Consider the following model.Minimize Z = c₁x₁ + c₂x₂,subject to a₁₁x₁ + a₁₂x₂ ≥ b₁ a₂₁x₂ + a₂₂x₂ ≤ b₂ and x₁ ≥ 0,x₂ ≥ 0.The estimates and ranges of uncertainty for the parameters are shown in the following table. Use robust optimization to formulate a conservative version of this model.

Question

Quizplus · Accepted Answer

The Answer is Robust optimization assigns the most conservative value to each parameter.Therefore,for the objective function in minimization form,it uses the maximum value of each c_j.Since the first functional constraint is in ≥ form,it uses the minimum value of each a₁_j and the maximum value of b₁.Since the second functional constraint is in ≤ form,it uses the maximum value of each a₂_j and the minimum value of b₂.The resulting model is Minimize Z = 22x₁ + 33x₂,subject to 28x₁ + 46x₂ ≥ 325 -48x₁ + -66x₂ ≤ -540 and x₁ ≥ 0,x₂ ≥ 0.

Consider the Following Model