Investigating a Dual-Channel Network in a Sustainable Closed-Loop Supply Chain Considering Energy Sources and Consumption Tax

. 2022 May 6;22(9):3547. doi: 10.3390/s22093547

Sets and Indicators:
I	Set of producers $i \in I$
J ₁	Set of existing distribution centers $j_{1} \in J_{1}$
$J_{2}$	Set of new distribution centers $j_{2} \in J_{2}$
J	$Set of all distribution centers j \in J = J_{1}$ ⋃ $J_{2}$
V	Set of pharmaceutical industries $v \in V$
F	Set of rice factories $f \in F$
K	Set of toiletries industries $k \in K$
M	$Set of retailers (market) m \in M$
O ₁	$Set of existing recycling centers o_{1} \in O_{1}$
O ₂	$Set of new recycling centers o_{2} \in O_{2}$
O	Set of all recycling centers o ∈ O = O₁ ⋃ O₂
C	Set of customers c ∈ C
$T$	$Set of time period t \in T = {1, 2, \dots t^{'}, \dots, t}$
T′	$Index for harvest period t^{'} \in T^{'} = {1, 2}$
U	Set of solar panel sites u ∈ U
B	Set of bio-refineries sites b ∈ B
X	Indicator for processed rice
Y	Indicator for rice bran
P	$Set of products p \in {X, Y}$
G	Indicator for mains electricity
R	$Set of energy sources r \in R$ ={ mains electricity, solarpanel, bio-refinery}
Parameters:
$f c j_{j}_{2}$	Fixed cost for launching new distribution center j₂
$f c s_{s}$	$Fixed \cos t for launching solar panel site s$
$f c o_{o 2}$	Fixed cost for launching recycling distribution center o₂
$f c b_{b}$	Fixed cost for launching bio-refinery b
${\tilde{p r m}}_{p m t}$	Cost of purchasing each kg of p-type product from market m (traditional purchase) during period t
${\tilde{p r f}}_{p f t}$	Cost of purchasing each kg of p-type product from factory f (online shopping) during period t
$p c a p f_{p f t}$	Production capacity of p-type product in factory f during period t
$c p a_{i}$	Cost of production per kg of rice plant for farmer i
$\tilde{c t a} x_{r}$	Tax on consumption per unit of electricity supplied from source r
$\tilde{c p} t_{p f r}$	Production cost per kg of p-type product in factory f, whose electricity is supplied from source r
$c h j_{j}_{t}$	Cost of per kg unprocessed rice maintenance at distribution center j during period t
$C T$	Cost of transporting by vehicle per kilometer
$d i s a_{i j}$	Distance between producer i and distribution center j
$d i s b_{j f}$	Distance between distribution center j and rice factory f
$d i s c_{f v}$	Distance between rice factory f and pharmaceutical industry v
$d i s d_{f k}$	Distance between rice factory f and toiletries industry k
$d i s e_{f m}$	Distance between rice factory f and market m
$d i s f_{f c}$	Distance between rice factory f and customer c
$d i s g_{m c}$	Distance between market m and customer c
$d i s h_{i o}$	Distance between producer i and recycling center o
$d i s i_{o i}$	Distance between recycling center o and producer i
$d i s j_{i b}$	Distance between producer i and bio-refinery b
$d i s k_{f b}$	Distance between rice factory f and bio-refinery b
$c a p_{i t^{'}}$	Product’s production capacity by producer i during period t′
$c a p r_{r t}$	Max energy level supplied from source r during period t
${\tilde{d c t}}_{p c t}$	Demand for p-type product by consumer c in traditional purchase during period t
${\tilde{d c o}}_{p c t}$	Demand for p-type product by consumer c in online shopping during period t
$d c i_{i t}$	Demand for compost by farm i during period t
$d v_{v t}$	Demand for rice bran by pharmaceutical industry v during period t
$d k_{k t}$	Demand for rice bran by toiletries industry k during period t
$E R$	Electrical energy required to process per kg of rice
M	A very large positive number
$η_{}$	Paddy to husk conversion rate
$δ$	Rice husk to electrical energy conversion rate in bio-refineries
$λ$	Straw to electrical energy conversion rate in bio-refineries
$ψ$	Straw to compost conversion rate
$c p o_{o}$	Cost of production per kg of compost at recycling center o
$π o_{o}$	CO₂ quantity released from constructing recycling center o
$π s_{s}$	CO₂ quantity released from constructing solar panel s
$π b_{b}$	CO₂ quantity released from constructing bio-refinery b
RF	Fuel required for vehicle per travel per k
$c a p v$	Capacity of vehicle
$β$	Rice plant to paddy conversion rate
$1 - β_{}$	Rice plant to straw conversion rate
$θ_{p}$	Paddy to product of type-p conversion rate
$f j_{j 2}$	Number of fixed job opportunities created by constructing new distribution centers j₂
$V J I_{i}$	Number of variable job opportunities created by producing per kg of product on farm i
$V J Q_{p f}$	Number of fixed job opportunities created by producing per kg of product p in factory f
Decision Variables
$X S e_{r t}$	Amount of electrical energy that should be supplied from source r during period t
$X h j_{j t}$	Quantity of paddy rice stored in the distribution center j during period t
$X a_{i j t^{'}}$	Quantity of rice plant transferred from producer i to distribution center j during period t′
$X b_{j f t}$	Quantity of paddy rice transferred from distribution center j to rice factory f during period t
$X c_{f v t}$	Quantity of rice bran transferred from rice factory f to pharmaceutical industry v during period t
$X d_{f k t}$	Quantity of rice bran transferred from rice factory f to toiletries industry k during period t
$X e_{p f m t}$	Quantity of type-p product transferred from rice factory f to market m during period t
$X f_{p f c t}$	Quantity of type-p product transferred from rice factory f to customer c during period t
$X g_{p m c t}$	Quantity of type-p product transferred from market r to customer c during period t
$X h_{i o t^{'}}$	Quantity of compost transferred from producer i to recycling center o during period t′
$X i_{o i t}$	Quantity of compost transferred from recycling center o to producer i during period t
$X j_{i b t}$	Quantity of rice straw transferred from farm i to bio-refinery b during period t
$X k_{f b t}$	Quantity of rice bran transferred from rice factory f to bio-refinery b during period t
$X q_{i t^{'}}$	Amount of rice plant produced by producer i during period t′
$X r h_{f p r t}$	Quantity of type-p product produced from rice factory f using source r during period t
$X S e_{r t}$	Quantity of electrical energy that should be supplied from source r during period t
Variables Zero and One:
W_j	if distribution center j is established, 1
V_s	if solar panel site s is established, 1
Z_b	if bio-refinery b is established, 1
Q_o	if recycling center o is established, 1