JAROSŁAW WTRÓBSKI Politechnika Szczeciska
Summary
Decision situations are related to various aspects of operations in an organisa-tion. Hence the content of information included in a decision maker’s expectations goes beyond defining criteria and setting a decision problematic. Finding a suitable approach is a task for an analyst who assists a decision maker in the decision proc-ess. The following paper synthesises premises used in analysing decision situations, which result in a choice of a multicriteria method to perform calculations. The con-cluded guidelines can be used as a vocabulary of analytical knowledge which allows to select a multicriteria method suitable for a given context of a decision situation. Keywords: information technology, internet usage, cluster analysis
1. Decision situations in operations of an economic organisation
Managing an economic organisation is filled with reactive actions against external stimulae. System theory defines an organisation as an open system, which goal is to reach stability in the environment with destabilising influence of disrupting factors. Considering an organisation more detailed than using the „black-box” approach defined by the system theory, a system intercon-nected subsystems and business processes emerges. Each process consists of communicating ac-tions, information processing and decisions.
Decision situations exist in every business process and in almost every business procedure. Significant importance to decisions should be given in interactive processes, based on interaction with humans. The common trend of automating all economic operations (processes) covers only simple and repetitive tasks. Whereas, the mentioned tasks include decision situations, in most cases those decisions are well described and codified. Hence it is possible to encode them as a single-criterion decision algorithm. Moreover, simple intra-procedural decisions are mostly binary (yes/no) decisions.
A difficulty arises when a decision involves choosing or grading (ranking) a number of avail-able alternatives. Such situations are encountered at the operational level, the tactical level as well as at the strategic level. Moreover, those situations are difficult to codify and to encode into an al-gorithm. Modelling decision processes in the mentioned situations is done by creating general guidelines for decisions and specifying desired outcomes of the implementation of a chosen deci-sion. The decision process itself is a manual operation of a business process and a burden of carry-ing tasks included in the process is on a person responsible for executcarry-ing a given instance of a process.
2. Expressing a decision situation as a criteria definition and a decision problematic
A decision problem according to B. Roy’s definition [1] is a representation of an element of a global decision. The literature distinguishes a number of types of decision alternatives. In the con-text of this paper, the essential division is the division on realistic alternatives (corresponding to a project, which implementation is feasible) and on unrealistic alternatives (which can include con-tradictory goals and can be only used for the discussion). The difficulty when solving multicriteria decision problems is the requirement of including alternatives’ judgements (choice alternatives) from various points of view, which refers to multicriteria judgements [2].
According to the outline presented above, the definition of a decision problem consists of a two-elements set presented below:
(
C
,
Φ
)
,where: C – a set of criteria, and – a set of meta-data of a decision situation.
The C set describes relations between properties of decision alternatives and preference levels of considered alternatives in respective aspects of consecutive elements of the description. The meta-data set consists of decision maker’s expectations about a decision situation. Determining decision criteria requires elaborating all properties of a desired post-implementation outcome of making the considered decision. An analytic task which is given to an analyst (an analyst and a decision makers states for roles and in practice can be assigned to a single person) is to reflect par-ticular aspects of considered implementation on characteristics describing possible options (deci-sion alternatives).
The fundamental element of the meta-data set is choice of a problematic of a decision situa-tion according to the division proposed in [1]:
a) problematic – the choice problematic (finding a subset of the A set which includes only the best solutions),
b) problematic – the sorting problematic (assigning alternatives to defined categories), c) problematic – the ordering problematic (constructing a ranking of alternatives in the set A from the best one to the worst one).
Fig. 3 Reference problematics (respectively choice α, ranking γ, and assignment β) in multicrite-ria decision aiding
Source: based on [1]
Determining a decision problematic is a very important, however not the only one determinant of a technique of carrying on the decision process. A problematic of a considered decision situation
depends on decision maker’s expectations for the process, as well as on characteristics of an ana-lysed decision. The following sample contexts determining the decision problematic are described in [4]: comparison (prioritise) of various technologies of energy production – problematic , choice of an investment plan – problematic , creating a set of projects – problematic .
3. Participation of an analyst in determining meta-data of a decision situation
Available tools for computer aided decision support are directed on calculating preference levels of considered decision alternatives using provided descriptions. Such an approach allows to automate only a part of the decision process. Applying multicriteria methods to analyse a decision situation requires making a deliberate choice of a method suitable for a given decision situation. The goal of the mentioned choice is to find the multicriteria transformation F which fulfils:
(
,
)
max
F C
Φ →
u
where u is an indicator of a decision maker’s satisfaction measured by his preferences.
Choosing a multicriteria method suitable for a given decision problem is made by an analyst who uses his knowledge about the environment of the problem and about characteristics of multicriteria methods. Particularly, in the aggregation phase, the way of dealing with differences between attrib-utes’ values is crucial. Nonetheless the impact of dispersion of those values on mutual preferences between decision alternatives shall not be neglected.
The purpose of the exploitation phase is to make an representation of the global preference which is the outcome of a decision maker’s expectations (meta-data) and mutual local preferences between particular decision alternatives.
4. Premises of the reality considered when analysing a decision situation
The environment of a decision situation is a factor which is not included in the decision process (a constant factor when compared to decision alternatives). The environment’s characteristics how-ever, have impact on judgements of decision alternatives and on outlining the preferred alterna-tives. Particularly, factors connected with the completeness of the description of a decision situa-tion included in a problem specificasitua-tion are the determinants of the mensitua-tioned completeness. An additional factor, which is important when choosing a suitable decision making approach, is the reality domain covering an analysed problem. Particular domains of decision situations are charac-terised by known dependencies among properties of actions and outcomes of their implementa-tions.
While researching guidelines for choosing a multicriteria approach for a decision situation, the pa-per focused on explanations provided by the scientific literature. The positions [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19] describe solving decision situations using one of the fol-lowing methods: PROMETHEE I/II, TOPSIS, ELECTRE III or AHP. The use of multicriteria methods for considered problems and claims supporting choices made were analysed. The conclu-sions drawn after analysing the literature were used to determine the structure of contextual infor-mation, which was used to analyse impacts of particular factors.
According to the mentioned above, a set of contextual determinants was created as the K set pre-sented below:
{
1,
2,
3,
4,
5,
6,
7,
8,
9}
where:
1
K
- Category of the subject of a decision, describes whether a decision is about an object, an ac-tion or a localisaac-tion (nominal variable)2
K
- Discipline of a decision, describes whether a decision is described by technical, social or economic determinants (nominal variable)3
K
- Describes whether conflicting criteria exist in a decision situation (binary variable)4
K
- Describes whether criteria covers the whole picture of a decision situation (binary variable)5
K
- Describes a number of criteria (ordinal variable)6
K
- Describes a number of alternatives (ordinal variable)7
K
- Describes a decision maker’s awareness level of a decision situation (ordinal variable)8
K
- Describes the scale of an analysed decision (ordinal variable)9
K
- The goal of a decision (nominal variable)It is suggested to consolidate the K set into the meta-data set of a decision situation as an in-tegral part of the decision process. The next step of the impact analysis of the outlined determi-nants was to discover significances of determidetermi-nants in choosing a multicriteria method suitable for a given decision situation.
5. Impact of identifying environmental factors on the results of decision aiding
Analysing the impact of the factors mentioned above was done using decision trees. The SAS En-terprise Miner software was used, and decision trees were induced using functions implemented into SAS Enterprise Miner. The entropy minimisation method was chosen. The following settings were used for inducing decision trees:
• minimum number observations in a leaf: 2, • observations required for a split search: 10,
• maximum number of branches from a node: 2 (binary tree), • splitting rules saved in each node: 5.
The analysis was performed for two types of the output: choosing a multicriteria method and choosing a decision aiding “school” (as a property dividing methods in two classes). The results of the analysis for choosing a particular method are presented on the Fig. 4. The naming was aligned to the format required by the LaTeX document preparation system, and was done as follows:
• $P_T$ - PROMETHEE I/II, • $T_P$ - TOPSIS,
• $A_H$ - AHP, • $E_3$ - ELECTRE III.
Fig. 4 Decision tree for choosing a method based on the context of a decision situation The correct classification rate for the decision tree choosing a multicriteria method equals 0,667. The induction process isolated the following subset of determinants which are sufficient in the as-pect of the analysed process:
{
2 6 7}
'
,
,
K
=
K K K
.It turned out that important factors of the context of a decision situation are: a decision discipline, a number of alternatives, and a decision maker’s awareness level of a decision situation.
de-scribes an approach based on the European school (outranking approach) and the value 2 dede-scribes the American school (utility value approach).
Fig. 5 Decision tree for choosing a decision aiding school based on a context of a decision situation
The correct classification rate for the decision tree choosing a decision aiding school method equals 0,714. The induction process isolated a single determinant which is sufficient in the aspect of the analysed process. Therefore the selected subset contains a single element, which is presented below:
{ }
8''
K
=
K
.It turned out that the scale of an analysed decision is the only significant factor. 6. Guidelines for improving reliability of the decision process
The paper proposes including the context of a decision situation in decision aiding tools. It was suggested to build a tool which would allow to define a set of parameters characterising environ-mental factors of a decision situation. A piece of software supporting multicriteria decisions was developed at the Szczecin University of Technology. The program allows to define not only crite-ria parameters, but also the meta-description of a decision situation. Users can define own proper-ties (meta-properproper-ties) describing a decision situation., which are used to make an assessment of the meta-information of a decision situation. A sample screenshot of a control defining an environ-mental factor in the program’s dictionary is presented on the Fig. 6.
Fig. 6 Definition of an environmental factor
The defined set of parameters describes the context of a decision situation using a dictionary of acceptable values. Two approaches are possible when using information gathered in the process. The first approach is to collect learning information in order to build a set of decision rules. The second approach is to use context information to activate rules in the knowledge base in order to choose a multicriteria method which is the most suitable for a given decision situation.
6. Concluding remarks
The choice of a multicriteria method based on the context of a decision situation allows to apply the same approach, which was used in the past with success. A chosen set of data gathered from scientific literature was used to discover four significant factors which are sufficient to describe suitability of a method to a decision situation. The isolated determinants are:
• the discipline of a decision, • a number of alternatives,
• the scale of an analysed decision.
The expected outcome of the program consists of marking methods suitable to solve a given deci-sion situation. During the research it was observed that that the more appropriate approach is to indicate a set of methods which is supported by a significant number of observations (above a mi-nimal level of support), along with the level of its support.
The Fig. 7 shows the list of methods included in the software with the suitable method checked.
Fig. 7 Choosing a multicriteria method to solve a decision problem
It is crucial to notice that some methods don’t include the full set of input information, which can be specified by a decision maker. For example the TOPSIS method doesn’t account veto, prefer-ence and indifferprefer-ence thresholds. Hprefer-ence, the research shall be continued on including a set of input information provided by a decision maker, in order to a better fir of a chosen multicriteria method to a given problem. Furthermore an available set of multicriteria methods should include a com-plete set of methods applied in situations which nature is similar to situations which are common in the organisation. Such an approach would allow making a choice of a method guided by real prem-ises, not by limitations of available tools.
5. Literature
1. B. Roy, The outranking approach and the foundations of ELECTRE methods, Theory and Decision, 31 (1991), pp. 49-73.
2. C. E. Escobar-Toledo, The Use of Multicriteria Decision Aid System in the Information Technology (IT) Allocation Problem, European Journal of Operational Research, 5/2(2005).
3. C. Araz and I. Ozkarahan, Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure, International Journal of Produc-tion Economics, 106 (2007), pp. 585-606.
4. J. P. Brans and P. Vincke, A PREFERENCE RANKING ORGANISATION METHOD, Management Science, 31 (1985), pp. 647-656.
5. J. P. Brans, P. Vincke and B. Mareschal, How to select and how to rank projects: The PROMETHEE method, European Journal of Operational Research, 24 (1986), pp. 228-238.
6. J.-J. Wang and D.-L. Yang, Using a hybrid multi-criteria decision aid method for informa-tion systems outsourcing, Computers & Operainforma-tions Research, 34 (2007), pp. 3691-3700.
7. M. Goumas and V. Lygerou, An extension of the PROMETHEE method for decision making in fuzzy environment: Ranking of alternative energy exploitation projects, Euro-pean Journal of Operational Research, 123 (2000), pp. 606-613.
8. A. Kangas, J. Kangas and J. Pykaelaeinen, Outranking Methods As Tools in Strategic Natural Resources Planning, Silva Fennica, 35 (2001), pp. 215-227.
9. G. Ozerol and E. Karasakal, A Parallel between Regret Theory and Outranking Methods for Multicriteria Decision Making Under Imprecise Information, Theory and Decision. 10. R. Rao and J. Davim, A decision-making framework model for material selection using a
combined multiple attribute decision-making method, The International Journal of Ad-vanced Manufacturing Technology, 35 (2008), pp. 751-760.
11. D.-F. Li, Compromise ratio method for fuzzy multi-attribute group decision making, Ap-plied Soft Computing, 7 (2007), pp. 807-817.
12. M.-T. Chu, J. Shyu, G.-H. Tzeng and R. Khosla, Comparison among three analytical methods for knowledge communities group-decision analysis, Expert Systems with Appli-cations, 33 (2007), pp. 1011-1024.
13. C.-C. Wei, C.-F. Chien and M.-J. J. Wang, An AHP-based approach to ERP system selec-tion, International Journal of Production Economics, 96 (2005), pp. 47-62.
14. C.-H. Cheng, K.-L. Yang and C.-L. Hwang, Evaluating attack helicopters by AHP based on linguistic variable weight, European Journal of Operational Research, 116 (1999), pp. 423-435.
15. T. L. Saaty, How to make a decision: The analytic hierarchy process, European Journal of Operational Research, 48 (1990), pp. 9-26.
16. T. L. Saaty, The Analytic Hierarchy and Analytic Network Processes for the Measure-ment of Intangible Criteria and for Decision-Making, Multiple Criteria Decision Analysis: State of the Art Surveys, 2005.
17. M. r. Augusto, J. o. Lisboa, M. Yasin and J. R. Figueira, Benchmarking in a multiple cri-teria performance context: An application and a conceptual framework, European Journal of Operational Research, 184 (2008), pp. 244-254.
18. J. Hokkanen and P. Salminen, ELECTRE III and IV Decision Aids in an Environmental Problem, Journal of Multi-Criteria Decision Analysis, 6 (1997), pp. 215-226.
19. M. Augusto, J. Lisboa, M. Yasin and J. R. Figueira, Benchmarking in a multiple criteria performance context: An application and a conceptual framework, European Journal of Operational Research, 184 (2008), pp. 244-254.
Zbigniew Piotrowski Jarosław Wtróbski
Instytut Systemów Informatycznych Wydział Informatyki
Politechnika Szczeciska
71-210 Szczecin ul. ołnierska 49 e-mail: zpiotrowski@wi.ps.pl e-mail: jwatrobski@wi.ps.pl
