Skip to main content
SpringerLink
Log in

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

  • Published:
Group Decision and Negotiation Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  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. 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. 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. 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).

References

  • Ackoff R (1967) Management misinformation systems. Manag Sci 14(4):B147–B156

    Article  Google Scholar 

  • Aho AV, Hopcroft JE, Ullmann JD (1974) The design and analysis of computer algorithms. Addison-Wesley, New York

    Google Scholar 

  • Aldous JM, Wilson RJ (2000) Graphs and applications: an introductory approach. Springer, London

    Book  Google Scholar 

  • Banxia (2005) Decision explorer online reference. Version 3.3. Banxia Software Limited, Kendal

    Google Scholar 

  • Barnard JM (1993) Substructure searching methods: old and new. J Chem Inf Comput Sci 33(4):532–538

    Article  Google Scholar 

  • Batagelj V (1991) Some mathematics of network analysis. Network seminar, Department of Sociology, University of Pittsburgh

  • Batagelj V (2003) Efficient algorithms for citation network analysis. University of Ljubljana, Institute of Mathematics, Physics and Mechanics, Department of Theoretical Computer Science, Preprint Series, 41, 1–27 (arXiv:cs/0309023v1, 14 September)

  • Batagelj V, Cerinšek M (2013) On bibliographic networks. Scientometrics 96(3):845–864

    Article  Google Scholar 

  • Batagelj V, Mrvar A (1998) Pajek: a program for large network analysis. Connections 21(2):47–57

    Google Scholar 

  • Batagelj V, Mrvar A (2008) Analysis of kinship relations with Pajek. Soc Sci Comput Rev 26(2):224–246

    Article  Google Scholar 

  • Batagelj V, Mrvar A (2014) Pajek. In: Alhajj R, Rokne J (eds) Encyclopedia of social network analysis and mining. New York: Springer, pp 1245–1256. [Also see the latest version online: Batagelj V, Mrvar A (2018) Pajek and PajekXXL. In: Alhajj R, Rokne J (eds) Encyclopedia of social network analysis and mining. Springer, New York. https://link.springer.com/referenceworkentry/10.1007/978-1-4939-7131-2_310. Accessed 14 Oct 2018

  • Batagelj V, Zaversnik M (2011) Fast algorithms for determining (generalized) core groups in social networks. Adv Data Anal Classif 59(2):129–145

    Article  Google Scholar 

  • Batagelj V, Doreian P, Ferligoj A, Kejžar N (2014) Understanding large temporal networks and spatial networks: exploration, pattern searching, visualization and network evolution. Wiley, Chichester

    Book  Google Scholar 

  • Bayazit N, Esin N, Ozsoy A (1981) Integrative approach to design techniques. Des Stud 2(4):215–223

    Article  Google Scholar 

  • Blandford S, Hope RP (1985) Systematic methods for the problem solving process with particular reference to design. IEE Proc A Phys Sci Meas Instrum Manag Educ Rev 132(4):199–212

    Article  Google Scholar 

  • Bonnici V, Giugno R, Pulvirenti A, Shasha D, Ferro A (2013) A subgraph isomorphism algorithm and its application to biochemical data. BMC Bioinform 14(7):S13

    Article  Google Scholar 

  • Brualdi RA (2018) Introductory combinatorics. Fifth edition [2018 reissue]. Pearson, New York

    Google Scholar 

  • Burbidge JL (1973) AIDA and group technology. Int J Prod Res 11(4):315–324

    Article  Google Scholar 

  • Cartwright D, Harary F (1956) Structural balance: a generalization of Heider’s theory. Psychol Rev 63(5):277–293

    Article  Google Scholar 

  • Chartrand G (1977) Introductory graph theory. Dover, New York

    Google Scholar 

  • Cohen MN (1995) Lewis carroll: a biography. Alfred A. Knopf, New York

    Google Scholar 

  • Conte D, Foggia P, Sansone C, Vento M (2004) Thirty years of graph matching in pattern recognition. Int J Pattern Recognit Artif Intell 18(03):265–298

    Article  Google Scholar 

  • Cook DJ, Holder LB (2007) Mining graph data. Wiley, Chichester

    Google Scholar 

  • de Nooy W, Mrvar A, Batagelj V (2018) Exploratory social network analysis with Pajek. Revised and expanded edition for updated software: third edition. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Dorst K, Royakkers L (2006) The design analogy: a model for moral problem solving. Des Stud 27(6):633–656

    Article  Google Scholar 

  • e Costa CAB, Lourenço JC, Oliveira MD, e Costa JCB (2014) A socio-technical approach for group decision support in public strategic planning: the Pernambuco PPA case. Group Decis Negot 23(1):5–29

    Article  Google Scholar 

  • Eppstein D (1999) Subgraph isomorphism in planar graphs and related problems. J Graph Algorithms Appl 3(3):1–27

    Article  Google Scholar 

  • Fillmore J, Williamson S (1974) On backtracking: a combinatorial description of the algorithm. Soc Ind Appl Math J Comput 3(1):41–55

    Google Scholar 

  • Foggia P, Percannella G, Vento M (2014) Graph matching and learning in pattern recognition in the last 10 years. Int J Pattern Recognit Artif Intell 28(01):1450001

    Article  Google Scholar 

  • Friend J (1989) The strategic choice approach. In: Rosenhead J (ed) Rational analysis for a problematic world: problem structuring methods for complexity, uncertainty and conflict. Wiley, Chichester, pp 121–157

    Google Scholar 

  • Friend J (1992) New directions in software for strategic choice. Eur J Oper Res 61(1–2):154–164

    Article  Google Scholar 

  • Friend J (2001) The strategic choice approach. In: Rosenhead J, Mingers J (eds) Rational analysis for a problematic world revisited: problem structuring methods for complexity, uncertainty and conflict, 2nd edn. Wiley, Chichester, pp 115–149

    Google Scholar 

  • Friend J (2014) Starting to build a useful science of public policy choice. Operational Research Society, Document Repository, IOR Legacy Section. Birmingham: West Midlands. Available at the following URL: http://www.theorsociety.com/DocumentRepository/Browse.aspx?CatID=1. Accessed 26 Nov 2018

  • Friend J, Hickling A (2005) Planning under pressure: the strategic choice approach, 3rd edn. Elsevier Butterworth Heinemann, Oxford

    Google Scholar 

  • Friend J, Norris ME, Stringer J (1988) The institute for operational research: an initiative to extend the scope of OR. J Oper Res Soc 39(8):705–713

    Article  Google Scholar 

  • Friend D, Friend J, Cushman M (2002) STRAD: the STRategic ADviser, version 2.3 for Windows, release 2.30 July 2002. User’s Manual. Stradspan Limited, Sheffield

    Google Scholar 

  • Gat D, Gonen A (1981) Orientation map for planning and design methods. Des Stud 2(3):171–175

    Article  Google Scholar 

  • Golomb SW, Baumert LD (1965) Backtrack programming. J Assoc Comput Mach 12(4):516–524

    Article  Google Scholar 

  • Hage P, Harary F (1983) Structural models in anthropology. Cambridge University Press, Cambridge

    Google Scholar 

  • Harary F (1957) Structural duality. Behav Sci 2(4):255–265

    Article  Google Scholar 

  • Harary F (1969) Graph theory. Addison Wesley, Reading

    Book  Google Scholar 

  • Harary F, Jessop N, Luckman J, Stringer J (1965) Analysis of interconnected decision areas: an algorithm for project development. Nature 206(4979):118

    Article  Google Scholar 

  • Hickling A (1978) AIDA and the levels of choice in structure plans. Town Plan Rev 49(4):459–475

    Article  Google Scholar 

  • Hope RP, Sharp JA (1989) The use of two planning decision support systems in combination for the redesign of an MBA information technology programme. Comput Oper Res 16(4):325–332

    Article  Google Scholar 

  • Hsiao S-W, Chou J-R (2004) A creativity-based design process for innovative product design. Int J Ind Ergon 34(5):421–443

    Article  Google Scholar 

  • Hsiao S-W, Chuang JC (2003) A reverse engineering based approach for product form design. Des Stud 24(2):155–171

    Article  Google Scholar 

  • Jones JC (1970/1992) Design methods, second edition. Wiley, Chichester

  • Jones JC (1979) Designing designing. Des Stud 1(1):31–35

    Article  Google Scholar 

  • Kammeier H (1998) A computer-aided strategic approach to decision making in urban planning: an exploratory case study in Thailand. Cities 15(2):105–119

    Article  Google Scholar 

  • Kirsh D (2000) A few thoughts on cognitive overload. Intellectica 30(1):19–51

    Google Scholar 

  • Knuth D (1997) The art of computer programming: volume 1, fundamental algorithms, 3rd edn. Addison Wesley, Upper Saddle River

    Google Scholar 

  • Knuth D (2015) The art of computer programming: volume 4, satisfiability, fascicle 6. Addison Wesley, Boston

    Google Scholar 

  • Krissinel EB, Henrick K (2004) Common subgraph isomorphism detection by backtracking search. Softw: Pract Exp 34(6):591–607

    Google Scholar 

  • Larrosa J, Valiente G (2002) Constraint satisfaction algorithms for graph pattern matching. Math Struct Comput Sci 12(4):403–422

    Article  Google Scholar 

  • Luckman J (1967) An approach to the management of design. OR 18(4):345–358

    Article  Google Scholar 

  • Norese MF, Rolando D, Fregonara E (2015) Integration of problem structuring methods: a methodological proposal for complex regional decision-making processes. Int J Decision Support Syst Technol 7(2):58–83

    Article  Google Scholar 

  • Phahlamohlaka J, Friend J (2004) Community planning for rural education in South Africa. Eur J Oper Res 152(3):684–695

    Article  Google Scholar 

  • Randic M (1978) Fragment search in acyclic structures. J Chem Inf Comput Sci 18(2):101–107

    Article  Google Scholar 

  • Randic M, Wilkins CL (1979) Graph-based fragment searches in polycyclic structures. J Chem Inf Comput Sci 19(1):23–31

    Article  Google Scholar 

  • Rosenhead J (1996) What’s the problem? An introduction to problem structuring methods. Interfaces 26(6):117–131

    Article  Google Scholar 

  • Rosenhead J, Mingers J (2001) Rational analysis for a problematic world revisted: problem structuring methods for complexity, uncertainty and conflict. Wiley, Chichester

    Google Scholar 

  • Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York

    Google Scholar 

  • Schoch D (2015) A positional approach for network centrality. Dissertation submitted for the degree of Doctor of Natural Sciences, Department of Computer and Information Science, Universität Konstanz. Available at the following URL: https://kops.uni-konstanz.de/handle/123456789/34821. Accessed 11 Oct 2018

  • Schoch D, Brandes U (2016) Re-conceptualizing centrality in social networks. Eur J Appl Math 27(6):971–985

    Article  Google Scholar 

  • Sharifzadegan MH, Fathi H, Zamanian R (2014) Using strategic choice approach in urban regeneration planning (Case study: Dolatkhah area in Tehran, Iran). Int J Archit Urban Dev 4(2):45–52

    Google Scholar 

  • Smith RP, Morrow JA (1999) Product development process modeling. Des Stud 20(3):237–261

    Article  Google Scholar 

  • Stradspan Ltd. (2014) http://www.stradspan.com/about.htm and http://www.stradspan.com/products.htm. Retrieved 10 Feb 2018

  • Tarjan RE (1972) Depth-first search and linear graph algorithms. Soc Ind Appl Math J Comput 1(2):146–160

    Google Scholar 

  • Todella E, Lami IM, Armando A (2018) Experimental use of strategic choice approach (SCA) by individuals as an architectural design tool. Group Decision and Negotiation https://doi.org/10.1007/s10726-018-9567-9 (online pending print publication)

  • Tsang E (1993) Foundations of constraint satisfaction. Academic Press, London

    Google Scholar 

  • Vento M (2015) A long trip in the charming world of graphs for pattern recognition. Pattern Recognit 48(2):291–301

    Article  Google Scholar 

  • Weas A, Campbell M (2004) Rediscovering the analysis of interconnected decision areas. Artif Intell Eng Des Anal Manuf 18(3):227–243

    Article  Google Scholar 

  • Wells MB (1971) Elements of combinatorial computing. Pergamon, Oxford

    Google Scholar 

  • Willett P, Barnard JM, Downs GM (1998) Chemical similarity searching. J Chem Inf Comput Sci 38(6):983–996

    Article  Google Scholar 

  • Wilson B (2001) Soft systems methodology: conceptual model building and its contribution. Wiley, Chichester

    Google Scholar 

  • Wu F-G, Sun H-H, Lin Y-C (2015) Innovative aid design of moving kitchenware for elders. Procedia Manuf 3:6266–6273

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Informática e Métodos Quantitativos (IMQ), Fundação Getulio Vargas (FGV), Escola de Administração de Empresas de São Paulo (EAESP), Rua Itapeva 474 – 9 andar, sala 901, Bairro Bela Vista, São Paulo, SP, 01332-000, Brazil

    Ion Georgiou & Joaquim Heck

  2. Faculty of Social Sciences, University of Ljubljana, Kardeljeva pl. 5, 1000, Ljubljana, Slovenia

    Andrej Mrvar

Authors
  1. Ion Georgiou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joaquim Heck
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrej Mrvar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ion Georgiou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10726-018-9607-5

Keywords

Search

Navigation