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Environmental and Economic Criteria in Ranking of Copper Concentrates

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Abstract

Influence of the economic criterion, called Profit, on the ranking of copper concentrates is investigated. Values of the criterion, which correspond to alternatives, are derived as earning values obtained by the exploitation of individual concentrates. Various scenarios with respect to the weight w 14, corresponding to the additional economical criterion, are defined and solved. A discrete set of results is generated, applying DECISION LAB software implementation of the PROMETHEE-GAIA methodology. Interpolating these results, we derived continuous interpolation functions which compute necessary quantities of concentrates for each real value of w 14 within the interval [0, 100].

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Authors and Affiliations

  1. Technical Faculty at Bor, University of Belgrade, Vojske Jugoslavije 12, Bor, Serbia

    Ivan Jovanović & Živan Živković

  2. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Predrag Stanimirović

Authors
  1. Ivan Jovanović
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  2. Predrag Stanimirović
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  3. Živan Živković
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Corresponding author

Correspondence to Ivan Jovanović.

Additional information

The authors gratefully acknowledge support from the Research Projects TR34023 and 174013 of the Serbian Ministry of Education and Science.

Appendix: Implementation in MATHEMATICA

Appendix: Implementation in MATHEMATICA

In the appendix, we describe the MATHEMATICA code for computing values E i . List P defines the percentages for all 14 products (the 14th product is the “miscellaneous” group) in 14 separate concentrates.

P={{12.62,0.018,0.0340,10.71,0.19,0.52,0.0025,0.0086,

      0.00003,0.004990,0.008,0.002192,0.000308,75.88},

    {16.21,0.021,0.0029,37.73,0.01,0.10,0.0025,0.0140,

      0.00001,0.004991,0.012,0.001234,0.000132,45.89},

    {14.59,0.024,0.0057,28.72,0.14,0.40,0.0025,0.0110,

      0.00002,0.004990,0.010,0.003300,0.000460,56.09},

    {25.87,0.018,0.0070,33.86,0.13,0.21,0.0025,0.0200,

      0.00002,0.004990,0.002,0.003350,0.000572,39.87},

    {21.45,0.021,0.0180,26.16,0.32,0.42,0.0050,0.0190,

      0.00003,0.004991,0.003,0.006350,0.000420,51.57},

    {21.72,0.018,0.9000,33.20,0.13,0.21,0.0030,0.0080,

      0.00005,0.005000,0.008,0.002510,0.000650,43.79},

    {23.51,0.016,1.2000,34.50,0.85,0.85,0.0250,0.0200,

      0.00009,0.004000,0.003,0.004520,0.001020,39.02},

    {24.21,0.030,0.8000,36.50,1.50,2.10,0.0300,0.0100,

      0.00008,0.008000,0.005,0.003850,0.000810,34.80},

    {19.15,0.060,0.0100,25.20,0.55,0.35,0.0020,0.0400,

      0.00020,0.005000,0.007,0.006510,0.000320,54.62},

    {21.32,0.030,0.3000,31.20,1.32,1.80,0.0020,0.0350,

      0.00010,0.004000,0.210,0.008230,0.000810,43.77},

    {17.50,0.015,0.2500,18.50,0.85,1.10,0.0150,0.0250,

      0.00009,0.005000,0.150,0.002510,0.000920,61.59},

    {25.20,0.017,0.0100,38.50,0.01,0.10,0.0025,0.0100,

      0.00020,0.006000,0.002,0.003320,0.000730,36.14},

    {22.30,0.040,0.0700,35.30,0.08,0.20,0.0020,0.0200,

      0.00009,0.006000,0.003,0.002810,0.000850,41.98},

    {20.18,0.025,0.0100,33.20,1.20,0.95,0.0450,0.0300,

      0.00009,0.007000,0.004,0.003820,0.000450,44.34}}/100

The list s defines the selling prices of the products.

$$ s = {7070.004, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 596835.923, 38279334.732, 0} $$

When all necessary parameters are defined, it is possible to calculate values E i , i = 1, ..., 14. To achieve this goal, it is necessary to perform the following steps A and B:

  1. Step A.

    Calculate the costs of the concentrates according to Eq. 2.4:

    $$ c = Table[s[[1]]*0.96*P[[i, 1]] - 400, {i, m}] $$
  2. Step B.

    Generate the list Profit = {E 1,...,E 14}:

    $$\begin{array}{rll} EV &=& Table[s[[1]]*0.92*P[[i, 1]]+s[[12]]*0.92*P[[i,12]] \\&&\quad+s[[13]]*0.92*P[[i,13]] -c[[i]], {i,n}] \end{array}$$

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Jovanović, I., Stanimirović, P. & Živković, Ž. Environmental and Economic Criteria in Ranking of Copper Concentrates. Environ Model Assess 18, 73–83 (2013). https://doi.org/10.1007/s10666-012-9327-1

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