M a x Z S . t . Z ≤ r i ( r j ( r k ( w i j k r k − w i j k r k + 1 ) ) ) ∀ i , j a n d r k Z ≤ r i r j r m w i j k r m ∀ i , j a n d r m ∑ i = 1 p ∑ j = 1 n ∑ k = 1 m w i j k = 1 w i j k ≥ 0 ∀ i , j a n d k Z : U n r e s t r i c t e d i n s i g n {\textstyle {\begin{aligned}&MaxZ\\&S.t.\\&Z\leq r_{i}{\bigg (}r_{j}{\big (}r_{k}(w_{ijk}^{r_{k}}-w_{ijk}^{{r_{k}}+1}){\big )}{\bigg )}\;\;\;\;\forall i,j\;and\;r_{k}\\&Z\leq r_{i}r_{j}r_{m}w_{ijk}^{r_{m}}\;\;\;\forall i,j\;and\;r_{m}\\&\sum _{i=1}^{p}\sum _{j=1}^{n}\sum _{k=1}^{m}w_{ijk}=1\\&w_{ijk}\geq 0\;\;\;\forall i,j\;and\;k\\&Z:Unrestricted\;in\;sign\\\end{aligned}}}
w k = ∑ i = 1 p ∑ j = 1 n w i j k ∀ k {\displaystyle {\begin{aligned}&w_{k}=\sum _{i=1}^{p}\sum _{j=1}^{n}w_{ijk}\;\;\;\;\forall k\\\end{aligned}}}
w j = ∑ i = 1 p ∑ k = 1 m w i j k ∀ j {\displaystyle {\begin{aligned}&w_{j}=\sum _{i=1}^{p}\sum _{k=1}^{m}w_{ijk}\;\;\;\;\forall j\\\end{aligned}}}
w i = ∑ j = 1 n ∑ k = 1 m w i j k ∀ i {\displaystyle {\begin{aligned}&w_{i}=\sum _{j=1}^{n}\sum _{k=1}^{m}w_{ijk}\;\;\;\;\forall i\\\end{aligned}}}
