Table 3.

Notation

Sets
I:	Set of suppliers indexed by i
J:	Set of candidate locations for manufacturing plants indexed by j
K:	Set of raw materials indexed by k
L:	Set of retailers indexed by l
T:	Set of periods indexed by t
S:	Set of scenarios indexed by s
Deterministic parameters
$d_{\mathit{ij}}$:	Distance between supplier i and manufacturing plant in candidate location j
$e_{\mathit{jl}}$:	Distance between manufacturing plant in candidate location j and retailer l
$f_j$:	Fixed cost of opening manufacturing plant in candidate location j
$o_i$:	Fixed cost of ordering from supplier i
$c_{\mathit{ik}}$:	Unit procurement cost of raw material k supplied from supplier i
$y_k$:	Amount of raw material k needed for one unit of product
$h_k$:	Unit holding cost of raw material k per period
u:	Unit shipment cost per unit per km
$\widehat{c_{\mathit{ik}}}$:	Unit emission dedicated to the manufacturing of raw material k in supplier i
$\widehat{h_k}$:	Unit emission of holding raw material k per period
$\widehat{u}$:	Unit shipment emission per unit per km
$C_{\mathit{env}}$:	Carbon cap
$m_i$:	Social responsibility score of supplier i
$n_j$:	Social responsibility score of manufacturing plant in candidate location j
$C_{\mathit{soc}}$:	Minimum social responsibility score that must be achieved
$p^s$:	Probability that $s^{\mathit{th}}$ scenario occurs
M	A big number
Random parameters
$a_{\mathit{ik}}^s$:	Supply capacity of supplier i for raw material k under scenario s
$b_{\mathit{lt}}^s$:	Demand of retailer l for product in period t under scenario s
Decision variables
${\psi }_{\mathit{ijkt}}^s$:	Amount of raw material k shipped from supplier i to plant j in period t under scenario s
${\delta }_{\mathit{jlt}}^s$:	Amount of product shipped from manufacturing plant j to retailer l in period t under scenario s
${\varphi }_{\mathit{jkt}}^s$:	Amount of raw material k kept in manufacturing plant j in period t under scenario s
${\chi }_{\mathit{it}}^s$:	1, if an order is made from supplier i in period t under scenario s, and 0 otherwise.
${\gamma }_j$:	1, if a manufacturing plant is opened in candidate location j, and 0 otherwise.