Urgent!! Mathematical modeling of the production line

1. I saw the title, this mainly uses the optimization method, and it is necessary to use multi-objective optimization, of course, you can also use single-objective optimization, and take one of the "both profit and energy saving" as the goal, and the other as a hard constraint, which is okay.

2. In the last question, it is necessary to formulate a "" importance index, I think this is not an index, but an indicator set, this indicator set has several indicators, including the efficiency of each machine, consumption and so on. These metrics are combined to produce a final score that is used to determine the importance of the machine. Of course, this is a comprehensive indicator system, and its formulation should be based on some readily available information, rather than arbitrarily decided.

In addition, the production speed of the production line depends on the speed of the slowest process, not the sum of the working hours of each process, and not the speed of the last process. I hope to give you a solution, you can also buy a book on mathematical modeling, which is very useful, I had a very useful one when I was in college, and it is not expensive about 10 yuan, which is generally available in the school library.

The optimization of the production line is one of the key points of our industrial engineering, you may wish to take a look at the book of method standards and operation design, which has a detailed introduction; There is also the production speed of the production line depends on the slowest process on the production line, the bottleneck process.

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The formula for the area of the cone side is pi r*l

r = under the root number (h(t) 2 2).

v＝1／3*pi*r*r*h

Volume vpi h(t) 3 6

dv dt=k*pi root number (h(t) 2 2) l=k*pi root number (h(t) 2 2) root number (r 2+h 2) = (root number 6) h(t) 2*k 2

dv dt=pi*h(t) 2*(dh(t) dt) 2= (6) h(t) 2*k 2

Simplified (3 under the root number) k=dh dt

At the same time, the two sides are integrated with t to obtain c-(root number 3) k*t=h(t) so that t=0, h(t)=10 (2) k under the root number

We get c = 10 (2 under the root number) k

Let h(t) 0, i.e. melt.

10 (2 under the root number) k (3 under the root number) k*tt=10 3 * (6 under the root number).

You are asking about Chen Wendeng's original question (Science and Engineering Mathematics I), which is an example question. (2005, 2006 editions). Go check it out. It's the section on the application of calculus!

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Zhou Cangyi et al., Mathematical Modeling Experiments are introduced.

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