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Файл:Моделирование и оптимизация технологических процессов. Учебное пособие
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ɗɥɟɦɟɧɬ
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ɂɬɨɝɨ
ɞɨɩɪɨɞɭɜɤɢ ɩɨɫɥɟɩɪɨɞɭɜɤɢ
ɦɚɫ ɤɝ ɦɚɫ ɤɝ ɦɚɫ ɤɝ ɦɚɫ ɤɝ
ɋɨɫɬɚɜɪɚɫɩɥɚɜɚ
ɍɝɚɪɨɛɳɢɣ
ɉɨɫɬɭɩɢɬ
ɜɲɥɚɤ
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Ɋɚɫɱɟɬɫɨɫɬɚɜɚɲɥɚɤɚɨɤɢɫɥɢɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚ
Ʉɨɦɩɨɧɟɧɬ
ɲɥɚɤɚ
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ɂɬɨɝɨ
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ɩɥɚɜɥɟɧɢɹɤɝ
ɇɚɢɦɟɧɨɜɚɧɢɟɫɬɚɬɶɢɩɪɢɯɨɞɚ
ɒɥɚɤ
ɨɤɢɫɥɢɬɟɥɶɧɨɝɨ
ɩɟɪɢɨɞɚɤɝ
Ɋɚɫɯɨɞɮɭɬɟɪɨɜɤɢɤɝ
ɫɬɟɧɵ ɫɜɨɞ
ɩɨɞɢɧɚ
ɨɬɤɨɫɵ
ɋɨɫɬɚɜɲɥɚɤɚ
ɤɝ ɦɚɫ
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ɏɢɦɢɱɟɫɤɢɣɫɨɫɬɚɜɦɟɬɚɥɥɚɦɚɫ
ɋ ɋU 6L 1L 0Q 0R : $O 7L
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ɏɢɦɢɱɟɫɤɢɣɫɨɫɬɚɜɲɥɚɤɚɦɚɫ
ɋ
6L2&D20Q0Q2$O
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ɉɪɨɬɨɤɨɥɩɥɚɜɤɢ
ɨɤɢɫɥɢɬɟɥɶɧɵɣɩɟɪɢɨɞ
ɂɧɬɟɧɫɢɜɧɨɫɬɶɩɪɨɞɭɜɤɢɦ
Ⱦɚɜɥɟɧɢɟɤɢɫɥɨɪɨɞɚɉɚ«««««««««««««««ā
ɦɢɧ«««««««««««««««
ȼɪɟɦɹɩɪɨɞɭɜɤɢɦɢɧ««««««««««««««««««««
Ɍɟɦɩɟɪɚɬɭɪɚɋ««««««««««««««««««««
Ɋɚɫɯɨɞɤɢɫɥɨɪɨɞɚɦ
«««««««««««««««««««
Ɇɚɫɫɚɪɚɫɩɥɚɜɚɤɝ«««««««««««««««««««
Ɇɚɫɫɚɲɥɚɤɚɤɝ«««««««««««««««««««««
Ɋɢɫ. 6.4 ɉɪɨɬɨɤɨɥ ɩɥɚɜɤɢ
ȼɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɣ ɩɟɪɢɨɞ. ɋɨɝɥɚɫɧɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɢɧɫɬɪɭɤɰɢɢ ɜɨɡ
ɦɨɠɧɵ ɫɥɟɞɭɸɳɢɟ ɜɚɪɢɚɧɬɵ ɪɚɫɤɢɫɥɟɧɢɹ ɦɟɬɚɥɥɚ ɩɨɫɥɟ ɩɪɨɜɟɞɟɧɢɹ ɨɤɢɫɥɢ
ɬɟɥɶɧɨɝɨɩɟɪɢɨɞɚɩɭɬɟɦɩɪɢɫɚɞɤɢ
Ɏɋɏ±ɤɝɬɚɥɸɦɢɧɢɣ±ɤɝɬ
Ɏɋ±ɤɝɬɚɥɸɦɢɧɢɣ±ɤɝɬ
ɨɬɯɨɞɵɚɥɸɦɢɧɢɟɜɨɝɨɩɪɨɢɡɜɨɞɫɬɜɚ±ɤɝɬɎɋ±ɤɝɬ
ɨɬɯɨɞɵɚɥɸɦɢɧɢɟɜɨɝɨɩɪɨɢɡɜɨɞɫɬɜɚ±ɤɝɬɎɋ±ɤɝɬ
ȼɵɛɢɪɚɟɦ ɜɬɨɪɨɣ ɜɚɪɢɚɧɬ ɪɚɫɤɢɫɥɟɧɢɹ ɩɨɥɚɝɚɹ ɪɚɫɯɨɞ ɮɟɪɪɨɫɢɥɢɰɢɹ
Ɏɋɢɚɥɸɦɢɧɢɹɜɤɨɥɢɱɟɫɬɜɟɤɝɬɢɤɝɬɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
ɉɪɢɦɟɦ ɫɬɟɩɟɧɶɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɨɣ ɫɩɨɫɨɛɧɨɫɬɢ ɤɪɟɦɧɢɹ ɪɚɜɧɨɣ ɚ
ɫɬɟɩɟɧɶ ɢɡɜɥɟɱɟɧɢɹɯɪɨɦɚ ɦɚɪɝɚɧɰɚ ɢ ɠɟɥɟɡɚ ɢɡ ɲɥɚɤɚ ɨɞɢɧɚɤɨɜɨɣɢɪɚɜɧɨɣ
Ɍɨɝɞɚɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶɞɚɧɧɵɦɢɬɚɛɥɦɨɠɧɨɪɚɫɫɱɢɬɚɬɶɤɨɥɢɱɟ
ɫɬɜɨɨɤɫɢɞɨɜɜɲɥɚɤɟɩɨɫɥɟɩɪɢɫɚɞɤɢɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɨɣɫɦɟɫɢ
m
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6L2
m
ā
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m
ā ɤɝ
&U2
m
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0Q2
m
ā ɤɝ
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ɤɝ
ɤɝ
Ɋɚɫɱɟɬ ɫɨɫɬɚɜɚ ɢ ɤɨɥɢɱɟɫɬɜɚ ɲɥɚɤɚ ɩɨɫɥɟ ɩɪɢɫɚɞɤɢ ɪɚɫɤɢɫɥɢɬɟɥɟɣ ɩɪɟɞ
ɫɬɚɜɥɟɧɵɜɬɚɛɥ
Ⱦɥɹ ɩɪɨɜɟɞɟɧɢɹ ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɨɝɨ ɩɟɪɢɨɞɚ ɜ ɧɨɪɦɚɥɶɧɵɯ ɬɟɦɩɟɪɚɬɭɪ
ɧɵɯɭɫɥɨɜɢɹɯɧɚɨɯɥɚɠɞɟɧɢɟɪɚɫɩɥɚɜɚɛɵɥɨɨɫɬɚɜɥɟɧɨɤɝɨɬɯɨɞɨɜɝɪɭɩɩɵ
Ȼɉɪɢɜɨɫɫɬɚɧɨɜɥɟɧɢɢɤɨɦɩɨɧɟɧɬɨɜɲɥɚɤɚɢɪɚɫɤɢɫɥɢɬɟɥɟɣɜɦɟɬɚɥɥɩɟɪɟɣ
ɞɟɬ
m
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m
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U
ɤɝ
ɤɝ
m
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0Q
m
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Ɋɚɫɱɟɬɫɨɫɬɚɜɚɲɥɚɤɚɪɚɫɤɢɫɥɟɧɢɹ
Ʉɨɦɩɨɧɟɧɬɲɥɚɤɚ
&
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ɂɬɨɝɨ
ɤɝ ɦɚɫ
ɋɨɫɬɚɜɲɥɚɤɚ
Ɋɚɫɱɟɬ ɫɨɫɬɚɜɚ ɦɟɬɚɥɥɚ ɩɨɫɥɟ ɪɚɫɤɢɫɥɟɧɢɹ ɲɥɚɤɚ ɢ ɩɪɢɫɚɞɤɢ ɨɯɥɚɠɞɚɸ
ɳɟɣɞɨɛɚɜɤɢɩɪɢɜɟɞɟɧɜɬɚɛɥɉɨɫɥɟɪɚɫɤɢɫɥɟɧɢɹɢɨɯɥɚɠɞɟɧɢɹɪɚɫɩɥɚɜɚ
ɩɪɨɜɨɞɢɬɫɹɨɩɟɪɚɰɢɹɫɤɚɱɢɜɚɧɢɹɲɥɚɤɚȾɨɩɭɫɤɚɟɦɱɬɨɭɞɚɥɹɟɬɫɹɲɥɚɤɚ
ɬɚɤɱɬɨɨɫɬɚɜɲɟɟɫɹɤɨɥɢɱɟɫɬɜɚɲɥɚɤɚɩɪɢɦɟɪɧɨɤɝ
Ⱦɥɹɧɚɜɟɞɟɧɢɹ ɪɚɮɢɧɢɪɨɜɨɱɧɨɝɨ ɲɥɚɤɚɢɫɩɨɥɶɡɭɟɦ ɫɥɟɞɭɸɳɢɟɲɥɚɤɨɨɛ
ɪɚɡɭɸɳɢɟɢɪɚɫɤɢɫɥɢɬɟɥɢɤɝɢɡɜɟɫɬɢɤɝɮɥɸɨɪɢɬɚɤɝɮɟɪɪɨɫɢɥɢɰɢɹ
Ɏɋɢɤɝɩɟɪɜɢɱɧɨɝɨɚɥɸɦɢɧɢɹ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
Ɋɚɫɱɟɬɫɨɫɬɚɜɚɪɚɫɩɥɚɜɚɩɨɫɥɟɪɚɫɤɢɫɥɟɧɢɹɢɨɯɥɚɠɞɟɧɢɹ
ɇɚɢɦɟɧɨɜɚɧɢɟɫɬɚɬɶɢɩɪɢɯɨɞɚ
ɗɥɟɦɟɧɬ
ɋ
ɋU
6L
1L
0Q
0R
:
$O
7L
)H
ɂɬɨɝɨ
Ɋɚɫɩɥɚɜ
ɦɚɫ ɤɝ ɤɝ ɤɝ ɤɝ ɦɚɫ
ɒɥɚɤ
ɢɪɚɫɤɢɫɥɢɬɟɥɢ
Ɉɬɯɨɞɵɝɪɭɩɩɵ
Ȼ
ɋɨɫɬɚɜɪɚɫɩɥɚɜɚ
Ɋɚɫɱɟɬɫɨɫɬɚɜɚ ɪɚɮɢɧɢɪɨɜɨɱɧɨɝɨɲɥɚɤɚɩɪɟɞɫɬɚɜɥɟɧ ɜɬɚɛɥ ɂɡɷɬɢɯ
U
ɞɚɧɧɵɯɫɥɟɞɭɟɬɱɬɨɫɨɫɬɚɜɩɨɥɭɱɟɧɧɨɝɨɪɚɫɩɥɚɜɚɨɬɥɢɱɚɟɬɫɹɨɬɫɪɟɞɧɢɯɡɧɚɱɟ
ɧɢɣɫɨɞɟɪɠɚɧɢɹɨɫɧɨɜɧɵɯɥɟɝɢɪɭɸɳɢɯɤɨɦɩɨɧɟɧɬɨɜɞɥɹɡɚɞɚɧɧɨɣɦɚɪɤɢɫɬɚɥɢ
ɉɨɷɬɨɦɭɧɟɨɛɯɨɞɢɦɨɩɪɨɢɡɜɟɫɬɢɤɨɪɪɟɤɬɢɪɨɜɤɭɫɨɫɬɚɜɚɦɟɬɚɥɥɚɫɢɫɩɨɥɶɡɨɜɚ
ɧɢɟɦɮɟɪɪɨɫɩɥɚɜɨɜɢɱɢɫɬɵɯɦɚɬɟɪɢɚɥɨɜȼɤɚɱɟɫɬɜɟɤɨɪɪɟɤɬɢɪɭɸɳɢɯɞɨɛɚɜɨɤ
ɜɵɛɢɪɚɟɦɎɏȺx
ɢȺȺȺxɩɪɢɦɚɫɫɟɪɚɫɩɥɚɜɚɬ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
Ɋɚɫɱɟɬɫɨɫɬɚɜɚɪɚɮɢɧɢɪɨɜɨɱɧɨɝɨɲɥɚɤɚ
ɇɚɢɦɟɧɨɜɚɧɢɟɫɬɚɬɶɢɩɪɢɯɨɞɚɤɝ
Ʉɨɦɩɨɧɟɧɬ
ɒɥɚɤɩɨɫɥɟ
ɫɤɚɱɢɜɚɧɢɹ
ɲɥɚɤɚ
ɦɚɫ ɤɝ
&
2
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ɂɡɜɟɫɬɶ &D) ɤɝ ɦɚɫ
ɩɟɪɜ
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0J2
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ɂɬɨɝɨ
ɋɨɫɬɚɜ
ɪɚɮɢɧɢɪɨɜɨɱɧɨɝɨ
ɲɥɚɤɚ
ɋɢɫɬɟɦɚ ɧɟɪɚɜɟɧɫɬɜ ɩɪɢ ɜɵɛɪɚɧɧɵɯ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɹɯ ɤɨɧɰɟɧɬɪɚɰɢɣ
ɤɨɦɩɨɧɟɧɬɨɜɜɪɚɫɩɥɚɜɟɞɥɹɷɬɨɣɦɚɪɤɢɫɬɚɥɢɢɢɯɪɟɚɥɶɧɵɦɫɨɞɟɪɠɚɧɢɢɜɦɟ
ɬɚɥɥɟɛɭɞɟɬɢɦɟɬɶɫɥɟɞɭɸɳɢɣɜɢɞ
xxx
xxx
xxx!
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Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɤɨɪɪɟɤɬɢɪɭɸɳɢɯ ɞɨɛɚɜɨɤ ɢ ɫɨɫɬɚɜɚ ɪɚɫɩɥɚɜɚ ɩɨɫɥɟ
ɤɨɪɪɟɤɬɢɪɨɜɤɢɩɪɟɞɫɬɚɜɥɟɧɵɜɬɚɛɥɢ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ɊɟɡɭɥɶɬɚɬɵɪɚɫɱɟɬɚɧɚɗȼɆɤɨɪɪɟɤɬɢɪɭɸɳɢɯɞɨɛɚɜɨɤ
Ɂɚɞɚɧɧɵɟ
ɗɥɟɦɟɧɬ
ɋ ± ɎɏȺ
&U ± ȺȺȺ
1L ± ɂɬɨɝɨ
ɩɪɟɞɟɥɵ
ɦɚɫ ɦɚɫ ɦɚɫ Ʉɨɦɩɨɧɟɧɬ Ɇɚɫɫɚɤɝ
ȼɪɚɫɩɥɚɜɟ
ɉɨɫɥɟ
ɤɨɪɪɟɤɬɢɪɨɜɤɢ
Ʉɨɪɪɟɤɬɢɪɭɸɳɢɟ
ɞɨɛɚɜɤɢ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
Ɋɚɫɱɟɬɫɨɫɬɚɜɚɪɚɫɩɥɚɜɚɩɨɫɥɟɤɨɪɪɟɤɬɢɪɨɜɤɢɢɥɟɝɢɪɨɜɚɧɢɹɬɢɬɚɧɨɦ
Ⱦɨ
ɗɥɟɦɟɧɬ
ɋ
&U
6L
1L
0Q
0R
:
$O
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ɂɬɨɝɨ
ɤɨɪɪɟɤɬɢɪɨɜɤɢ
ɦɚɫ ɤɝ ɤɝ ɤɝ ɤɝ ɦɚɫ
Ʉɨɪɪɟɤɬɢɪɭɸɳɢɟ
ɞɨɛɚɜɤɢ
ɉɪɢɥɟɝɢɪɨɜɚɧɢɢ
ɮɟɪɪɨɬɢɬɚɧɨɦ
ɉɨɫɥɟ
ɤɨɪɪɟɤɬɢɪɨɜɤɢ
ɢɥɟɝɢɪɨɜɚɧɢɹ
ɉɪɢ ɥɟɝɢɪɨɜɚɧɢɢ ɦɟɬɚɥɥɚɬɢɬɚɧɨɦ ɜɨɡɦɨɠɧɵ ɫɥɟɞɭɸɳɢɟ ɜɚɪɢɚɧɬɵ ɩɪɢ
ɫɚɞɤɚɮɟɪɪɨɬɢɬɚɧɚɜɩɟɱɶɢɢɫɩɨɥɶɡɨɜɚɧɢɟɮɟɪɪɨɬɢɬɚɧɚɢɥɢɦɟɬɚɥɥɢɱɟɫɤɨɝɨɬɢ
ɬɚɧɚɜɤɨɜɲɟɉɪɢɦɟɦ ɱɬɨɥɟɝɢɪɨɜɚɧɢɟɦɟɬɚɥɥɚɩɪɨɢɡɜɨɞɢɬɫɹɜ ɤɨɜɲɟɮɟɪɪɨ
ɬɢɬɚɧɨɦɎ7ɢɫɨɞɟɪɠɚɳɢɦɦɚɫɋ 6L 0R$Oɢ
7Lɇɟɨɛɯɨɞɢɦɨɟɤɨɥɢɱɟɫɬɜɨɮɟɪɪɨɬɢɬɚɧɚɦɨɠɧɨɪɚɫɫɱɢɬɚɬɶɩɨɮɨɪɦɭɥɟ
ªº
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ɝɞɟ>7L@±ɤɨɧɟɱɧɨɟɫɨɞɟɪɠɚɧɢɟɬɢɬɚɧɚɜɪɚɫɩɥɚɜɟɩɨɫɥɟɥɟɝɢɪɨɜɚɧɢɹ
m
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ɎɌX
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±ɫɨɞɟɪɠɚɧɢɟɬɢɬɚɧɚɜɮɟɪɪɨɫɩɥɚɜɟɦɚɫ
ɌL
±ɫɬɟɩɟɧɶɭɫɜɨɟɧɢɹɬɢɬɚɧɚɢɡɮɟɪɪɨɫɩɥɚɜɚɦɚɫ
η
ɌL
M
±ɦɚɫɫɚɪɚɫɩɥɚɜɚɤɝ
S
ȾɥɹɩɨɥɭɱɟɧɢɹɝɚɪɚɧɬɢɪɨɜɚɧɧɨɝɨɜɩɪɟɞɟɥɚɯȽɈɋɌɚɫɨɞɟɪɠɚɧɢɹɬɢɬɚɧɚɜ
ɦɟɬɚɥɥɟ ɩɪɢɦɟɦ> 7L@ ɉɪɢ ɡɚɞɚɧɧɨɣ ɦɚɫɫɟɪɚɫɩɥɚɜɚ M
ɫɬɟɩɟɧɢɭɫɜɨɟɧɢɹ ɬɢɬɚɧɚɢɚɥɸɦɢɧɢɹ ɢɡɮɟɪɪɨɬɢɬɚɧɚ η
ɲɟɩɪɢɜɟɞɟɧɧɨɝɨɫɨɨɬɧɨɲɟɧɢɹɩɨɥɭɱɢɦm
ɤɝɆɚɫɫɚɪɚɫɩɥɚɜɚɩɪɢɷɬɨɦ
ɎɬX
ɌL
ɤɝ ɢ
S
ɦɚɫɢɡ ɜɵ
ɫɨɫɬɚɜɢɬɤɝ
ȼɦɟɬɚɥɥɩɟɪɟɣɞɟɬ
ɋ±ā ɤɝ6L±ā ɤɝ
0R±ā ɤɝ$O±āā ɤɝ
7L±āā ɤɝ
ɋ ɭɱɟɬɨɦ ɫɨɫɬɚɜɚ ɦɟɬɚɥɥɚ ɩɨɫɥɟ ɤɨɪɪɟɤɬɢɪɨɜɤɢ ɢ ɩɪɢɜɟɞɟɧɧɵɯ ɞɨɛɚɜɨɤ
ɩɪɢɥɟɝɢɪɨɜɚɧɢɢɩɨɥɭɱɢɦɫɨɫɬɚɜɝɨɬɨɜɨɝɨɫɩɥɚɜɚɬɚɛɥ
Ɍ ɚ ɛ ɥ ɢ ɰ ɚ
ɏɢɦɢɱɟɫɤɢɣɫɨɫɬɚɜɠɢɞɤɨɣɫɬɚɥɢɜɤɨɜɲɟɩɨɫɥɟɥɟɝɢɪɨɜɚɧɢɹɫɬɚɥɢ
ɋ ɋU 6L 1L 0Q 0R : $O 7L
Ɋɟɡɭɥɶɬɚɬɵɪɚɫɱɟɬɚɩɨɤɨɦɩɶɸɬɟɪɧɨɣɦɨɞɟɥɢɩɪɟɞɫɬɚɜɥɟɧɵɧɚɪɢɫ
ɉɪɨɬɨɤɨɥɩɥɚɜɤɢ
ɜɨɫɫɬɚɧɨɜɢɬɟɥɶɧɵɣɩɟɪɢɨɞ
Ɋɚɫɤɢɫɥɢɬɟɥɶɧɵɟɞɨɛɚɜɤɢ
ɎɟɪɪɨɫɢɥɢɰɢɣɎɋɤɝ«««««««««««««««««
Ⱥɥɸɦɢɧɢɣ«««««««««««««««««««««««
Ɉɯɥɚɠɞɚɸɳɢɟɞɨɛɚɜɤɢ
Ɉɬɯɨɞɵɝɪɭɩɩɵ Ȼ ɤɝ «««««««««««««««««
Ƚɨɞɧɨɝɨ ɤɝ «««««««««««««««««««««
Ʉɨɥɢɱɟɫɬɜɨɫɥɢɬɤɨɜɦɚɫɫɨɣ ɤɝɲɬ«««««««««««
ȼɵɯɨɞ ɝɨɞɧɨɝɨ ɦɚɫ «««««««««««««««««
Ɋɢɫ. 6.5 ɉɪɨɬɨɤɨɥ ɩɥɚɜɤɢ
ɋɅɈȼȺɊɖɌȿɊɆɂɇɈȼ
Ⱥɛɫɬɪɚɝɢɪɨɜɚɧɢɟ
DEVWUDFWLRQ ɚɧɝɥ 'LH $EVWUDNWLRQ ɧɟɦ ODEVWUDFWLRQ
ɮɪɚɧɰ±ɨɞɧɚɢɡɨɫɧɨɜɧɵɯɦɵɫɥɢɬɟɥɶɧɵɯɨɩɟɪɚɰɢɣɩɨɡɜɨɥɹɸɳɚɹɦɵɫɥɟɧɧɨɜɵ
ɱɥɟɧɢɬɶɢɩɪɟɜɪɚɬɢɬɶɜɫɚɦɨɫɬɨɹɬɟɥɶɧɵɣɨɛɴɟɤɬɪɚɫɫɦɨɬɪɟɧɢɹɨɬɞɟɥɶɧɵɟɫɬɨɪɨɧɵ
ɫɜɨɣɫɬɜɚɢɥɢɫɨɫɬɨɹɧɢɹɨɛɴɟɤɬɚɜɱɢɫɬɨɦɜɢɞɟ
Ⱥɞɟɤɜɚɬɧɨɫɬɶ ɦɨɞɟɥɢ DGHTXDF\ RI WKH PRGHO ɚɧɝɥ $QJHPHVVHQKHLW GHV
0RGHOOVɧɟɦDGpTXDWLRQGXPRGqOH ɮɪɚɧɰ±ɬɪɟɛɨɜɚɧɢɟɤ ɦɨɞɟɥɢɫɨɫɬɨɹɳɟɟ ɜ
ɟɟ ɫɩɨɫɨɛɧɨɫɬɢ ɜɨɫɩɪɨɢɡɜɨɞɢɬɶ ɫɜɨɣɫɬɜɚ ɫɨɫɬɨɹɧɢɟ ɢ ɩɨɜɟɞɟɧɢɟ ɢɫɫɥɟɞɭɟɦɨɝɨ
ɨɛɴɟɤɬɚɫɞɨɫɬɚɬɨɱɧɨɣɞɥɹɩɨɫɬɚɜɥɟɧɧɵɯɰɟɥɟɣɬɨɱɧɨɫɬɶɸɢɜɞɨɫɬɚɬɨɱɧɨɲɢɪɨɤɨɦ
ɞɢɚɩɚɡɨɧɟ ɢɡɦɟɧɟɧɢɹ ɟɟ ɫɨɫɬɨɹɧɢɹɢ ɫɨɫɬɨɹɧɢɹ ɟɟ ɫɪɟɞɵ Ⱦɨɫɬɚɬɨɱɧɵɦ ɭɫɥɨɜɢɟɦ
ɚɞɟɤɜɚɬɧɨɫɬɢɦɨɞɟɥɢɹɜɥɹɟɬɫɹɟɟɝɨɦɨɦɨɪɮɢɡɦɢɫɫɥɟɞɭɟɦɨɦɭɨɛɴɟɤɬɭ
Ⱥɥɝɨɪɢɬɦ DOJRULWKP ɚɧɝɥ 'HU $OJRULWKPXV ɧɟɦ ODOJRULWKPH ɮɪɚɧɰ±
ɧɚɛɨɪɢɧɫɬɪɭɤɰɢɣ ɨɩɢɫɵɜɚɸɳɢɯ ɩɨɪɹɞɨɤ ɞɟɣɫɬɜɢɣɢɫɩɨɥɧɢɬɟɥɹ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ
ɪɟɡɭɥɶɬɚɬɚɪɟɲɟɧɢɹɡɚɞɚɱɢɡɚɤɨɧɟɱɧɨɟɱɢɫɥɨɞɟɣɫɬɜɢɣȼɫɬɚɪɨɣɬɪɚɤɬɨɜɤɟɜɦɟɫɬɨ
ɫɥɨɜɚ©ɩɨɪɹɞɨɤªɢɫɩɨɥɶɡɨɜɚɥɨɫɶɫɥɨɜɨ©ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶªɧɨɩɨɦɟɪɟɪɚɡɜɢɬɢɹ
ɩɚɪɚɥɥɟɥɶɧɨɫɬɢɜɪɚɛɨɬɟɤɨɦɩɶɸɬɟɪɨɜɫɥɨɜɨ©ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶªɫɬɚɥɢɡɚɦɟɧɹɬɶ
ɛɨɥɟɟɨɛɳɢɦɫɥɨɜɨɦ©ɩɨɪɹɞɨɤªɗɬɨɫɜɹɡɚɧɨɫɬɟɦɱɬɨɪɚɛɨɬɚɤɚɤɢɯɬɨɢɧɫɬɪɭɤɰɢɣ
ɚɥɝɨɪɢɬɦɚɦɨɠɟɬɛɵɬɶɡɚɜɢɫɢɦɚɨɬɞɪɭɝɢɯɢɧɫɬɪɭɤɰɢɣɢɥɢɪɟɡɭɥɶɬɚɬɨɜɢɯɪɚɛɨɬɵ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɧɟɤɨɬɨɪɵɟ ɢɧɫɬɪɭɤɰɢɢ ɞɨɥɠɧɵ ɜɵɩɨɥɧɹɬɶɫɹ ɫɬɪɨɝɨ ɩɨɫɥɟ ɡɚɜɟɪ
ɲɟɧɢɹɪɚɛɨɬɵɢɧɫɬɪɭɤɰɢɣɨɬɤɨɬɨɪɵɯ ɨɧɢɡɚɜɢɫɹɬɇɟɡɚɜɢɫɢɦɵɟɢɧɫɬɪɭɤɰɢɢɢɥɢ
ɢɧɫɬɪɭɤɰɢɢɫɬɚɜɲɢɟɧɟɡɚɜɢɫɢɦɵɦɢɢɡɡɚɡɚɜɟɪɲɟɧɢɹɪɚɛɨɬɵɢɧɫɬɪɭɤɰɢɣɨɬɤɨɬɨ
ɪɵɯɨɧɢɡɚɜɢɫɹɬɦɨɝɭɬɜɵɩɨɥɧɹɬɶɫɹɜɩɪɨɢɡɜɨɥɶɧɨɦɩɨɪɹɞɤɟɩɚɪɚɥɥɟɥɶɧɨɢɥɢɨɞ
ɧɨɜɪɟɦɟɧɧɨɟɫɥɢɷɬɨɩɨɡɜɨɥɹɸɬɢɫɩɨɥɶɡɭɟɦɵɟɩɪɨɰɟɫɫɨɪɢɨɩɟɪɚɰɢɨɧɧɚɹɫɢɫɬɟɦɚ
Ⱥɥɝɨɪɢɬɦɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ DOJRULWKPLF PRGHOLQJ ɚɧɝɥ
$OJRULWKPLVFKH0RGHOOLHUXQJɧɟɦPRGpOLVDWLRQDOJRULWKPLTXHɮɪɚɧɰ± ɪɚɡɧɨɜɢɞ
ɧɨɫɬɶɢɦɢɬɚɰɢɨɧɧɨɝɨɦɨɞɟɥɢɪɨɜɚɧɢɹɫɢɫɩɨɥɶɡɨɜɚɧɢɟɦɭɧɢɜɟɪɫɚɥɶɧɨɝɨɹɡɵɤɚɩɪɨ
ɝɪɚɦɦɢɪɨɜɚɧɢɹɉɚɫɤɚɥɶȻɟɣɫɢɤɢɥɢɞɪɢɫɩɟɰɢɚɥɶɧɵɯɚɥɝɨɪɢɬɦɨɜȻɨɥɟɟɬɪɭɞɨ
ɟɦɤɨɩɨɫɪɚɜɧɟɧɢɸɫɩɪɢɦɟɧɟɧɢɟɦɦɨɞɟɥɢɪɭɸɳɢɯɫɢɫɬɟɦɢɬɟɯɧɨɥɨɝɢɣȼɧɚɫɬɨɹ
ɳɟɟɜɪɟɦɹɩɪɢɦɟɧɹɟɬɫɹɜɧɟɤɨɬɨɪɵɯɜɭɡɚɯɞɥɹɩɪɟɩɨɞɚɜɚɧɢɹɨɫɧɨɜɤɨɦɩɶɸɬɟɪɧɨɝɨ
ɦɨɞɟɥɢɪɨɜɚɧɢɹ
Ⱥɧɚɥɢɬɢɱɟɫɤɢɟɦɨɞɟɥɢ DQDO\WLFDOPRGHOV ɚɧɝɥ $QDO\WLVFKH0RGHOOH ɧɟɦ
PRGqOHV GDQDO\VH ɮɪɚɧɰ ± ɱɢɫɥɟɧɧɨɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɪɚɡɪɚɛɚɬɵɜɚɟɦɵɟ
ɞɥɹɢɫɫɥɟɞɨɜɚɧɢɹɫɬɪɭɤɬɭɪɵɦɨɞɟɥɢɪɭɟɦɨɣɫɢɫɬɟɦɵȼɷɤɨɧɨɦɢɤɨɦɚɬɟɦɚɬɢɱɟɫɤɨɦ
ɦɨɞɟɥɢɪɨɜɚɧɢɢɤɚɤɩɪɚɜɢɥɨɢɦɟɸɬɰɟɥɶɸɜɵɹɜɥɟɧɢɟɪɟɡɟɪɜɨɜɩɨɜɵɲɟɧɢɹɷɮɮɟɤ
ɬɢɜɧɨɫɬɢɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹɦɨɞɟɥɢɪɭɟɦɨɣɫɢɫɬɟɦɵɥɢɛɨɮɚɤɬɨɪɨɜɜɥɢɹɸɳɢɯɧɚ
ɢɫɫɥɟɞɭɟɦɵɟɩɨɤɚɡɚɬɟɥɢɯɨɡɹɣɫɬɜɟɧɧɨɣɞɟɹɬɟɥɶɧɨɫɬɢɚɬɚɤɠɟɮɨɪɦɵɢɫɬɟɩɟɧɢɢɯ
ɜɥɢɹɧɢɹ
Ⱥɩɨɫɬɟɪɢɨɪɧɨɟɪɟɲɟɧɢɟ SRVWHULRUGHFLVLRQ ɚɧɝɥ$SRVWHULDOH /|VXQJɧɟɦ
GpFLVLRQDSRVWpULHOOHɮɪɚɧɰ±ɜɫɬɨɯɚɫɬɢɱɟɫɤɢɯɞɜɭɯɷɬɚɩɧɵɯɦɨɞɟɥɹɯ±ɜɟɤɬɨɪɨɩ
ɬɢɦɚɥɶɧɵɯɡɧɚɱɟɧɢɣɩɟɪɟɦɟɧɧɵɯɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯɩɥɚɧɨɜɵɟɡɚɞɚɧɢɹ ɜɵɩɨɥɧɹɟ
ɦɵɟɩɨɫɥɟɩɨɫɬɭɩɥɟɧɢɹɢɧɮɨɪɦɚɰɢɢɨɧɚɫɬɭɩɥɟɧɢɢɨɩɪɟɞɟɥɟɧɧɨɝɨɫɥɭɱɚɣɧɨɝɨɫɨ
ɛɵɬɢɹ ɜɥɢɹɸɳɟɝɨ ɧɚ ɯɨɡɹɣɫɬɜɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ Ⱦɥɹ ɤɚɠɞɨɝɨ ɜɚɪɢɚɧɬɚ ɢɫɯɨɞɚ
ɫɥɭɱɚɣɧɵɯɫɨɛɵɬɢɣɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹɨɬɞɟɥɶɧɨɟɚɩɨɫɬɟɪɢɨɪɧɨɟɪɟɲɟɧɢɟ
Ⱥɩɪɢɨɪɧɨɟ ɪɟɲɟɧɢɟ D SULRUL GHFLVLRQ ɚɧɝɥ (LQH DSULRULVFKH /|VXQJ
ɧɟɦVROXWLRQDSULRULɮɪɚɧɰ±ɜɫɬɨɯɚɫɬɢɱɟɫɤɢɯɞɜɭɯɷɬɚɩɧɵɯɦɨɞɟɥɹɯ±ɜɟɤ
ɬɨɪ ɨɩɬɢɦɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɩɟɪɟɦɟɧɧɵɯɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɩɥɚɧɨɜɵɟ ɡɚɞɚɧɢɹ
ɬɪɟɛɭɸɳɢɟ ɜɵɩɨɥɧɟɧɢɹ ɞɨ ɩɨɫɬɭɩɥɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɨ ɫɥɭɱɚɣɧɵɯ ɫɨɛɵɬɢɹɯ
ɜɥɢɹɸɳɢɯɧɚɨɠɢɞɚɟɦɵɟɯɨɡɹɣɫɬɜɟɧɧɵɟɪɟɡɭɥɶɬɚɬɵ
ȻɚɥɚɧɫEDODQFHɚɧɝɥ'LH%LODQ]ɧɟɦODEDODQFHɮɪɚɧɰ±ɜɷɤɨɧɨɦɢ
ɤɨɦɚɬɟɦɚɬɢɱɟɫɤɨɦɦɨɞɟɥɢɪɨɜɚɧɢɢ±ɭɪɚɜɧɟɧɢɟɢɥɢɧɟɪɚɜɟɧɫɬɜɨɭɫɬɚɧɚɜɥɢɜɚ
ɸɳɟɟɫɨɨɬɜɟɬɫɬɜɢɟɦɟɠɞɭɢɫɬɨɱɧɢɤɚɦɢɪɟɫɭɪɫɚɢɧɚɩɪɚɜɥɟɧɢɹɦɢɟɝɨɢɫɩɨɥɶɡɨ
ɜɚɧɢɹ ɍɪɚɜɧɟɧɢɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɟɫɥɢ ɢɦɟɸɳɢɟɫɹ ɢɫɬɨɱɧɢɤɢ ɪɟɫɭɪɫɚɞɨɥɠɧɵ
ɛɵɬɶɢɫɩɨɥɶɡɨɜɚɧɵɛɟɡɨɫɬɚɬɤɚ ɥɢɛɨɟɫɥɢɧɚɥɢɱɢɟɨɫɬɚɬɤɚɜɥɢɹɟɬ ɧɚɷɤɨɧɨɦɢ
ɱɟɫɤɢɣɷɮɮɟɤɬɬɪɟɛɭɟɬɡɚɬɪɚɬɧɚɭɬɢɥɢɡɚɰɢɸɥɢɛɨɦɨɠɟɬɛɵɬɶɫɜɵɝɨɞɨɣɩɪɨ
ɞɚɧɧɚɪɵɧɤɟȼɩɪɨɬɢɜɧɨɦɫɥɭɱɚɟɛɚɥɚɧɫɵɡɚɩɢɫɵɜɚɸɬɫɹɜɮɨɪɦɟɧɟɪɚɜɟɧɫɬɜ
ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɵɦ ɫɨɜɨɤɭɩɧɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɪɟɫɭɪɫɚ ɧɟ ɩɪɟɜɵɲɚɟɬ ɪɚɡɦɟɪɚ
ɢɦɟɸɳɢɯɫɹɟɝɨɢɫɬɨɱɧɢɤɨɜ
ȼɟɤɬɨɪɧɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ YHFWRU SURJUDPPLQJ ɚɧɝɥ
9HNWRUSURJUDPPLHUXQJɧɟɦSURJUDPPDWLRQYHFWRULHOOHɮɪɚɧɰ±ɪɚɡɞɟɥɦɚ
ɬɟɦɚɬɢɤɢɢɫɫɥɟɞɭɸɳɢɣɦɟɬɨɞɵɪɟɲɟɧɢɹɡɚɞɚɱɜɟɤɬɨɪɧɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ɮɨɪɦɚɥɢɡɦɢɫɩɨɥɶɡɭɟɦɵɣɞɥɹɩɪɟɞɫɬɚɜɥɟɧɢɹɡɧɚɧɢɣɨɫɬɪɭɤɬɭɪɟɦɨɞɟɥɢɪɭ
ɟɦɵɯɨɛɴɟɤɬɨɜɜɮɨɪɦɟɡɚɞɚɱɢɜɟɤɬɨɪɧɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ȼɡɚɢɦɧɨɫɬɶ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ UHFLSURFLW\ ɚɧɝɥ
*HJHQVHLWLJNHLW ɧɟɦ UpFLSURFLWp ɮɪɚɧɰ± ɫɜɨɣɫɬɜɨ ɡɚɞɚɱ ɜɵɩɭɤɥɨɝɨ ɜ ɬɨɦ
ɱɢɫɥɟ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɫɨɫɬɨɹɳɟɟ ɜ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ ɨɩɬɢɦɚɥɶ
ɧɨɝɨɪɟɲɟɧɢɹɢɢɧɜɚɪɢɚɧɬɧɨɫɬɢɫɬɨɱɧɨɫɬɶɸɞɨɦɚɫɲɬɚɛɚɦɧɨɠɢɬɟɥɟɣɅɚɝɪɚɧ
ɠɚɤ ɡɚɦɟɧɟɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢɥɸɛɵɦ ɷɮɮɟɤɬɢɜɧɵɦɨɝɪɚɧɢɱɟɧɢɟɦɩɪɢ ɞɨɩɨɥ
ɧɢɬɟɥɶɧɨɦɭɫɥɨɜɢɢɱɬɨɡɧɚɱɟɧɢɟɩɪɟɠɧɟɣɰɟɥɟɜɨɣɮɭɧɤɰɢɢɨɫɬɚɧɟɬɫɹɪɚɜɧɵɦ
ɨɩɬɢɦɚɥɶɧɨɦɭ
Ƚɪɚɮ ɦɨɞɟɥɢ PRGHO JUDSK ɚɧɝɥ 0RGHOOGLDJUDPP ɧɟɦ JUDSKLTXH GX
PRGqOHɮɪɚɧɰ± ɨɛɴɟɤɬɢɦɢɬɚɰɢɨɧɧɨɣɦɨɞɟɥɢ ɩɪɟɞɫɬɚɜɥɹɸɳɢɣɧɚɩɪɚɜɥɟɧ
ɧɵɣ ɝɪɚɮɨɛɴɟɞɢɧɹɸɳɢɣ ɜɫɟ ɩɪɨɰɟɫɫɵ ɢɦɢɬɚɰɢɨɧɧɨɣ ɦɨɞɟɥɢɧɟɡɚɜɢɫɢɦɨ ɨɬ
ɤɨɥɢɱɟɫɬɜɚ ɭɪɨɜɧɟɣ ɫɬɪɭɤɬɭɪɧɨɝɨ ɚɧɚɥɢɡɚ Ɇɨɠɟɬ ɢɦɟɬɶ ɬɪɟɯɦɟɪɧɨɟ ©ɦɧɨɝɨ
ɫɥɨɣɧɨɟªɢɡɨɛɪɚɠɟɧɢɟɉɨɥɭɱɚɟɬɫɹɩɪɢɫɬɪɭɤɬɭɪɧɨɦɚɧɚɥɢɡɟɩɪɨɰɟɫɫɚ
Ⱦɜɨɣɫɬɜɟɧɧɚɹ ɨɰɟɧɤɚ ɨɝɪɚɧɢɱɟɧɢɹ GXDO FRQVWUDLQW DVVHVVPHQW ɚɧɝɥ
'RSSHOWH(LQVFKlW]XQJGHU %HVFKUlQNXQJɧɟɦGRXEOH pYDOXDWLRQGHODOLPLWDWLRQ
ɮɪɚɧɰ±ɜɟɥɢɱɢɧɚɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹɩɪɢɪɨɫɬɡɧɚɱɟɧɢɹɰɟɥɟɜɨɣɮɭɧɤɰɢɢɡɚ
ɞɚɱɢɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹɩɪɢɦɚɥɨɦɢɡɦɟɧɟɧɢɢɜɟɥɢɱɢɧɵɫɜɨ
ɛɨɞɧɨɝɨɱɥɟɧɚɞɚɧɧɨɝɨɨɝɪɚɧɢɱɟɧɢɹɱɚɫɬɧɚɹɩɪɨɢɡɜɨɞɧɚɹɨɩɬɢɦɚɥɶɧɨɝɨɡɧɚɱɟ
ɧɢɹɰɟɥɟɜɨɣɮɭɧɤɰɢɢɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨɜɤɚɱɟɫɬɜɟɮɭɧɤɰɢɢɫɜɨɛɨɞɧɵɯɱɥɟɧɨɜ
ɨɝɪɚɧɢɱɟɧɢɣɡɚɞɚɱɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɩɨɜɟɥɢɱɢɧɟɫɜɨɛɨɞ
ɧɨɝɨ ɱɥɟɧɚ ɞɚɧɧɨɝɨ ɨɝɪɚɧɢɱɟɧɢɹ ɂɡɦɟɪɹɟɬɫɹ ɜ ɟɞɢɧɢɰɚɯ ɢɡɦɟɪɟɧɢɹɰɟɥɟɜɨɣ
ɮɭɧɤɰɢɢɜɪɚɫɱɟɬɟɧɚɟɞɢɧɢɰɭɢɡɦɟɪɟɧɢɹɨɝɪɚɧɢɱɟɧɢɹ
Ⱦɟɫɤɪɢɩɬɢɜɧɵɟ ɦɨɞɟɥɢ GHVFULSWLYH PRGHOV ɚɧɝɥ 'HVNULSWLHUWH 0RGHOOH
ɧɟɦɶRGqOHVGHVFULSWLIVɮɪɚɧɰ±ɦɨɞɟɥɢɰɟɥɶɸɤɨɬɨɪɵɯɹɜɥɹɟɬɫɹɮɨɪɦɚɥɢ
ɡɨɜɚɧɧɨɟɩɪɟɞɫɬɚɜɥɟɧɢɟɡɧɚɧɢɹɨɫɬɪɭɤɬɭɪɟɦɨɞɟɥɢɪɭɟɦɨɝɨɨɛɴɟɤɬɚ
ȾɢɧɚɦɢɱɟɫɤɚɹɦɨɞɟɥɶG\QDPLFPRGHOɚɧɝɥ'\QDPLVFKHV0RGHOOɧɟɦ
PRGqOHG\QDPLTXHɮɪɚɧɰ±ɦɨɞɟɥɶɜɤɨɬɨɪɨɣɫɨɫɬɨɹɧɢɟɨɛɴɟɤɬɚɹɜɧɨɢɥɢɧɟ
ɹɜɧɨɡɚɜɢɫɢɬɨɬɜɪɟɦɟɧɢȾɚɠɟɟɫɥɢɧɚɷɬɭɦɨɞɟɥɶɧɟɜɨɡɞɟɣɫɬɜɨɜɚɬɶɢɡɜɧɟɬɨ
ɩɪɢɞɜɢɠɟɧɢɢɜɪɟɦɟɧɢɜɧɟɣɜɫɟɪɚɜɧɨɛɭɞɭɬɢɡɦɟɧɹɬɶɫɹɜɵɯɨɞɧɵɟɯɚɪɚɤɬɟɪɢ
ɫɬɢɤɢɉɪɢɦɟɪɨɦ ɞɢɧɚɦɢɱɟɫɤɨɣɫɢɫɬɟɦɵ ɦɨɠɟɬɫɥɭɠɢɬɶ ɬɟɥɨɛɪɨɲɟɧɧɨɟ ɩɨɞ
ɭɝɥɨɦɤɝɨɪɢɡɨɧɬɭ
Ɂɚɞɚɱɚ ɜɟɤɬɨɪɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ YHFWRU SURJUDPPLQJ WDVNɚɧɝɥ
YHNWRUSURJUDPPLHUDXIJDEH ɧɟɦ WkFKH GH SURJUDPPDWLRQ YHFWRULHOOH ɮɪɚɧɰ ±
ɡɚɞɚɱɚɨɬɵɫɤɚɧɢɹ ɨɩɬɢɦɭɦɚ ɩɨ ɉɚɪɟɬɨɡɚɞɚɧɧɨɣ ɜɟɤɬɨɪɮɭɧɤɰɢɢ ɧɚɡɚɞɚɧɧɨɦ
ɦɧɨɠɟɫɬɜɟɞɨɩɭɫɬɢɦɵɯɡɧɚɱɟɧɢɣɩɟɪɟɦɟɧɧɵɯ
Ɂɧɚɤɨɜɨɟɦɨɞɟɥɢɪɨɜɚɧɢɟ6LJQPRGHOLQJɚɧɝɥ6LJQDOPRGHOOLHUXQJɧɟɦ
PRGpOLVDWLRQHPEOpPDWLTXHɮɪɚɧɰ±ɩɪɨɰɟɫɫɩɨɫɬɪɨɟɧɢɹɦɨɞɟɥɢɫɢɫɩɨɥɶɡɨɜɚ
ɧɢɟɦɫɩɟɰɢɚɥɶɧɵɯ ɡɧɚɤɨɜ ɫɢɦɜɨɥɨɜ ɧɚɨɫɧɨɜɟ ɨɛɳɢɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɨɦɟɪ
ɧɨɫɬɟɣ
ɂɞɟɚɥɢɡɚɰɢɹLGHDOL]DWLRQ ɚɧɝɥ LGHDOLVLHUXQJ ɧɟɦ LGpDOLVDWLRQ
ɮɪɚɧɰ± ɦɵɫɥɟɧɧɨɟ ɤɨɧɫɬɪɭɢɪɨɜɚɧɢɟɩɪɟɞɫɬɚɜɥɟɧɢɣ ɨɛ ɨɛɴɟɤɬɚɯ ɧɟ ɫɭɳɟ
ɫɬɜɭɸɳɢɯɢɥɢɧɟɨɫɭɳɟɫɬɜɢɦɵɯɜɞɟɣɫɬɜɢɬɟɥɶɧɨɫɬɢɧɨɬɚɤɢɯɞɥɹɤɨɬɨɪɵɯɫɭ
ɳɟɫɬɜɭɸɬɩɪɨɨɛɪɚɡɵɜɪɟɚɥɶɧɨɦɦɢɪɟ
ɂɦɢɬɚɰɢɨɧɧɚɹɦɨɞɟɥɶVLPXODWLRQPRGHOɚɧɝɥVLPXODWLRQVPRGHOOɧɟɦ
PRGqOH GH VLPXODWLRQ ɮɪɚɧɰ ± ɫɩɟɰɢɚɥɶɧɵɣ ɩɪɨɝɪɚɦɦɧɵɣ ɤɨɦɩɥɟɤɫ ɩɨɡɜɨ
ɥɹɸɳɢɣɢɦɢɬɢɪɨɜɚɬɶɞɟɹɬɟɥɶɧɨɫɬɶɤɚɤɨɝɨɥɢɛɨɫɥɨɠɧɨɝɨɨɛɴɟɤɬɚɈɧɡɚɩɭɫɤɚ
ɟɬɜɤɨɦɩɶɸɬɟɪɟɩɚɪɚɥɥɟɥɶɧɵɟɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɟɜɵɱɢɫɥɢɬɟɥɶɧɵɟɩɪɨɰɟɫɫɵ
ɤɨɬɨɪɵɟɹɜɥɹɸɬɫɹɩɨɫɜɨɢɦɜɪɟɦɟɧɧɵɦɩɚɪɚɦɟɬɪɚɦɫɬɨɱɧɨɫɬɶɸɞɨɦɚɫɲɬɚɛɨɜ
ɜɪɟɦɟɧɢɢɩɪɨɫɬɪɚɧɫɬɜɚɚɧɚɥɨɝɚɦɢɢɫɫɥɟɞɭɟɦɵɯɩɪɨɰɟɫɫɨɜ
ɂɦɢɬɚɰɢɨɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟVLPXODWLRQ PRGHOLQJɚɧɝɥVLPXODWLRQV
PRGHOOLHUXQJ ɧɟɦ PRGpOLVDWLRQ SDU VLPXODWLRQ ɮɪɚɧɰ ± ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɚɹ
ɪɚɡɧɨɜɢɞɧɨɫɬɶ ɚɧɚɥɨɝɨɜɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɟɚɥɢɡɭɟɦɨɝɨ ɫ ɩɨɦɨɳɶɸ ɧɚɛɨɪɚ
ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɵɯ ɫɪɟɞɫɬɜ ɫɩɟɰɢɚɥɶɧɵɯ ɢɦɢɬɢɪɭɸɳɢɯ ɤɨɦ
ɩɶɸɬɟɪɧɵɯ ɩɪɨɝɪɚɦɦ ɢ ɬɟɯɧɨɥɨɝɢɣ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɩɨɡɜɨɥɹɸɳɢɯ ɩɨɫɪɟɞ
ɫɬɜɨɦɩɪɨɰɟɫɫɨɜɚɧɚɥɨɝɨɜɩɪɨɜɟɫɬɢɰɟɥɟɧɚɩɪɚɜɥɟɧɧɨɟɢɫɫɥɟɞɨɜɚɧɢɟɫɬɪɭɤɬɭɪɵ
ɢɮɭɧɤɰɢɣɪɟɚɥɶɧɨɝɨɫɥɨɠɧɨɝɨɩɪɨɰɟɫɫɚɜɩɚɦɹɬɢɤɨɦɩɶɸɬɟɪɚɜɪɟɠɢɦɟ©ɢɦɢ
ɬɚɰɢɢªɜɵɩɨɥɧɢɬɶɨɩɬɢɦɢɡɚɰɢɸɧɟɤɨɬɨɪɵɯɟɝɨɩɚɪɚɦɟɬɪɨɜ
ɂɧɬɟɪɚɤɬɢɜɧɨɟ ɨɛɭɱɟɧɢɟLQWHUDFWLYH OHDUQLQJɚɧɝɥLQWHUDNWLYHV /HUQHQ
ɧɟɦ DSSUHQWLVVDJH LQWHUDFWLI ɮɪɚɧɰ ± ɷɬɨ ɫɩɟɰɢɚɥɶɧɚɹ ɮɨɪɦɚ ɨɪɝɚɧɢɡɚɰɢɢ
ɩɨɡɧɚɜɚɬɟɥɶɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɋɭɬɶ ɢɧɬɟɪɚɤɬɢɜɧɨɝɨ ɨɛɭɱɟɧɢɹ ɫɨɫɬɨɢɬ ɜ ɬɨɦ
ɱɬɨɭɱɟɛɧɵɣɩɪɨɰɟɫɫɨɪɝɚɧɢɡɨɜɚɧɬɚɤɢɦɨɛɪɚɡɨɦɱɬɨɩɪɚɤɬɢɱɟɫɤɢɜɫɟɭɱɚɳɢɟ
ɫɹ ɨɤɚɡɵɜɚɸɬɫɹ ɜɨɜɥɟɱɟɧɧɵɦɢ ɜ ɩɪɨɰɟɫɫ ɩɨɡɧɚɧɢɹ ɨɧɢ ɢɦɟɸɬ ɜɨɡɦɨɠɧɨɫɬɶ
ɩɨɧɢɦɚɬɶɢɪɟɮɥɟɤɬɢɪɨɜɚɬɶɩɨɩɨɜɨɞɭɬɨɝɨɱɬɨɨɧɢɡɧɚɸɬɢɞɭɦɚɸɬ
ɂɧɬɭɢɬɢɜɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟLQWXLWLYH OHDUQLQJɚɧɝɥLQWXLWLYHV /HUQHQ
ɧɟɦDSSUHQWLVVDJHLQWXLWLIɮɪɚɧɰ ±ɩɪɨɰɟɫɫɫɨɡɞɚɧɢɹɦɨɞɟɥɢɧɚ ɨɫɧɨɜɟɢɧ
ɬɭɢɰɢɢɩɪɟɞɫɬɚɜɥɟɧɢɣɢɠɢɡɧɟɧɧɨɝɨɨɩɵɬɚ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹɤɨɦɩɟɬɟɧɬɧɨɫɬɶLQIRUPDWLRQFRPSHWHQFHɚɧɝɥ,QIRU
PDWLRQVNRPSHWHQ] ɧɟɦ FRPSpWHQFH LQIRUPDWLRQQHOOH ɮɪɚɧɰ ± ɷɬɨ ɢɧɬɟɝɪɚ
ɬɢɜɧɨɟ ɤɚɱɟɫɬɜɨ ɥɢɱɧɨɫɬɢ ɩɪɟɞɫɬɚɜɥɹɸɳɟɟ ɫɨɛɨɣ ɟɞɢɧɫɬɜɨ ɦɨɬɢɜɚɰɢɨɧɧɨɣ
ɬɟɨɪɟɬɢɱɟɫɤɨɣɢɩɪɚɤɬɢɱɟɫɤɨɣɝɨɬɨɜɧɨɫɬɢɢɫɩɨɫɨɛɧɨɫɬɢɫɬɭɞɟɧɬɚɤɨɫɭɳɟɫɬɜ
ɥɟɧɢɸɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢɨɫɧɨɜɚɧɧɨɣɧɚ ɭɫɜɨɟɧɢɢɫɩɨɫɨɛɨɜ ɩɪɢ
ɨɛɪɟɬɟɧɢɹɡɧɚɧɢɣɢɡɪɚɡɥɢɱɧɵɯɢɫɬɨɱɧɢɤɨɜɢɧɮɨɪɦɚɰɢɢ
Ʉɨɦɩɟɬɟɧɬɧɨɫɬɶ FRPSHWHQFH ɚɧɝɥ .RPSHWHQ] ɧɟɦ FRPSpWHQFH
ɮɪɚɧɰ±ɫɨɜɨɤɭɩɧɨɫɬɶɤɨɦɩɟɬɟɧɰɢɣɧɚɥɢɱɢɟɡɧɚɧɢɣɢɨɩɵɬɚɧɟɨɛɯɨɞɢɦɵɯ
ɞɥɹɷɮɮɟɤɬɢɜɧɨɣɞɟɹɬɟɥɶɧɨɫɬɢɜɡɚɞɚɧɧɨɣɩɪɟɞɦɟɬɧɨɣɨɛɥɚɫɬɢ
ɄɨɦɩɟɬɟɧɬɧɨɫɬɧɵɣɩɨɞɯɨɞFRPSHWHQFHDSSURDFKɚɧɝɥ.RPSHWHQ]DQVDW]
ɧɟɦDSSURFKHSDUFRPSpWHQFHɮɪɚɧɰ± ɷɬɨɦɟɬɨɞɦɨɞɟɥɢɪɨɜɚɧɢɹɪɟɡɭɥɶɬɚ
ɬɨɜɨɛɭɱɟɧɢɹɢɢɯɩɪɟɞɫɬɚɜɥɟɧɢɹɤɚɤɧɨɪɦɤɚɱɟɫɬɜɚɜɵɫɲɟɝɨɨɛɪɚɡɨɜɚɧɢɹɉɨɞ
ɪɟɡɭɥɶɬɚɬɚɦɢɩɨɧɢɦɚɸɬɫɹɧɚɛɨɪɵ ɤɨɦɩɟɬɟɧɰɢɣɜɤɥɸɱɚɸɳɢɟɡɧɚɧɢɹ ɩɨɧɢɦɚ
ɧɢɟɢɧɚɜɵɤɢɨɛɭɱɚɟɦɨɝɨɤɨɬɨɪɵɟɨɩɪɟɞɟɥɹɸɬɫɹɤɚɤɞɥɹɤɚɠɞɨɝɨɦɨɞɭɥɹɩɪɨ
ɝɪɚɦɦɵɬɚɤɢɞɥɹɩɪɨɝɪɚɦɦɵɜɰɟɥɨɦ
Ʌɢɧɟɣɧɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ OLQHDU SURJUDPPLQJ ɚɧɝɥ /LQHDUH
3URJUDPPLHUXQJɧɟɦSURJUDPPDWLRQOLQpDLUHɮɪɚɧɰ±ɪɚɡɞɟɥɦɚɬɟɦɚɬɢɱɟ
ɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢɫɫɥɟɞɭɸɳɢɣ ɡɚɞɚɱɢ ɨɬɵɫɤɚɧɢɹ ɷɤɫɬɪɟɦɭɦɚ ɥɢɧɟɣ
ɧɨɣ ɮɭɧɤɰɢɢ ɧɚ ɦɧɨɠɟɫɬɜɟ ɞɨɩɭɫɬɢɦɵɯ ɡɧɚɱɟɧɢɣ ɩɟɪɟɦɟɧɧɵɯ ɡɚɞɚɧɧɨɦ ɫɢ
ɫɬɟɦɨɣɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣɢɢɥɢ ɧɟɪɚɜɟɧɫɬɜ ɮɨɪɦɚɥɢɡɦɢɫɩɨɥɶɡɭɟɦɵɣ
ɞɥɹɩɪɟɞɫɬɚɜɥɟɧɢɹɡɧɚɧɢɣɨɫɬɪɭɤɬɭɪɟɦɨɞɟɥɢɪɭɟɦɵɯɨɛɴɟɤɬɨɜɜɮɨɪɦɟɡɚɞɚɱɢ
ɨɬɵɫɤɚɧɢɹɷɤɫɬɪɟɦɭɦɚɥɢɧɟɣɧɨɣɮɭɧɤɰɢɢɧɚɦɧɨɠɟɫɬɜɟɞɨɩɭɫɬɢɦɵɯɡɧɚɱɟɧɢɣ
ɩɟɪɟɦɟɧɧɵɯɡɚɞɚɧɧɨɦɫɢɫɬɟɦɨɣɥɢɧɟɣɧɵɯɭɪɚɜɧɟɧɢɣɢɢɥɢɧɟɪɚɜɟɧɫɬɜ
Ɇɚɤɪɨɷɤɨɧɨɦɢɱɟɫɤɚɹ ɦɨɞɟɥɶ PDFURHFRQRPLF PRGHO ɚɧɝɥ
0DNUR|NRQRPLVFKHV 0RGHOO ɧɟɦ PRGqOH PDFURpFRQRPLTXHɮɪɚɧɰ ± ɷɤɨɧɨ
ɦɢɤɨɦɚɬɟɦɚɬɢɱɟɫɤɚɹɦɨɞɟɥɶɜ ɤɨɬɨɪɨɣɧɟɜɵɞɟɥɹɸɬɫɹ ɩɟɪɟɦɟɧɧɵɟɨɩɢɫɵɜɚ
ɸɳɢɟɨɬɞɟɥɶɧɵɯ ɯɨɡɹɣɫɬɜɭɸɳɢɯ ɫɭɛɴɟɤɬɨɜɩɪɟɞɩɪɢɹɬɢɹ ɨɬɪɚɫɥɢ ɫɨɫɬɚɜɥɹ
ɸɳɢɯɦɨɞɟɥɢɪɭɟɦɭɸɯɨɡɹɣɫɬɜɟɧɧɭɸɫɢɫɬɟɦɭɢɤɨɬɨɪɚɹɨɬɪɚɠɚɟɬɬɨɥɶɤɨɫɜɹɡɢ
ɩɪɢɫɭɳɢɟɷɬɨɣɫɢɫɬɟɦɟɤɚɤɰɟɥɨɦɭ
Ɇɚɫɲɬɚɛ ɜɪɟɦɟɧɢ WLPH VFDOH ɚɧɝɥ =HLWVWUDKO ɧɟɦ pFKHOOH GH WHPSV
ɮɪɚɧɰ±ɱɢɫɥɨɤɨɬɨɪɨɟɡɚɞɚɟɬɞɥɢɬɟɥɶɧɨɫɬɶɦɨɞɟɥɢɪɨɜɚɧɢɹɨɞɧɨɣɟɞɢɧɢɰɵ
ɦɨɞɟɥɶɧɨɝɨ ɜɪɟɦɟɧɢɩɟɪɟɫɱɢɬɚɧɧɨɣ ɜ ɫɟɤɭɧɞɵ ɜ ɫɟɤɭɧɞɚɯ ɚɫɬɪɨɧɨɦɢɱɟɫɤɨɝɨ
ɪɟɚɥɶɧɨɝɨɜɪɟɦɟɧɢɩɪɢɜɵɩɨɥɧɟɧɢɢɦɨɞɟɥɢ
Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ PDWKHPDWLFDO PRGHO ɚɧɝɥ PDWKHPDWLVFKHV
0RGHOO ɧɟɦ PRGqOH PDWKpPDWLTXH ɮɪɚɧɰ ± ɫɨɜɨɤɭɩɧɨɫɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ
ɡɚɜɢɫɢɦɨɫɬɟɣɝɨɦɨɦɨɪɮɧɚɹɢɫɫɥɟɞɭɟɦɨɣɫɢɫɬɟɦɟɢɢɫɩɨɥɶɡɭɟɦɚɹɞɥɹɫɭɠɞɟɧɢɹ
ɨɛɟɟɫɜɨɣɫɬɜɚɯɢɩɨɜɟɞɟɧɢɢ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ PDWK PRGHOLQJ ɚɧɝɥ PDWKHPDWLVFKH
0RGHOOLHUXQJɧɟɦ PRGpOLVDWLRQPDWKpPDWLTXH ɮɪɚɧɰ ±ɦɟɬɨɞɢɫɫɥɟɞɨɜɚɧɢɹ
ɪɟɚɥɶɧɵɯɨɛɴɟɤɬɨɜ ɩɪɢɩɨɦɨɳɢ ɩɨɫɬɚɧɨɜɤɢɷɤɫɩɟɪɢɦɟɧɬɨɜɧɚ ɢɯɦɚɬɟɦɚɬɢɱɟ
ɫɤɢɯɦɨɞɟɥɹɯ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ PDWKHPDWLFDO SURJUDPPLQJ ɚɧɝɥ
0DWKHPDWLVFKH 3URJUDPPLHUXQJ ɧɟɦ SURJUDPPDWLRQ PDWKpPDWLTXH ɮɪɚɧɰ ±
ɪɚɡɞɟɥɦɚɬɟɦɚɬɢɤɢ ɢɫɫɥɟɞɭɸɳɢɣɦɟɬɨɞɵɪɟɲɟɧɢɹ ɡɚɞɚɱɨɬɵɫɤɚɧɢɹɷɤɫɬɪɟ
ɦɭɦɚɧɚɡɚɞɚɧɧɨɦɦɧɨɠɟɫɬɜɟɞɨɩɭɫɬɢɦɵɯɡɧɚɱɟɧɢɣɩɟɪɟɦɟɧɧɵɯɮɨɪɦɚɥɢɡɦ
ɢɫɩɨɥɶɡɭɟɦɵɣɞɥɹɩɪɟɞɫɬɚɜɥɟɧɢɹɡɧɚɧɢɣɨɫɬɪɭɤɬɭɪɟɦɨɞɟɥɢɪɭɟɦɵɯɨɛɴɟɤɬɨɜɜ
ɮɨɪɦɟɡɚɞɚɱɢ ɨɬɵɫɤɚɧɢɹɷɤɫɬɪɟɦɭɦɚɧɚ ɡɚɞɚɧɧɨɦɦɧɨɠɟɫɬɜɟ ɞɨɩɭɫɬɢɦɵɯɡɧɚ
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