Kak_ijcccv11n5.pdf INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL ISSN 1841-9836, 11(5):666-683, October 2016. Degree of Project Utility and Investment Value Assessments A. Kaklauskas Arturas Kaklauskas Vilnius Gediminas Technical University, Vilnius, Lithuania arturas.kaklauskas@vgtu.lt Abstract: This article recommends a new INVAR Method for a multiple crite- ria analysis (Degree of Project Utility and Investment Value Assessments along with Recommendation Provisions). Its use can be for a sustainable building assessment. The INVAR Method can additionally assist in determining the investment value of a project under deliberation and provide digital recommendations for improving projects. Furthermore, the INVAR Method can optimize the selected criterion seek- ing that the project under deliberation would be equally competitive in the market, as compared to the other projects under comparison. The INVAR Method is addi- tionally able to calculate the value that the project under deliberation should be for this project to become the best among those under deliberation. The case studies presented in this research are for demonstrating this developed method. Keywords: COPRAS, DUMA and INVAR Methods, Multiple criteria analysis, In- vestment value, Utility degree, Recommendations. 1 Introduction The increased awareness about building energy consumption and sustainability has resulted in the development of various means for predicting performance and rating sustainability. The Building Research Establishment Environmental Assessment Method (BREEAM) and Leader- ship in Energy and Environmental Design (LEED) are the most commonly used Performance Rating Systems [1]. According to Lee [2], statistical analysis reveals a moderate degree of agree- ment amongst the five schemes (BREEAM, LEED, CASBEE, BEAM Plus and the Chinese ESGB) on weights and ranks of weights allocated to five key assessment aspects. Ferreira [3] compare the criteria weighting process of four sustainable construction assessment tools (LiderA, SB ToolPT, Code for Sustainable Homes and LEED for Homes 2012) and show that the four different weighting sets are robust and generally similar. A discussion on BREEAM and multiple criteria decision making follows as an example. The hierarchical structures of key criteria and features of BREEAM Offices are by levels of Issues, Categories and Criteria. The top level contains ten distinct issues (the maximum number of obtainable credits appears in parentheses): Management (22), Health & Well-being (14), Energy (30), Transport (9), Water (9), Materials (12), Waste (7), Land Use & Ecology (12), Pollution (13), Innovation (10). The second level includes 69 categories and the third level – 114 criteria. Expert opinion determines the total number of credits for each category [4]. The use of the BREEAM credits scoring system is for determining the overall assessment grade, which may be Pass (≥ 30%), Good (≥ 45%), Very Good (≥ 55%), Excellent (≥ 70%) and Outstanding (≥ 85%). No weightings are applied to credits awarded under different categories, as the number of obtainable credits assigned to each category already reflects the weight assigned to a category of assessment relative to other categories (as per [2]). For example, BREEAM (Code for Sustainable Homes) divides into nine categories, which subdivide into 34 issues (criteria). The award for each issue according to its performance can be a maximum number of credits. Then, for each category, the percentage of the total credits awarded for all its issues is determined. That percentage is Copyright © 2006-2016 by CCC Publications 668 A. Kaklauskas multiplied by its weight [5,6]. In the end, the weighted values of all those nine categories are added up to obtain one of the six possible certification classes. Thus there is maintenance of the weighting structure with natural adjustments to market needs [3]. Multiple criteria decision making (MCDM) comprises a finite set of alternatives, which deci- sion makers must select, evaluate or rank according to the weights of a finite set of criteria. The multiple criteria nature of the problem regarding energy performance assessment of buildings makes the MCDM Method ideal for coping with the complexity of the problem [7]. Berardi [8] emphasizes sustainability assessments in a built environment using multiple criteria rating sys- tems. Other scientists [9–15] have also done multiple criteria and multi-aspect analysis of green buildings. COPRAS method [9,10] was found to be an effective method for the green buildings assessment. COPRAS (Complex Proportional Assessment Method) method was developed by E. Zavad- skas and A. Kaklauskas [16]. The COPRAS method consists of five stages. Later, this method has been supplemented with a new “Method of Defining the Utility and Market Value of a Property” (DUMA) developed by Kaklauskas [14], see [17]. The degrees of utility of the prop- erty considered as well as the market value of a property being valuated is determined in seven DUMA method stages. The newly developed INVAR (Degree of Project Utility and Investment Value Assessments along with Recommendations) method by Kaklauskas integrates the philosophy of COPRAS and DUMA methods and offers the new opportunities. These new opportunities are as follows: defin- ing the investment value of a project; providing digital tips for improving projects; optimizing a selected criterion; calculating the value of the project, which would permit it to be best among others under deliberation. Determining the priorities and utility degree of projects applying Stages 1-5 of the INVAR method are identical to COPRAS method. Other INVAR method 6-11 stages are different from the COPRAS and DUMA methods. According to the International Valuation Standards [18], investment value is the value of an asset to the owner or a prospective owner for individual investment or operational objectives. As stated in Business Dictionary, investment value reflects the value of an asset to its owner, depending on his or her expectations and requirements. Schmidt [19] believes that investment value refers to the value to a specific investor, based on requirements of that investor, tax rate, and financing. The INVAR Method for an analysis of sustainable buildings (see case studies) use the same initial data as the BREEAM Method uses. The INVAR Method was applied in research in various EU projects (INTELLITIES, IDES- EDU, Brita in Pubs); the author took part in the research. The results of these projects were discussed in a number of publications by the author in conjunction with colleagues [20–25]. The structure of this paper is as follows: after this introduction, Section 2 describes the INVAR Method. Section 3 follows with Case Studies. Finally the discussion and conclusions appear in Section 4. 2 INVAR Method Assessing utility degree and the value of a project under investigation along with the es- tablishment of priorities for this project’s implementation is not especially difficulty. However, this first requires obtaining the numerical values and weights of criteria and applying multiple criteria decision making methods. The presentation of the analysis of projects under comparison is in the form of a grouped decision making matrix, where columns contain n alternative projects under consideration. Meanwhile the rows represent all the pertinent quantitative and conceptual information (see Table 1) [14]. Degree of Project Utility and Investment Value Assessments 669 Table 1: Grouped decision making matrix of the multiple criteria analysis of projects under comparison Criteria describing the alternatives * Projects under comparison W ei g h ts M ea su re m en t u n it s a1 a2 ... aj ... an X1 z1 q1 m1 x11 x12 ... x1j ... x1n X2 z2 q2 m2 x21 x22 ... x2j ... x2n X3 z3 q3 m3 x31 x32 ... x3j ... x3n ... ... ... ... ... ... ... ... ... ... Xi zi qi mi xi1 xi2 ... xij ... xin ... ... ... ... ... ... ... ... ... ... Xm zm qm mm xm1 xm2 ... xmj ... xmn Conceptual information pertinent to projects (i.e., texts, drawings, graphics, video tapes and virtual and augmented realities) * – The sign zi(+(−)) indicates that a greater (lesser) criterion value corresponds to greater (lesser) significance for stakeholders. The INVAR method [14] assumes direct and proportional dependence of significance and a priority of investigated versions in a system of criteria that adequately describe the alternatives and on the values and weights of those criteria. Significance, priority, utility degree and invest- ment value of alternatives, presentation of quantitative recommendations and optimization of different criteria are determined in 11 stages. INVAR method stages 1-5 are identical as COPRAS method [9,10,14]. Stage 1. First, form a weighted, normalized decision making matrix D. The purpose of this stage is to receive dimensionless, weighted values from the comparative indices. Upon establishing the dimensionless values of the indices, all criteria, originally having different dimensions, become comparable. The following formula for this purpose is: dij = xij · qi n∑ j=1 xij , i = 1, m; j = 1, n, (1) where xij is the value of the i-th criterion in the j-th alternative of a solution, m – the number of criteria, n – the number of the alternatives compared and qi – the weight of the i-th criterion. The sum of dimensionless, weighted index values dij of each criterion xi is always equal to the weight qi of this criterion: qi = n∑ j=1 dij, i = 1, m; j = 1, n. (2) In other words, the value of the weight qi of the investigated criterion proportionally distributes over all the alternative versions aj according to their values xij. Stage 2. The sums of weighted, normalized indices describing the j-th version are calculated. The minimizing of index S −j and maximizing of index S+j describe the versions. The lower value of minimizing indices is better (investment). The greater value of maximizing indices is better (management, health & wellbeing, energy, transport, water, materials, waste, land use & ecology, 670 A. Kaklauskas pollution, innovation). The formula for calculating the sums is: S+j = m∑ i=1 d+ij; S−j = m∑ i=1 d −ij, i = 1, m; j = 1,n. (3) In this case, the values S+j (the greater the project "pluses" of this value, the greater the satis- faction of interested parties) and S −j (the lower the project "minuses" of this value, the better the goal attainments by interested parties) express the degree of goals attained by interested parties pertinent to each alternative project. In any case, the sum of the "pluses" S+j and the "minuses" S −j of all alternative projects is always respectively equal to all the sums of the weights of the maximizing and minimizing criteria: S+ = n∑ j=1 S+j = m∑ i=1 n∑ j=1 d+ij, S − = n∑ j=1 S −j = m∑ i=1 n∑ j=1 d −ij, i = 1, m, j = 1, n. (4) This way the calculations performed may be additionally checked. Stage 3. Thebasis pertinent todetermining the significance (efficiency) of the versionsunder comparison constitutes the descriptions of the features pertinent to positive project "pluses" and to negative project "minuses". The formula for finding the relative significance Qj of each project aj is: Qj = S+j + S −min · n∑ j=1 S −j S −j · n∑ j=1 S −min S −j , j = 1, n, (5) where S −min is the least value of the S−j. Stage 4. Determining the priorities of projects pertains to the axiom that the greater the Qj the higher the efficiency (priority) of the project. The analysis of the method presented allows stating that it may be easily applied for evaluating projects and selecting the most efficient of them, while fully aware of the physical meaning of the process. Moreover, it allows formulating a reduced criterion Qj directly proportional to the relative effect of the compared criteria values dij and weights qi on the end result (see Table 2). Determining the utility degrees of the project under consideration as well as the investment value of a project under valuation occurs in seven stages. Stage 5. The formula used for the calculation pertinent to project aj utility degree Nj is: Nj = (Qj ÷ Qmax) · 100% (6) Here Qj and Qmax are the significances of the project obtained from Equation 5. The utility degree Nj of project aj indicates the satisfaction level of the interested parties. The more goals achieved and the more important they are, the higher is the degree of project utility. Stage 6. Calculating the investment value x1j cycle e of the project under deliberation aj can be by means of e approximation. The problem may be stated as follows: What investment value x1j cycle e of the assessed project aj will make it equally competitive on the market with the projects under comparison (a1 − an) (see Table 3)? The measurement of the value x1j cycle e is by price (Euro, British pounds, U.S. dollar or others) per square meter. Degree of Project Utility and Investment Value Assessments 671 Table 2: Alternative results of a multiple criteria analysis Criteria describing the alternatives * Projects under comparison W ei g h ts M ea su re m en t u n it s a1 a2 ... aj ... an X1 z1 q1 m1 d11 d12 ... d1j ... d1n X2 z2 q2 m2 d21 d22 ... d2j ... d2n X3 z3 q3 m3 d31 d32 ... d3j ... d3n ... ... ... ... ... ... ... ... ... ... Xi zi qi mi di1 di2 ... dij ... din ... ... ... ... ... ... ... ... ... ... Xm zm qm mm dm1 dm2 ... dmj ... dmn Sums of weighted, normalized, maximizing in- dices (project "pluses”) of the project S+1 S+2 ... S+j ... S+n Sums of weighted, normalized, minimizing in- dices (project "minuses”) of the project S −1 S−2 ... S−j ... S−n Significance of the project Q1 Q2 ... Qj ... Qn Priority of the project P1 P2 ... Pj ... Pn Utility degree of the project (%) N1 N2 ... Nj ... Nn * – The sign zi(+(−)) indicates that a greater (lesser) criterion value corresponds to greater (lesser) significance for stakeholders. Assuming Nje > n∑ j=1 Nj÷n, then continue increasing the value x1j cycle e of this project aj (see Table 3) by 1 unit costs per square meter (e.g., 1 Euro/m2) and performing calculations as per Stages 1-6 with the gained decision making matrix until arriving at Inequality Nje < n∑ j=1 Nj ÷ n during e approximations. Then the final value x1j cycle e (while Nje > n∑ j=1 Nj ÷ n) equals the investment value: x1j iv = x1j cycle e (7) Assuming Nje < n∑ j=1 Nj ÷ n , then continue reducing the value x1j cycle e of this project aj (see Table 3) by 1 unit costs per square meter (e.g., 1 Euro/m2) and performing calculations as per Stages 1-6 with the gained decision making matrix until arriving at Inequality Nje > n∑ j=1 Nj ÷ n during e approximations. Then the final value x1j cycle e (while Nje < n∑ j=1 Nj ÷ n) equals the investment value (see Formula 7). Stage 7. Performing the optimization of value xij is possible for any criterion during e approximations. It is necessary to determine, what the optimized value xij cycle e should be for alternative aj to be equally competitive in the market with the other alternatives under comparison (a1 − an) (see Table 3). The optimization of value xij for any criterion pertinent to the project under deliberation aj may be determined by performing complex analyses of the benefits and drawbacks of these projects. Development of a grouped, decision making matrix for the multiple criteria analysis of a project transpires by calculating the optimization of value xij during e approximations of a 672 A. Kaklauskas Table 3: Grouped decision making matrix for the investment value assessment of project aj (optimization of value xij for any criterion) Criteria describing the alternatives * Project under valuation and projects under comparison W ei g h ts M ea su re m en t u n it s a1 a2 ... aj ... an X1 z1 q1 m1 x11 x12 ... x1j cycle e ... x1n X2 z2 q2 m2 x21 x22 ... x2j ... x2n X3 z3 q3 m3 x31 x32 ... x3j ... x3n ... ... ... ... ... ... ... ... ... ... Xi zi qi mi xi1 xi2 ... xij cycle e ... xin ... ... ... ... ... ... ... ... ... ... Xm zm qm mm xm1 xm2 ... xmj ... xmn Nje N1e N2e ... Nje ... Nne Conceptual information pertinent to projects (i.e., texts, drawings, graphics, video tapes and virtual and augmented realities) * – The sign zi(+(−)) indicates that a greater (lesser) criterion value corre- sponds to greater (lesser) significance for stakeholders. project under valuation by the block-diagram, as presented in Figure 1. Use of Stages 1-5 and 7 accomplishes a set assessment of all the positive and negative features of a project (criteria, its values and weights). Perform calculations by using a grouped decision making matrix (see Table 3) and Stages 1-5 and 7. The calculation for the corrected optimization of value xij cycle e for any criterion aj is by formula: Assuming Nje > n∑ j=1 Nj ÷ n and Xi is Xi−, then xij cycle e = xij cycle 0 × (1 + e × r), e = 1, r Assuming Nje > n∑ j=1 Nj ÷ n and Xi is, Xi+, then xij cycle e = xij cycle 0 × (1 − e × r), e = 1, r (8a) Assuming Nje < n∑ j=1 Nj ÷ n and Xi is Xi−, then xij cycle e = xij cycle 0 × (1 − e × r), e = 1, r Assuming Nje < n∑ j=1 Nj ÷ n and Xi is Xi+, then xij cycle e = xij cycle 0 × (1 + e × r), e = 1, r (8b) where e is the number of cycles during which optimization value xij cycle e can be determined by means of e approximation of the project under deliberation aj. Meanwhile r is the amount by which the optimization value xij cycle e of the project under deliberation aj increases (decreeses) by means of cycling, to satisfy Inequality 9. Xi+(Xi−) – indicates that a greater (lesser) criterion value corresponds to a greater (lesser) significance for stakeholders. Assuming the utility degree Nje of the project under deliberation aj is greater than the average utility degree (Formula 8a) of the projects under comparison, it means project aj is more ben- eficial on average than the projects under comparison are. For the project under deliberation Degree of Project Utility and Investment Value Assessments 673 Figure 1: Block-diagram for a project’s optimization value assessment to be equally competitive on the market with the projects under comparison (a2 − an), reduce (increase) the value xij cycle e of its criterion (see formula 8a) under deliberation by an r amount over e cycles, until satisfying the next inequality: |Nje − n∑ j=1 Nje ÷ n| < s (9) where s is the accuracy, by percentage, to be achieved by calculating the value xij cycle e of the criterion under deliberation of project aj. For example, given that s = 0.5%, the number of calculation approximations will be lower than it is at s = 0.1%. The decision maker selects the r and s amounts depending on the accuracy needed for the calculations. Assuming the utility degree Nje of the project under deliberation ax is lower than the utility degree (Formula 8b) is on average of the projects under comparison, it means project aj is less beneficial on average than the projects under comparison are. For the project under deliberation to be equally competitive on the market with comparison projects (a1 − an), increase (reduce) the value xij cycle e of its criterion (see formula 8b) under deliberation by an r amount over e cycles, until satisfying Inequality 9. Assuming Inequality 9 is not satisfied, it means the calculation of the value xij cycle e of the criterion under deliberation of the project under valuation aj is not sufficiently accurate, and it is necessary to repeat the approximation cycle. Thereby the corrected revision of value xij cycle e of the project under valuation substitutes into a grouped decision making matrix of a project’s multiple criteria analysis. Recalculate Formulae 1-8 until satisfying Inequality 9. There is a determination of the optimization value xij cycle e for any criterion of the project under valuation aj. Upon satisfaction of Inequality 9, the application of the next, Formula 10 is to determine the optimization value xij cycle e for any criterion of project aj: xij opt value = xij cycle e (10) Stage 9. Presenting indicator xij of the quantitative recommendation iij showing thepercentage of a possible improvement in the value of indicator xij for it to become equal to the best value 674 A. Kaklauskas xi max of criterion Xi is by the formula (see Tables 4 and 8): iij = |xij − xi max|÷ xij × 100% (11) where iij is the quantitative recommendation iij of indicator xij showing the percentage of a possible improvement in the value of indicator xij for it to become equal to the best value xi max of criterion Xi. Meanwhile xi max is the value of the indicator of the best criterion Xi of the variants under comparison. Stage 10. Indicator xij of quantitative recommendation rij showing the percentage of pos- sible improvement of utility degree Nj of alternative aj upon presentation of xij = xi max. In other words, rij shows the percentage of possible improvement in the utility degree Nj of alter- native aj, assuming the value of indicator xij can be improved up to the best value xi max of the indicator of criterion Xi. The calculation is by formula: rij = (qi × xi max) ÷ (S−j + S+j) × 100% (12) where rij is the indicator xij of the quantitative recommendation rij showing the percentage of possible improvement in the utility degree Nj of alternative aj, when xij = xi max. The submission of the quantitative recommendations iij and rij of value xij is in a matrix form (see Table 4). Stage 11. This stage involves calculation by approximation e cycle to determine, what the value x1j cycle e should be for the project under deliberation aj to become the best among those under deliberation. The problem may be stated as follows: What investment value x1j cycle e of the project under valuation aj will make it the best on the market, as per the projects under comparison (a1−an) (see Table 3)? The measurement of value x1j cycl e is by price (Euro, British pounds, U.S. dollar or others) per square meter. The reduction in the price of this project per 1 square meter unit (e.g., 1 Euro/m2) continues until utility degree Nj e of the project under deliberation aj equals 100%. 3 Case Studies: Describing the sustainability of buildings as- sessed by the INVAR Method 3.1 Case Study 1: Calculations of the IKEA shopping center utility degree A specific example appears next to demonstrate the INVAR method more clearly. Five buildings for retail operations a1 – a5 are under analysis for this case study. All the data come from the BREEAM pre-assessment reports and other sources pertinent to IKEA shopping center a1 [26,27], Orchard Park District Centre a2 [28], Friargate Court & Retail Units a3 [29], Dorking Store a4 [30] and Retail Foodstore a5 [31]. Table 5 shows this data. Table 5 consists of criteria (BREEAM Sections and investment), their values (BREEAM Section scores and prices per square meter) and weights. The sum of the weights of all the BREEAM criteria (BREEAM Sections) is equal to one, because the calculation of the section score section has assessed the weighting. The weight of the Investment criterion is compared to the sum of the weights from all the other criteria (BREEAM Sections). This associates with the requirement that the price of these projects must equal the achieved results. The basis for performing an assessment of the sustainability of retail buildings consists of the 11 INVAR method stages. These calculations appear in brief below. Stage 1: The weighted normalized decision making matrix D is formed (see Formula 1, Table 5 and 9). The first formula for this purpose is: Degree of Project Utility and Investment Value Assessments 675 Table 4: Quantitative recommendations submitted in a matrix form Criteria describing the alternatives * Compared projects W ei g h ts M ea su re m en t u n it s a1 a2 ... aj ... an X1 z1 q1 m1 x11 x12 ... x1j ... x1n Possible improvement of the value of indicator x1j for it to become equal to the best value x1 max of criterion X1 % i11 i12 ... i1j ... i1n Possible improvement of the utility degree Nj of al- ternative aj upon presentation of x1j = x1 max % r11 r12 ... r1j ... r1n X2 z2 q2 m2 x21 x22 ... x2j ... x2n Possible improvement in the value of indicator x2j for it to become equal to the best value x2 max of criterion X2 % i21 i22 ... i2j ... i2n Possible improvement of utility degree Nj of alterna- tive aj upon presentation of x2j = x2 max % r21 r22 ... r2j ... r2n ... ... ... ... ... ... ... ... ... ... Xi zi qi mi xi1 xi2 ... xij ... xin Possible improvement in the value of indicator xij for it to be equal to the best value xi max of criterion Xi % ii1 ii2 ... iij ... iin Possible improvement in utility degree Nj of alter- native aj upon presentation of xij = xi max % ri1 ri2 ... rij ... rin ... ... ... ... ... ... ... ... ... ... Xm zm qm mm xm1 xm2 ... xmj ... xmn Possible improvement in the value of indicator xmj for it to be equal to the best value xm max of criterion Xm % im1 im2 ... imj ... imn Possible improvement of utility degree Nj of alterna- tive aj upon presentation of xmj = xm max % rm1 rm2 ... rmj ... rmn d11 = 10 × 1774 ÷ (1774 + 1953.8 + 2370 + 1890 + 2045) = 1.7682 d12 = 1.1 × 1953.8 ÷ (1774 + 1953.8 + 2370 + 1890 + 2045) = 1.9474 d13 = 1.1 × 2370 ÷ (1774 + 1953.8 + 2370 + 1890 + 2045) = 2.3623 The value of weight qi of the investigated criterion distributes proportionally among retail build- ings under analysis aj according to their values xij (see Table 6). For example: q2 = 0.1068 + 0.2403 + 0.1942 + 0.2403 + 0.2185 = 1.0 q4 = 0.2709 + 0.1996 + 0.0925 + 0.1913 + 0.2457 = 1.0 Stage 2: The sums of weighted normalized indices describing the j-th version are calculated. Formula 3 calculates the sums: S+1 = 0.1068+ 0.2293 + 0.2709 + 0.2056+ 0.0957 + 0.1186 + 0.13 + 0.1944 + 0.2557+ 0.0 = 1.607 S −1 = 1.7682 etc. In any case, the sums of the “pluses” S+j and “minuses” S−j of all alternative projects are always, respectively, equal to all sums of the weights of maximizing and minimizing criteria (see Formula 4): S+ = 1.607 + 1.7515 + 2.2967 + 1.6557 + 2.689 = 10.0 S − = 1.7682 + 1.9474 + 2.3623 + 1.8838 + 2.0383 = 10.0 676 A. Kaklauskas Table 5: Initial data for INVAR method calculations (see [32]) Quantitative and qualitative information pertinent to retail buildings Criteria describing the retail buidlings * Measurement units Weight Compared retail buidlings a1 a2 a3 a4 a5 Investment - Euro/m2 10 1774 1953.8 2370 1890 2045 Management + Points 1 4.8 10.8 8.73 10.8 9.82 Health & Wellbeing + Points 1 10.65 10 7.5 8.3 10 Energy + Points 1 14.44 10.64 4.93 10.2 13.1 Transport + Points 1 5.6 4.92 7.11 2.5 7.11 Water + Points 1 1.98 5.33 4 4.7 4.67 Materials + Points 1 4.12 5.77 9.62 4.8 10.42 Waste + Points 1 3.22 4.69 3.75 5.6 7.5 Land Use & Ecology + Points 1 7 6 7 7 9 Pollution + Points 1 5.8 3.08 6.15 3.8 3.85 Innovation + Points 1 0 0 2 0 2 * – The sign “+/-” indicates that a greater (lesser) criterion value corresponds to greater (lesser) significance for a user (stakeholder). Stage 3: Formula 5 finds the relative significance Qj of each project aj (see Table 6): Q1 = 1.607 + 1.7682 × (1.7682 + 1.9474 + 2.3623 + 1.8838 + 2.0383) 1.7682 × (1.7682 ÷ 1.7682 + 1.7682 ÷ 1.9474 + 1.7682 ÷ 2.3623+ + 1.7682 ÷ 1.8838 + 1.7682 ÷ 2.0383) = 3.8478 Q2 = 1.7515 + 1.7682 × (1.7682 + 1.9474 + 2.3623 + 1.8838 + 2.0383) 1.9474 × (1.7682 ÷ 1.7682 + 1.7682 ÷ 1.9474 + 1.7682 ÷ 2.3623+ + 1.7682 ÷ 1.8838 + 1.7682 ÷ 2.0383) = 3.7861 Stage 4: The greater the Qj, the higher is the efficiency (priority) of the retail buildings: Q5 > Q3 > Q1 > Q2 > Q4 (see Table 6: 4.6329 > 3.974 > 3.8478 > 3.7861 > 3.759). Stage 5: Formula 6 is used for calculating utility degree Nj: N1 = (3.8478 ÷ 4.6329) × 100% = 83.05% N2 = (3.7861 ÷ 4.6329) × 100% = 81.72% N3 = (3.974 ÷ 4.6329) × 100% = 85.78% N4 = (3.759 ÷ 4.6329) × 100% = 81.14% N5 = (4.6329 ÷ 4.6329) × 100% = 100% The results of a multiple criteria evaluation of the sustainable retail buildings under analysis appear in Table 6. Table 6 shows that the fiftht version a5 is the best by utility degree equaling N5 = 100%. The third version a3 was second according to priority, and its utility degree was equal to N3 = 85.78%. 3.2 Case Study 2: Calculations of the IKEA shopping center investment value The calculations of the investment value of the IKEA shopping center under valuation are according to data from Table 5 and Stages 1-6. Construction of the IKEA shopping center for furniture and home furnishings was in several stages. First, there was selection of a lot and then, the detailed planning for merging two lots. Upon approval of the detailed plan, there were Degree of Project Utility and Investment Value Assessments 677 Table 6: INVAR method calculation results Quantitative and qualitative information pertinent to retail buildings Criteria describing retail buidlings * Measurement units Weight Retail buidings under comparison a1 a2 a3 a4 a5 Investment - Euro/m2 10 1.7682 1.9474 2.3623 1.8838 2.0383 Management + Points 1 0.1068 0.2403 0.1942 0.2403 0.2185 Health &Wellbeing + Points 1 0.2293 0.2153 0.1615 031787 0.2153 Energy + Points 1 0.2709 0.1996 0.0925 0.1913 0.2457 Transport + Points 1 0.2056 0.1806 0.261 0.0918 0.261 Water + Points 1 0.0957 0.2577 0.1934 0.2273 0.2258 Materials + Points 1 0.1186 0.1661 0.277 0.1382 0.3 Waste + Points 1 0.13 0.1894 0.1515 0.2262 0.3029 Land Use & Ecology + Points 1 0.1944 0.1667 0.1944 0.1944 0.25 Pollution + Points 1 0.2557 0.1358 0.2712 0.1675 0.1698 Innovation + Points 1 0 0 0.5 0 0.5 Sums of weighted, normalized maximizing indices (pro- ject “pluses”) of the retail buildings 1.607 1.7515 2.2967 1.6557 2.689 Sums of weighted, normalized minimizing (projects “mi- nuses”) indices of the retail buildings 1.7682 1.9474 2.3623 1.8838 2.0383 Significance of the retail buildings 3.8478 3.7861 3.974 3.759 4.6329 Priority of the retail buildings 3 4 2 5 1 Utility degree of the retail buildings (%) 83.05% 81.72% 85.78% 81.14% 100% * – The sign “+/-” indicates that a greater (lesser) criterion value corresponds to greater (lesser) significance for a user (stakeholder). ecological tests conducted on the lot, followed by the design and then the arrangement of the lot. Some 2,400 units of garages and their foundations were demolished. The partial use of processed construction materials was for new construction, and the remaining materials, for transferring to other waste handlers. The amount of contaminated soil removed was 1,000 tons (see Figure 2). The retail buildings designed a parking lot for 953 automobiles of which 37 are for the disabled and 36 for families with children. The unused areas of the lot have planted greenery. The water supply of the city provides the water for the building. Centralized sewage networks of the city handle the captured wastewater from the facilities and rainwater that then flow into appropriate piping. The facility contains an installed, autonomous water heating system using solar energy. Air conditioning installations consist of efficient heat pumps and the ventilation – of productive recovery systems. The centralized heating network supplies heat. The design and construction of the building were according to customer specifications and were in consideration of permissible noise level maintenance. The project blueprint stipulates an external enclosure that insulates noise to no less than 32 dB. The main indicators of the project are total building area – 25,359 m2, main area – 21,533 m2, building height – 15.84 m, drinking water supply pipeline – 3,300 m, wastewater pipeline – 1,900 m and rainwater pipeline – 2,358 m. Air conditioning and ventilation systems are installed in the retail buildings for assuring hygienic stipulations for the facilities and the required, stable air temperature and moisture stipulations for the administrative facilities of the work environment. The lighting for the building divides into zones that are all independently controlled. Only certified materials having the least impact on the environment over the life of the building were used for the building’s internal and external systems. The insulation materials used were those having the least impact on the environment but containing the best thermal insulation properties. The investment of the IKEA shopping center was 47.2 mln. Euro. The aim was to establish, what the investment value x11 cycle e (see the bold-faced numbers 678 A. Kaklauskas a b Figure 2: IKEA shopping center for furniture and home furnishings: a) IKEA lot under arrange- ment and b) operating IKEA shopping center in Tables 5 and 7) of the investment should be for a1 to be equally competitive in the market against the other retail buildings under comparison (a2 – a5). Applications of INVAR Stages 1-6 serve to accomplish a set assessment of the positive and negative features of all these retail buildings. As Table 7 shows, the most beneficial retail building during the 124th cycle of approxima- tion (e = 124), according to its designation for use, is a5 (N5 124 = 100%). The second under comparison that is most beneficial is a1 (N1 124 = 86.43%) and the third under comparison – a3 (N3 124 = 85.77%). The calculated utility degrees of the sustainable retail buildings under comparison make it apparent that the cost x11 124 = 1650 (Euro/m 2) for IKEA shopping center under valuation a1 is still too high. Therefore this retail buildings a1 is not equally competi- tive in the market, as compared to the sustainable retail buildings under comparison, once the assessment of their sets of specific positive and negative features is complete. Stage 6 also af- firms the same fact: the calculation of the investment value for retail building a1 during the 124th cycle of approximation was not sufficiently accurate (see column 9 in Table 7). Table 7 shows that Inequality (see column 9 in Table 7) was unsatisfactory for the first 144 cycles. The determination of the investment value of a1 under valuation with respect to the other retail build- ings under comparison appears in the final, 145th approximation cycle – N1 145cycle = 87.04% (N2 145cycle = 81.53%, N3 145cycle = 85.77%, N4 145cycle = 80.91% and N5 145cycle = 100%). In the 144th approximation cycle, the utility degree of project under comparison a1 calculates at N1 = 87.02%. The degrees of utility for the retail buildings under analysis show that a1 under valuation in the 145th approximation cycle is more beneficial than is the second retail building under comparison a2 by 5.51% and more beneficial than retail building under comparison a4 by 6.13%. There was a revision of the investment value x11 in every cycle (from x11 cycle 0 = 1774 Euro/m2), each by 1 Euro/m2 by size until Inequality (see column 9 in Table 7) was satisfied (x11 cycle 145 = 1629 Euro/m 2). Thus investment value x11 cycle e (respectively, 1774, ..., 1629) is checked for accuracy pertinent to retail building a1 by placing them into the bold cell of the decision making matrix (see Table 5). All calculations were repeated according to Stages 1-6 until Inequality (see column 9 in Table 7) was satisfied in the 145th cycle. Table 7 shows that the calculations of investment value x11 cycle e become more and more accurate with each, next e approximation cycle for retail building a1 under analysis. 3.3 Case Study 3: Provision of recommendations The results of the provision of recommendations by applying Stages 1-5, 9 and 10 of the INVAR method for the retail buildings appear in Table 8. Initial data for the calculations are presented in Table 5. Meanwhile, the recommendations for bettering the criteria for these retail buildings under comparison appear in Table 8. Recommendations arrive in a matrix (see Table Degree of Project Utility and Investment Value Assessments 679 Table 7: Revised changes in value and investment valuedeterminations for IKEAshopping center under valuation a1 Utility degree change in retail buildings under deliberation by rationalizing the corrected value x11 cycle e of building a1 Appro- ximation cycle * Utility degree N1e Utility degree N2e Utility degree N3e Utility degree N4e Utility degree N5e ** *** 1 2 3 4 5 6 7 8 9 0 1774 83.05% 81.72% 85.78% 81.14% 100% 86.34% |− 4.11%| < 0.02% ... ... ... ... ... ... ... ... ... 124 1650 86.43% 81.56% 85.77% 80.95% 100% 86.94% |− 0.64%| < 0.02% ... ... ... ... ... ... ... ... ... 134 1640 86.72% 81.55% 85.77% 80.93% 100% 87.00% |− 0.34%| < 0.02% ... ... ... ... ... ... ... ... ... 144 1630 87.02% 81.53% 85.77% 80.91% 100% 87.05% |− 0.03%| < 0.02% 145 x1j iv = 1629 87.04% 81.53% 85.77% 80.91% 100% 87.05% |− 0.01 %| < 0.02 % * - revised changes in value and investment value x11 cycle e (Euro/m 2) of IKEA shopping center under valuation a1. ** (N1e + N2e + N3e + N4e + N5e) ÷ 5 *** Inequality to determine, whether the calculation of revised value x11 cycle e of IKEA shopping center under valuation a1 is sufficiently accurate. 8) by using Formulae 10 and 11 during Stages 9 and 10. Every window in Table 8 describing Alternative aj consists of three parts: xij – the value of the i-th criterion (Xi) in the j-th alternative; quantitative recommendation iij showing the percentage of a possible improvement in the value of indicator xij for it to become equal to the best value xi max of criterion Xi (xij = xi max); and quantitative recommendation rij showing the percentage of possible improvement of utility degree Nj of alternative aj upon presentation of xij = xi max. If, for example, it would be possible to improve the assessment of the Health &Wellbeing criterion for building a3 (i33 = 42%) from the x33 = 7.5 value achieved up to the best value for a1 (x34 = 10.65), then the utility degree N3 for building a3 would increase by r33 = 2.1%. Analogically, if the assessment of the Energy criterion for building a3 (x43 = 5.1) could be improved up to the amount of the best assessment for building a1 (x41 = 14.44), then the effectiveness of the criterion Energy for building a3 would increase by i43 = 183.14%, and the utility degree N3 would increase by r43 = 9.1569% (see Table 8). 3.4 Case Study 4: Optimization of the value This example, based on Stages 1-5 and 7, will determine, what the value x43 cycle e of the BREEAM Energy Section (see the number in bold in Table 5) must be for project a3 to be equally competitive on the market, as compared to the other retail buildings under comparison (a1, a2, a4, a5) by a set assessment of all their positive and negative features. It is possible to optimize any one of the criteria or their composite parts by the new INVAR method, which deliberates the sustainability of retail buildings under analysis in an integrated manner by using Pre-assessment Reports. The optimization of the score of the Energy Section of BREEAM, which appears next, will serve as an example (see Table 5). The determination of the optimized score x43 cycle e for the project under valuation a3 appears 680 A. Kaklauskas Table 8: Quantitative recommendations submitted in a matrix form Quantitative and qualitative information pertinent to alternatives Criteria describing the alternatives * Measurement units Weight Alternatives a1 a2 a3 a4 a5 Health &Wellbeing + Points 1 x31 = 10.65 10 x33 = 7.5 8.3 10 (0%) (6.5%) (i33 = 42%) (28.31%) (6.5%) (0%) (0.325%) (r33 = 2.1%) (1.4157%) (0.325%) Energy + Points 1 x41 = 14.44 10.64 x43 = 5.1 10.2 13.1 (0%) (35.71%) (i43 = 183.14%) (41.57%) (10.23%) (0%) (1.7857%) (r43 = 9.1569%) (2.0784%) (0.5115%) *- The sign “+/-” indicates that a greater (lesser) criterion value corresponds to a greater (lesser) signifi- cance for a user (stakeholder). in Table 9. The formulation of this task is the following: determine, what the optimized score x43 cycle e should be for building under valuation a3 for it to be equally competitive in the market, as compared with the sustainable retail buildings (a1, a2, a4, a5) after a complex assessment of their positive and negative features. The decision making matrix (see Table 5), the amalgamated block diagram submitted in Figure 1 and the calculations performed by Stages 1-5 and 7 serve as the basis for these calculations. The results of the e approximation cycles of these calculations appear in Table 9. The aim was to establish, what the score x43 cycle e should be (see the numbers Table 9: What score x43 cycle e should be for building a3 to be equally competitive in the market with other retail buildings under comparison (a1, a2, a4, a5) Appro- ximation cycle Score x43 cycle e Utility degree N1e Utility degree N2e Utility degree N3e Utility degree N4e Utility degree N5e * ** 0 4.93 83.05% 81.72% 85.78% 81.14% 100% 86.34% |− 0.7%| > 0.1% ... ... ... ... ... ... ... 7 5 83.05% 81.72% 85.81% 81.14% 100% 86.34% |− 0.67%| > 0.1% ... ... ... ... ... ... ... 57 5.5 83.04% 81.72% 86.03% 81.14% 100% 86.39% |− 0.45%| > 0.1% ... ... ... ... ... ... ... 107 6 83.02% 81.72% 86.25% 81.14% 100% 86.43% |− 0.19%| > 0.1% ... ... ... ... ... ... ... 157 6.5 83.01% 81.72% 86.47% 81.14% 100% 86.47% |0%| < 0.1% * (N1e + N2e + N3e + N4e + N5e) ÷ 5 ** Inequality 9 to determine, whether the calculation of revised value x43 cycle e of under valuation a3 is sufficiently accurate. in bold in Tables 5 and 9) for building a3 to be equally competitive in the market with other retail buildings under comparison (a1, a2, a4, a5). Applications of INVAR Stages 1-5 and 7 serve to accomplish a set assessment of the positive and negative features of all these retail buildings. Table 9 shows that Inequality 9 was unsatisfactory for the first 156 cycles. The score x43 was increased in every cycle (from x43 cycle 0 = 4.93) by an amount of 0.01 until Inequality 9 was satisfied (x43 cycle 157 = 6.5). Then scores x43 cycle e (respectively, 4.94, ... and 6.5) are checked for accuracy pertinent to building a3 by placing these results into the bold cell of the decision making matrix (see Tables 5 and 9). All the calculations were repeated according to Formulae Stages 1-5 and 7 until Inequality 9 was satisfied in the 157th cycle. Table 9 shows the Degree of Project Utility and Investment Value Assessments 681 Table 10: What should the value x11 cycle e of IKEA shopping center be for this project to become the best among those under deliberation? Approxı- mation cycle Investment value x11 cycle e (Euro/m2) Utility degree N1e N2e N3e N4e N5e 0 1774 83.05% 81.72% 85.78% 81.14% 100% 124 1650 86.43% 81.56% 85.77% 80.95% 100% 134 1640 86.72% 81.55% 85.77% 80.93% 100% 174 1600 87.92% 81.49% 85.77% 80.86% 100% 274 1500 91.14% 81.34% 85.77% 80.68% 100% 424 1350 96.73% 81.07% 85.76% 80.37% 100% 474 1300 98.84% 80.97% 85.76% 80.25% 100% 484 1290 99.27% 80.95% 85.76% 80.23% 100% 494 1280 99.72% 80.93% 85.76% 80.20% 100% 499 1275 99.94% 80.92% 85.76% 80.19% 100% 504 1270 100% 80.78% 85.62% 80.04% 99.84% calculations of score x43 cycle e becoming more and more accurate with each, next approximation cycle for building under analysis a3. 3.5 Case Study 5: What should the value of the IKEA shopping center be for this project to be the best among those under deliberation? The calculations in this example are by approximation e cycle to determine, what the value x11 cycle e of IKEA shopping center a1 should be for this project to become best among those under deliberation a1-a5. The price of this project continues being reduced by 1 Euro/m 2 until N1e becomes equal to 100% (Stages 1-5 and 11). Table 10 shows that N1e = 100% had not been satisfied over 503 cycles. That is the reason the investment value x11 cycle e of the project under valuation a1, which had been revised 504 times, was entered into the decision making matrix (Table 5) for the multiple criteria analysis of retail building. Table 10 shows that, in each following approximation cycle, the calculation of the revised investment value x11 cycle e of building under valuation a1 became more and more accurate. All the calculations by Stages 1-5 and 11 were repeated, until N1e = 100% was satisfied in the 504th cycle. It can be stated that this project can become the most effective among the projects under comparison, once the value x11 cycle e of the IKEA shopping center = 1270 Euro/m 2. 4 Conclusion This article recommends a new multiple criteria analysis, the INVAR method (Degree of project Utility and investment value Assessments along with recommendation provisions). IN- VAR method stages 1-5 are identical as COPRAS method [9, 10, 14]. It generates conditions to assess management, health & wellbeing, energy, transport, water, materials, waste, land use 682 A. Kaklauskas & ecology, pollution, innovation, comfort, quality of life and aesthetics as well as its techni- cal, economic, legal/regulatory, educational, social, cultural, ethical, psychological, emotional, religious and ethnic aspects in conformity with requirements and opportunities for clients, de- signers, contractors, users and other stakeholders. The systems and the values and weights of the quantitative and qualitative criteria express these requirements. The INVAR method allows determining the strongest and weakest aspects of each project pertinent to a sustainable building and its constituent parts. Performance of the analyses is to learn by what degree one alternative is better than is another. Furthermore, this discloses the details, why this is so. The practical case studies presented in this research validate this developed method. An analysis of the results reached by the INVAR method permits making the following claims: • The INVAR method can determine the utility degree and investment values of the projects under deliberation. • The INVAR method can provide digital tips for improving projects. • The INVAR method can define, what the value of a selected criterion needs to be for the project under deliberation to be equally competitive in the market, as compared with others under comparison after a set assessment of all their positive and negative features. • The INVAR method can calculate, what the value of the project under deliberation should be for this project to become the best among others under deliberation. Acknowledgment The author thanks Ms. Vijole Arbas for her help in translating to English and editing this article. Bibliography [1] Schwartz, Y., Raslan, R. 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