Grouping means proportion of main group, normal group and production group and scale means its absolute quantitative size.
To define group and scale of highbred pigs is of significance not only in completing production plan but in reducing unnecessary cost to the minimum.
To produce F1 pigs pig farms have to divide pigs into main group, normal group and production group, and in case of renewing groups they have to divide pigs according to the age.
If you take the large scale of highbred pigs, you can be in favour of getting piglets for pork production, but you can increase production expenses such as feed cost. On the contrary if you take too small scale of highbred pigs, you can't manage to complete the production plan owing to production decrease of piglets.
Rational grouping of highbred pigs also has great effects on high productivity with less cost.
If you increase the rates of main group and highbred boars, you can get into the trouble with livestock breeding and expenses.
If you decrease those, you can't renew the general groups in a planned way.
Increase of mating times makes them impossible and results in malproduction of piglets.
As you can see here, we can solve the grouping with the economic mathematical model as follows.
X1 - Rate of main group
X2 - Rate of normal group
X3 - Rate of production group
K1 - Yearly average productivity of main group
K2 - Yearly average productivity of normal group
R1 - Yearly average renewal rate of main group
R2 - Yearly average renewal rate of normal group
R3 - Yearly average renewal rate of production group
α - Rate of sow which are transferred into normal group
β - Rate of sow which are transferred into normal group
Formula (1) is the limit that the sum of the grouping rates must be 100(or 1).
Formula (2) is the limit that piglets should be bred enough to update the yearly normal group of pigs.
Formula (3) is the limit that piglets should be bred enough to update the yearly production group of pigs.
Formula (4) is the limit every grouping rate must be more than 0.
Formula (5) is that the productivity of every group must be maximum.
Thus economic mathematical model result in linear planning problems which ensure the practical benefits providing the relation between groups.
Thus we discussed some problems for putting management and production on a scientific and modern basis in pig farms.
Based on such a method, pig farms can assess the overall composition rates of highbred pigs and take measures for their grouping.
