**4. Results and Discussion**

In this section, priorities of allocating gas to different sectors of consumption as coefficients of proximity (rank) and relative proportional weight and priority of six different sectors of gas consumption are shown in Table 4. It should be noted that the relative weight of each sector is calculated by dividing the corresponding coefficient of affinity into the total coefficients of the proximity of all sectors of consumption. Regarding Table 4, the first rank of consumption is assigned to export and then injection to oil fields and petrochemical industries are in order, respectively.


**Table 4.** Rating, relative weight, and priority of the different sectors (*Pi*) of consumption.

At this stage, the optimal allocation of gas resources to different sectors of consumption is implemented using the GP multi-purpose decision-making technique. Therefore, the solution for the objective function, the goal and system constraints of GP multi-purpose decision-making technique for 2018–2025 by using the relative weight of the various consumption sectors (presented in Table 4), as well as information extracted from the trend of the gas industry and energy balance sheet documents of Iran is to be found. The goal share of the various gas sectors, the amount of consumption of the various departments of consumption (based on the balance sheet of energy and hydrocarbons), the base gas volume, the allocable and predicted amount of each year is summarized in Figure 2, Tables 5 and 6.

Inputs of GP consists the goal portion (*FCij*) of consumption, price per cubic meter of natural gas in consumption areas, *Pij*, base gas volume (*Zi*), limited, allocated and predicted value, the volume of gas deficit (*Fj*), and minimum natural gas consumption of each consumption sector (*ACij*) in Figure 2, Tables 5–9, respectively.

**Figure 2.** The goal portion (*FCij*) of various gas sectors (MCM: Million Cubic Meter).




**Table 6.** Base gas volume (*Zi*), limited, allocated and predicted value (MCM).

**Table 7.** The volume of gas deficit (*Fj*) (MCM).


**Table 8.** Minimum natural gas consumption of each sector (*ACij*) (MCM).


**Table 9.** The Gas surplus in different years (*Ej*) (MCM).


## *Calculate Security Costs*

Considering the equations, the cost of energy security in different sectors is calculated. The probability of occurrence of each of the threats in the gas security disorder is based on the recurrence of the expert's opinion as outlined in the following tables (Tables 10 and 11).

**Table 10.** The probability of occurrence of each of the threats (*PRij* ) (Percentage).


**Table 11.** Price per cubic meter of gas per consumption unit (*Cij* ) (Rials).


The goal programming model mentioned in the previous section after substituting numerical values associated with different input parameters is as follows:

$$\text{Minin } P\_6d\_1^+ \text{ , } P\_4d\_2^+ \text{ , } P\_3d\_3^+ \text{ , } P\_5d\_4^+ \text{ , } P\_2d\_5^+ \text{ , } P\_1d\_6^+$$

Such that:

*X*<sup>11</sup> + 3941*X*<sup>12</sup> + 4021*X*<sup>13</sup> + 4102*X*<sup>14</sup> + 4184*X*<sup>15</sup> + 4265*X*<sup>16</sup> + 4347*X*<sup>17</sup> + 4430*X*<sup>18</sup> + *d*<sup>−</sup> <sup>1</sup> <sup>−</sup> *<sup>d</sup>*<sup>+</sup> = 4, 221, 000 *X*<sup>21</sup> + 1320*X*<sup>22</sup> + 1320*X*<sup>23</sup> + 1320*X*<sup>24</sup> + 1320*X*<sup>25</sup> + 1320*X*<sup>26</sup> + 1320*X*<sup>27</sup> + 1320*X*<sup>28</sup> + *d*<sup>−</sup> <sup>2</sup> <sup>−</sup> *<sup>d</sup>*<sup>+</sup> = 1, 009, 000 *X*<sup>31</sup> + 3445*X*<sup>32</sup> + 3445*X*<sup>33</sup> + 3445*X*<sup>34</sup> + 3445*X*<sup>35</sup> + 3445*X*<sup>36</sup> + 3445*X*<sup>37</sup> + 3445*X*<sup>38</sup> + *d*<sup>−</sup> <sup>3</sup> <sup>−</sup> *<sup>d</sup>*<sup>+</sup> = 960, 000 *X*<sup>41</sup> + 80*X*<sup>42</sup> + 80*X*<sup>43</sup> + 80*X*<sup>44</sup> + 80*X*<sup>45</sup> + 80*X*<sup>46</sup> + 80*X*<sup>47</sup> + 80*X*<sup>48</sup> + *d*<sup>−</sup> <sup>4</sup> <sup>−</sup> *<sup>d</sup>*<sup>+</sup> = 2, 581, 000 *X*<sup>51</sup> + 130*X*<sup>52</sup> + 130*X*<sup>53</sup> + 130*X*<sup>54</sup> + 130*X*<sup>55</sup> + 130*X*<sup>56</sup> + 130*X*<sup>57</sup> + 130*X*<sup>58</sup> + *d*<sup>−</sup> <sup>5</sup> <sup>−</sup> *<sup>d</sup>*<sup>+</sup> = 327, 000 26, 000*X*<sup>61</sup> + 26, 000*X*<sup>62</sup> + 26, 000*X*<sup>63</sup> + 26, 000*X*<sup>64</sup> + 26, 000*X*<sup>65</sup> + 26, 000*X*<sup>66</sup> + 26, 000*X*<sup>67</sup> + 26, 000*X*<sup>68</sup> + *d*<sup>−</sup> <sup>6</sup> <sup>−</sup> *<sup>d</sup>*<sup>+</sup> = 628, 000

*X*<sup>11</sup> + *X*<sup>21</sup> + *X*<sup>31</sup> + *X*<sup>41</sup> + *X*<sup>51</sup> + *X*<sup>61</sup> ≤ 588 *X*<sup>12</sup> + *X*<sup>22</sup> + *X*<sup>32</sup> + *X*<sup>42</sup> + *X*<sup>52</sup> + *X*<sup>62</sup> ≤ 709 *X*<sup>13</sup> + *X*<sup>23</sup> + *X*<sup>33</sup> + *X*<sup>43</sup> + *X*<sup>53</sup> + *X*<sup>63</sup> ≤ 809 *X*<sup>14</sup> + *X*<sup>24</sup> + *X*<sup>34</sup> + *X*<sup>44</sup> + *X*<sup>54</sup> + *X*<sup>64</sup> ≤ 818 *X*<sup>15</sup> + *X*<sup>25</sup> + *X*<sup>35</sup> + *X*<sup>45</sup> + *X*<sup>55</sup> + *X*<sup>65</sup> ≤ 825 *X*<sup>16</sup> + *X*<sup>26</sup> + *X*<sup>36</sup> + *X*<sup>46</sup> + *X*<sup>56</sup> + *X*<sup>66</sup> ≤ 827 *X*<sup>17</sup> + *X*<sup>27</sup> + *X*<sup>37</sup> + *X*<sup>47</sup> + *X*<sup>57</sup> + *X*<sup>67</sup> ≤ 824 *X*<sup>18</sup> + *X*<sup>28</sup> + *X*<sup>38</sup> + *X*<sup>48</sup> + *X*<sup>58</sup> + *X*<sup>68</sup> ≤ 807


$$d\_1^+ \cdot d\_1^- = 0, \; d\_2^+ \cdot d\_2^- = 0, \; d\_3^+ \cdot d\_3^- = 0, \; d\_4^+ \cdot d\_4^- = 0, \; d\_5^+ \cdot d\_5^- = 0, \; d\_6^+ \cdot d\_6^- = 0$$

$$X\_{ij\prime} \; d\_k^+ \; d\_k^- \; \geq 0 \; \models \; k = 1,2,3,4,5,6$$

In the lexicographer method, the objective functions of the goal programming model are considered and solved separately to minimize the deviation from the specified goal according to their priority. Then, if it obtained a unique point, it is considered to be the optimal point. If multiple solutions are found in the space of multiple solutions, lower important functions are checked for the points.

According to the results obtained by solving the model with the first priority objective function (the first objective function), the obtained point is unique and the negative deviation of the first objective function from the specified cause is minimum and zero. The answer (Table 12 and Figure 3) is final and efficient and acceptable:


**Table 12.** Optimal allocation of gas to sectors based on cost minimization (MCM).

Allocation of household surplus gas to other sectors is calculated as follows:

*Min Z* = 3864*X*<sup>11</sup> +3941*X*<sup>12</sup> + 4021*X*<sup>13</sup> + 4102*X*<sup>14</sup> + 4184*X*<sup>15</sup> + 4265*X*<sup>16</sup> + 4347*X*<sup>17</sup> + 4430*X*<sup>18</sup> + 1320*X*<sup>21</sup> +1320*X*<sup>22</sup> + 1320*X*<sup>23</sup> + 1320*X*<sup>24</sup> + 1320*X*<sup>25</sup> + 1320*X*<sup>26</sup> + 1320*X*<sup>27</sup> + 1320*X*<sup>28</sup> + 3445*X*<sup>31</sup> +3445*X*<sup>32</sup> + 3445*X*<sup>33</sup> + 3445*X*<sup>34</sup> + 3445*X*<sup>35</sup> + 3445*X*<sup>36</sup> + 3445*X*<sup>37</sup> + 3445*X*<sup>38</sup> + 80*X*<sup>41</sup> +80*X*<sup>42</sup> + 80*X*<sup>43</sup> + 80*X*<sup>44</sup> + 80*X*<sup>45</sup> + 80*X*<sup>46</sup> + 80*X*<sup>47</sup> + 80*X*<sup>48</sup> + 130*X*<sup>51</sup> + 130*X*<sup>52</sup> + 130*X*<sup>53</sup> +130*X*<sup>54</sup> + 130*X*<sup>55</sup> + 130*X*<sup>56</sup> + 130*X*<sup>57</sup> + 130*X*<sup>58</sup> + 26, 000*X*<sup>61</sup> + 26, 000*X*<sup>62</sup> + 26, 000*X*<sup>63</sup> +26, 000*X*<sup>64</sup> + 26, 000*X*<sup>65</sup> + 26, 000*X*<sup>66</sup> + 26, 000*X*<sup>67</sup> + 26, 000*X*<sup>68</sup>

*X*<sup>21</sup> + *X*<sup>31</sup> + *X*<sup>41</sup> + *X*<sup>51</sup> + *X*<sup>61</sup> ≤ 91.46 *X*<sup>22</sup> + *X*<sup>32</sup> + *X*<sup>42</sup> + *X*<sup>52</sup> + *X*<sup>62</sup> ≤ 59.4 *X*<sup>23</sup> + *X*<sup>33</sup> + *X*<sup>43</sup> + *X*<sup>53</sup> + *X*<sup>63</sup> ≤ 89.1 *X*<sup>24</sup> + *X*<sup>34</sup> + *X*<sup>44</sup> + *X*<sup>54</sup> + *X*<sup>64</sup> ≤ 51 *X*<sup>25</sup> + *X*<sup>35</sup> + *X*<sup>45</sup> + *X*<sup>55</sup> + *X*<sup>65</sup> ≤ 40.2 *X*<sup>26</sup> + *X*<sup>36</sup> + *X*<sup>46</sup> + *X*<sup>56</sup> + *X*<sup>66</sup> ≤ 66.7 *X*<sup>27</sup> + *X*<sup>37</sup> + *X*<sup>47</sup> + *X*<sup>57</sup> + *X*<sup>67</sup> ≤ 70.46 *X*<sup>28</sup> + *X*<sup>38</sup> + *X*<sup>48</sup> + *X*<sup>58</sup> + *X*<sup>68</sup> ≤ 247.68 *X*<sup>21</sup> + *X*<sup>31</sup> + *X*<sup>41</sup> + *X*<sup>51</sup> + *X*<sup>61</sup> ≥ 3.7 *X*<sup>22</sup> + *X*<sup>32</sup> + *X*<sup>42</sup> + *X*<sup>52</sup> + *X*<sup>62</sup> ≥ 39.8 *X*<sup>23</sup> + *X*<sup>33</sup> + *X*<sup>43</sup> + *X*<sup>53</sup> + *X*<sup>63</sup> ≥ 15.1 *X*<sup>24</sup> + *X*<sup>34</sup> + *X*<sup>44</sup> + *X*<sup>54</sup> + *X*<sup>64</sup> ≥ 55.4 *X*<sup>25</sup> + *X*<sup>35</sup> + *X*<sup>45</sup> + *X*<sup>55</sup> + *X*<sup>65</sup> ≥ 104.3 *X*<sup>26</sup> + *X*<sup>36</sup> + *X*<sup>46</sup> + *X*<sup>56</sup> + *X*<sup>66</sup> ≥ 176.3 *X*<sup>27</sup> + *X*<sup>37</sup> + *X*<sup>47</sup> + *X*<sup>57</sup> + *X*<sup>67</sup> ≥ 182.1 *X*<sup>28</sup> + *X*<sup>38</sup> + *X*<sup>48</sup> + *X*<sup>58</sup> + *X*<sup>68</sup> ≥ 360.8 *Xij* ≥ 0;

According to the solution of the above formula, the optimal allocation of surplus gas to each of the sources of consumption is as follows (Table 13 and the Figure 4).


**Table 13.** Optimal allocation of surplus gas (MCM).

**Figure 4.** Optimal allocation of surplus gas.

Minimizing the cost of energy security is calculated as follows:

$$\text{Min } P\_1 d\_1^+ \text{ } \text{ } P\_2 d\_2^+ \text{ } \text{ } P\_3 d\_3^+ \text{ } \text{ } P\_3 d\_4^+ \text{ } \text{ } P\_5 d\_5^+ \text{ } \text{ } P\_6 d\_6^+$$

#### Such that:

```
13, 369.5X11 +14, 818X12 + 16, 920X13 + 17, 550X14 + 18, 040X15 + 18, 117X16 + 18, 762X17 + 18, 411X18 + 269.2X21
             +332.6X22 + 237.6X23 + 293X24 + 293.1X25 + 205.9X26 + 316.8X27 + 356.4X28 + 72.3X31
             +217X32 + 24.1X33 + 337.6X34 + 578.7X35 + 1519.2X36 + 378.6X37 + 48.2X38 + 100.4X41
             +190.6X42 + 209.6X43 + 217.2X44 + 216.8X45 + 198.8X46 + 187.2X47 + 268.8X48 + 2340X51
             +11, 180X52 + 3380X53 + 9620X54 + 35, 880X55 + 32, 760X56 + 66, 560X57 + 22, 620X58 + 0.7X61
             +37.7X62 + 54.6X63 + 54.6X64 + 54.6X65 + 54.6X66 + 54.6X67 + 54.6X68 <= 327, 712
```

$$\begin{array}{c}X\_{11} + X\_{12} + X\_{13} + X\_{14} + X\_{15} + X\_{16} + X\_{17} + X\_{18} < = 4\\X\_{21} + X\_{22} + X\_{23} + X\_{24} + X\_{25} + X\_{26} + X\_{27} + X\_{28} < = 6\\X\_{31} + X\_{32} + X\_{33} + X\_{34} + X\_{35} + X\_{36} + X\_{37} + X\_{38} < = 7\\X\_{41} + X\_{42} + X\_{43} + X\_{44} + X\_{45} + X\_{46} + X\_{47} + X\_{48} < = 5\\X\_{51} + X\_{52} + X\_{53} + X\_{54} + X\_{55} + X\_{56} + X\_{57} + X\_{58} < = 2\\X\_{61} + X\_{62} + X\_{63} + X\_{64} + X\_{65} + X\_{66} + X\_{67} + X\_{68} < = 10\\d\_{1}^{+} \cdot d\_{1}^{-} = 0d\_{2}^{+} \cdot d\_{2}^{-} = 0\\d\_{3}^{+} \cdot d\_{3}^{-} = 0d\_{4}^{+} \cdot d\_{4}^{-} = 0\\d\_{5}^{+} \cdot d\_{5}^{-} = 0d\_{6}^{+} \cdot d\_{6}^{-} = 0\\X\_{ij} \cdot d\_{k}^{+} \cdot d\_{k}^{-} \ge 0; \ k = 1, 2, 3, 4, 5, 6\end{array}$$

Considering the above problem in Lingo 17 software, the optimal allocation of energy security is as follows (Table 14 and Figure 5).


**Table 14.** Optimal allocation of energy security costs (Rials).

**Figure 5.** Optimal allocation of energy security costs.

According to Table 14, the optimal cost of energy security is calculated as follows:

(1 × 332.6)+ (1.23 × 237.6) + (1.23 × 293) + (1.23 × 293.1) + (1.23 × 205.9) + (1.23 × 14, 818) + (1.23 × 18, 920) +(1.23 × 17, 550) + (0.29 × 18, 040) + (0.7 × 11, 180) + (1.23 × 3380) + (1.23 × 19.6) +(1.23 × 209.6) + (1.23 × 217.6) + (1.23 × 216.8) + (0.61 × 198.8) + (0.8 × 217) + (1.23 × 44.1) +(1.23 × 337.6) + (1.23 × 578.7) + (1.23 × 1519.2) + (1.23 × 378.6) + (1.23 × 0.7) +(1.23 × 37.7) + (7.5 × 54.6) = 90, 201.802

> Regarding Table 13 gas surplus was present throughout the gas system. It shows that the gas surplus is allocated to different consumption sectors. Table 14 shows the cost of energy security which is only calculated for the sectors which do not have a supply shortage. In other words, this cost is assigned to the various sectors according to the cost of gas production and the priority of the consumer sector as specified in Table 14.
