Practical production scheduling at big factory

Question

At this big factory:

$3$ production lines:Line$_1$,Line$_2$,Line$_3$;

$10$ products: $p_1,p_2,p_3,p_4,p_5,p_6,p_7,p_8,p_9,p_{10}$;

Each production line can produce each of the products, but each product still is recommended to should be produced on certain special line; the time of producing one of some product is invariable; each product line runs all the time; switch from producing one product to another on production line would waste extra time;

Now I receive many orders which record information as below: enter image description here

Now I treat them as below:

1. merge the orders which have the same product name and deadline;
2. for deadline day, I range all the orders on the recommended lines;
3. if the recommended lines are not enough then switch to other free lines;
4. if all the lines on the current day are not enough, then switch to lines of the next day;
5. if all the products were arranged on the current day and still some of lines are a little free, then these free lines would be arranged to produce products of next day(then next next day);

I have coded according to above steps but I still think maybe there is some system method for this problem; I guess maybe I should use linear programming, but I don't know how since lack of these experience;

so shall I get some advice for resolving this problem or some demo/examples materials for similar problems?

thanks a lot!