I would like to know about the travel backpack problem in operations research. Thank you! 50

The backpack problem is a very well-known problem. It can be described as follows. Let's say there are n items, denoted as d1, d2, d3, ,......dn。For each item di (1==0, and is an integer, i=1,2,..n

where: ck is the unit value of the kth item, wk is the unit weight or volume of the kth item, and w is the weight or volume limit of the backpack.

The relevant elements of dynamic programming are as follows:

Stage K: The kth loading of the kth item (k=1,2,...,n）

State variable SK: The weight (or volume) that the backpack can still be loaded on the kth load

Decision variable xk: the number of items of the kth type loaded for the kth time.

Decision Allowed Collection: dk(sk)=

State transition equation: sk+1=sk wkxk

Stage metric: vk=ckxk

Generally speaking, the methods used to solve the backpack problem include the recursive method and the greedy method, etc., but the two methods used to solve the backpack problem have their inevitable shortcomings, although the recursive method can traverse the search space and find the optimal solution, but because the space of the solution of this problem grows by the n level of 2, it is only suitable for solving the small-scale backpack problem, and the greedy method is difficult to really find the optimal solution, and the optimal solution found by this method is often far from the real optimal solution. As a random optimization and search method, the genetic algorithm has good parallelism, and the genetic algorithm only needs to use the value information of the target, without the value information such as the degree, so it is suitable for any scale. The optimization of highly non-linear discontinuous multimodal functions and the optimization of objective functions without analytic expressions of genetic algorithms have strong generality.

Seek ...... togetherI can also give points to ......

In general, the optimal solution of the transportation scheme has one optimal solution or multiple optimal solutions, and there will be no infinite number of solutions to the real problem, unless it can be decimalized.

Multiple optimal solutions exist when the number of closed loop tests is 0. At this time, the corresponding increase or decrease of the volume of transportation on this closed loop, as long as the amount of transportation and the amount of transportation in each row and column are not the same, it is the optimal solution.

No wealth value is required. Hope it helps.

This is a linear programming problem:

Set up No. 1 cargo hold to load x1 parts 1, load x2 parts 2; Cargo hold No. 2 is loaded with x3 parts 1, and x4 parts are loaded with 2

According to the title, the equipment must be transported in a matching manner, that is, the total number of all parts 1 is equal to the total number of all parts 2, which is also equal to the total number of sets of transportation equipment. Yes.

maxs=40(x1+x3)

250x1+80x2 6600 (because the maximum load is 6000*110%=6600).

70x1+100x2≤2500

250x3+80x4≤4400 (4000*110%=4400)

70x3+100x4≤2500

x1-x2+x3-x4=0 (x1+x3=x2+x4)

The calculation process of the simplex table is omitted. ）

Optimal solution (ignoring integer requirements) x1 = x2 = x3 = maxs = 10,000.

Optimal solution (integer solution) x1=17 x2=13 x3=12 x4=16 maxs=11.6 million.

ps: I have done this question several times, and I have tested it several times, and the final answer is correct, I don't know if you want the rebasing iteration process table of the simplex table, but it is really a bit troublesome to write it here, hehe, operations research is a bit difficult, learn hard! Come on!

These are the course names. The principles of management and the theory of management can be said to be almost identical. But the management zhi

Operations Research and DAO Operations Research are slightly different. For example, there is a method for solving linear programming problems in operations research called the simplex method, if the name of the course you are studying is "Operations Research", then you should master the principles and calculation methods of the simplex method; "Management Operations Research", on the other hand, only requires you to know that this method exists, and the specific solution using the simplex method is done by computer software. In other words, "operations research" is more demanding than "management operations research".

Of course, this difference is not absolute, and the teaching purpose of different schools is different, and it must be analyzed according to the actual situation.

in[1]:= maximize[,

out[1]= }

Such as upstairs **.

The result is the same, maximum.

The specific value is 20

Is there a problem with this question?

Multiply this formula by 2.

The answer is equal to 20.

Students in these grades will be assigned to three other secondary schools the following year. The school provides pick-up and drop-off for all students who are more than 1 mile from the school, so in order to save on bus fares, the school will allocate students to the school. From the city's six residential areas to the schools, the annual bus fare for each student is shown in the table below (some other basic figures for the following year are also given).

Where 0 indicates that the year slip does not require bus service, and ** indicates that this allocation is not possible.

Set up one by one, with the problem of transportation.

1.Operational research.

This discipline has been widely used in the overall planning and coordination of research organizations such as industrial and commercial enterprises, military departments, and civil affairs, so its application is not limited by industries and departments. Operations research not only conducts creative scientific research on various operations, but also involves the actual management of organizations, which has a strong practicality, and should ultimately be able to provide constructive suggestions to decision-makers and receive practical results; It aims at the overall optimality, and from the perspective of the system, it tries to solve the conflict of interests between the various departments of the system in the best way for the whole system. It can also be regarded as an optimization technique that provides optimization methods to solve various problems. Operations research has been applied to various management projects and plays an important role in modernization.

Therefore, operations research is very promising, and it can also be changed to management in the future.

2.Cybernetics.

With the continuous improvement of the level of automation, the control system itself is becoming more and more complex, the number of control variables in the system also increases, the requirements for control performance are also gradually improved, many situations require the performance of the system to be optimal, such as the shortest time, the smallest error, the most economical fuel, the highest output, the lowest cost, the greatest benefit, etc., and requires a strong ability to adapt to the change of the environment, but the design indicators such as stability, rapidity and accuracy based on now are difficult to meet the new control requirements. Therefore, the requirements of the society for the control of talents are getting higher and higher, and the employment prospects of graduates of this major are also very good.

3.Direction of employment.

After graduation, students can be engaged in academic research, technology management, teaching in scientific research, education and other departments, as well as in production, design, development and other enterprises and institutions engaged in applied technology research and management decision-making.

I am a graduate student in Mathematics and Applied Mathematics (non-teacher) and want to take the Operational Research and Cybernetics Examination. Therefore, the requirements of the society for the control of talents are getting higher and higher, and the employment prospects of graduates of this major are also very good.

Go back to the college entrance examination to fill in the career planning master.

Copy page 1It has a wide range of commercial applications.

2.There are many companies in the company, and there are also in the bank, teachers and other industries, in general, this is a relatively good major in mathematics.

3.Bank ** R&D department, logistics management, software development are all fine, depending on what kind of project you did with your mentor during your master's and doctoral studies.

4.Like logistics, it is a system engineering, involving all aspects, and it must be used.