Competition and Integration in Closed-Loop Supply Chain Network with Variational Inequality

Table 2

Notation for the closed-loop supply chain network after horizontal merger of partial firms.

Notation	Definition
𝐿𝑖^2𝑁	The set of all forward links for the Firm i, where 𝑖=1,2,…,𝑆
𝐿𝑖^2𝑅	The set of all reverse links for the Firm i, where 𝑖=1,2,…,𝑆
𝑃^2𝑁𝑖𝑗	The set of all forward paths connecting the first layer node 𝑖 (𝑖=1,2,…,𝑆) with demand market j, where 𝑗=1,2,…,𝐽
𝑃^2𝑅𝑖𝑗	The set of all reverse paths connecting the demand market j with the first layer node 𝑖 (𝑖=1,2,…,𝑆)
𝑃𝑗^2𝑁	The set of all forward paths between all S nodes with demand market j
𝑃𝑗^2𝑅	The set of all reverse paths between all S nodes with demand market j
𝑃𝑖^2𝑁	The set of all forward paths between the node 𝑖 (𝑖=1,2,…,𝑆) with all demand markets
𝑃𝑖^2𝑅	The set of all reverse paths between the node 𝑖 (𝑖=1,2,…,𝑆) with all demand markets
𝑃^2𝑁	The set of all forward paths
𝑀^2𝑁	The number of all forward paths
𝑃^2𝑅	The set of all reverse paths
𝑀^2𝑅	The number of all reverse paths
𝑥^2𝑝	The nonnegative remanufactured product flow on the path p (𝑝∈𝑃^2𝑁)
𝑥^2	𝑀^2𝑁-dimensional vector of all remanufactured product flows on the paths in 𝑝∈𝑃^2𝑁
𝑦^2𝑝	The nonnegative manufactured product flow on the path p (𝑝∈𝑃^2𝑁)
𝑦^2	𝑀^2𝑁-dimensional vector of all manufactured product flows on the paths in 𝑝∈𝑃^2𝑁
𝑧^2𝑝	The nonnegative recovered EOL product flow on the path p (𝑝∈𝑃^2𝑅)
𝑧^2	𝑀^2𝑅-dimensional vector of all EOL product flows on the paths in 𝑝∈𝑃^2𝑅
𝑋^2	The set of all product flows, 𝑋^2≡𝑥^2,𝑦^2,𝑧^2