Table AIV Indices, parameters, decision...

Table AIV

Indices, parameters, decision variables and constrains for CSP_TS

Symbol	Description
Decision variables
X_k,p,c,o,s	The same meaning as for the CSP₁
XO_k,c,p,o,s	If product p is delivered from the manufacturer (factory) k to the distribution center c using means of transport s, then XO_k,c,p,o,s=1, otherwise XO_k,c,p,o,s=0
XH_f,i,j	The same meaning as for the CSP₃
TH_f,o	The total time of delivery to the customer o
Constrain
It determines the time of delivery, i.e. how long it takes for the delivery from the manufacturer (factory) to the customer
$\begin{array}{l} X O_{k . p . c . o, s} \cdot S t ⩾ X_{k, p, c, o, s} \forall k \in K, c \in C, p \in P, o \in O, s \in S \\ T H_{f, o} = \sum_{i \in O \cup C} \sum_{j \in O \cup C} D O_{i, j} \cdot X H_{f, i, j} \forall f \in F, h \in H, o \in O : D O F_{h, f} = 1 \\ \sum_{k \in K} \sum_{c \in C} \sum_{s \in S} (D O_{k, c} \cdot X O_{k, p, c, o, s} + T C_{c} \cdot X O_{k, p, c, o, s}) + \sum_{h \in H} T H_{f, o} = T O_{p, o} \forall p \in P, o \in O \end{array}$	(C27)

Symbol	Description
Decision variables
X_k,p,c,o,s	The same meaning as for the CSP₁
XO_k,c,p,o,s	If product p is delivered from the manufacturer (factory) k to the distribution center c using means of transport s, then XO_k,c,p,o,s=1, otherwise XO_k,c,p,o,s=0
XH_f,i,j	The same meaning as for the CSP₃
TH_f,o	The total time of delivery to the customer o
Constrain
It determines the time of delivery, i.e. how long it takes for the delivery from the manufacturer (factory) to the customer
$\begin{array}{l} X O_{k . p . c . o, s} \cdot S t ⩾ X_{k, p, c, o, s} \forall k \in K, c \in C, p \in P, o \in O, s \in S \\ T H_{f, o} = \sum_{i \in O \cup C} \sum_{j \in O \cup C} D O_{i, j} \cdot X H_{f, i, j} \forall f \in F, h \in H, o \in O : D O F_{h, f} = 1 \\ \sum_{k \in K} \sum_{c \in C} \sum_{s \in S} (D O_{k, c} \cdot X O_{k, p, c, o, s} + T C_{c} \cdot X O_{k, p, c, o, s}) + \sum_{h \in H} T H_{f, o} = T O_{p, o} \forall p \in P, o \in O \end{array}$	(C27)