Optimization - multi objective planning

1、 effect

Programming solution is a mathematical theory and method to study the extreme value problem of objective function under constraints .

2、 Input / output description

Input ： Objective function , Constraints and value range of decision variables .
Output ： Programming solution result , And the derivation of programming equation .

3、 Relevant concepts

Positive deviation variable ： The amount by which the actual value exceeds the target value , Greater than or equal to 0

Negative deviation variable ： The amount by which the actual value is less than the target value , Greater than or equal to 0

Absolute constraint ： Conditions to be met

Goal constraints ： Try to meet the conditions , Add the negative deviation variable and subtract the positive deviation variable to form the equation

Priority factor ： The subjective weight given to each goal

4、 Case example

Two products , product 1  Each consumable is 1, Time consuming to 2 God , Profit is 8 ten thousand ; product 2 Each consumable is 2, Time consuming to 1 God , Profit is 10 ten thousand . The total material quantity is 10. requirement 11 It must be done in days . Determine respective production , Try to meet the following conditions

Conditions 1： product 1 The output of is not greater than that of the product 2;
Conditions 2： Materials should be used as fully as possible ;
Conditions 3： The planned profit target should be reached and exceeded as far as possible 56 Ten thousand yuan ;

  Determining priorities ,, after , Then the objective function and constraints are ：

  In this way, multi-objective programming is transformed into single objective programming .

5、 Modeling steps

1. Determining priorities

2. Build the objective function

3. Set the value range and constraints

4. Model solving