lable at ScienceDirect

Journal of Environmental Management 91 (2009) 509–515

Contents lists avai

Journal of Environmental Management

journal homepage: www.elsevier .com/locate/ jenvman

Multi-criteria ranking of copper concentrates according to their quality – Anelement of environmental management in the vicinity of copper – Smeltingcomplex in Bor, Serbia

Djordje Nikolic*, Ivan Jovanovic, Ivan Mihajlovic, Zivan ZivkovicUniversity of Belgrade, Technical Faculty in Bor, Vojske Jugoslavije 12, 19210 Bor, Serbia

a r t i c l e i n f o

Article history:Received 1 April 2009Received in revised form1 September 2009Accepted 10 September 2009Available online 14 October 2009

Keywords:Copper concentrateHeavy metalsRankingPROMETHEE/GAIA

* Corresponding author. Tel.: þ381 64 204 57 51; fE-mail address: djnikolic@tf.bor.ac.rs (D. Nikolic).

0301-4797/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.jenvman.2009.09.019

a b s t r a c t

The results of multi-criteria ranking of copper concentrates by their quality, according to their content ofuseful and harmful components, are presented in this paper. Cu, Ag and Au were taken as usefulcomponents, while Pb, Zn, As, Cd, Hg, Bi and Sb were considered as harmful with adequate weightparameters. Considering its specific role in copper metallurgy, sulfur in the concentrate was consideredin two scenarios. In the first scenario S was considered as a useful and in the other one as a harmfulcomponent. The ranking is done by implementing the PROMETHEE/GAIA method with an additionalimplementation of the special PROMETHEE V method, using the standard limitations of the heavy metalscontent in the concentrate. In this way, it is possible to perform an optimization of the input charge forthe copper extraction from two aspects. The first aspect covers benefits from the content of useful metals,while the second deals with the protection of the environment, considering the content of harmfulcomponents of the charge.

Using multi-criteria decision making for the sake of ranking the quality of copper concentrates, asdescribed in this paper, could be considered as a contribution to the methodology of forming the marketprice of this product.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

In the last 50 years, the evolutionary development of techno-logical process has been recorded in the extractive metallurgy ofnonferrous metals (King, 2007). The thing which is especiallyspecific is the development of pyrometallurgical technologicalprocesses for copper production. The classical process of oxidationroasting, followed by melting in reverberatory furnace and subse-quent converting, with the use of SO2 process gas for sulfuricacid production, could be regarded as the starting point for themodern copper metallurgy development. Great progress was madeby introducing Outokumpu flesh furnace, Mitsubishi smeltingconcept, Noranda reactor, Peirce–Smith converting, El Tenienteconverter and others. The purposes of these improvements were anincrease in technological exploitations, better environmentalprotection, and the reduction of anode copper production costs(King, 2007). These improvements of technological processes led toan increase in capacities of the copper extraction facilities and anincrease in the overall world copper production (Filipou et al.,

ax: þ381 30 421 078.

All rights reserved.

2007). This, at the same time led to an enlargement of the problemsdue to the environmental pollution (Franzin et al., 1979; Faitondjievet al., 2000; Zhukovsky, 2000; Gidhagen et al., 2002; Hedberg et al.,2005; Aznar et al., 2008).

Many copper ore bodies, besides copper minerals, contain otherheavy metal minerals, such as: Ni, As, Pb, Bi, Zn, Sb, and others, which,during the process of selective separation and concentration (Guoand Yen, 2005) mostly get into the content of copper concentrate.

Arsenic is especially characteristic since it is often found in theform of double sulfides with copper as enargite (Cu3AsS4) or ten-nantite (Cu12As4S13) mineral. Thus, in the process of differentialflotation of copper minerals, it is hard to separate it from the copperand usually it remains in the concentrate (Filipou et al., 2007).

During the process of pyrometallurgical copper production,which yields more than 90% of entire world copper production(King, 2007), sulfides of heavy metals oxidize or sublimate insulfide form on increased temperatures (Magaeva et al., 2000;Moldovanska et al., 2000). Due to an incomplete treatment of wastefumes, they pollute the environment in the form of PM10 particles.Modern copper smelting plants, although having installed thelatest technological devices for removal of the airborne particlesfrom the waste fumes and maximum degree of SO2 gas utilization,still represent the main polluters in their regions (Hedberg et al.,

Table 2Given weight coefficients on the basis of present metals harmfulness.

Element Weight Influence on health Regulated values

Cu 30.0% Harmful, but removable 25%Bi 4.0% 0.05%As 7.0% First category, easy removing

from organism in period 3–5 days0.20%

S 4.0% 32% minPb 8.5% First category, stays in human

organism, also cancerous2%

Zn 4.0% 3%Cd 8.5% First category, stays in human

organism, also cancerous0.01%

Se 4.0% 0.005%Hg 4.0% Poisonous, not cancerous, removing

from organism after one month5 ppm

Sb 4.0% 0.30%Ni 7.0% Cancerous 0.10%Ag 5.0% 150 ppmAu 10.0% 10 ppm

S¼ 100%

D. Nikolic et al. / Journal of Environmental Management 91 (2009) 509–515510

2005). In the case of an old copper extraction technology (oxidationroasting – smelting in reverberatory furnace – converting) which isstill present in the Bor Smelting Plant (Serbia) within the RTB –company (Copper Smelter Complex), PM10 and SO2 emissions arefar over the limited values, which is a serious hazard for peoples’health in this region and consequently, this is one of the mostpolluted areas in Europe (Dimitrijevic et al., 2008).

Considering that heavy metals: Cu, Ni, Cd, Pb, Zn, Hg, As, Sb, Bi.in airborne dust (PM10) present a certain danger for human healthin the surroundings of copper smelting plant, the World HealthOrganization (WHO, 2001) proscribes limited values of SO2, PM10

and heavy metals content in the air. This way peoples’ health insuch areas would be somehow protected. Also, EU commission islimiting values of the contents of these pollutants in the air (TheCouncil of the European Union EU, 1999, 2004) and that obligescompanies to respect these regulations.

However, in the world market for copper concentrates, the priceof copper concentrate is mostly formed on the basis of offers anddemands. The content of harmful components in the concentratehas not a dominant influence on its price, and it is, unfortunately,considered only in some cases. This way, available copperconcentrates, besides the useful components: Cu, Ag, Au, containother harmful heavy metals, such as: As, Pb, Zn, Cd, Bi, Ni, Hg, Se,and Sb.

Authors of this paper believe that the market price of copperconcentrate should be formed according to the present offer anddemand, but also to be accompanied by the principle of ‘‘bonus’’and ‘‘penal’’. ‘‘The Bonus’’ should be given considering the contentof useful components (Cu and noble metals), and on the other hand,‘‘the penal’’ should be given regarding the content of harmfulelements. However, according to the international standards, limitsof harmful elements are not set for the penalty, given as a signifi-cant factor in the copper concentrate trade. Sometimes theeconomic factor overtakes, especially in the countries where thelaw is not rigorous to this matter, so the ‘‘dirty’’ concentrates cometo the market, and hence the profit is the highest, but with thelargest environmental pollution. The global principles of the envi-ronmental protection do not meet the implementation at the locallevel (Parnell, 2006; Yorgun, 2007), which in many cases is theethical dilemma (Halis et al., 2007).

This paper consists of two parts. The aim of the first part is topresent the results of the PROMETHEE/GAIA method for thecomplete ranking of copper concentrates on the basis of severalcriteria at the same time, aiming to find the least bad solutionfrom the set of the available concentrates, according to theiruseful and harmful content. The second part of this paper, byinvolving a special PROMETHEE V method, optimizes the resultsof previous PROMETHEE II ranking, based on the additional

Table 1Chemical composition of ranked concentrates.

Alternatives Criteria-elements concentration

Cu Bi As S Pb Zn

Max/min Max Min Min Mina,b Min MPreference function Linear Linear Linear Linear Linear LinIndifference threshold (Q) 5% 5% 5% 5% 5% 5%Preference threshold (P) 30% 30% 30% 30% 30% 30Unit % % % % % %Conc. 1 12.62 0.018 0.0340 10.71 0.190000 0.5Conc. 2 16.21 0.021 0.0029 37.73 0.009999 0.1Conc. 3 14.59 0.024 0.0057 28.72 0.140000 0.4Conc. 4 25.87 0.018 0.0070 33.86 0.130000 0.2Conc. 5 21.45 0.021 0.0180 26.16 0.320000 0.4

a Stands min for Scenario 1.b Stands max for Scenario 2.

standardized limitations of harmful heavy metals in theconcentrates.

2. Method for data analysis

For ranking the copper concentrates, according to their contentof useful and harmful components, we decided to apply the Multi-Criteria Decision Making (MCDM) method (Rousis et al., 2008).Many authors use the MCDM for solving environmental decisionproblems (Al-Rashdan et al., 1999; Khalil et al., 2004; Lim et al.,2005, 2006). In this work, the PROMETHEE method was used forranking the concentrate quality taking in consideration the contentof useful and harmful components at the same time, while the GAIAplane, as an option, gives a graphical interpretation of the PROM-ETHEE method and this way shows a clear picture of the problem ofmaking the decision according to the PROMETHEE ranking (VisualDecision Inc., 2007). The reason for using the PROMETHEE/GAIAmethod, for processing the starting data set, is in certain advan-tages of this method over the other MCDM methods. Theseadvantages are reflecting, in a way of problem structuring, takinginto consideration the amount of data that is possible to process,the ability for quantification of qualitative data type, good softwaresupport and presentation of obtained results. (Macharis et al.,2004; Visual Decision Inc., 2004)

The PROMETHEE presents an outranking method, for the finalset of alternatives (Vego et al., 2008). When this method is used, itis required to define the corresponding preference function and togive the weight criteria (weight coefficient) to each input variable.The preference function defines how a particular option is ranked,

Cd Se Hg Sb Ni Ag Au

in Min Min Min Min Min Max Maxear Linear Linear Linear Linear Linear Linear Linear

5% 5% 5% 5% 5% 5% 5%% 30% 30% 30% 30% 30% 30% 30%

% % g/t % % g/t g/t2 0.0025 0.0086 0.3000 0.004990 0.00800 21.92 3.080 0.0025 0.0140 0.0990 0.004991 0.01200 12.34 1.320 0.0025 0.0110 0.2000 0.004990 0.01000 33.00 4.601 0.0025 0.0200 0.2000 0.004990 0.00199 33.50 5.722 0.0050 0.0190 0.3000 0.004991 0.00300 63.50 4.20

Table 3Net flow preferences for Scenario 1 and Scenario 2.

Alternatives Sc. 1 Sc. 2

Fþ F� F Fþ F� F

Con. 1 0.2002 0.5932 �0.3931 0.1602 0.6332 �0.4731Con. 2 0.3664 0.4143 �0.0479 0.3990 0.3847 0.0143Con. 3 0.2901 0.3565 �0.0665 0.2904 0.3601 �0.0698Con. 4 0.6293 0.1319 0.4974 0.6521 0.1133 0.5388Con. 5 0.4224 0.4123 0.0101 0.4137 0.4240 �0.0103

Table 4Weight stability intervals for referent scenarios.

Element Weight Stability intervals

Sc. 1 Sc. 2

Min Max Min Max

Cu 0.3 0.2274 Infinity 0.2433 0.3308Bi 0.04 0.0000 0.3890 0.0000 0.4710As 0.07 0.0398 0.1086 0.0536 0.1371S 0.04 0.0000 0.0650 0.0177 0.3217Pb 0.085 0.0620 0.1140 0.0727 0.1349Zn 0.04 0.0259 0.0827 0.0219 1.0889Cd 0.085 0.0000 0.1314 0.0653 0.1326Se 0.04 0.0000 0.0815 0.0077 0.0892Hg 0.04 0.0152 0.0731 0.0259 0.0995Sb 0.04 0.0000 Infinity 0.0000 InfinityNi 0.07 0.0276 0.1257 0.0125 0.0880Ag 0.05 0.0210 0.0649 0.0000 0.0623Au 0.1 0.0519 0.1137 0.0000 0.1204

D. Nikolic et al. / Journal of Environmental Management 91 (2009) 509–515 511

related to the other and it transfers the deviation between twoparallel alternatives into one unique parameter, which is attachedto the preference degree. The preference degree represents theincreasing function of deviation, where, if the deviation is small, itrelates to week preference, or in the case when the deviation islarge, it then stands for strong preference of a referent alternative.In the PROMETHEE method it is possible to chose one out of sixforms of the preference function (Usual, U-shape; V-shape; Level,Linear, Gaussian) where each form could be described with twothresholds (Q and P). The indifference threshold (Q) represents thelargest deviation which the decision-maker considers not to beimportant, while the preference threshold (P) represents thesmallest deviation that is considered to be crucial for the makingthe decision. The P value should not be smaller than Q. TheGaussian threshold (s) is representing the median value of P and Qthresholds (Brans, 1982; Brans et al., 1984; Brans and Vincke, 1985;Herngren et al., 2006).

The PROMETHEE method is based on determining the positive(Fþ) and negative flow (F�) for each alternative according to out-ranking relations and proportionally with resulting weight coeffi-cients for each criteria-attribute. The positive flow of preference isexpressing how much a certain alternative dominates compared toother alternatives. This means, if the value is larger (Fþ/ 1), thealternative is more important. The negative flow of preference isexpressing how much a certain alternative is preferred by the otheralternatives. The alternative is more important if the value ofa negative flow is smaller (F�/ 0). Complete ranking (PROM-ETHEE II) is based on the calculation of a net flow (F), whichrepresents the difference between the positive and the negativepreference flow. The alternative with the highest value of the netflow is ranked the best (Brans and Mareschal, 1994; Albadvi et al.,2007; Anand and Kodali, 2008).

The PROMETHEE V extends the field of application of thePROMETHEE II method. It can be used to solve the problem of theselection of several alternatives with the given set of constraints.This approach is particularly useful when the set of alternatives issegmented and should be verified both between and within thecluster (Brans and Mareschal, 1992).

The PROMETHEE V procedure includes two steps:

Step 1. At this stage the multi-criteria problem, without theconstraints is considered. The net outranking flow (F) iscomputed based on the PROMETHEE II ranking.

Fig. 1. PROMETHEE II complete ranking o

Step 2. A binary type (0–1) linear program is built in order totake into account the additional constraints:

MaxXm

i¼1

FðaiÞ$xi (1)

where: m is a number of alternatives.

The coefficients of the function (1) are the values of the netoutranking flow. The aim is thus to collect as much outranking flowas possible within the subset of selected alternatives. The linearconstraints of function (1) can include the cardinality, budget,return, investment, marketing constraints, or other threshold thatthe selected alternatives must satisfy. This binary type program canbe developed by using classical methods (e.g. branch and boundmethods) (Brans and Mareschal, 1994).

3. Results and discussion

For the multi-variation ranking of copper concentrates, basedon their quality, comparison was made for five different types ofcopper concentrates, which are available at RTB – Bor Company(Serbian Mining and Copper Smelter Complex), one of the largestcopper smelting plants in Europe. The first three concentrates(Conc. 1, Conc. 2 and Conc. 3) were obtained by the exploitationof local resources from ore deposits around the RTB – BorCompany, while the remaining two (Conc. 4 and Conc. 5) areoriginated from abroad. As useful components in concentrateswe considered Cu, Au, and Ag, while Ni, Bi, As, Pb, Zn, Cd, Se, Hg,Sb and S (Scenario 1) were considered as harmful components. Inthe second scenario, sulfur was considered as a useful compo-nent due of its combustion potential in the charge of the roastingand smelting operation (Scenario 2). The results of chemicalanalysis of the copper concentrates used in this ranking proce-dure are presented in Table 1. The choice of an optimal

f alternatives for defined scenarios.

Fig. 2. GAIA plain for defined Scenario 1 (D¼ 85.07%).

D. Nikolic et al. / Journal of Environmental Management 91 (2009) 509–515512

composition of the copper concentrate, to be processed in thissmelting plant, is a key element for managing the protection ofthe environment in this region.

For ranking the concentrates, considering the aspect of theirmetal content, the PROMETHEE/GAIA method was used. Regardingthat, the data in Table 1 are of quantitative nature, the linearfunction for all defined criteria (with thresholds of indifferenceQ¼ 5% and of preference P¼ 30%) was chosen as the preferencefunction (Visual Decision Inc., 2007; Vego et al., 2008).

For the definition of the weight criteria, the fact was consideredthat all the metals of the concentrate are not of the same impor-tance, considering their influence on the smelting process as well astheir ecological importance or influence on health and environ-ment, which is shown in Table 2.

For both defined scenarios, discussed above, the PROMETHEEranking was done, with Decision Lab 2000 software package. Basedon the data from Tables 1 and 2, the resulted values of positive (Fþ)and negative (F�) flows were obtained (see Table 3).

Complete ranking of the concentrates was performed using thePROMETHEE II method, from the best to the worst option accordingto the given criteria and for both defined scenarios (see Fig. 1). Theresults indicate that in both cases considered, the best concentrateis one marked as the alternative no. 4 (concentrate 4) while theleast preferred alternative is alternative no. 1 (concentrate 1). Also,it can be noticed that if changing ‘‘the role’’ of the element, (theSulfur in Scenario 1 taken as harmful, while in the Scenario 2considered as useful factor) the shifting of the concentrate 5 andconcentrate 2 at the second ranking position appears.

In order to determine the size of preferred relations withgiven ranking, the analyses of interval of stability for bothscenarios was done (see Table 4). By this analysis, it is possible todetermine the intervals of stability for each criterion. The intervalof stability defines the limits within which the range of theweight coefficient of the given criteria can be obtained withoutinfluencing the obtained result of PROMETHEE II ranking. Here, itmust be taken into consideration that changes of weight can bedone only by one criterion, while relative weights of the othercriteria stay the same. On the basis of relatively wide stabilityintervals, it can be concluded that the final order of ranking doesnot change even when the weight coefficients vary in relativelywide limits.

Another advantage of the Decision Lab software package is it’sreflecting the possibility of using the GAIA (Geometrical Analysisfor Interactive Assistance) plane. After determining that the D

value is satisfactory for both considered scenarios, with amounts:Sc. 1 – 85.07%; Sc. 2 – 85.28, the validity of using this tool wasproved, where, D represents the measure of the quantity ofinformation being preserved by defined model. In the real worldapplications, the value of D should always be larger than 60% andin most cases even larger than 80% (Brans and Mareschal, 1994).

Based on the GAIA plane, it is possible and easy to determinethe discriminative strength of each criterion, as well as theaspects of consistency or inconsistency as the indicator of eachalternative for all criterions. The alternatives are shown astriangles, and the criterions are presented as axes with squareendings in Figs. 2 and 3.

Fig. 3. GAIA plain for defined Scenario 2 (D¼ 85.28%).

Table 5PROMETHEE V constraints.

K1 x1þ x2þ x3þ x4þ x5� 1K2 10.71x1þ 37.73x2þ 28.72x3þ 33.86x4þ 26.16x5� 32K3 12.62x1þ 16.21x2þ 14.59x3þ 25.87x4þ 21.45x5� 21K4 0.0025x1þ 0.0025x2þ 0.0025x3þ 0.0025x4þ 0.005x5� 0.01K5 0.034x1þ 0.003x2þ 0.0057x3þ 0.007x4þ 0.018x5� 0.2K6 0.52x1þ 0.1x2þ 0.4x3þ 0.21x4þ 0.42x5� 3K7 0.19x1þ 0.01x2þ 0.14x3þ 0.13x4þ 0.32x5� 2K8 0.008x1þ 0.012x2þ 0.01x3þ 0.002x4þ 0.003x5� 0.1

D. Nikolic et al. / Journal of Environmental Management 91 (2009) 509–515 513

The eccentricity of position of square criterion is representingthe strength of influence of that criterion while the similarityin preference between certain criterions is defined with almostthe same direction of these criterions axes. For the Scenario 1 (seeFig. 2) it is possible to observe the similarity in preference betweenmetals: Ag, Au, Ni, Cu, (cluster C), also metals: Pb, As, Hg, Zn,(cluster B) while S (cluster A) is in an obvious conflict with allcriteria. Also the positions of alternatives (triangles) determine thestrength or weakness of the alternative in relation to the criteria.The closer to the axe direction of a single criterion, the better thealternative is in accordance with the criteria. For the alternatives –concentrates 4 and 5 (cluster C) for the Scenario 1, it can bedetermined that they are the best options because they are laying inthe direction of criteria axes with the strongest influence of Cu andAu with the position closest to the decision stick pi, which isdefining the compromising solution in accordance with the givenweight criteria.

On the basis of the GAIA plains analyses for the Scenario 2 (seeFig. 3), it can be determined that a certain difference hasappeared in ranking in favor of alternative 2. The reason for thisdifference is the change of the sulfur influence, from negative topositive. The S position in the GAIA plain has joined the harmo-nized group of criteria: Pb, As, Hg, Zn (cluster D); in that way thealternative 2 preference has grown in relation to alternative 5.The best and the worst alternative rank is the same in this case as

well: alternative – concentrate 4 (cluster E) is the best, whilealternative 1 (cluster F) is the concentrate with the worst pref-erence. Also it should be noted that criteria Bi and Sb have noinfluence on making the final decision on ranking the concen-trates in both considered cases, as both are placed close to thecoordinate beginning.

Although the ranking according to PROMETHEE II method gavethe answer to the hierarchy of available concentrates from theaspect of their heavy metals content, it is evident that the values ofcertain heavy metals in those concentrates exceed the prescribedcontent. To overcome this problem, the authors of this paper havedecided to apply the PROMETHEE V method with constraints, sothe choice of the most optimal alternative was introduced in theframework of ecological limits for heavy metals content.

Table 6Optimal set of alternatives for given constraints.

Defined scenario Optimal solutions Objective function value

Scenario 1 X4, X5 0.5075Scenario 2 X2, X4 0.5531

D. Nikolic et al. / Journal of Environmental Management 91 (2009) 509–515514

As for the formation of optimization model, for both alternativescenarios, the results of a net flow (Table 3) previously completedwith the PROMETHEE II method, were considered for defining thegoal functions in accordance with the objectives of the Eq. (1).

The following constraints were taken in consideration:

� K1: there must be at least one solution for the establishedmodel;� K2: concentrate must contain a minimum of 32% of sulfur;� K3: concentrate must contain a minimum of 21% of copper;� K4: cadmium content in the concentrate should not exceed the

value of 0.01%;� K5: content of arsenic in the concentrate should not exceed the

value of 0.2%;� K6: content of zinc in concentrate should not exceed the value

of 3%;� K7: lead content in the concentrate should not exceed the value

of 2%;� K8: content of nickel in concentrate should not exceed the

value of 0.1%.

Prescribed limited values for the content of certain elements incopper concentrates are defined by the authorities of Serbia andshould be applied when importing such concentrate. The import ofcopper concentrate, containing harmful elements over the limitedvalues, is not allowed. In the Table 5, for the defined limits,constraints are shown according to the formulation of the PROM-ETHEE V method.

Appropriate models of binary (0–1) linear programming forboth scenarios are developed using the method of calculatingbranch and bound, and the results obtained present the optimalalternatives, which meet the set limitations, as shown in Table 6.

In order to determine the ideal mixture of available concentratesfrom the aspect of given criteria, the additional modification of theinitial PROMETHEE V method was performed with the one extrarestriction added (the percentage of copper in concentrate shouldnot exceed 25%). This is demanded by the technological process ofthe Bor copper smelting plant due to the copper losses in the slagduring the melting operation. To determine the participation ofeach concentrates in the ideal charge, according to the prescribedlimits (see Table 7), the binary model was replaced with a classicalmodel of linear programming.

Obtained values which are the solution of this set of linearprogramming problem, for both scenarios are: X1¼0, X2¼ 0, X3¼

Table 7Set of limits for modified PROMETHEE V method.

K1 x1þ x2þ x3þ x4þ x5¼ 1a

K2 10.71x1þ 37.73x2þ 28.72x3þ 33.86x4þ 26.16x5� 32K3 12.62x1þ 16.21x2þ 14.59x3þ 25.87x4þ 21.45x5� 25K4 12.62x1þ 16.21x2þ 14.59x3þ 25.87x4þ 21.45x5� 21K5 0.0025x1þ 0.0025x2þ 0.0025x3þ 0.0025x4þ 0.005x5� 0.01K6 0.034x1þ 0.003x2þ 0.0057x3þ 0.007x4þ 0.018x5� 0.2K7 0.52x1þ 0.1x2þ 0.4x3þ 0.21x4þ 0.42x5� 3K8 0.19x1þ 0.01x2þ 0.14x3þ 0.13x4þ 0.32x5� 2K9 0.008x1þ 0.012x2þ 0.01x3þ 0.002x4þ 0.003x5� 0.1

a Condition for the formation of mixtures.

0.077128; X4¼ 0.922872; X5¼ 0. This means that the ideal mixtureshould contain 7.7% of concentrate (3) and 92.3% of concentrate (4).Such a mixture will meet the prescribed criteria in accordance withthe standardized values for a certain heavy metals content.

4. Conclusions

Multi-criteria ranking of copper concentrates, according to thecontent of useful components (Cu, Au and Ag) and, at the sametime, harmful elements (Bi, As, Pb, Zn, Cd, Se, Hg, Cr and Ni), gave asthe opportunity to select the optimal solution from the differentconcentrate offer. Two different scenarios were taken in toconsideration. For both scenarios, the best solution is concentratenumber 4. Depending on the status of the sulfur – as the atmo-sphere polluter (Scenario 1) or combustion element and rawmaterial for sulfuric acid production (Scenario 2), the position ofthe second, in the rank of the best solutions, changes from theconcentrate 5 to the concentrate 2 respectively.

Applying the PROMETHEE V methodology and moving from thebinary to the classical linear programming model, there has beencreated the opportunity to make the optimal ranking of the avail-able concentrates – which is a mixture of optimal charge compo-sition both from the aspect of the useful components content andfrom the aspect of minimizing the environmental pollutionresulting from the emission of smelter plant gases.

By using multiple analyses described in this paper, dependingon the given situation – the market offer and the available tech-nology, the concentrate buyers can make the best possible choiceand impose the ‘‘bonus’’ and ‘‘penal’’ methodology when negoti-ating the sales price with potential concentrate sellers. The ethicalprinciples of environment protection, besides economic ones, mustbe considered as well (Halis et al., 2007). At the same time, theglobal relationship regarding environmental protection must beapplied at the local level (Parnell, 2006; Yorgun, 2007). Theproposed methodology for multi-criteria ranking of copperconcentrates, according to their quality, presents a good startingpoint for the development of the methodology that can be used forforming the selling price of copper concentrate with the intro-duction of additional variables such as: the use of technology,pricing, content of inert components, etc. This is undoubtedlysuggested with this paper. In further research of this topic, theauthors of this paper will integrate the analysis of environmentalwith the analysis of economic criteria, using the PROMETHEEmethodology. This, we believe, will give an additional dimension tothe ranking of available copper concentrates.

Acknowledgements

The authors feel indebted to the company Visual Decision Inc.Montreal, Canada; for software package Decision Lab 2000provided to them free of charge.

References

Al-Rashdan, D., Al-Kloub, B., Dean, A., Al-Shemmeri, T., 1999. Environmental impactassessment and ranking the environmental projects in Jordan. European Journalof Operational Research 118 (1), 30–45.

Albadvi, A., Chaharsooghi, S.K., Esfahanipour, A., 2007. Decision making in stocktrading: an application of PROMETHEE. European Journal of OperationalResearch 177 (2), 673–683.

Anand, G., Kodali, R., 2008. Selection of lean manufacturing systems using thePROMETHEE. Journal of Modelling in Management 3 (1), 40–70.

Aznar, J.C., Richer-Lafleche, M., Cluis, D., 2008. Metal contamination in the lichenAlectoria sarmentosa near the copper smelter of Murdochville, Quebec. Envi-ronmental Pollution 156 (1), 76–81.

Brans, J.P., 1982. L’ingenierie de la decision; Elaboration d’instruments d’aide a ladecision. La methode PROMETHEE. In: Nadeau, R., Landry, M. (Eds.), L’aide a la

D. Nikolic et al. / Journal of Environmental Management 91 (2009) 509–515 515

decision: Nature, Instruments et Perspectives d’Avenir. Presses de l’UniversiteLaval, Quebec, Canada, pp. 183–213.

Brans, J.P., Mareschal, B., Vincke, Ph, 1984. PROMETHEE: a new family of outrankingmethods in multi-criteria analysis. In: Brans, J.P. (Ed.), Operational Research ’84.North-Holland, Amsterdam, pp. 477–490.

Brans, J.P., Vincke, Ph, 1985. A preference ranking organisation method: thePROMETHEE method for MCDM. Management Science 31 (6), 647–656.

Brans, J.P., Mareschal, B., 1992. Promethee-V – MCDM problems with segmentationconstraints. INFOR 30 (2), 85–96.

Brans, J.P., Mareschal, B., 1994. The PROMCALC and GAIA decision support systemfor MCDA. Decision Support Systems 12, 297–310.

Dimitrijevic, M., Kostov, A., Tasic, V., Milosevic, N., 2008. Influence of pyrometal-lurgical copper production on the environment. Journal of Hazardous Materials.doi:10.1016/j.jhazmat.2008.08.099.

Filipou, D., St.German, P., Grammatikopolus, T., 2007. Recovery of metal values fromcopper – arsenic minerals and other related resources. Mineral Processing &Extractive Metallurgy Review 28, 247–298.

Faitondjiev, L., Stanislavova, L., Tchuldjian, H., Gupta, S.K., Schulin, R., 2000. Toxicelements in soils of the region of Kremikovtzi. Soil Science Agrochemistry andEcology 35 (5), 3–9.

Franzin, W.G., McFarlane, G.A., Lutz, A., 1979. Atmospheric fallout in the vicinity ofa base metal smelter at Flin Flon, Manitoba, Canada. Environmental Science &Technology 13 (12), 1513–1522.

Gidhagen, L., Kahelin, H., Schmidt-Thome, P., Johansson, C., 2002. Anthropogenicand natural levels of arsenic in PM10 in central and northern Chile. AtmosphericEnvironment 36 (23), 3803–3817.

Guo, B.H., Yen, W.T., 2005. Selective flotation of enargite by electrochemical control.Minerals Engineering 18 (6), 605–612.

Halis, M., Akowa, O., Tagraf, H., 2007. The relationship between ethics andquality: conflicts and common grounds. Serbian Journal of Management 2 (2),127–145.

Hedberg, E., Gidhagen, L., Johansson, C., 2005. Source contributions to PM10 andarsenic concentrations in central Chile using positive matrix factorization.Atmospheric Environment 39 (3), 549–561.

Herngren, L., Goonetilleke, A., Ayoko, G.A., 2006. Analysis of heavy metals in road-deposited sediments. Analytica Chimica Acta 571 (2), 270–278.

Khalil, W. Al-Shiekh, Goonetilleke, A., Kokot, S., Carroll, S., 2004. Use of chemo-metrics methods and multicriteria decision-making for site selection forsustainable on-site sewage effluent disposal. Analytica Chimica Acta 506 (1),41–56.

King, G.M., 2007. The evolution of technology for extractive metallurgy over the last50 years – is the best yet to come? Journal of Metals 59 (2), 21–27.

Lim, Mc.C.H., Ayoko, G.A., Morawska, L., 2005. Characterization of elemental andpolycyclic aromatic hydrocarbon compositions of urban air in Brisbane.Atmospheric Environment 39 (3), 463–476.

Lim, Mc.C.H., Ayoko, G.A., Morawska, L., Ristovski, Z.D., Jayaratne, E.R., Kokot, S.,2006. A comparative study of the elemental composition of the exhaustemissions of cars powered by liquefied petroleum gas and unleaded petrol.Atmospheric Environment 40 (17), 3111–3122.

Macharis, C., Springael, J., De Brucker, K., Verbeke, A., 2004. PROMETHEE and AHP:the design of operational synergies in multicriteria analysis. StrengtheningPROMETHEE with ideas of AHP. European Journal of Operational Research 153(2), 307–317.

Magaeva, S., Patronov, G., Lenchev, A., Granchorov, I., 2000. Energy analysis ofprocessing SO2 containing gases in metallurgy into sulphuric acid and sulphur.Journal of Mining and Metallurgy, Section B: Metallurgy 36 (1–2B), 77–92.

Moldovanska, N., Dimitrov, R., Ladev, L., 2000. Kinetic study of CdS oxidationprocess in non-isothermal conditions. Journal of Mining and Metallurgy,Section B:Metallurgy 36 (1–2B), 103–110.

Parnell, J., 2006. Reassessing the ‘‘think global, act local’’ mandate: evaluation andsynthesis. Serbian Journal of Management 1 (1), 21–28.

Rousis, K., Moustakas, K., Malamis, S., Papadopoulos, A., Loizidou, M., 2008. Multi-criteria analysis for the determination of the best WEEE management scenarioin Cyprus. Waste Management 28 (10), 1941–1954.

The Council of the European Union EU, 1999. 1999/30/CE Council Directive relatingto limit values for sulphur dioxide, nitrogen dioxide and oxide of nitrogen,particulate matter and lead in ambient air.

The Council of the European Union EU, 2004. 2004/107/CE Council Directiverelating to arsenic, cadmium, mercury, nickel and polycyclic aromatic hydro-carbons in ambient air.

Visual Decision Inc., 2007. Getting Started Guide, Decision Lab 2000, ExecutiveEdition, Montreal, Quebec, Canada.

Vego, G., Kucar-Dragicevic, S., Koprivanac, N., 2008. Application of multi-criteriadecision-making on strategic municipal solid waste management in Dalmatia,Croatia. Waste Management 28 (11), 2192–2201.

WHO (World Health Organization), 2001. Air Quality Guidelines for Europe, seconded. WHO Regional Publications, Regional Office for Europe, Copenhagen,Denmark.

Yorgun, S., 2007. New trends in Turkish union movement in the global world.Serbian Journal of Management 2 (2), 247–257.

Zhukovsky, V.M., 2000. Thermodynamics of environment. Journal of Mining andMetallurgy, Section B: Metallurgy 36 (1–2B), 93–102.

Web References

Visual Decision Inc., 2004. Why to Us PROMETHEE/GAIA instead AHP? Montreal,Quebec, Canada. http://www.visualdecision.com/promethee_vs_ahp.htm.