2.4 Подготовка исходной информации.
Целевая функция (1) в числовом виде запишется как:
Условие обязательного выполнения перевозок (2.2) примет вид:
Декада I
У1=170*X1+183,6*X2+153*X3+119*X4+221*X5+62,9*X6 = 2700
У2=120*X7+129,6*X8+108*X9+84*X10+156*X11+44,4*X12 = 18300
У3=260*X13+280,8*X14+234*X15+182*X16+338*X17+96,2*X18 = 9200
У4=100*X19+108*X20+90*X21+70*X22+130*X23+37*X24 = 13866
Декада II
У5=170*X25+183,6*X26+153*X27+119*X28+221*X29+62,9*X30 = 2700
У6=110*X31+118,8*X32+99*X33+77*X34+143*X35+40,7*X36 = 8500
У7=130*X37+140,4*X38+117*X39+91*X40+169*X41+48,1*X42 =17100
У8=260*X43+280,8*X44+234*X45+182*X46+338*X47+96,2*X48 =9200
У9=100*X49+108*X50+90*X51+70*X52+130*X53+37*X54 = 13866
Декада III
У10=110*X55+118,8*X56+99*X57+77*X58+143*X59+40,7*X60 = 8500
У11=260*X61+280,8*X62+234*X63+182*X64+338*X65+96,2*X66 = 9200
У12=100*X67+108*X68+90*X69+70*X70+130*X71+37*X72 = 13866
У13=100*X73+108*X74+70*X75+90*X76+130*X77+37*X78 = 8300
Условие не превышения количества транспортных средств в парке (2.3) представится как:
Декада I
У14=X1+X7+X13+X19 = 12
У15=X2+X8+X14+X20 = 3
У16=X3+X9+X15+X21 = 10
У17=X4+X10+X16+X22 = 6
У18=X5+X11+X17+X23 = 3
У19=X6+X12+X18+X24 = 3
Декада II
У20=X25+X31+X37+X43+X49= 12
У21=X26+X32+X38+X44+X50= 3
У22=X27+X33+X39+X45+X51= 10
У23=X28+X34+X40+X46+X52= 6
У24=X29+X35+X41+X47+X53= 3
У25=X30+X36+X42+X48+X54= 3
Декада III
У26=X55+X61+X67+X73 = 12
У27=X56+X62+X68+X74 = 3
У28=X57+X63+X69+X75 = 10
У29=X58+X64+X70+X76 = 6
У30=X59+X65+X71+X77 = 3
У31=X60+X66+X72+X78 = 3
Задачу решили симплекс-методом на компьютере. Оптимальный план использования автомобилей представлен в таблице 2.3
Таблица 2.3 Оптимальный план
|
Марка автомобиля |
Расстояние перевозок, км |
W, т |
QН, л |
Количество ТС по декадам |
Производительность, т |
Расход топлива, л |
||||||||
|
I |
II |
III |
I |
II |
III |
I |
II |
III |
||||||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
||
|
КамАЗ 65111 |
6,7
|
170 |
86,3 |
--- |
0,1 |
--- |
--- |
170 |
--- |
--- |
86,3 |
--- |
||
|
--- |
1 |
--- |
--- |
1700 |
--- |
--- |
863 |
--- |
||||||
|
КрАЗ 6510 |
183,6 |
113,6 |
1,4 |
--- |
--- |
2570,4 |
--- |
--- |
1590,4 |
--- |
--- |
|||
|
1 |
--- |
--- |
1836 |
--- |
--- |
1136 |
--- |
--- |
||||||
|
УРАЛ 5557 |
153 |
74,9 |
--- |
10 |
--- |
--- |
15300 |
--- |
--- |
7490 |
--- |
|||
|
--- |
10 |
--- |
--- |
15300 |
--- |
--- |
7490 |
--- |
||||||
|
УРАЛ 48072 |
119 |
104,5 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КамАЗ 55111 |
221 |
87,4 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
САЗ 3508 |
62,9 |
68 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КамАЗ 65111 |
11,7 |
110 |
95,4 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КрАЗ 6510 |
118,8 |
126,3 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
УРАЛ 5557 |
99 |
82,5 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
УРАЛ 48072 |
77 |
116 |
--- |
6 |
--- |
--- |
4620 |
--- |
--- |
6960 |
--- |
|||
|
--- |
6 |
--- |
--- |
4620 |
--- |
--- |
6960 |
--- |
||||||
|
КамАЗ 55111 |
143 |
96,7 |
--- |
--- |
2,36 |
--- |
--- |
3374,8 |
--- |
--- |
2282,1 |
|||
|
--- |
--- |
2 |
--- |
--- |
2860 |
--- |
--- |
1934 |
||||||
|
САЗ 3508 |
40,7 |
74,8 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КамАЗ 65111 |
10,7 |
120 |
95,4 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КрАЗ 6510 |
129,6 |
126,3 |
1,5 |
--- |
--- |
1944 |
--- |
--- |
1894,5 |
--- |
--- |
|||
|
2 |
--- |
--- |
2592 |
--- |
--- |
2592 |
--- |
--- |
||||||
|
УРАЛ 5557 |
108 |
82,6 |
10 |
--- |
--- |
10800 |
--- |
--- |
8260 |
--- |
--- |
|||
|
10 |
--- |
--- |
10800 |
--- |
--- |
8260 |
--- |
--- |
||||||
|
УРАЛ 48072 |
84 |
116 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КамАЗ 55111 |
156 |
96,7 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
САЗ 3508 |
44,4 |
74,9 |
0,8 |
--- |
--- |
355,2 |
--- |
--- |
599,2 |
--- |
--- |
|||
|
1 |
--- |
--- |
444 |
--- |
--- |
749 |
--- |
--- |
||||||
|
КамАЗ 65111 |
9,5 |
130 |
92,2 |
--- |
8,36 |
--- |
--- |
10868 |
--- |
--- |
7707,9 |
--- |
||
|
--- |
8 |
--- |
--- |
10400 |
--- |
--- |
7376 |
--- |
||||||
|
КрАЗ 6510 |
140,4 |
121,8 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
УРАЛ 5557 |
117 |
79,8 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
УРАЛ 48072 |
91 |
111,9 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
КамАЗ 55111 |
169 |
93,4 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
|
САЗ 3508 |
48,1 |
72,4 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|||
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||||
Продолжение таблицы 2.3
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
|
КамАЗ 65111 |
3,2 |
260 |
66,4 |
3,45 |
--- |
0,08 |
8970 |
--- |
208 |
2290,8 |
--- |
53,12 |
|
4 |
--- |
1 |
10400 |
--- |
2600 |
2656 |
--- |
664 |
||||
|
КрАЗ 6510 |
280,8 |
86,4 |
--- |
--- |
3 |
--- |
--- |
8424 |
--- |
--- |
2592 |
|
|
--- |
--- |
3 |
--- |
--- |
8424 |
--- |
--- |
2592 |
||||
|
УРАЛ 5557 |
234 |
58,1 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
УРАЛ 48072 |
182 |
79,7 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
КамАЗ 55111 |
338 |
67,2 |
--- |
1,73 |
--- |
--- |
5847,4 |
--- |
--- |
1162,5 |
--- |
|
|
--- |
2 |
--- |
--- |
6760 |
--- |
--- |
1344 |
--- |
||||
|
САЗ 3508 |
96,2 |
53,1 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
КамАЗ 65111 |
14 |
100 |
103,3 |
8,54 |
--- |
--- |
8540 |
--- |
--- |
8821,8 |
--- |
--- |
|
9 |
--- |
--- |
9000 |
--- |
--- |
9297 |
--- |
--- |
||||
|
КрАЗ 6510 |
108 |
136,9 |
--- |
2,34 |
--- |
--- |
2527,2 |
--- |
--- |
3203,5 |
--- |
|
|
--- |
2 |
--- |
--- |
2160 |
--- |
--- |
2738 |
--- |
||||
|
УРАЛ 5557 |
90 |
89,3 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
УРАЛ 48072 |
70 |
125,7 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
КамАЗ 55111 |
130 |
104,7 |
--- |
1,26 |
0,02 |
--- |
1638 |
26 |
--- |
1319,2 |
20,94 |
|
|
--- |
1 |
1 |
--- |
1300 |
1300 |
--- |
1047 |
1047 |
||||
|
САЗ 3508 |
37 |
80,9 |
2,16 |
3 |
3 |
799,2 |
1110 |
1110 |
1747,4 |
2427 |
2427 |
|
|
2 |
3 |
3 |
740 |
1110 |
1110 |
1618 |
2427 |
2427 |
||||
|
КамАЗ 65111 |
12,1 |
110 |
98,6 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
КрАЗ 6510 |
118,8 |
130,5 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
УРАЛ 5557 |
99 |
85,3 |
--- |
--- |
10 |
--- |
--- |
9900 |
--- |
8530 |
--- |
|
|
--- |
--- |
10 |
--- |
--- |
9900 |
--- |
8530 |
--- |
||||
|
УРАЛ 48072 |
77 |
119,9 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
КамАЗ 55111 |
143 |
99,9 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
||||
|
САЗ 3508 |
40,7 |
77,3 |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
|
|
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
--- |
ВЫВОДЫ
После решения задачи симплекс-методом у меня вышел оптимальный план использования автомобилей. По первой декаде у меня получилось что работы выполняются только на 97%, по второй декаде на 63%, по третьей декаде на 94%. Чтобы использовать автомобили примерно на 100% нужно либо увеличить план выполнения работ, либо увеличить количество автомобилей. Можно сделать заказ на несколько автомобилей с другими фирмами.