Optimizing resources with Linear Programming
Modeling problems theory
To be able to solve a problem intervening an algorithm, first must extract all the information that contributes itself, and arranging the problem for the aforementioned algorithm.
The steps to model a problem are the following:
- Step 1: Determining decision variables and expressing them algebraically.
- Step 2: Determining the restrictions and expressing them as equations or inequalities in function of the decision variables:
- A11·X1 + A12·X2 + ... + A1n·Xn ≥, ≤, ó = b1
- A21·X1 + A22·X2 + ... + A 2n·Xn ≥, ≤, ó = b2
- Am1·X1 + Am2·X2 + ... + Amn·Xn ≥, ≤, ó = bm
- Step 3: Expressing all implicit conditions established by the origin of variables: negativeness, integer, only a few allowed values, ...
- X1,..., Xn ≥ 0
- X1,..., Xn are integers, or boolean,...
- Step 4: Determining Objective Function.
- Maximize or minimize Z = C1·X1 + C2·X2 + ... + Cn·Xn
As example, let see how to model some typical problems:
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