Method SNOD for Investment Projects Analysis of Buildings Reconstruction Oleg I. Larichev, Dmitry Yu. Kochin (Institute for Systems Analysis, Moscow, Russia) Leonas L. Ustinovicius (Gediminas University, Vilnus, Lithuania)

A company is looking for a construction site to build a large supermarket. The preliminary analysis has shown that there are four potential construction sites : Practical example Var 1Var 2Var 3Var 4 Parking capacity, max Presence of competitors, min 1 Low 5 High 3 Medium 5 High Population density within 1 km radius, max Price of the site, min Public transport flow, max 1 Low 3 Medium 5 High 7 Very High Visibility from a principal street, max 5 High 3 Medium 1 Low Communications infrastructure, max 3 Medium 5 High 7 Very High

Formal problem statement Given: N – number of criteria. Q – number of given alternatives w ij, 1 i N, 1 j Q – evaluation on the scale of the i-th criterion (there can be both qualitative and quantitative criteria). Required : To select the best alternative from Q set on the basis of a decision- maker's (DM) preferences.

DM's capabilities 1. DM is capable of comparing evaluations of two alternatives by separate criteria ; 2. DM is capable of comparing multicriteria alternatives, which are different by evaluations on two criteria only; 3. DM is capable of comparing an advantage of one alternative against two or three advantages of the other one.

DM answers 1. One of two compared objects is more preferable. 2. The compared objects are equally preferable.

Method SNOD a Scale of Normalized and Ordered Differences The method is based on the pair-compensation principle, when an attempt is made to counterbalance the advantages of one alternative by advantages of another alternative. is consists of two stages: 1. formal analysis – preparing a series of questions to be posed to DM 2. obtaining the information from DM –DM-DSS dialogue

Formal analysis - the purpose The analysis is aimed at preparing a series of questions to be posed to DM that could provide: - a minimum load for DM: the least number of questions to be posed ; - gradual ascending of questions difficulty ; - the greatest possible use of DM information.

Formal analysis Stages: 1. A pair comparison of all alternatives. For each pair of alternatives: a. Normalization of evaluations of alternatives in each pair b. The normalized estimations are summarized c. Alternative with greatest sum - winner in pair 2. Preparation of questions sequence to be posed to DM a. The choice of potentially best alternative (PBA) b. The other alternatives are compared in accordance with PBA is founded on de Condorce principle : "The alternative, which wins over all other alternatives in the course of pair comparisons, shall be considered the best one".

Example: the stage of formal analysis Difference: Result: : Var 1 is better than Var 2

Possible cycles on the stage of formal analysis A B C Criterion 1, max Criterion 2, max Criterion 3, max De Condorce principle could lead to cyclic relations on the set of alternatives It turns out that B > A, A > C, but B < C by the results of the formal analysis.

Condition of cycles absence jk N,,, 21 - mean values of alternative estimations by criteria calculated for pairwise comparison of alternativesA j and A k. N,, 1 - mean values of all alternative estimations by criteria group of given alternatives jk C - a set of criteria, by whichA j is more preferable thanA k, jk C - a set of criteria, by whichA j is less preferable than A k A sufficientcondition of cycles absence on the set of alternatives A is satisfaction of the following conditions for any pair of alternativesA j and A k : jk ii Ci, jk ii Ci,

Dialogue DM-DSS Stage 1.: Preparation of comparisons (for alternative group). 1. Association of close estimations. 2. Elimination of alternatives with inadmissibly low estimations. Stage 2.: Ordering relative advantages and disadvantages in a pair of alternatives. Elaboration of SNOD – Scale of the Normalized Ordered Differences for alternatives pair. Stage 3. Main comparisons made by DM DM is trying to compensate relative disadvantages of PBA by its advantages.

Main Comparisons made by DM Criteria Alt 1 Is better Alt 2 Is better

DSS – alternative comparison

DSS – Results of the comparisons inadmissibly low estimation After all comparisons Alt 3 has the leading position. 2 pair wise alternative comparisons have been made. The comparisons completed:

Features of the method SNOD 1. The method uses rather simple (from the psychological point of view) procedures for the elicitation of DM preferences. 2. The language of DM and his organization is used in DM-DSS dialogue. The quantitative, verbal and mark estimations may be used. 3. The method enables to compare a large number of alternatives by using the minimum number of questions to DM. 4. The method can easily adapt to a concrete problem (set of alternatives) and always results in best or presumably best alternative. 5. The method checks for the consistency of information obtained from DM. 6. The method provides the DM with an opportunity to receive explanations of the results by displaying those of his/her answers, which have led to the result obtained.