A Software Decision Support System

MKA-2 1. Purpose of MKA-2 system Different tasks in planning, control, analysis and monitoring in economy,

transport, industrial production, education, ecology and other spheres can be reduced to multicriteria decision making problems. Multicriteria decision making problems can be divided into two separate classes depending on their formal statement. In the first class a finite number of explicitly set constraints in the form of functions define an infinite number of feasible alternatives. These problems are called continuous multicriteria decision making problems or multicriteria optimization problems. In the second class of problems a finite number of alternatives are explicitly given in a tabular form. These problems are called discrete multicriteria decision making problems or multicriteria analysis problems.

In multicriteria analysis problems several criteria are simultaneously optimized in the feasible set of alternatives. In the general case there does not exist one alternative, which optimizes all the criteria. There is a set of alternatives however, characterized by the following: each improvement in the value of one criterion leads to deterioration in the value of at least one other criterion. This set of alternatives is called a set of the non-dominating alternatives. Each alternative in this set could be a solution of the multicriteria problem. In order to select one alternative, it is necessary to have additional information set by the so-called decision maker (DM). The information that the DM provides reflects his/her global preferences with respect to the quality of the sought alternative.

The multicriteria analysis problems can be divided into three types: problems of multicriteria choice, problems of multicriteria ranking and problems of multicriteria sorting. Many real life problems in management practice may be formulated as problems of choice, ranking and sorting of resources, strategies, projects, offers, policies, credits, products, innovations, designs, costs, profits, portfolios, etc.

For the purpose of better understanding of these problems, we shall discuss one real example, described by Mladineo, N., Margeta, J., Brans, J.P. and Mareshal, B. (1987): Multicriteria Ranking of Alternative Locations for Small Scale Hydroplants, EJOR, 31, 215-222.

The aim of the problem is to choose a building site for an European electric power station. The criteria to be evaluated can be grouped in four classes:

• economic criteria (costs, manpower, etc.); • technical criteria (power and others); • ecological criteria (influence on the environment); • other criteria (safety level and others). Six probable locations for building the electric power station in Europe

and six criteria for their evaluation are considered.

The possible alternatives are as follows: • Italy; • Belgium; • Germany; • Great Britain; • Portugal; • France. The criteria for evaluation are the following: • Manpower for running the plant (number of persons); • Power (Megawatts); • Construction costs (106 USD); • Annual maintenance costs (106 USD); • Ecology (number of villages to evacuate); • Safety level.

The criterion “Manpower for running the plant” reflects the number of

persons, who would be necessary for running the station. It has to be minimized.

The criterion “Power” reflects the quantity of the produced energy. This criterion has to be maximized.

The criterion “Construction costs” reflects the cost price of the project in USD, hence it has to be minimized.

The criterion “Annual maintenance costs” has to be minimized as well. In order to find an appropriate site, satisfying the requirements for electric

power station building, it is supposed that some inhabited places will be necessarily evacuated. The criterion “Ecology (number of evacuated villages)” has to be minimized.

The criterion “Safety level” is maximized. This real problem of multicriteria choice is presented in the following

table:

Table 1 Criteria

Alternatives

Manpower for

running the plant

(number of persons)

Power

(Megawatt)

Construction Cost

(106 USD)

Annual maintenance

cost (106 USD)

Villages to

evacuate (number)

Safety level

ITALY 80 90 600 54 8 Satisfactory BELGIUM 65 58 200 97 1 Very low

GERMANY 83 60 400 72 4 High U.K. 40 80 1000 75 7 Exclusively

high PORTUGAL 52 72 600 20 3 Very high

FRANCE 94 96 700 36 5 High

In this example the criteria “Manpower running the plant”, “Power”, “Construction costs”, “Annual maintenance costs” and “Ecology” have quantitative measures – a number, Megawatts and 106 USD. This type of criteria is called quantitative.

The qualitative criteria are such criteria, which have qualitative estimates that are defined by experts. In this example the criterion Safety level is a qualitative criterion.

MKA-2 software system is designed to support the solution of problems

for multicriteria choice and for multicriteria ranking. The system includes three types of methods: weighting method – AHP, outranking methods – PROMETHEE II, ELECTRE III and interactive method.

2. Functional possibilities MKA-2 system enables: • entry, correction and storing of data for different problems of

multicriteria choice and of multicriteria ranking; • solution of these problems with the help of four methods:

o AHP (Analytic-Hierarchy Process); o PROMETHEE II; o ELECTRE III; o Classification-based interactive method;

• presentation of the final solution of the problem digitally and graphically;

• saving of the input data for the solved problems and saving of the results obtained in a file and on a paper carrier.

3. System requirements MKA-2 system operates with the following computer configuration: • Pentium 200MMX processor or quicker (recommended); • 32 MB RAM or more (64 MB RAM recommended); • 32-bit operation system like MS Windows 95, 98, NT 4.0, 2000, XP; • 10 MB free disk space for optimal productivity; • XVGA display (1024x768 resolution or higher recommended).

4. Install and uninstall MKA-2 system can be installed on a computer, which satisfies the system

requirements described in section 3. In order to install the system, the following operations have to be

accomplished: • Start Windows; • Insert the disk in the CD-ROM device; • The installation program is self-started. If your CD-ROM device or your

Windows version does not support the option Automatic starting, choose RUNN from the Start menu of Windows; RU

• Enter x:\setup.exe in the command line, where x is the letter assigned to your CD-ROM device;

• Press the OKK button; O• Follow the instructions given in the installation program to continue with

the installation process; • When the installation is over, restart your computer.

In order to uninstall MKA-2 system from your computer, open CCoonnttrrooll PPaanneell and choose AAdddd//RReemmoovvee PPrrooggrraammss, then select MKA-2 from the list and follow the instructions, appearing in the opened window.

5. Operation with MKA-2 system The system is built on the principle of Multidocument interface. The main

window contains a drop-down menu with the following commands: • File (New problem, Open, Save, Printt and Exitt); File (New problem, Open, Save, Prin Exi• Setups (Languagee and Startingg); Setups (Languag Startin• Review (Adviser, Messages, Selection of a Methodd and Graphicss); Review (Adviser, Messages, Selection of a Metho Graphic• Window (Horizontal ranking, Vertical rankingg and Cascade rankingg); Window (Horizontal ranking, Vertical rankin Cascade rankin• Help (User’s manuall and About the programm). Help (User’s manua About the progra The main window contains a band with the following buttons: NNeeww

pprroobblleemm,, OOppeenn,, SSaavvee,, PPrriinntt,, SSeettuuppss and GGrraapphhiiccss. 5.1. Operation with files The system creates and opens files with *.mka extension. The entry of the data for a new problem is started by the NNeeww pprroobblleemm

command from FFiillee menu. The OOppeenn command loads an existing *.mka file and you can continue the operation with the information stored in it.

The storing of the currently solved problem in a *.mka file is accomplished with the help of the SSaavvee command. When a solution of the problem is obtained with the help of one of the methods, it can be saved in a file, preserving also information about DM’s preferences used to find the solution.

The exit from the system is realized with the help of the EExxiitt command.

5.2. Entry of the data for the problem solved The entry of the data for the solved problem includes several stages. • The name of the problem is entered – a text string is filled in the field

labeled Objectivee, which describes the solved problem. For example: “Choice of a construction site” or “Choice of a project”.

Objectiv

• The names of the criteria are input in the field with the label Criteria. A criterion is defined as quantitative, qualitative, arranging or weight by the group of radio buttons: Criterion Type. Information is given whether the criterion has to be minimized or maximized with the help of the radio buttons group MinMax. The button named Insertt Criterion confirms the data, which has been entered for the current criterion. Pressing the Delete criterion button deletes the entered criterion, which is without influence on the information input for the other criteria. With the help of the Edit criterion button some corrections can be made in the name or in the characteristics set for the chosen criterion, but the information entered for the alternatives concerning this criterion is lost.

Criteria

Criterion Type

MinMax Inser riterion

Delete criterion

Edit criterion

• The names of the alternatives are successively entered in the field with a label Alternatives. The button Insertt Alternative confirms the entry of the alternative.

Alternatives Inser Alternative

Example: The initial information entered for the example discussed in section 1, is shown in Fig. 1.

With the help of the NNeexxtt button in the window IInniittiiaallllyy aaddddiinngg ffoorr ccrriitteerriiaa aanndd aalltteerrnnaattiivveess, the task passes to windows for successive entry of the alternatives values with respect to each criterion. Setting successively numeric values for the separate alternatives does the entry of a quantitative criterion. The entry of values for the qualitative criteria is done with apriori defined qualitative estimates, available in a drop-down list. It is necessary to choose primarily an alternative (the field for a value is coloured in green) and afterward to select a qualitative estimate from a drop-down list, containing the following elements:

• Exceptionally bad (low); • Essential bad (low); • Very bad (low); • Bad (Low); • Average (Fair); • Good (High); • Very good (or very high); • Essential good (high); • Exceptionally good (high).

Fig. 1

The usage of different adjectives to define a qualitative estimate from the drop-down list is implied by the different specifics of the qualitative criteria. For example, to describe the qualitative criterion MMaannooeeuuvvrraabbiilliittyy, adjectives like bad or good are used, while for the qualitative criterion SSaaffeettyy, the adjectives high or low are used.

Example: Fig. 2 shows the entry of the alternatives estimates with respect

to the qualitative criterion SSaaffeettyy lleevveell in the example discussed in section 1. When values for a weighted criterion are entered, the window RReellaattiivvee

iimmppoorrttaannccee ooff aalltteerrnnaattiivveess appears, with the help of which the DM must do pair-wise comparison for all of the alternatives with respect to the current criterion. A table is shown on the screen, the left column of which comprises all pairs of alternatives and the right column – the relative significance of the first alternative with respect to the second one in the given pair. The relative significance is defined with the help of a slider. If the slider is positioned to the left, the first alternative is more important than the second one, and if it is to the right – the opposite.

At the arranging criterion, the alternatives are ranked by the DM with regard to their importance in relation to the current criterion. The alternatives ranking is accomplished by selection of the desired alternative and its replacement by mouse dragging to the desired position.

Fig. 2 5.3. Selection of a method After the whole information about the criteria set is entered, a window,

containing the names of the dominating alternatives and a CChhoooossee mmeetthhoodd window are automatically opened. The preferred method is selected with the

help of a group of three radio-buttons. If the Classification-Based IInntteerraaccttiivvee mmeetthhoodd is selected, the way for finding of an initial solution has to be indicated – AAuuttoo ggeenneerraattiioonn or EEnntteerreedd bbyy uusseerr.

5.4. Entry of DM’s preferences

5.4.1. Analytic hierarchy process method

When AAnnaallyyttiicc hhiieerraarrcchhyy pprroocceessss method is selected, a window Relative iimmppoorrttaannccee ooff ccrriitteerriiaa appears, with the help of which the DM has to compare pair-wise all the criteria according to their importance for him/her. A table is shown on the screen, the left column of which comprises all the criteria pairs and the right column – the relative significance of the first criterion with respect to the second one in the given pair. The relative significance is defined with the help of a slider found to the right, under the scales image. If the slider is positioned to the left with respect to 1 (the middle), the first criterion is more important than the second one, and if it is to the right – the opposite. With the help of NNeexxtt button a new window appears where the information already entered about the relative significance of one criterion compared to another is shown and also the criteria relative weights calculated on this basis.

Fig. 3 Example: Fig. 3 shows a table with the pair-wise comparison of the

criteria in the example, considered in section 1 and the criteria relative weights calculated on the basis of this information.

The alternatives ranking with respect to their significance, which is obtained, is shown in Fig. 4.

Fig. 4 This result is obtained on the basis of the alternatives evaluations

regarding each one of the criteria, and also on the basis of the defined relative significance of every criterion with respect to the other which is determined by the DM during the pair-wise comparison. This method is convenient, when the DM is competent and is able to do comparative evaluation of the criteria importance correlated one to another and also concerning the defined objective of selection.

5.4.2. PROMETHEE II method When PPRROOMMEETTHHEEEE IIII method is selected, a window is opened, in which

the alternatives table is visualized. Each one of the criteria is successively chosen. The information about this criterion already entered is visualized and corrected, if needed and additional information, necessary for the method operation, is entered. The type (quantitative, qualitative, arranging or weight) and the kind (maximum or minimum) are shown for every criterion.

The additional parameters, which must be determined by the DM, are as follows:

• Weight – characterizes the importance of the criterion, set in the field labeled Weight. If it is considered that one criterion is more important than the others, it is assigned a greater weight. In case several or all criteria have equal significance, they must be given equal weights.

Weight

• Selection of a preference function – from a drop-down menu one of the six possible preference functions is selected. Depending on the alternatives preference function chosen with respect to the criterion selected, the values of the parameters necessary for it are set: indifference threshold, preference threshold and Gaussian threshold. The values of these parameters can be given as absolute or percent values. This is indicated selecting one of the two radio buttons – Absolutee or Percent. Absolut Percent

The DM is offered 6 functions in order to express the intensity of preference between two alternatives with regard to the corresponding criterion. For every one of them 0, 1 or 2 parameters are given, each one with

real economic significance. The indifference threshold defines the size of the difference among the alternatives, at which no preference can be expressed, i.e. appoint the better one. The preference threshold defines the difference between two alternatives, which determines strict preference, i.e. one of them is distinctly better than the other. The value of the Gaussian threshold has to be between the indifference threshold and the preference threshold. The threshold’s values cannot be larger than the difference between the maximal and the minimal valuation of the alternatives for the corresponding criterion. The DM selects one of the following functions:

Usual criterion: It expresses strict preference always when the difference between the two alternatives is not zero. It has no parameters.

U-shape criterion: It requires setting of an indifference threshold and at difference smaller than it there is no preference, at greater difference – strict preference is defined.

V-shape criterion: It requires setting of a preference threshold. The degree of preference rises linearly with the increase of the difference among the alternatives. At difference greater than the preference threshold set, it gives strict preference.

Level criterion: It requires setting of two parameters: an indifference threshold and a preference threshold. A current average value between these two thresholds is also considered. It is recommended for criteria with a finite arranged set of values (very bad, bad, average, etc.).

V-shape criterion with indifference: It requires again setting of two parameters, the preference between them growing linearly with difference increase.

Gaussian criterion: The preference degree grows continuously with difference increase. It requires one parameter, the value of which is located between the indifference and the preference thresholds.

Fig. 5

The average value of the criterion is visualized on the screen as well as the difference between the maximal and the minimal value with respect to all the alternatives. This information helps the DM to choose appropriate values for the indifference and preference thresholds.

In the field labeled UUnniittss, the DM is enabled to set the measuring units for the respective criterion.

With the help of the SSeett VVaalluueess button, the values for each criterion entered by the DM, are confirmed. After the information concerning all the criteria is entered, the button SSoollvvee becomes active and the final ranking of the alternatives is output. The result can be seen, as graphics as well, if the GGrraapphhiicc button is pressed. It is located in the band of the quick access buttons, found under the menus.

Example: Fig. 5 shows a screen with defined additional parameters for one

of the criteria – Construction costs, related to the example from section 1. In case that equal weights are assigned to all the criteria and the

preference selected functions are: Manpower – U-shape criterion, indifference threshold – 10; Power – V-shape criterion, preference threshold – 30; Construction costs – V-shape criterion with an indifference area,

indifference threshold – 50; preference threshold – 500; Maintenance costs – a level criterion, indifference threshold – 10,

preference threshold – 60; Villages to evacuate – Gaussian criterion, Gaussian threshold – 5; Safety level – Usual criterion;

then the alternatives ranking with respect to their significance obtained with the help of PROMETHEE II method is shown in Fig. 6.

Fig. 6

5.4.3. ELECTRE III method

If the EELLEECCTTRREE ІІІІІІ method is chosen, a window with the table of alternatives opens. It contains the information already entered about the

values of the alternatives (rows) for each of the criteria (columns). Each of the criteria is successively chosen. For each criterion is shown its type (quantitative, qualitative, arranging or weight) and whether it has to be maximized or minimized. Additional information necessary for the operation of the method is entered and if it is already input, it may be modified. The additional information, required by the decision maker is:

• Weight – shows the relative importance of the criteria. It is entered in the field with a label Weight. If it is considered that one criterion is more important than the others, it is assigned a greater weight. If several or all of the criteria have equal significance for the DM, they are assigned equal weights.

Weight

• Indifference threshold – defines the size of the difference between the evaluations of two alternatives, at which no preference can be expressed, i.e. one alternative cannot be appointed as better than the other with respect to the corresponding criterion.

• Preference threshold – the difference between the values of two alternatives, which defines strict preference, i.e. one of the alternatives is explicitly better than the other with respect to the corresponding criterion.

• Veto threshold – defines the difference between the values of two alternatives for the corresponding criterion, when the worse alternative is rejected, irrespectively of its values on the other criteria.

The difference between the values of two alternatives, which is between

the indifference threshold and the preference threshold, defines the area of “weak preference” and it reflects DM's hesitation in his choice between such two alternatives. The values of the thresholds cannot be greater than the difference between the maximal and the minimal value of the alternatives with respect to the corresponding criterion. This difference is shown for convenience in the field labeled MMaaxx VVaall –– MMiinn VVaall.. The values of all thresholds may be given in absolute or in percent computing units. This is indicated selecting of one of the two radio-buttons − AAbbssoolluuttee or PPeerrcceenntt.

In the field with a label UUnniitt, the DM has the possibility to set the units for measuring the respective criterion.

The DM is enabled to choose not to use a veto threshold for the corresponding criterion, marking the field DDiissaabbllee VVeettoo TThhrreesshhoolldd.

The values for the weight and the thresholds on the corresponding criterion are obligatory to be entered. By clicking on the SSeett VVaalluueess button, the DM confirms these values for each criterion. The weight and the threshold values can be modified by choosing the respective criterion in the table of alternatives, then entering the new values and clicking on the SSeett VVaalluueess button.

After the information for all the criteria is input, the button SSoollvvee becomes active and with its help the final ranking of the alternatives can be seen. The result can also be viewed in a graphic form, by selecting the GGrraapphhiicc button, which is positioned in the band of the quick access buttons under the menus.

Example: Fig. 7 shows a screen with the additional parameters set by the decision maker for one of the criteria – Staff, for the example in Section1.

Fig. 7

Let all the criteria be assigned equal weights and the thresholds selected be:

Staff – Indifference threshold – 10, Preference threshold – 12, Veto threshold – 54;

Power – Indifference threshold – 10, Preference threshold – 30, Veto threshold – 38;

Building expenses – Indifference threshold – 50, Preference threshold – 500;

Maintenance expenses – Indifference threshold – 10, Preference threshold – 60;

Evacuation strength – Indifference threshold – 1, Preference threshold – 2;

Security level – Indifference threshold – 1, Preference threshold – 2. In this case the ranking of the alternatives in relation to their importance,

obtained with the help of the EELLEECCTTRREE ІІІІІІ method, is shown in Fig. 8.

Fig.8 5.4.4. Classification-Based interactive method

There are two possibilities to set the initial solution if the CCllaassssiiffiiccaattiioonn--BBaasseedd iinntteerraaccttiivvee mmeetthhoodd is selected.

In case AAuuttoo ggeenneerraattiioonn is chosen, the window DDeeffiinnee tthhee ddeessiirreedd cchhaannggeess is opened, in which the current preferred alternative automatically chosen, is shown.

In case EEnntteerreedd bbyy uusseerr is selected, the window CCuurrrreenntt ggeenneerraatteedd pprreeffeerrrreedd aalltteerrnnaattiivvee is opened, in which the DM selects the initial current preferred alternative. With the help of the NNeexxtt button, the DDeeffiinnee tthhee ddeessiirreedd cchhaannggeess window is opened, in which the chosen alternative is indicated.

The values of the criteria for the current preferred alternative are visualized in the DDeeffiinnee tthhee ddeessiirreedd cchhaannggeess window and the DM sets his/her preferences for alteration of the criteria values. After a given criterion is selected (green-lighted), a context menu is invoked with the help of the right button of the mouse, by which the DM sets the desired or acceptable alteration in the value of this criterion for the next iteration. The desired or acceptable alterations in the values of a given criterion are the following:

• Improve – free; • Improve with aspiration level; • Improve with max. value; • Worse – free; • Worse with aspiration level; • Worse with max. value; • Possible changes in an interval; • Save current value; • Indifferent. If the choice is connected with the necessity to enter a concrete value, a

complementary dialogue window is opened and setting of the corresponding

digital information is expected. One iteration of the method is executed with the help of the NNeexxtt button and the window CCuurrrreenntt ggeenneerraatteedd pprreeffeerrrreedd aalltteerrnnaattiivvee is opened. A table of the alternatives is shown, in which the DM makes his/her selection. The blue-coloured alternatives are infeasible with respect to the preferences set and cannot be chosen. The yellow-coloured alternative is the one, which responds to the greatest extent to the preferences set by the DM at the previous iteration. In case the DM wants, some other alternatives, close to this alternative, can be shown with the help of the RReessuulltt button. The DM selects the new currently preferred alternative from these alternatives, which can be different than the one suggested by the system (yellow coloured). With the help of the NNeexxtt button, DDeeffiinnee tthhee ddeessiirreedd cchhaannggeess window appears.

Example: Fig. 9 shows the DDeeffiinnee tthhee ddeessiirreedd cchhaannggeess window for the automatically generated alternative at the first iteration for the example in section 1. This is Great Britain, which is the best with respect to the first criterion Manpower. The DM’s wishes for alteration in the criteria values are shown.

Fig. 9 Fig. 10 shows the alternatives table. Portugal (yellow coloured) is the

alternative, which satisfies to the greatest extent the preferences concerning the criteria values, expressed by the DM.

Fig. 10

6. Options

6.1. Language The interface of the system may be applied in two languages – Bulgarian

and English. The language selected is indicated by the respective radio-button.

6.2. Startup Marking this option when MKA-2 system is started will show TTiipp ooff tthhee ddaayy.

7. View

7.1. Hint The hint is context-oriented system providing help information about the

visual components of the system. After the selection of this option a HHiinntt window is opened and when the cursor moves to any visual element of the system, an explanatory text appears in this window.

7.2. Messages The selection of this option opens a MMeessssaaggeess window. All MKA-2 system

modules output service information about their operation in this window. With the help of a context menu the window content may be deleted, printed or stored in a file.

7.3. Evaluation table After this option is chosen, a window appears that shows the evaluation

table. It contains the information already entered of the alternatives values (in rows) for each one of the criteria (in columns).

7.4. Choose method After the selection of this option, a CChhoooossee mmeetthhoodd window is opened. This

window is automatically opened after the entry of the problem data. 7.5. Graphic After the selection of this option, GGrraapphhiicc view window is opened, in which

the final result is graphically presented if a result is already obtained with any of the methods.

8. Help 8.1. User’s manual Choosing this option, a window appears, in which the User’s manual is

shown.

9. Print MKA-2 system makes possible the DM’s very flexible printing

(documenting) of the description and solution of the current problem. When the problem input data are entered, the following choice options are

active: • inclusion of criteria and alternatives; • inclusion of the alternatives table; • inclusion of the actual date and hour. In case the problem is solved with the help of any of the methods, the

respective options for the method become active for selection and the information entered by the DM can be printed.

If a final result of the problem being solved is found, the option PPrriinntt of the final result also becomes active.

Some setups are possible for alteration of: • font and size; • print quality; • printer selection; • number of copies.

10. Dictionary of terms Criteria – measurable or evaluated properties of the problems/processes

considered, which describe them to a great extent in the context of the problem considered; synonyms are: attributes, parameters, characteristics, factors, components, etc.

Alternatives - a set of resources, strategies, projects, offers, policies, credits, products, innovations, designs, portfolios, etc., which have to be evaluated with respect to the criteria set in order to select the best.

Non-dominated alternatives – these alternatives, for which no other alternatives exist, simultaneously better with respect to all the criteria.

Dominated alternatives – these alternatives, for which at least one different alternative exists, which is simultaneously better with respect to all the criteria.

Decision maker (DM) – the person that realizes the alternatives evaluation and selects the most preferred alternative.

Qualitative criteria – such criteria that have a qualitative estimate only, defined by experts.

Ranking – arrangement of the alternatives related to their significance with respect to all the criteria.

CBIM interactive method– the search for the most preferred non-dominated alternative is accomplished in several steps. At each step the DM is presented the alternative closest to his/her preferences and if it does not satisfy him/her, sets his/her preferences again and a new step is executed.

Currently preferred alternative – the alternative being selected by the DM at the current step.