(1.1) max(∑i, j[P ij·X ij]) Subject to the constraints (1.2)∑j X ij ≤ 1 , ∀ i ∈ E (1.3)∑i X ij ≤ N j  , ∀ j ∈ J (1.4) X ij ≤ q ij  , ∀ i ∈ E, j ∈ J (1.5) X ij ∈ {0, 1} , ∀ i ∈ E, j ∈ J