Моделирование и оптимизация технологических процессов. Учебное пособие

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ȺȼɊɹɛɨɜɂȼɑɭɦɚɧɨɜɈɘɌɚɪɚɫɨɜɚ

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ɍɱɟɛɧɨɟɩɨɫɨɛɢɟ

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ɋɚɦȽɌɍɡɚɜɟɞɭɸɳɢɣɤɚɮɟɞɪɨɣɥɢɬɟɣɧɵɯɢɜɵɫɨɤɨɷɮɮɟɤɬɢɜɧɵɯɬɟɯɧɨɥɨɝɢɣ

ɞɢɪɟɤɬɨɪɐɟɧɬɪɚɥɢɬɟɣɧɵɯɬɟɯɧɨɥɨɝɢɣɩɪɟɞɫɟɞɚɬɟɥɶɩɪɚɜɥɟɧɢɹɋɚɦɚɪɫɤɨɝɨ

ɨɬɞɟɥɟɧɢɹɊɨɫɫɢɣɫɤɨɣɚɫɫɨɰɢɚɰɢɢɥɢɬɟɣɳɢɤɨɜɊȺɅɢɤɨɦɢɬɟɬɚɰɜɟɬɧɨɝɨ

ɥɢɬɶɹɊȺɅɞɬɧȼɥɚɞɢɦɢɪ ɂɜɚɧɨɜɢɱ ɇɢɤɢɬɢɧ

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 ȼȼȿȾȿɇɂȿ ɈɋɇɈȼɇɕȿɉɈɇəɌɂəɌȿɈɊɂɂɆɈȾȿɅɂɊɈȼȺɇɂə ɌȿɏɇɈɅɈȽɂɑȿɋɄɂɏɉɊɈɐȿɋɋɈȼɂɈȻɔȿɄɌɈȼ Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟɦɟɬɨɞɵ Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹɦɨɞɟɥɶ Ⱥɥɝɨɪɢɬɦ ɆȿɌɈȾɈɅɈȽɂəɉɈɋɌɊɈȿɇɂəɆȺɌȿɆȺɌɂɑȿɋɄɂɏɆɈȾȿɅȿɃ ɇȿɈȻɏɈȾɂɆɈɋɌɖɋɂɋɌȿɆɇɈȽɈɂɋɋɅȿȾɈȼȺɇɂə ɂɋɈȼȿɊɒȿɇɋɌȼɈȼȺɇɂəɋɉɈɋɈȻɈȼɆɈȾȿɅɂɊɈȼȺɇɂə Ʉɥɚɫɫɢɮɢɤɚɰɢɹɦɟɬɨɞɨɜɦɨɞɟɥɢɪɨɜɚɧɢɹ ȼɢɞɵɩɟɪɟɦɟɧɧɵɯɢɫɩɨɥɶɡɭɟɦɵɯɜɦɨɞɟɥɢ Ʉɥɚɫɫɢɮɢɤɚɰɢɹɢɫɨɞɟɪɠɚɧɢɟɡɚɞɚɱɨɩɬɢɦɢɡɚɰɢɢɢɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯɩɪɨɰɟɫɫɨɜ ɈɉɌɂɆɂɁȺɐɂəɊȿɒȿɇɂɃɉɈɈȻȿɋɉȿɑȿɇɂɘɉɊȿȾɉɊɂəɌɂɃ ɂɈɊȽȺɇɂɁȺɐɂɂɂɏɊȺȻɈɌɕɆȿɌɈȾȺɆɂɅɈȽɂɋɌɂɄɂ Ɉɫɧɨɜɧɚɹɡɚɞɚɱɚɢɨɫɧɨɜɧɵɟɩɨɧɹɬɢɹɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ Ʉɥɚɫɫɢɮɢɤɚɰɢɹɡɚɞɚɱɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ Ɇɟɬɨɞɵɨɞɧɨɦɟɪɧɨɣɨɩɬɢɦɢɡɚɰɢɢ Ɉɩɬɢɦɢɡɚɰɢɹɪɟɲɟɧɢɣɩɨɨɛɟɫɩɟɱɟɧɢɸɩɪɟɞɩɪɢɹɬɢɣɢɨɪɝɚɧɢɡɚɰɢɢ ɢɯɪɚɛɨɬɵɦɟɬɨɞɚɦɢɥɨɝɢɫɬɢɤɢɧɚɨɫɧɨɜɟɥɢɧɟɣɧɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɊȺɋɑȿɌɒɂɏɌɕɈɉɌɂɆȺɅɖɇɈȽɈɋɈɋɌȺȼȺɇȺɗȼɆ ɈɉɌɂɆɂɁȺɐɂəɋɈɋɌȺȼȺɄɈɊɊȿɄɌɂɊɍɘɓɂɏȾɈȻȺȼɈɄ ɋɈȼȿɊɒȿɇɋɌȼɈȼȺɇɂȿɌȿɏɇɈɅɈȽɂɂȼɕɉɅȺȼɄɂ ɄɈɊɊɈɁɂɈɇɇɈɋɌɈɃɄɂɏɋɌȺɅȿɃɁȺɋɑȿɌɋɌȺȻɂɅɂɁȺɐɂɂ ɌȿɏɇɈɅɈȽɂɑȿɋɄɂɏɉȺɊȺɆȿɌɊɈȼ Ⱥɧɚɥɢɡɢɡɦɟɧɟɧɢɹɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯɩɚɪɚɦɟɬɪɨɜɩɪɢɜɵɩɥɚɜɤɟɫɬɚɥɢ ɏɇɌɜɨɬɤɪɵɬɵɯɞɭɝɨɜɵɯɩɟɱɚɯ Ɋɚɡɪɚɛɨɬɤɚɫɬɚɛɢɥɶɧɨɣɬɟɯɧɨɥɨɝɢɢɜɵɩɥɚɜɤɢɤɨɪɪɨɡɢɨɧɧɨɫɬɨɣɤɨɣ ɫɬɚɥɢɫɤɨɪɪɟɤɬɢɪɭɸɳɢɦɩɟɪɢɨɞɨɦ Ʉɨɦɩɶɸɬɟɪɧɨɟɦɨɞɟɥɢɪɨɜɚɧɢɟɩɪɨɰɟɫɫɚɜɵɩɥɚɜɤɢɫɬɚɥɢ ɋɅɈȼȺɊɖɌȿɊɆɂɇɈȼ ȻɂȻɅɂɈȽɊȺɎɂɑȿɋɄɂɃɋɉɂɋɈɄ ɉɊɂɅɈɀȿɇɂə ɉɪɢɥɨɠɟɧɢɟ ɉɪɢɥɨɠɟɧɢɟ ɉɪɢɥɨɠɟɧɢɟ ɉɪɢɥɨɠɟɧɢɟ 



ɂɡɜɟɫɬɧɨ ɱɬɨ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɯ ɥɢɧɢɣ ɢ ɫɨɨɬɜɟɬ ɫɬɜɟɧɧɨɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯɩɪɨɰɟɫɫɨɜɫɭɳɟɫɬɜɭɟɬɨɝɪɨɦɧɨɟɤɨɥɢɱɟɫɬɜɨɪɚɡɥɢɱ ɧɵɯ ɤɨɦɛɢɧɚɰɢɣ ɮɚɤɬɨɪɨɜ ɩɪɨɢɡɜɨɞɫɬɜɚ ɧɨ ɩɪɢ ɷɬɨɦ ɜɟɫɶɦɚ ɨɝɪɚɧɢɱɟɧɧɨɟ ɱɢɫɥɨɜɚɪɢɚɧɬɨɜɢɯɪɚɰɢɨɧɚɥɶɧɵɯɤɨɦɛɢɧɚɰɢɣɇɚɩɨɢɫɤɢɨɛɨɫɧɨɜɚɧɢɟɬɚɤɢɯ ɜɚɪɢɚɧɬɨɜɨɪɢɟɧɬɢɪɨɜɚɧɤɭɪɫ©Ɇɨɞɟɥɢɪɨɜɚɧɢɟɢɨɩɬɢɦɢɡɚɰɢɹɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜª

Ȼɨɥɶɲɨɟɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɬɚɤɠɟ ɜɵɛɨɪɬɢɩɚ ɦɨɞɟɥɢ Ɇɨɞɟɥɢ ɪɚɡɥɢɱɚɸɬɫɹ ɫɥɨɠɧɨɫɬɶɸ ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɦɟɬɨɞɨɥɨɝɢɱɟɫɤɨɝɨ ɚɩɩɚɪɚɬɚ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ± ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨȾɥɹɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɣɩɪɨɦɵɲɥɟɧɧɨɫɬɢɚɤɬɭɚɥɶɧɵɦɹɜɥɹɟɬ ɫɹɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɟɢɮɢɡɢɱɟɫɤɨɟɦɨɞɟɥɢɪɨɜɚɧɢɟ

Ɉɫɨɛɨɪɚɫɫɦɨɬɪɟɧɵɡɚɞɚɱɢɨɩɬɢɦɢɡɚɰɢɢɫɜɵɛɨɪɨɦɢɧɬɟɧɫɢɜɧɨɫɬɢɢɫɩɨɥɶɡɨ ɜɚɧɢɹɪɚɡɥɢɱɧɵɯɫɩɨɫɨɛɨɜɜɵɩɨɥɧɟɧɢɹɷɬɨɝɨɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɝɨɩɪɨɰɟɫɫɚ



ȼ ɭɫɥɨɜɢɹɯ ɨɝɪɚɧɢɱɟɧɧɨɫɬɢ ɮɢɧɚɧɫɨɜɵɯ ɪɟɫɭɪɫɨɜ ɦɧɨɝɢɟ ɩɪɟɞɩɪɢɹɬɢɹ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɜɚɪɢɚɧɬɵ ɩɪɢɜɥɟɱɟɧɢɹ ɤɪɟɞɢɬɧɵɯ ɫɪɟɞɫɬɜ Ⱦɥɹ ɩɪɚɜɢɥɶɧɨɝɨ ɪɟɲɟɧɢɹɷɬɨɝɨɜɚɠɧɨɝɨ ɜɨɩɪɨɫɚɫɥɟɞɭɟɬɨɛɪɚɬɢɬɶɫɹ ɤɡɚɞɚɱɟɦɢɧɢɦɢɡɚɰɢɢɰɟ ɥɟɜɨɝɨɮɨɧɞɚɉɪɢɥɢɦɢɬɟɬɪɚɧɫɩɨɪɬɧɵɯɡɚɬɪɚɬɢɬɟɪɪɢɬɨɪɢɢɩɪɨɞɚɠɨɫɨɛɟɧɧɨ ɜɩɪɚɤɬɢɤɟɦɚɥɵɯɩɪɟɞɩɪɢɹɬɢɣɚɤɬɭɚɥɶɧɵɬɚɤɧɚɡɵɜɚɟɦɵɟɬɪɚɧɫɩɨɪɬɧɵɟɡɚɞɚ ɱɢɤɨɬɨɪɵɟɪɟɲɚɸɬɫɹɡɞɟɫɶɫɢɦɩɥɟɤɫɦɟɬɨɞɨɦɢɜɟɧɝɟɪɫɤɢɦɦɟɬɨɞɨɦ



Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ – ɪɚɡɥɢɱɧɵɟ ɫɩɨɫɨɛɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɦɚɬɟɦɚ ɬɢɱɟɫɤɨɝɨɚɩɩɚɪɚɬɚɬɟɯɢɥɢɢɧɵɯɦɚɬɟɦɚɬɢɱɟɫɤɢɯɬɟɨɪɢɣ

í Ⱥɥɝɟɛɪɚ

í ȼɵɫɲɚɹɚɥɝɟɛɪɚ

í Ƚɟɨɦɟɬɪɢɹ

í Ɍɪɢɝɨɧɨɦɟɬɪɢɹ

í Ɍɟɨɪɢɹɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯɭɪɚɜɧɟɧɢɣ

í Ɍɟɨɪɢɹɜɟɪɨɹɬɧɨɫɬɟɣ









Ⱥɧɚɥɨɝɨɜɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɢɥɢɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɫɧɨɜɚɧɧɨɟɧɚ ɩɪɨɰɟɫɫɭ ɚɥɶɧɨɦɩɨɞɨɛɢɢɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹɬɟɦɱɬɨɩɪɨɬɨɬɢɩɢɨɛɴɟɤɬɢɦɟɸɬɪɚɡɥɢɱɧɭɸ ɩɪɢɪɨɞɭɧɨ ɩɪɨɰɟɫɫɵ ɜ ɧɢɯɨɩɢɫɵɜɚɸɬɫɹ ɨɞɢɧɚɤɨɜɵɦɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɢɫɨ ɨɬɧɨɲɟɧɢɹɦɢ ɨɛɵɱɧɨ ɨɞɧɢɦɢ ɢ ɬɟɦɢ ɠɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ ɏɚɪɚɤɬɟɪɧɵɦ ɩɪɢɦɟɪɨɦ ɚɧɚɥɨɝɨɜɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɢɫɫɥɟɞɨɜɚɧɢɟ ɪɚɡɥɢɱɧɵɯɦɟɯɚɧɢɱɟɫɤɢɯɫɢɫɬɟɦɧɚɢɯɷɥɟɤɬɪɢɱɟɫɤɢɯɷɥɟɤɬɪɨɧɧɵɯɚɧɚɥɨɝɚɯ

ɉɨɞɤɨɧɰɟɩɬɭɚɥɶɧɨɣɦɨɞɟɥɶɸɨɛɵɱɧɨɩɨɧɢɦɚɟɬɫɹɦɨɞɟɥɶɨɬɪɚɠɚɸɳɚɹɫ ɧɟɨɛɯɨɞɢɦɨɣɩɨɥɧɨɬɨɣɩɪɨɬɨɬɢɩɢɡɚɩɢɫɚɧɧɚɹɧɚɟɫɬɟɫɬɜɟɧɧɨɦɹɡɵɤɟɫɢɫɩɨɥɶ ɡɨɜɚɧɢɟɦɩɨɥɨɠɟɧɢɣɧɚɢɜɧɨɣɥɨɝɢɤɢ

Ɋɚɡɥɢɱɚɸɬɞɟɫɤɪɢɩɬɢɜɧɨɟ ɤɨɧɰɟɩɬɭɚɥɶɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ