiou, I., Heck, J. & Mrvar, A. The Analysis of Interconnected Decision Areas: A Computational Approach to Finding All Feasible Solutions. Group Decis Negot 28, 543–563 (2019). https://doi.org/10.1007/s10726-018-9607-5

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Keywords

  • Computational model
  • Computer supported design
  • Networks
  • Decision-making
  • Pajek software