“…In this paper, it can be transformed into a max-max problem by dual theory. Let θ ik , μ ik , λ ik 1 , λ ik 2 , π ik 1 , π ik 2 , γ i , e ik 1 , e ik 2 , v ik , ϕ i jk 1 , ϕ i jk 2 , ϕ i jk 3 , l ik 1 , l ik 2 , ξ ik be dual variables for constraints (1), (2), (13), (14), (17), (20), (22), (27) and (29). Dual constraints can be obtained as follows:…”