“…Since we suppose the change of criteria from original value ݔ , to new value ݕ , and the prices for the unit improvement, the overall prices for the improvement of specific criteria are given by the values ܿ , ൫ݕ , − ݔ , ൯ and ݐ , ൫ݕ , − ݔ , ൯. To ensure that the budgets will be not exceeded, we sum the prices of all improvements and the constraints are given by )ݕ(ܿ ≤ ,ܥ where )ݕ(ܿ = ∑ ∑ ܿ , ൫ݕ , − ݔ , ൯ ୀଵ ୀଵ (11) )ݕ(ݐ ≤ ܶ, where )ݕ(ݐ = ∑ ∑ ݐ , ൫ݕ , − ݔ , ൯ ୀଵ ୀଵ (12) The optimal new criteria values with budget constraints are given by the solution of integer linear optimization problem (9) with constraints (11), (12), and min ܪ ≤ ݕ , ≤ max ܪ , ݆ = 1, … , ,ܬ ݇ = 1, … , ܭ (13) (i.e., ݕ , ∈ )ܪ and ݕ , ≥ ݔ , , ݆ = 1, … , ,ܬ ݇ = 1, … , ,ܭ (14) i.e., the new values are larger or equal to original values -there is not a possibility to "sell" values.…”