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0 Ideas for the competition
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https://blog.csdn.net/dc_sinor?type=blog
1 description
The human resources arrangement problem of a mathematics department in a university is an optimization problem of integer programming. By analyzing the existing technical strength and constraints of the mathematics department in detail, in the solution of problem 1, the integer with the largest direct income in a day can be listed Planning, the maximum direct benefit obtained is 42,860 yuan; and in the solution of problem 2, since the professor can only work four days a week, and the associate professor can only work five days a week, under such constraints, list a week Integer programming model of the maximum direct income, the maximum direct income is 198720 yuan.
2 Problem summary
The faculty resources of the Department of Mathematics are limited. There are currently four projects from four different clients. The difficulty of the work is different, and the remuneration for the technical personnel involved in each project is different. so:
1. In the case of meeting the job requirements, how to allocate the existing technical force of the Department of Mathematics so as to maximize the direct benefits of the day?
2. Under the condition that the working hours of professors and associate professors are constrained, how to allocate the existing technical force of the Department of Mathematics so as to maximize its direct benefits in a week?
3 Modeling process
3.1 Boundary description
1. People with different technical strengths have the same probability of being assigned to work every day, and where individuals with the same professional title go to work is random;
2. In addition to paying the stipulated wages, the customer must also pay all related expenses (such as meals, bus fares, etc.) during the working period;
3. The work will be completed on the same day.
3.2 Notation Conventions
3.3 Analysis
It can be seen from the meaning of the question that each project has different restrictions and requirements on the number of personnel with different professional titles. For customers, quality assurance is the key, and professors are relatively scarce, so each project has a limit of no less than a certain number of professors. Among them, due to the high technical requirements of the project, teaching assistants cannot participate. The main work of the two projects is completed in the office, so there is a management fee of 50 yuan per person per day.
From the above analysis, it can be obtained: the maximum direct income = total income - technical staff wages -, storage fees in both places.
3.4 Model establishment
3.5 Model solution
The relevant data tables are as follows:
Title Structure and Salary of the Department of Mathematics
4 Model Evaluation and Promotion
This model uses reasonable assumptions and fully considers various constraints to obtain personnel arrangements and direct benefits
Both are the optimal solution and optimal value of this model, which can guide the human resources arrangement of the Mathematics Department of Wuhan University. But from the model assumptions, we know that the logarithm
The arrangement of the existing technical force of the department is random. In the same working hours, some people may work more times and some people work less unfairly.
Therefore, in the case of meeting the work needs, when assigning work, we should artificially try to make the number of work of each person not too far apart, or equal.
This model obtains the maximum direct benefit of the Department of Mathematics from the perspective of quantification through the deployment of human resources. All linear programming models similar to this model can be obtained by using the method of this model. However, this model is only a single-objective planning, and the objective requirements can be added on this basis. For example, on the basis of maximizing the direct benefits of the Department of Mathematics, the client spends the least amount of money, and so on. In this way, a multi-objective programming model is established. Solve more complex practical problems.
5 Implementation code
f=[-1000;-800;-550;-450;-1500;-800;-650;-550;-1300;-900;-650;-350;-1000;-800;-650;-450];
A=zeros(9,16);
for i=1:1
for j=1:16
A(i,j)=1;
end
end
for i=2:5
for j=i-1:4:11+i
A(i,j)=1;
end
end
i0=0;
for i=6:9
for j=i0+1:(i-5 )*4
A(i,j)=1;
end
i0=j;
end
b=[64;17;20;15;18;12;25;17;10];
Aeq=zeros(1,16);
Aeq(1,3)=1;
beq=[2];
LB=[1;2;2;1;2;2;2;2;2;2;2;1;1;3;1;0];
UB=[3;5;2;2;inf;inf;inf;8;inf;inf;inf;inf;inf;inf;inf;0];
[x,fval]=linprog(f,A,b,Aeq,beq,LB,UB)
f=[-1000;-1000;-1000;-1000;-1000;-1000;-1000;-1500;-1500;-1500;-1500;-1500;-1500;-1500;-1250;-1250;-1250;-1250;-1250;-1250;-1250;-950;-950;-950;-950;-950;-950;-950;-800;-800;-800;-800;-800;-800;-800;-800;-800;-800;-800;-800;-800;-800;-850;-850;-850;-850;-850;-850;-850;-750;-750;-750;-750;-750;-750;-750;-600;-600;-600;-600;-600;-600;-600;-700;-700;-700;-700;-700;-700;-700;-650;-650;-650;-650;-650;-650;-650;-650;-650;-650;-650;-650;-650;-650;-500;-500;-500;-500;-500;-500;-500;-600;-600;-600;-600;-600;-600;-600;-350;-350;-350;-350;-350;-350;-350;-450;-450;-450;-450;-450;-450;-450];
A=zeros(60,112);
for i=1;1
for j=1:112
A(i,j)=1;
end
end
i0=0;
for i=2:4
for j=i0+1:(i-1)*28
A(i,j)=1;
end
i0=j;
end
for i=5:32
for j=(i-4):28:80+i
A(i,j)=1;
end
end
for i=33:39
for j= i-32:7:(i-11)
A(i,j)=1;
end
end
j0=j;
for i=40:46
for j=j0+(i-39):7:(i-18)+j0
A(i,j)=1;
end
end
j0=j;
for i=47:53
for j=j0+(i-46):7:j0+(i-25)
A(i,j)=1;
end
end
j0=j;
for i=54:60
for j=j0+(i-53):7:j0+(i-32)
A(i,j)=1;
end
end
b=[362;48;125;119;17;17;17;17;17;17;17;20;20;20;20;20;20;20;15;15;15;15;15;15;15;18;18;18;18;18;18;18;12;12;12;12;12;12;12;25;25;25;25;25;25;25;17;17;17;17;17;17;17;10;10;10;10;10;10;10];
UB=[3;3;3;3;3;3;3;5;5;5;5;5;5;5;3;3;3;3;3;3;3;2;2;2;2;2;2;2;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;8;8;8;8;8;8;8;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;+inf;0;0;0;0;0;0;0];
LB=[1;1;1;1;1;1;1;2;2;2;2;2;2;2;1;1;1;1;1;1;1;1;1;1;1;1;1;1;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;2;1;1;1;1;1;1;1;1;1;1;1;1;1;1;3;3;3;3;3;3;3;1;1;1;1;1;1;1;0;0;0;0;0;0;0];
Aeq=zeros(7,112);
for i=1:7
Aeq(i,i+14)=1;
end
beq=[2;2;2;2;2;2;2];
[x,fval]=linprog(f,A,b,Aeq,beq,LB,UB)
Modeling data
Data Sharing: The strongest modeling data
