# Sustainable Supply Chain Network Design with Carbon Footprint Consideration: A Case Study in China

Authors: Yue Jiang; Yang Zhao; Mengyuan Dong; Shuihua Han
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

With the environment concern increasing, corporations are facing new challenges on carbon management in supply chain network. In this paper, environmental consideration is introduced to traditional supply chain management, and the sustainable supply chain (SSC) is designed considering carbon footprint. We develop a mixed integer linear programming (MILP) model to get the optimal decisions on partner selection, technology selection, and transportation mode selection, as well as material procurement, product supply, and recovery mode. For validating the model, a beverage company in China is used. We also analyze the impact of supply chain uncertainties such as carbon emission price and recovery rate of returned products on the decision of SSC design.


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## Body

## 1. Introduction

Greenhouse gases are produced by human activities, such as methane and carbon dioxide, which has resulted in the increasing concern of environmental issues in the last few decades. Recently, due to the increasing concern of these serious environment problems, the sustainability is coming. At the same time, companies are increasingly aware of the environmental responsibility of their partners [1–3]. In order to fully realize sustainable management of supply chain, a sustainable network of supply chain should be firstly designed from the strategic perspective. Then, sustainable procurement, manufacturing, distribution, and recovery can be achieved from the operations management perspective. Carbon emission is one of the most important criteria to measure the sustainability of supply chain. The research about supply chain with considering carbon emissions is inadequate. Many research works are only confined to carbon emission management in transportation and warehousing links; few works have analyzed the impact of internal (procurement, manufacturing, etc.) and external factors (carbon price, recovery rate, etc.) on the optimal decisions, the operating cost, and carbon emission of sustainable supply chain.In this paper, carbon emissions are introduced into traditional supply chain management, and a MILP model is proposed to solve the SSC design problems. Our work focuses on the following streams: the first is about the decisions in the process of procurement, manufacturing, distribution, and recycling; the second is about the impact of carbon price and recovery rate on the decision of SSC network design. A real-world case of a beverage company in China is used to validate the model we proposed.We organize this paper as follows. The first and second sections are the introductory and relevant literature. Conceptual model is introduced in Section3. A MILP model for the design of SSC with the consideration of carbon footprint is presented and described in Section 4. Section 5 focuses on analyzing the results of the model, followed by sensitivity analysis in Section 6. The last section is about the conclusions and future research.


## 2. Literature Review

The research about the design of traditional supply chain network is rich. A MILP model is used to develop a supply chain management system by Jang; this system can give the optimal decisions on production, inventory, and transportation selection [4]. Chan developed a simulation model in order to design supply chain; in their research, five models are proposed to get optimal decisions considering the stock, lead time, and transportation cost [5]. A discrete-event simulation model is used by Bottani and Montanari; in their research, the impact of supply chain configurations on the cost of holding, ordering, transportations, and shipping is analyzed [6]. For more about traditional supply chain design, readers are referred to Mexiell and Gareya which gives a good literature survey [7].With the growing awareness of environment, some researchers proposed the concept of closed-loop supply chain management (CLSC) which incorporates the concept of recycling and remanufacturing [8]. Some research focused on the process of recycling and remanufacturing. Bottani investigated the issue of minimizing the environmental burden of a real CLSC, consisting of a pallet provider, a manufacturer, and several retailers; they find that asset retrieving operations contribute to the environmental impact of the system to the greatest extent [9]. Savaskan pointed out that there are three recycling modes, encouraging retailers to recover, recycling directly from consumers and outsourcing the recycling business to a third party. They also used the game method to analyze the optimal price and sales volume [10]. The recovery network of supply chain is designed by Beamon and Fernandes; the network can make the optimal decision about the recycling center selection, the storage capacities, and the amount of materials transported from this site to that site [11]. Some papers have also tried to integrate recycling and remanufacturing into traditional supply chain networks. Ovchinnikov provided integration decisions for OEM based on management of closed-loop remanufacturing supply chain with combining remanufacturing and recycling process. They considered pricing and remanufacturing strategies of firms, which offer two kinds of its products in the market with the consideration of demand cannibalization [12]. Yang used MILP method to design closed-loop supply chain, and supplier, manufacturer, retailer, consumer, and recycling center are all considered in this design. The impact of return rate, the transformation rate of raw, and recovery material on the decision of supply chain is also analyzed in this research [13].Despite the research about CLSC, the research of supply chain with the consideration of carbon emissions, recycling, and remanufacturing is inadequate. We find that previous studies on carbon emissions mainly focused on the definition and calculation of carbon footprint. Hertwich defined carbon footprint; he indicated carbon footprint measures the amount of CO2 or GHG emitted by an activity or product during the life cycle. The carbon emission of transportation and storage process are calculated in the supply of food and beverage. The impact of supply chain design on the carbon emission is analyzed in their research [14].Recently, global awareness on sustainability and environmental protection inspire many researchers, industry, and other organizations to develop a green and low carbon supply chain management [15, 16]. Luo proposed a MILP to design the supply chain; in this model, the author analyzes the impact of product cost, quality and carbon emission on the supply chain design [17]. Following this idea, considering the impact of carbon market, Ramudhin developed a MILP model to design the supply chain with considering carbon market; they found the external control variables have impact on supply chain network, so, in the supply chain network design, we must not ignore the carbon policy [18]. Based on this, Chaabane designed the supply chain network with different carbon emission policies; they found current carbon emission policies and regulations should be further strengthened and unified [19]. Daryanto considered an integrated three-echelon supply chain with carbon emissions from transportation and warehousing, as well as disposing of the deteriorated items; they find that the benefit of supply chain integration in terms of total supply chain cost and carbon emission reduction [20]. Nagurney and Abdallah also studied the design of SSC network with the consideration of carbon footprint [21, 22]. For more about the design with considering carbon emission, readers are referred to Cynthia which gives a good literature on sustainable supply chain network design between 2010 and mid-2017 [23]Different from existing research, there are several contributions of our research. First, the decision model that blends life cycle assessment (LCA) criteria and supply chain management method is limited, and many research works are confined to carbon emission management in transportation and warehousing links. SSC network design is studied with the consideration of procurement, manufacturing, distribution, and recovery based on the LCA as design criteria in our paper. Secondly, it is different from existing paper like Kuo in which the operating cost and carbon emission are individually minimized [24]. In this paper, the operating cost and carbon emission are both simultaneously considered. Third, our paper not only identifies the largest emission source of supply chain, but also analyzes the decisions of supply chain, such as procurement decision, manufacturing decision, distribution decision, and recycling decision. Lastly, our paper analyzes the impact of internal and external factors (carbon price and recovery rate) on the decisions, the operating cost, and carbon emission of sustainable supply chain which cannot be found in existing papers.


## 3. Conceptual Model Development

In this paper, the considered sustainable supply chain is based on a beverage Corporation C located in Xiamen in China. Corporation C is a subsidiary company of global beverage giant; the core business is to produce and sell a well-known drinks. It has a leading market share and position in the industry. It also occupies a very important position in beverage supply chain and is regarded as the core enterprise of this industry. The headquarters of Corporation C focus on the issue of sustainable development and implemented carbon reduction plans in some business areas. Corporation C adopts relevant measures to reduce carbon emission in the production process of beverage, and most significant is a reduction in the use of PET (Polyester) chip. Figure1 depicts the operational processes of the supply chain of beverage product.Figure 1
The supply chain network of beverage product.The supplier, distribution center, and recycling center are named for the name of location, for example, the supplier located in Xiamen; we call the supplier as Xiamen supplier. There are two types of raw materials: ingredient and wrappage. The main component of wrappage is PET (polyester) chip. The ingredient of beverage product is a secret recipe; thus there is only one supplier of the ingredient. Ingredient purchasing has no relation with the design of supply chain network; hence relevant cost and carbon emission are ignored in our research. The sources of PET chip are divided into two parts: new and recovery PET chip. There are two new PET chip suppliers; they are located in Xiamen and Jiangsu, and they are called Xiamen supplier and Jiangsu supplier. All suppliers can meet the demand of manufacturer without delivery delay and shortage; the qualities of the new PET chip from different suppliers are the same, but the prices and carbon emissions are different. There are also two recycling centers located in Xiamen and Fuzhou; they are called Xiamen Recycling Center and Fuzhou recycling center.All manufacturing processes are completed in an independent manufacturing center of Corporation C, which comprises five potential technology options. Each technology has different production cost and carbon emission. Technology 1 to technology 5 are used to produce 32g, 26g, 21.6g, 17.02g, and 16.6g bottles, respectively. There are three phases in manufacturing processes, which are preform manufacturing, bottle manufacturing, and beverage filling, as shown in Figure2. In preform manufacturing process, the fixed cost increases with decreasing of bottle weight from Technology 1 to Technology 5, whilst the variable cost and carbon emission decrease from Technology 1 to Technology 5. In bottle manufacturing process, all cost and carbon emission are constant from Technology 1 to Technology 5. In beverage filling process, all cost and carbon emission are irrelevant with bottle weight, but relevant to filling technology, there are two kinds of filling technology; they are hot-filling and aseptic cold-filling technology. Hot-filling technology is used in Technologies 1, 2, and 3 and aseptic cold-filling is used in Technologies 4 and 5. The cost and carbon emission of aseptic cold-filling technology are higher than hot-filling technology.Figure 2
Main manufacturing processes.After manufacturing process, the products will be transported to distribution center. There are two distribution centers; they are Xiamen Distribution Center and Quanzhou Distribution Center which are located in Xiamen and Quanzhou, respectively. Since the distribution centers have different distances to Corporation C and market as well as different operating costs, maximum stocks, and distribution capability, Corporation C supplies the products for regional markets located in Xiamen, Quanzhou, Fuzhou, Nanping, Longyan, Zhangzhou, and Ningde. The demand of each market must be satisfied; stock out and backlog are not allowed. Figure3 shows the distribution map of markets. The distance between each supply chain node can be obtained from Google map. Used bottles are returned to recycling centers where they are either discarded or turned into recovery PET chip according to the conditions of recycling. There are four transportation modes, which are plane, ship, truck, and van. The transportation capacity is close to full in each delivery, and there is no special requirement about the delivery time of the product.Figure 3
Distribution map of markets.


## 4. Model Formulation

### 4.1. Notations

In this part, we first define the decision variable, and Appendix gives the parametersDecision Variables in Procurement Process
Y
s
i
t: 0-1 variable, in period t, if the supplier s supplies raw material i, the value of this variable is 1; otherwise the value of the variable is 0.
Y
F
s
v
t: 0-1 variable, in period t, if the raw materials are transported by transport v from supplier s to manufacturing center, the value of the variable is 1, otherwise the value of the variable is 0.
Y
F
r
v
t: The 0-1 variable. in period t, if the vehicle v is used to transport the recovered materials from the recycling center r to the manufacturing center, the value of the variable is 1, otherwise the value of the variable is 0.
Q
F
s
i
v
t: In period t, the total transport volume of raw material i transported from supplier s to manufacturing center using vehicle v.
Q
F
r
j
v
t: In period t, the total transport volume of recovered materials j transported from recycling center r to manufacturing center using vehicle v.Decision Variables in Manufacturing Process
Y
h
t: 0-1 variable, in period t, if the technology h is chosen for production, the value of the variable is 1; otherwise the value of the variable is 0.
Q
i
t: In period t, the total amount of raw material i consumed by the production.
Q
j
t: In period t, the total amount of recovered material j consumed by the production.
Q
h
t: In period t, produce or assemble the output of the product using technology h
I
i
t: In period t, the inventory of raw material i of manufacturing center.
I
j
t: In period t, the inventory of recovered material j of manufacturing center.
I
t: In period t, the inventory of final product of manufacturing center.Decision Variables in Distribution Process
Y
d
t: 0-1 variable, in period t, if the distribution center d is selected for product distribution, the value of the variable is 1,; otherwise the value of the variable is 0.
I
d
t: In period t, the inventory of finished product of distribution center d.
Y
F
d
v
t: 0-1 variable, in period t, if the vehicle v is used to transport the finished product from the manufacturing center to the distribution center d, the value of the variable is 1, otherwise the value of the variable is 0.
Y
d
c
v
t: 0-1 variable, in period t, if the final product is transported by vehicle v from the distribution center d to the market c, the value of the variable is 1, otherwise the value of the variable is 0.
Q
F
d
v
t: In period t, the total transport volume of finished product from the manufacturing center to the distribution center d transported by vehicle v
Q
d
c
v
t: In period t, the total transport volume of the final product transported by vehicle v from the distribution center d to market c.Decision Variables in Recycling Process
Y
r
t: 0-1 variable, in period t, if the recycling center r is selected for material recovery, the value of the variable is 1; otherwise the value of the variable is 0.
Q
r
t: In period t, the total amount of returned products processed in the recycling center r during the current period.
D
r
t: In period t, the total amount of recycled products discarded directly in the recycling center r
Q
r
j
t: In period t, the total amount of recycled material j recovered from the recycling center r
I
r
t: In period t, the inventory of returned product of recycling center r
I
r
j
t: In period t, the inventory of recovered material j of recycling center r
Y
c
r
v
t: 0-1 variable, in period t, if the returns are transported by vehicle v from market c to recycling center r, the value of the variable is 1, otherwise the value of the variable is 0.
Q
c
r
v
t: in period t, the total quantity of returned goods transported from recycling center r by vehicle v


### 4.2. Operating Cost Function

The operating cost function (1) consists of four major components: procurement cost (PC), manufacturing cost (MC), distribution cost (DC), and recovery cost (RC). (1)
F
1
=
P
C
+
M
C
+
D
C
+
R
CProcurement cost function (2) measures costs related to new and recovered PET chips. The first part is fixed ordering cost, second and third parts are purchasing cost, and fourth and fifth parts are transportation cost.(2)
P
C
=
∑
s
=
1
S
∑
i
=
1
I
∑
t
=
1
T
O
C
s
i
t
Y
s
i
t
+
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
P
s
i
t
Q
F
s
i
v
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
v
=
1
V
∑
t
=
1
T
P
r
j
t
Q
F
r
j
v
t
+
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
F
s
Q
F
s
i
v
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
F
r
Q
F
r
j
v
tManufacturing cost function (3) refers to the cost incurred in the production process. The first part is fixed operating cost of manufacturing center, second part is fixed investment cost of production line, third part is the variable production cost of the product, the fourth, fifth, and sixth parts are inventory cost of raw material, recovery material, and final product in manufacturing center.(3)
M
C
=
∑
t
=
1
T
F
O
t
+
∑
h
=
1
H
∑
t
=
1
T
F
C
h
t
Y
h
t
+
∑
h
=
1
H
∑
t
=
1
T
V
C
h
t
Q
h
t
+
∑
i
=
1
I
∑
t
=
1
T
H
i
t
I
i
t
+
∑
j
=
1
J
∑
t
=
1
T
H
j
t
I
j
t
+
∑
t
=
1
T
H
t
I
tDistribution cost function (4) refers to the cost of distributing finished products from manufacturing centers to markets. The first part is fixed operating cost of distribution center, the second part is distribution cost of product, the third part is transportation cost of final products between manufacturing and distribution center, and the fourth item is the transportation cost of finished products between distribution center and market.(4)
D
C
=
∑
d
=
1
D
∑
t
=
1
T
F
O
d
t
Y
d
t
+
∑
d
=
1
D
∑
t
=
1
T
V
C
d
t
I
d
t
+
∑
d
=
1
D
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
F
d
Q
F
d
v
t
+
∑
d
=
1
D
∑
c
=
1
C
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
d
c
Q
d
c
v
tRecycling cost function (5) refers to the cost of recovered returns and the cost of discarded unusable recycled materials. The first item is fixed operating cost of recycling center, the second item is purchasing cost of returned product, the third item is discarding cost of returned product, the fourth item is recovery cost of material, the fifth item is inventory cost of returned product at recycling center, the sixth item is inventory cost of recovery material at recycling center, and the seventh item is transportation cost of returned product between market and recycling center.(5)
R
C
=
∑
r
=
1
R
∑
t
=
1
T
F
O
r
t
Y
r
t
+
∑
r
=
1
R
∑
v
=
1
V
∑
t
=
1
T
P
r
t
Q
C
r
v
t
+
∑
r
=
1
R
∑
t
=
1
T
V
C
D
r
t
D
r
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
t
=
1
T
V
C
r
j
t
Q
r
j
t
+
∑
r
=
1
R
∑
t
=
1
T
H
r
t
I
r
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
t
=
1
T
H
r
j
t
I
r
j
t
+
∑
c
=
1
C
∑
r
=
1
R
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
c
r
Q
c
r
v
t


### 4.3. Carbon Emission Function

The carbon emission function (6) consists of four major components: procurement carbon emission (PE), manufacturing carbon emission (ME), distribution carbon emission (DE), and recycling carbon emission (RE).(6)
F
2
=
P
E
+
M
E
+
D
E
+
R
EProcurement carbon emissions function (7) measures the carbon emissions related to acquisition of new and recovered material. The first item is initial carbon footprint of raw material, second item is transportation carbon emission of raw material from supplier to manufacturing center, and third item is transportation carbon emission of recovery material from recycling center to manufacturing center.(7)
P
E
=
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
C
O
s
i
t
Q
F
s
i
v
t
+
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
F
s
Q
F
s
i
v
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
F
r
Q
F
r
j
v
tThe manufacturing carbon emission function (8) is the carbon emission in manufacturing process; it is equal to the total production of products multiplied by the unit carbon emissions. (8)
M
E
=
∑
h
=
1
H
∑
t
=
1
T
C
O
h
t
Q
h
tThe distribution carbon emission function (9) is the carbon emission of distributing final product from manufacturing center to distribution center and from distribution center to market. The first item is transportation carbon emission of final product from manufacturing center to distribution center, and the second item is transportation carbon emission of final products from distribution center to market.(9)
D
E
=
∑
d
=
1
D
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
F
d
Q
F
d
v
t
+
∑
d
=
1
D
∑
c
=
1
C
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
d
c
Q
d
c
v
tThe recycling carbon emission function (10) is the carbon emission in recycling process. The first item is carbon emission of discarding the product at recycling center, the second item is carbon emission of material recovery, and the third item is transportation carbon emission of returned product from market to recycling center.(10)
R
E
=
∑
r
=
1
R
∑
t
=
1
T
C
O
D
r
t
D
r
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
t
=
1
T
C
O
r
j
t
Q
r
j
t
+
∑
c
=
1
C
∑
r
=
1
R
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
c
r
Q
c
r
v
t


### 4.4. Objective Function

Performance of SSC can be evaluated from two aspects: economics and environment. In order to unify the two different goals, we introduce a parameter, the price of carbonP
c
e, to transform the carbon emission function into carbon emission cost function. Then, the objective function becomes(11)
min
⁡
Z
=
F
1
+
P
c
e
F
2


### 4.5. Constraints

#### 4.5.1. Supplier Constraints

(12)
∑
v
=
1
V
Q
F
s
i
v
t
≤
S
-
s
i
t
Y
s
i
t
,
∀
s
∈
1
,
⋯
,
S
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(13)
Y
s
i
t
-
1
≤
Y
s
i
t
,
∀
s
∈
1
,
⋯
,
S
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
TConstraint (12) shows the capacity of supplier. Constraint (13) ensures that if a supplier is selected, the manufacturer will cooperate with this supplier in all decision-making periods.


#### 4.5.2. Manufacturing Center Constraints

(14)
Q
h
t
≤
Q
-
h
t
Y
h
t
,
∀
h
∈
1
,
⋯
,
H
,
∀
t
∈
1
,
⋯
,
T
(15)
Q
i
t
+
Q
j
t
=
∑
h
=
1
H
α
h
i
Q
h
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(16)
I
i
t
-
1
+
∑
s
=
1
S
∑
v
=
1
V
Q
F
s
i
v
t
=
I
i
t
+
Q
i
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(17)
I
j
t
-
1
+
∑
r
=
1
R
∑
v
=
1
V
Q
F
r
j
v
t
=
I
j
t
+
Q
j
t
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(18)
I
t
-
1
+
∑
h
=
1
H
Q
h
t
=
I
t
+
∑
d
=
1
D
∑
v
=
1
V
Q
F
d
v
t
,
∀
t
∈
1
,
⋯
,
T
(19)
I
_
i
t
≤
I
i
t
≤
I
-
i
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(20)
I
_
j
t
≤
I
j
t
≤
I
-
j
t
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(21)
I
_
t
≤
I
t
≤
I
-
t
,
∀
t
∈
1
,
⋯
,
T
(22)
Y
h
t
-
1
≤
Y
h
t
,
∀
h
∈
1
,
⋯
,
H
,
∀
t
∈
1
,
⋯
,
TConstraint (14) relates to production capacity of manufacturing center. Constraint (15) computes the material consumption of manufacturing center. Constraints (16), (17), and (18) are inventory variations of manufacturing center. Constraints (19), (20), and (21) ensure the inventory of raw materials; recovery material and final product are more than safety stock and less than the maximum stock. Constraint (22) ensures that if a technology is selected, this technology will be used in all decision-making periods.


#### 4.5.3. Distribution Center Constraints

(23)
I
d
t
-
1
+
∑
v
=
1
V
Q
F
d
v
t
=
I
d
t
+
∑
c
=
1
C
∑
v
=
1
V
Q
d
c
v
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(24)
Y
d
t
I
_
d
t
≤
I
d
t
≤
Y
d
t
I
-
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(25)
∑
v
=
1
V
Q
F
d
v
t
+
∑
c
=
1
C
∑
v
=
1
V
Q
d
c
v
t
≤
D
-
d
t
Y
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(26)
Y
d
t
-
1
≤
Y
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
TConstraint (23) shows the inventory variation of distribution center. Constraints (24) and (25) relate to the inventory and distribution capacity of distribution center. Constraint (26) ensures that if a distribution center is selected, this distribution center will be used in entire periods.


#### 4.5.4. Market Constraint

(27)
∑
d
=
1
D
∑
v
=
1
V
Q
d
c
v
t
=
D
E
c
t
,
∀
c
∈
1
,
⋯
,
C
,
∀
t
∈
1
,
⋯
,
TConstraint (27) expresses the demand of each market.


#### 4.5.5. Recycling Center Constraint

(28)
∑
r
=
1
R
∑
v
=
1
V
Q
c
r
v
t
=
θ
t
D
E
c
t
,
∀
c
∈
1
,
⋯
,
C
,
∀
t
∈
1
,
⋯
,
T
(29)
I
r
t
-
1
+
∑
c
=
1
C
∑
v
=
1
V
Q
c
r
v
t
=
I
r
t
+
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(30)
I
r
j
t
-
1
+
Q
r
j
t
=
I
r
j
t
+
∑
v
=
1
V
Q
F
r
j
v
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(31)
Y
r
t
I
_
r
t
≤
I
r
t
≤
Y
r
t
I
-
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(32)
Y
r
t
I
_
r
j
t
≤
I
r
j
t
≤
Y
r
t
I
-
r
j
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(33)
D
r
t
=
β
r
t
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(34)
Q
r
j
t
=
∑
h
=
1
H
γ
h
j
Y
h
t
1
-
β
r
t
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(35)
Q
r
t
≤
R
-
r
t
Y
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(36)
Y
r
t
-
1
≤
Y
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
TConstraint (28) calculates the quantity of returned product. Constraints (29) and (30) show the inventory variation of recycling center. Constraints (31) and (32) relate to the inventory capacity of recycling center. Constraint (33) determines the quantity of discarded materials. Constraint (34) calculates the quantity of recovery material. Constraint (35) ensures the recovery capacity of recycling center. Constraint (36) ensures that if a recycling center is selected, it will be used for the entire periods.


#### 4.5.6. Initial Settings

(37)
I
i
0
=
0
,
I
j
0
=
0
,
I
0
=
0
,
I
d
0
=
0
,
I
r
0
=
0
,
I
r
j
0
=
0
∀
i
∈
1
,
⋯
,
I
,
∀
j
∈
1
,
⋯
,
J
,
∀
d
∈
1
,
⋯
,
D
,
∀
r
∈
1
,
⋯
,
RConstraint (37) shows that the initial value of related decision variables is 0.


#### 4.5.7. Binary Variables

(38)
Y
s
i
t
,
Y
F
s
v
t
,
Y
F
r
v
t
,
Y
h
t
,
Y
d
t
,
Y
F
d
v
t
,
Y
d
c
v
t
,
Y
r
t
,
Y
c
r
v
t
are  binary  variableConstraint (38) ensures that the variables are binary variable.


## 4.1. Notations

In this part, we first define the decision variable, and Appendix gives the parametersDecision Variables in Procurement Process
Y
s
i
t: 0-1 variable, in period t, if the supplier s supplies raw material i, the value of this variable is 1; otherwise the value of the variable is 0.
Y
F
s
v
t: 0-1 variable, in period t, if the raw materials are transported by transport v from supplier s to manufacturing center, the value of the variable is 1, otherwise the value of the variable is 0.
Y
F
r
v
t: The 0-1 variable. in period t, if the vehicle v is used to transport the recovered materials from the recycling center r to the manufacturing center, the value of the variable is 1, otherwise the value of the variable is 0.
Q
F
s
i
v
t: In period t, the total transport volume of raw material i transported from supplier s to manufacturing center using vehicle v.
Q
F
r
j
v
t: In period t, the total transport volume of recovered materials j transported from recycling center r to manufacturing center using vehicle v.Decision Variables in Manufacturing Process
Y
h
t: 0-1 variable, in period t, if the technology h is chosen for production, the value of the variable is 1; otherwise the value of the variable is 0.
Q
i
t: In period t, the total amount of raw material i consumed by the production.
Q
j
t: In period t, the total amount of recovered material j consumed by the production.
Q
h
t: In period t, produce or assemble the output of the product using technology h
I
i
t: In period t, the inventory of raw material i of manufacturing center.
I
j
t: In period t, the inventory of recovered material j of manufacturing center.
I
t: In period t, the inventory of final product of manufacturing center.Decision Variables in Distribution Process
Y
d
t: 0-1 variable, in period t, if the distribution center d is selected for product distribution, the value of the variable is 1,; otherwise the value of the variable is 0.
I
d
t: In period t, the inventory of finished product of distribution center d.
Y
F
d
v
t: 0-1 variable, in period t, if the vehicle v is used to transport the finished product from the manufacturing center to the distribution center d, the value of the variable is 1, otherwise the value of the variable is 0.
Y
d
c
v
t: 0-1 variable, in period t, if the final product is transported by vehicle v from the distribution center d to the market c, the value of the variable is 1, otherwise the value of the variable is 0.
Q
F
d
v
t: In period t, the total transport volume of finished product from the manufacturing center to the distribution center d transported by vehicle v
Q
d
c
v
t: In period t, the total transport volume of the final product transported by vehicle v from the distribution center d to market c.Decision Variables in Recycling Process
Y
r
t: 0-1 variable, in period t, if the recycling center r is selected for material recovery, the value of the variable is 1; otherwise the value of the variable is 0.
Q
r
t: In period t, the total amount of returned products processed in the recycling center r during the current period.
D
r
t: In period t, the total amount of recycled products discarded directly in the recycling center r
Q
r
j
t: In period t, the total amount of recycled material j recovered from the recycling center r
I
r
t: In period t, the inventory of returned product of recycling center r
I
r
j
t: In period t, the inventory of recovered material j of recycling center r
Y
c
r
v
t: 0-1 variable, in period t, if the returns are transported by vehicle v from market c to recycling center r, the value of the variable is 1, otherwise the value of the variable is 0.
Q
c
r
v
t: in period t, the total quantity of returned goods transported from recycling center r by vehicle v


## 4.2. Operating Cost Function

The operating cost function (1) consists of four major components: procurement cost (PC), manufacturing cost (MC), distribution cost (DC), and recovery cost (RC). (1)
F
1
=
P
C
+
M
C
+
D
C
+
R
CProcurement cost function (2) measures costs related to new and recovered PET chips. The first part is fixed ordering cost, second and third parts are purchasing cost, and fourth and fifth parts are transportation cost.(2)
P
C
=
∑
s
=
1
S
∑
i
=
1
I
∑
t
=
1
T
O
C
s
i
t
Y
s
i
t
+
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
P
s
i
t
Q
F
s
i
v
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
v
=
1
V
∑
t
=
1
T
P
r
j
t
Q
F
r
j
v
t
+
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
F
s
Q
F
s
i
v
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
F
r
Q
F
r
j
v
tManufacturing cost function (3) refers to the cost incurred in the production process. The first part is fixed operating cost of manufacturing center, second part is fixed investment cost of production line, third part is the variable production cost of the product, the fourth, fifth, and sixth parts are inventory cost of raw material, recovery material, and final product in manufacturing center.(3)
M
C
=
∑
t
=
1
T
F
O
t
+
∑
h
=
1
H
∑
t
=
1
T
F
C
h
t
Y
h
t
+
∑
h
=
1
H
∑
t
=
1
T
V
C
h
t
Q
h
t
+
∑
i
=
1
I
∑
t
=
1
T
H
i
t
I
i
t
+
∑
j
=
1
J
∑
t
=
1
T
H
j
t
I
j
t
+
∑
t
=
1
T
H
t
I
tDistribution cost function (4) refers to the cost of distributing finished products from manufacturing centers to markets. The first part is fixed operating cost of distribution center, the second part is distribution cost of product, the third part is transportation cost of final products between manufacturing and distribution center, and the fourth item is the transportation cost of finished products between distribution center and market.(4)
D
C
=
∑
d
=
1
D
∑
t
=
1
T
F
O
d
t
Y
d
t
+
∑
d
=
1
D
∑
t
=
1
T
V
C
d
t
I
d
t
+
∑
d
=
1
D
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
F
d
Q
F
d
v
t
+
∑
d
=
1
D
∑
c
=
1
C
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
d
c
Q
d
c
v
tRecycling cost function (5) refers to the cost of recovered returns and the cost of discarded unusable recycled materials. The first item is fixed operating cost of recycling center, the second item is purchasing cost of returned product, the third item is discarding cost of returned product, the fourth item is recovery cost of material, the fifth item is inventory cost of returned product at recycling center, the sixth item is inventory cost of recovery material at recycling center, and the seventh item is transportation cost of returned product between market and recycling center.(5)
R
C
=
∑
r
=
1
R
∑
t
=
1
T
F
O
r
t
Y
r
t
+
∑
r
=
1
R
∑
v
=
1
V
∑
t
=
1
T
P
r
t
Q
C
r
v
t
+
∑
r
=
1
R
∑
t
=
1
T
V
C
D
r
t
D
r
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
t
=
1
T
V
C
r
j
t
Q
r
j
t
+
∑
r
=
1
R
∑
t
=
1
T
H
r
t
I
r
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
t
=
1
T
H
r
j
t
I
r
j
t
+
∑
c
=
1
C
∑
r
=
1
R
∑
v
=
1
V
∑
t
=
1
T
V
C
v
t
L
c
r
Q
c
r
v
t


## 4.3. Carbon Emission Function

The carbon emission function (6) consists of four major components: procurement carbon emission (PE), manufacturing carbon emission (ME), distribution carbon emission (DE), and recycling carbon emission (RE).(6)
F
2
=
P
E
+
M
E
+
D
E
+
R
EProcurement carbon emissions function (7) measures the carbon emissions related to acquisition of new and recovered material. The first item is initial carbon footprint of raw material, second item is transportation carbon emission of raw material from supplier to manufacturing center, and third item is transportation carbon emission of recovery material from recycling center to manufacturing center.(7)
P
E
=
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
C
O
s
i
t
Q
F
s
i
v
t
+
∑
s
=
1
S
∑
i
=
1
I
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
F
s
Q
F
s
i
v
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
F
r
Q
F
r
j
v
tThe manufacturing carbon emission function (8) is the carbon emission in manufacturing process; it is equal to the total production of products multiplied by the unit carbon emissions. (8)
M
E
=
∑
h
=
1
H
∑
t
=
1
T
C
O
h
t
Q
h
tThe distribution carbon emission function (9) is the carbon emission of distributing final product from manufacturing center to distribution center and from distribution center to market. The first item is transportation carbon emission of final product from manufacturing center to distribution center, and the second item is transportation carbon emission of final products from distribution center to market.(9)
D
E
=
∑
d
=
1
D
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
F
d
Q
F
d
v
t
+
∑
d
=
1
D
∑
c
=
1
C
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
d
c
Q
d
c
v
tThe recycling carbon emission function (10) is the carbon emission in recycling process. The first item is carbon emission of discarding the product at recycling center, the second item is carbon emission of material recovery, and the third item is transportation carbon emission of returned product from market to recycling center.(10)
R
E
=
∑
r
=
1
R
∑
t
=
1
T
C
O
D
r
t
D
r
t
+
∑
r
=
1
R
∑
j
=
1
J
∑
t
=
1
T
C
O
r
j
t
Q
r
j
t
+
∑
c
=
1
C
∑
r
=
1
R
∑
v
=
1
V
∑
t
=
1
T
C
O
v
t
L
c
r
Q
c
r
v
t


## 4.4. Objective Function

Performance of SSC can be evaluated from two aspects: economics and environment. In order to unify the two different goals, we introduce a parameter, the price of carbonP
c
e, to transform the carbon emission function into carbon emission cost function. Then, the objective function becomes(11)
min
⁡
Z
=
F
1
+
P
c
e
F
2


## 4.5. Constraints

### 4.5.1. Supplier Constraints

(12)
∑
v
=
1
V
Q
F
s
i
v
t
≤
S
-
s
i
t
Y
s
i
t
,
∀
s
∈
1
,
⋯
,
S
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(13)
Y
s
i
t
-
1
≤
Y
s
i
t
,
∀
s
∈
1
,
⋯
,
S
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
TConstraint (12) shows the capacity of supplier. Constraint (13) ensures that if a supplier is selected, the manufacturer will cooperate with this supplier in all decision-making periods.


### 4.5.2. Manufacturing Center Constraints

(14)
Q
h
t
≤
Q
-
h
t
Y
h
t
,
∀
h
∈
1
,
⋯
,
H
,
∀
t
∈
1
,
⋯
,
T
(15)
Q
i
t
+
Q
j
t
=
∑
h
=
1
H
α
h
i
Q
h
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(16)
I
i
t
-
1
+
∑
s
=
1
S
∑
v
=
1
V
Q
F
s
i
v
t
=
I
i
t
+
Q
i
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(17)
I
j
t
-
1
+
∑
r
=
1
R
∑
v
=
1
V
Q
F
r
j
v
t
=
I
j
t
+
Q
j
t
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(18)
I
t
-
1
+
∑
h
=
1
H
Q
h
t
=
I
t
+
∑
d
=
1
D
∑
v
=
1
V
Q
F
d
v
t
,
∀
t
∈
1
,
⋯
,
T
(19)
I
_
i
t
≤
I
i
t
≤
I
-
i
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(20)
I
_
j
t
≤
I
j
t
≤
I
-
j
t
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(21)
I
_
t
≤
I
t
≤
I
-
t
,
∀
t
∈
1
,
⋯
,
T
(22)
Y
h
t
-
1
≤
Y
h
t
,
∀
h
∈
1
,
⋯
,
H
,
∀
t
∈
1
,
⋯
,
TConstraint (14) relates to production capacity of manufacturing center. Constraint (15) computes the material consumption of manufacturing center. Constraints (16), (17), and (18) are inventory variations of manufacturing center. Constraints (19), (20), and (21) ensure the inventory of raw materials; recovery material and final product are more than safety stock and less than the maximum stock. Constraint (22) ensures that if a technology is selected, this technology will be used in all decision-making periods.


### 4.5.3. Distribution Center Constraints

(23)
I
d
t
-
1
+
∑
v
=
1
V
Q
F
d
v
t
=
I
d
t
+
∑
c
=
1
C
∑
v
=
1
V
Q
d
c
v
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(24)
Y
d
t
I
_
d
t
≤
I
d
t
≤
Y
d
t
I
-
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(25)
∑
v
=
1
V
Q
F
d
v
t
+
∑
c
=
1
C
∑
v
=
1
V
Q
d
c
v
t
≤
D
-
d
t
Y
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(26)
Y
d
t
-
1
≤
Y
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
TConstraint (23) shows the inventory variation of distribution center. Constraints (24) and (25) relate to the inventory and distribution capacity of distribution center. Constraint (26) ensures that if a distribution center is selected, this distribution center will be used in entire periods.


### 4.5.4. Market Constraint

(27)
∑
d
=
1
D
∑
v
=
1
V
Q
d
c
v
t
=
D
E
c
t
,
∀
c
∈
1
,
⋯
,
C
,
∀
t
∈
1
,
⋯
,
TConstraint (27) expresses the demand of each market.


### 4.5.5. Recycling Center Constraint

(28)
∑
r
=
1
R
∑
v
=
1
V
Q
c
r
v
t
=
θ
t
D
E
c
t
,
∀
c
∈
1
,
⋯
,
C
,
∀
t
∈
1
,
⋯
,
T
(29)
I
r
t
-
1
+
∑
c
=
1
C
∑
v
=
1
V
Q
c
r
v
t
=
I
r
t
+
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(30)
I
r
j
t
-
1
+
Q
r
j
t
=
I
r
j
t
+
∑
v
=
1
V
Q
F
r
j
v
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(31)
Y
r
t
I
_
r
t
≤
I
r
t
≤
Y
r
t
I
-
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(32)
Y
r
t
I
_
r
j
t
≤
I
r
j
t
≤
Y
r
t
I
-
r
j
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(33)
D
r
t
=
β
r
t
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(34)
Q
r
j
t
=
∑
h
=
1
H
γ
h
j
Y
h
t
1
-
β
r
t
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(35)
Q
r
t
≤
R
-
r
t
Y
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(36)
Y
r
t
-
1
≤
Y
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
TConstraint (28) calculates the quantity of returned product. Constraints (29) and (30) show the inventory variation of recycling center. Constraints (31) and (32) relate to the inventory capacity of recycling center. Constraint (33) determines the quantity of discarded materials. Constraint (34) calculates the quantity of recovery material. Constraint (35) ensures the recovery capacity of recycling center. Constraint (36) ensures that if a recycling center is selected, it will be used for the entire periods.


### 4.5.6. Initial Settings

(37)
I
i
0
=
0
,
I
j
0
=
0
,
I
0
=
0
,
I
d
0
=
0
,
I
r
0
=
0
,
I
r
j
0
=
0
∀
i
∈
1
,
⋯
,
I
,
∀
j
∈
1
,
⋯
,
J
,
∀
d
∈
1
,
⋯
,
D
,
∀
r
∈
1
,
⋯
,
RConstraint (37) shows that the initial value of related decision variables is 0.


### 4.5.7. Binary Variables

(38)
Y
s
i
t
,
Y
F
s
v
t
,
Y
F
r
v
t
,
Y
h
t
,
Y
d
t
,
Y
F
d
v
t
,
Y
d
c
v
t
,
Y
r
t
,
Y
c
r
v
t
are  binary  variableConstraint (38) ensures that the variables are binary variable.


## 4.5.1. Supplier Constraints

(12)
∑
v
=
1
V
Q
F
s
i
v
t
≤
S
-
s
i
t
Y
s
i
t
,
∀
s
∈
1
,
⋯
,
S
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(13)
Y
s
i
t
-
1
≤
Y
s
i
t
,
∀
s
∈
1
,
⋯
,
S
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
TConstraint (12) shows the capacity of supplier. Constraint (13) ensures that if a supplier is selected, the manufacturer will cooperate with this supplier in all decision-making periods.


## 4.5.2. Manufacturing Center Constraints

(14)
Q
h
t
≤
Q
-
h
t
Y
h
t
,
∀
h
∈
1
,
⋯
,
H
,
∀
t
∈
1
,
⋯
,
T
(15)
Q
i
t
+
Q
j
t
=
∑
h
=
1
H
α
h
i
Q
h
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(16)
I
i
t
-
1
+
∑
s
=
1
S
∑
v
=
1
V
Q
F
s
i
v
t
=
I
i
t
+
Q
i
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(17)
I
j
t
-
1
+
∑
r
=
1
R
∑
v
=
1
V
Q
F
r
j
v
t
=
I
j
t
+
Q
j
t
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(18)
I
t
-
1
+
∑
h
=
1
H
Q
h
t
=
I
t
+
∑
d
=
1
D
∑
v
=
1
V
Q
F
d
v
t
,
∀
t
∈
1
,
⋯
,
T
(19)
I
_
i
t
≤
I
i
t
≤
I
-
i
t
,
∀
i
∈
1
,
⋯
,
I
,
∀
t
∈
1
,
⋯
,
T
(20)
I
_
j
t
≤
I
j
t
≤
I
-
j
t
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(21)
I
_
t
≤
I
t
≤
I
-
t
,
∀
t
∈
1
,
⋯
,
T
(22)
Y
h
t
-
1
≤
Y
h
t
,
∀
h
∈
1
,
⋯
,
H
,
∀
t
∈
1
,
⋯
,
TConstraint (14) relates to production capacity of manufacturing center. Constraint (15) computes the material consumption of manufacturing center. Constraints (16), (17), and (18) are inventory variations of manufacturing center. Constraints (19), (20), and (21) ensure the inventory of raw materials; recovery material and final product are more than safety stock and less than the maximum stock. Constraint (22) ensures that if a technology is selected, this technology will be used in all decision-making periods.


## 4.5.3. Distribution Center Constraints

(23)
I
d
t
-
1
+
∑
v
=
1
V
Q
F
d
v
t
=
I
d
t
+
∑
c
=
1
C
∑
v
=
1
V
Q
d
c
v
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(24)
Y
d
t
I
_
d
t
≤
I
d
t
≤
Y
d
t
I
-
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(25)
∑
v
=
1
V
Q
F
d
v
t
+
∑
c
=
1
C
∑
v
=
1
V
Q
d
c
v
t
≤
D
-
d
t
Y
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
T
(26)
Y
d
t
-
1
≤
Y
d
t
,
∀
d
∈
1
,
⋯
,
D
,
∀
t
∈
1
,
⋯
,
TConstraint (23) shows the inventory variation of distribution center. Constraints (24) and (25) relate to the inventory and distribution capacity of distribution center. Constraint (26) ensures that if a distribution center is selected, this distribution center will be used in entire periods.


## 4.5.4. Market Constraint

(27)
∑
d
=
1
D
∑
v
=
1
V
Q
d
c
v
t
=
D
E
c
t
,
∀
c
∈
1
,
⋯
,
C
,
∀
t
∈
1
,
⋯
,
TConstraint (27) expresses the demand of each market.


## 4.5.5. Recycling Center Constraint

(28)
∑
r
=
1
R
∑
v
=
1
V
Q
c
r
v
t
=
θ
t
D
E
c
t
,
∀
c
∈
1
,
⋯
,
C
,
∀
t
∈
1
,
⋯
,
T
(29)
I
r
t
-
1
+
∑
c
=
1
C
∑
v
=
1
V
Q
c
r
v
t
=
I
r
t
+
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(30)
I
r
j
t
-
1
+
Q
r
j
t
=
I
r
j
t
+
∑
v
=
1
V
Q
F
r
j
v
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(31)
Y
r
t
I
_
r
t
≤
I
r
t
≤
Y
r
t
I
-
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(32)
Y
r
t
I
_
r
j
t
≤
I
r
j
t
≤
Y
r
t
I
-
r
j
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(33)
D
r
t
=
β
r
t
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(34)
Q
r
j
t
=
∑
h
=
1
H
γ
h
j
Y
h
t
1
-
β
r
t
Q
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
j
∈
1
,
⋯
,
J
,
∀
t
∈
1
,
⋯
,
T
(35)
Q
r
t
≤
R
-
r
t
Y
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
T
(36)
Y
r
t
-
1
≤
Y
r
t
,
∀
r
∈
1
,
⋯
,
R
,
∀
t
∈
1
,
⋯
,
TConstraint (28) calculates the quantity of returned product. Constraints (29) and (30) show the inventory variation of recycling center. Constraints (31) and (32) relate to the inventory capacity of recycling center. Constraint (33) determines the quantity of discarded materials. Constraint (34) calculates the quantity of recovery material. Constraint (35) ensures the recovery capacity of recycling center. Constraint (36) ensures that if a recycling center is selected, it will be used for the entire periods.


## 4.5.6. Initial Settings

(37)
I
i
0
=
0
,
I
j
0
=
0
,
I
0
=
0
,
I
d
0
=
0
,
I
r
0
=
0
,
I
r
j
0
=
0
∀
i
∈
1
,
⋯
,
I
,
∀
j
∈
1
,
⋯
,
J
,
∀
d
∈
1
,
⋯
,
D
,
∀
r
∈
1
,
⋯
,
RConstraint (37) shows that the initial value of related decision variables is 0.


## 4.5.7. Binary Variables

(38)
Y
s
i
t
,
Y
F
s
v
t
,
Y
F
r
v
t
,
Y
h
t
,
Y
d
t
,
Y
F
d
v
t
,
Y
d
c
v
t
,
Y
r
t
,
Y
c
r
v
t
are  binary  variableConstraint (38) ensures that the variables are binary variable.


## 5. Computational Results

For illustration and evaluation purposes, two periods of decision-making are considered. The price of carbon is 40 yuan/ton with reference to the EU’s price of carbon emission rights. Other relevant parameters are given in the Appendix. LINGO 11.0 is used to solve the problem. Supply chain network structure is shown in Figure4.Figure 4
Supply chain network structure for the case.


### 5.1. Procurement Decisions

Considering the problem of selecting new PET supplier, Jiangsu supplier is selected, not Xiamen supplier, due to the following reasons. Although Jiangsu supplier is farther than Xiamen supplier to Corporation C, and hence carbon emission, transportation cost, and initial carbon footprint of Jiangsu supplier are higher than that of Xiamen supplier, but the price of Jiangsu supplier is lower than Xiamen supplier; lower procurement cost can make up for the higher initial carbon footprint, higher transportation cost and carbon emission. Table1 depicts the procurement volume of raw materials and recovery PET chip is greater than zero. Although the initial carbon footprint of new PET chip is lower than that of recovery PET chip, new PET chip is more expensive than recovery PET chip. Savings from carbon emission cost of purchasing a new PET chip are lower than the savings from procurement cost of purchasing recovered PET chips, so Corporation C will purchase recovered PET chips as more as possible.Table 1
Procurement plan of raw materials and recovery materials (ten thousand tons).
Period
New PET chip (Jiangsu)
Recovery PET chip (Xiamen)
1
0.1214
0.0042
2
0.1112
0.0118Table2 shows that ship will be chosen if plane, ship, truck, and van are given between Jiangsu supplier and the Corporation C; truck will be chosen if truck and van are given between Corporation C and Xiamen Recycling Center. Analyzing this phenomenon, the transportation cost and carbon emission of the plane, truck, and van are higher than that of ship, so ship is the best choice without considering the transportation time. The unit transportation cost of truck is lower than that of van, but the carbon emission of truck is higher than that of van, because the price of carbon is not high. The cost saving of carbon emission using van is lower than the increasing transportation cost using truck. So truck is better than van considering transportation cost and carbon emission.Table 2
The selection of vehicle and traffic volume about materials in each period (ten thousand tons).
Period
Vehicle
Traffic volume
From new PET chip supplier (Jiangsu) to Corporation C
Period 1
ship
0.1214
Period 2
ship
0.1112
From recycling center (Xiamen) to Corporation C
Period 1
truck
0.0042
Period 2
truck
0.0118


### 5.2. Manufacturing Decisions

Technology 5 is chosen in the manufacturing process. Figure5(a) shows recovery cost, distribution cost, manufacturing cost, procurement cost, and total operating cost of different technologies. Figure 5(a) shows the total operating cost of supply chain declines from Technology 1 to Technology 5. On the other hand, Figure 5(b) shows total carbon emission of Technology 4 and Technology 5 is higher than that of Technologies 1, 2, and 3. Table 3 shows the consumption of materials and manufacturing plan in each period. Table 4 is the inventory plan of product and material in manufacturing center in each period.Table 3
Consumption of materials and manufacturing plan in each period.
Period
New PET chip(Jiangsu)(Ten thousand tons)
Recovery PET chip(Xiamen)(Ten thousand tons)
Final product(Ten thousand)
1
0.1014
0.001
3200
2
0.1062
0.009
3600Table 4
Inventory plan of material in manufacturing center in each period.
Period
New PET chip(Jiangsu)(Ten thousand tons)
Recovery PET chip(Xiamen)(Ten thousand tons)
1
0.02
0.0032
2
0.025
0.006Figure 5
(a)
Recovery cost, distribution cost, manufacturing cost procurement cost, and total operating cost with different technology
(b)
Recycling, distribution, manufacturing, procurement carbon emission, and total carbon emission with different technology


### 5.3. Distribution Decisions

In the distribution process, Quanzhou Distribution Center is selected. Although Xiamen distribution center is closer to Corporation C than Quanzhou Distribution Center, fixed operating cost and unit distribution cost of Xiamen distribution center are higher than that of Quanzhou Distribution Center. The lower operating cost of Quanzhou Distribution Center can make up for the higher transportation cost and transportation carbon emission, so Quanzhou Distribution Center is selected. Table5 shows the inventory of product in distribution center in each period. Table 6 shows that truck will be chosen if truck and van are given from the distribution center to market. The analysis of this selection is the same as Table 2.Table 5
Inventory of product in distribution center in each period (ten thousand).
Period
1
2
inventory
1200
1300Table 6
Selection of vehicle and traffic volume about product in each period (ten thousand).
Vehicle
Traffic volume
From Corporation C to distribution center (Quanzhou)
Period 1
truck
3200
Period 2
truck
3600
From distribution center(Quanzhou) to market
Period 1
truck
2000
Period 2
truck
3500


### 5.4. Recovery Decisions

In the recovery, Xiamen Recycling Center is selected. There are some reasons leading to this phenomenon. Although the discarding carbon emission of returned product and regeneration carbon emission of recovery material of Xiamen Recycling Center are higher than that of Fuzhou recycling center, the operating cost, the price of recovery PET chip, the fixed operation cost, the purchase cost of returned product, and discarding cost of Xiamen Recycling Center are lower than that of Fuzhou recycling center. Lower operating cost can make up for higher carbon emission. So Xiamen Recycling Center is better than Fuzhou recycling center.Tables7 and 8 show that the inventory of recovered PET chips and returned products is equal to the safety stock (see Tables 18 and 19), and the total amounts of returned product which is reprocessed in the current period and recovered PET chip which is regenerated are equal to the maximum value of reprocessing capability. There are several reasons for this phenomenon. (1) If the inventory of recovery PET chip and returned product are lower, the inventory cost will be less and this also can save more resources and energy. (2) From the analysis of Table 1, Corporation C is encouraged to purchase recovery PET chip in order to meet the demand of Corporation C and obtain high profit. The recycling center should try to reprocess the returned product in current period, which is recycled in current period according to the reprocessing capacity, so that the inventory of returned products is equal to safety stock. Recovered PET chips should be transported to Corporation C as many as possible on the premise of the safety stock in recycling center. Table 9 shows that truck will be chosen if truck and van are given from market to distribution center. The analysis of this selection is the same as Table 2.Table 7
Recovery and processing in each period.
Period
Returned product which is reprocessed in current period(Ten thousand)
Returned product which is discarded(Ten thousand)
Recovery PET chipwhich is regenerated(Ten thousand tons)
1
540
54
0.0078
2
1010
101
0.0145Table 8
Inventory of recovery PET chip and of returned product in recycling center.
Period
Inventory of recovery of PET chip
Inventory of returned product
(Ten thousand tons)
(Ten thousand)
1
0.0036
60
2
0.0063
100Table 9
The selection of vehicle and traffic volume about returned product in each period.
Vehicle
Traffic volume(Ten thousand)
From market to recycling center
Period 1
truck
600
Period 2
truck
1050


## 5.1. Procurement Decisions

Considering the problem of selecting new PET supplier, Jiangsu supplier is selected, not Xiamen supplier, due to the following reasons. Although Jiangsu supplier is farther than Xiamen supplier to Corporation C, and hence carbon emission, transportation cost, and initial carbon footprint of Jiangsu supplier are higher than that of Xiamen supplier, but the price of Jiangsu supplier is lower than Xiamen supplier; lower procurement cost can make up for the higher initial carbon footprint, higher transportation cost and carbon emission. Table1 depicts the procurement volume of raw materials and recovery PET chip is greater than zero. Although the initial carbon footprint of new PET chip is lower than that of recovery PET chip, new PET chip is more expensive than recovery PET chip. Savings from carbon emission cost of purchasing a new PET chip are lower than the savings from procurement cost of purchasing recovered PET chips, so Corporation C will purchase recovered PET chips as more as possible.Table 1
Procurement plan of raw materials and recovery materials (ten thousand tons).
Period
New PET chip (Jiangsu)
Recovery PET chip (Xiamen)
1
0.1214
0.0042
2
0.1112
0.0118Table2 shows that ship will be chosen if plane, ship, truck, and van are given between Jiangsu supplier and the Corporation C; truck will be chosen if truck and van are given between Corporation C and Xiamen Recycling Center. Analyzing this phenomenon, the transportation cost and carbon emission of the plane, truck, and van are higher than that of ship, so ship is the best choice without considering the transportation time. The unit transportation cost of truck is lower than that of van, but the carbon emission of truck is higher than that of van, because the price of carbon is not high. The cost saving of carbon emission using van is lower than the increasing transportation cost using truck. So truck is better than van considering transportation cost and carbon emission.Table 2
The selection of vehicle and traffic volume about materials in each period (ten thousand tons).
Period
Vehicle
Traffic volume
From new PET chip supplier (Jiangsu) to Corporation C
Period 1
ship
0.1214
Period 2
ship
0.1112
From recycling center (Xiamen) to Corporation C
Period 1
truck
0.0042
Period 2
truck
0.0118


## 5.2. Manufacturing Decisions

Technology 5 is chosen in the manufacturing process. Figure5(a) shows recovery cost, distribution cost, manufacturing cost, procurement cost, and total operating cost of different technologies. Figure 5(a) shows the total operating cost of supply chain declines from Technology 1 to Technology 5. On the other hand, Figure 5(b) shows total carbon emission of Technology 4 and Technology 5 is higher than that of Technologies 1, 2, and 3. Table 3 shows the consumption of materials and manufacturing plan in each period. Table 4 is the inventory plan of product and material in manufacturing center in each period.Table 3
Consumption of materials and manufacturing plan in each period.
Period
New PET chip(Jiangsu)(Ten thousand tons)
Recovery PET chip(Xiamen)(Ten thousand tons)
Final product(Ten thousand)
1
0.1014
0.001
3200
2
0.1062
0.009
3600Table 4
Inventory plan of material in manufacturing center in each period.
Period
New PET chip(Jiangsu)(Ten thousand tons)
Recovery PET chip(Xiamen)(Ten thousand tons)
1
0.02
0.0032
2
0.025
0.006Figure 5
(a)
Recovery cost, distribution cost, manufacturing cost procurement cost, and total operating cost with different technology
(b)
Recycling, distribution, manufacturing, procurement carbon emission, and total carbon emission with different technology


## 5.3. Distribution Decisions

In the distribution process, Quanzhou Distribution Center is selected. Although Xiamen distribution center is closer to Corporation C than Quanzhou Distribution Center, fixed operating cost and unit distribution cost of Xiamen distribution center are higher than that of Quanzhou Distribution Center. The lower operating cost of Quanzhou Distribution Center can make up for the higher transportation cost and transportation carbon emission, so Quanzhou Distribution Center is selected. Table5 shows the inventory of product in distribution center in each period. Table 6 shows that truck will be chosen if truck and van are given from the distribution center to market. The analysis of this selection is the same as Table 2.Table 5
Inventory of product in distribution center in each period (ten thousand).
Period
1
2
inventory
1200
1300Table 6
Selection of vehicle and traffic volume about product in each period (ten thousand).
Vehicle
Traffic volume
From Corporation C to distribution center (Quanzhou)
Period 1
truck
3200
Period 2
truck
3600
From distribution center(Quanzhou) to market
Period 1
truck
2000
Period 2
truck
3500


## 5.4. Recovery Decisions

In the recovery, Xiamen Recycling Center is selected. There are some reasons leading to this phenomenon. Although the discarding carbon emission of returned product and regeneration carbon emission of recovery material of Xiamen Recycling Center are higher than that of Fuzhou recycling center, the operating cost, the price of recovery PET chip, the fixed operation cost, the purchase cost of returned product, and discarding cost of Xiamen Recycling Center are lower than that of Fuzhou recycling center. Lower operating cost can make up for higher carbon emission. So Xiamen Recycling Center is better than Fuzhou recycling center.Tables7 and 8 show that the inventory of recovered PET chips and returned products is equal to the safety stock (see Tables 18 and 19), and the total amounts of returned product which is reprocessed in the current period and recovered PET chip which is regenerated are equal to the maximum value of reprocessing capability. There are several reasons for this phenomenon. (1) If the inventory of recovery PET chip and returned product are lower, the inventory cost will be less and this also can save more resources and energy. (2) From the analysis of Table 1, Corporation C is encouraged to purchase recovery PET chip in order to meet the demand of Corporation C and obtain high profit. The recycling center should try to reprocess the returned product in current period, which is recycled in current period according to the reprocessing capacity, so that the inventory of returned products is equal to safety stock. Recovered PET chips should be transported to Corporation C as many as possible on the premise of the safety stock in recycling center. Table 9 shows that truck will be chosen if truck and van are given from market to distribution center. The analysis of this selection is the same as Table 2.Table 7
Recovery and processing in each period.
Period
Returned product which is reprocessed in current period(Ten thousand)
Returned product which is discarded(Ten thousand)
Recovery PET chipwhich is regenerated(Ten thousand tons)
1
540
54
0.0078
2
1010
101
0.0145Table 8
Inventory of recovery PET chip and of returned product in recycling center.
Period
Inventory of recovery of PET chip
Inventory of returned product
(Ten thousand tons)
(Ten thousand)
1
0.0036
60
2
0.0063
100Table 9
The selection of vehicle and traffic volume about returned product in each period.
Vehicle
Traffic volume(Ten thousand)
From market to recycling center
Period 1
truck
600
Period 2
truck
1050


## 6. Sensitivity Analysis

In this section, the impact of related parameters on the SSC design is analyzed for Corporation C.


### 6.1. The Impact of Carbon Emission Price

Table10 summarizes the decisions of supply chain network with different carbon emission prices. Figures 6(a)–6(c) show the impact of carbon price on (a) the total operating and procurement cost, (b) manufacturing, distribution, and recovery cost, and (c) total carbon footprint and carbon emission of procurement, manufacturing, distribution, and recycling, respectively. We can see that if the increasing of carbon price is between 1 and 5 times of the original price, the original price is 40 yuan and the operating cost and carbon emission remain constant. When the increase reaches 6 times, the total operation and distribution cost increase and the total carbon emission of supply chain and the distribution carbon emission decrease, but the other costs and carbon emission do not change. When the increasing reaches 10 times, the total operation and procurement cost increase and the total carbon emission of supply chain and procurement carbon emission decrease, but the other costs and carbon emission remain unchanged. When the increase is between 10 and 12 times of the original price, all are the same as 10 times of original value.Table 10
Decisions of supply chain network with different carbon price.
Carbon price
1,2,…,5 times
6,7,…,9 times
10,11,…,12 times
Supplier of PET chip
Jiangsu
Jiangsu
Xiamen
Manufacturing technology
Technology 5
Technology 5
Technology 5
Distribution center
Quanzhou
Quanzhou
Quanzhou
Recycling center
Xiamen
Xiamen
Xiamen
Vehicle selection
truck
van
van
The percentage of recovery PET chip
6.44%
6.44%
6.44%Figure 6
Impact of carbon price on supply chain network design.
(a)
Total operating cost and procurement cost of the supply chain
(b)
Manufacturing cost, distribution cost, and recovery cost
(c)
Total carbon footprint and the carbon emissions of procurement, manufacturing, distribution, and recyclingManagement Analysis. If the increasing of carbon emission price is between 1 and 5 times, marginal cost of reducing carbon emissions in any part of supply chain is much higher than the expense. Hence, the corporation needs not to change the strategy of current supply chain design. One to 5 times increasing in carbon price will only increase the cost of carbon emission, but have no impact on the total operating cost and carbon emission. If the increasing of carbon price reaches 6 times, the savings in carbon emission cost of using van are more than the savings in transportation cost of using truck. So, under this condition, van should be selected. Distribution process is affected the most because the transportation volume and distance of product in distribution process is very large, and the change of vehicle increases the unit transportation cost and reduces unit carbon emission, so the cost increases and the carbon emission in distribution process decreases greatly. Although the change of vehicle has some impact on procurement and recycling process, lower purchase volume leads to lower transportation volume of raw materials in procurement process, and lower recovery rate leads to lower transportation volume of recovery material for recycling process. Furthermore, since recycling center, corporation, and markets are in the same region, the distance between each other is small. So the proportion of transportation cost of procurement process in total procurement cost, the proportion of transportation carbon emission of procurement process in total procurement carbon emission, the transportation cost of recycling process in total recovery cost, and the transportation emission of the recycling process in total recovery carbon emission are relatively small. Therefore, procurement cost and carbon footprint, recovery cost, and carbon footprint are hardly affected. In addition, the increasing of carbon price 6 times does not change other decisions, so manufacturing cost and carbon emission do not change. Therefore, the total operating cost will increase with the increasing of distribution cost and the total carbon footprint will decrease with the decreasing of distribution carbon emission. When the increasing of carbon price reaches 10 times, the advantage on price of foreign supplier cannot make up higher initial carbon footprint of product, higher procurement cost, and higher transportation carbon emission cost. At this time, the corporation should give up foreign supplier and choose the local supplier. Because the price of raw material from local suppliers is higher and the initial carbon footprint is lower, procurement cost will increase and procurement carbon emission will decrease if the purchase amount does not change. In additional, the 10 times increasing of carbon price does not change in other decisions except procurement. So, the total operating cost will increase with the increasing of procurement cost and the total carbon footprint will decrease with the decreasing of procurement carbon emission.


### 6.2. The Impact of Recovery Rate

Table11 summarizes the decisions of supply chain network with different recovery rates. Figures 7(a) and 7(b) show the impact of recovery rate. As shown, recovery cost increases and procurement cost decreases, but manufacturing cost and distribution costs do not change with the increasing of recovery rate. Moreover, total operating cost first decreases and then increases, total carbon footprint and recycling carbon emission increases, and procurement carbon emission decreases, but the carbon emissions of manufacturing and distribution do not change with the increasing of recovery rate.Table 11
Decisions of supply chain network design with different recovery rates.
Recovery rate
30%
50%
80%
100%
Supplier of PET chip
Jiangsu
Jiangsu
Jiangsu
Jiangsu
Manufacturing technology
Technology 5
Technology 5
Technology 5
Technology 5
Distribution center
Quanzhou
Quanzhou
Quanzhou
Quanzhou
Recycling center
Xiamen
Xiamen
Xiamen
Xiamen
Vehicle selection
truck
truck
truck
truck
The percentage of recovery PET chip
6.44%
12.80%
22.37%
26.26%Figure 7
Impact of recovery rate.
(a)
Total operating cost, procurement cost, manufacturing cost, distribution cost, and recovery cost of the supply chain
(b)
The total carbon footprint and carbon emissions of procurement, manufacturing, distribution, and recyclingManagement Analysis. The first analysis is related to the recycling process. When the demand of product is constant, if the recovery rate increases, the quantity of returned products will increase constantly from market to recycling center which can increase the transportation cost and transportation carbon emission. The saving cost of purchasing recovery material is more than the carbon footprint cost saving of purchasing raw material. Its results show that the demand of recovery material is more than that of raw material. Therefore, the recycling center will change the arrangements of recycling. It is recommended to expand the scale of reprocessing returned products and recovering material in order to satisfy the demand. Expanded recycling and reprocessing lead recovery cost and carbon emission to increase constantly. At last, the cost of recycling process increases constantly with the impact of recovery cost, reprocessing cost, and transportation cost in recycling process. The total carbon emission in recycling process also increases constantly with the impact of the recovery carbon emission, reprocessing carbon emission and transportation carbon emission of returned products. Second analysis is related to procurement process. With recovery material deliverability increasing, corporation will change the procurement proportion between raw material and recovery material. It causes more and more recovery materials to be purchased and relatively less raw materials to be purchased. So this causes purchasing cost of materials to decrease constantly, and the decreasing in the procurement quantity of raw materials leads to a reduction of initial carbon footprint of procurement. On the other hand, the distance between recycling center and corporation is less than the distance between the supplier of raw material and corporation, so this decision causes the transportation cost and transportation of carbon emission decreasing. At last, the total cost in procurement process continuously reduces with the impact of the decreasing of purchasing materials cost and transportation cost. The total carbon emission in procurement process reduces with the increasing of recovery rate under the impact of the decreasing of the initial carbon emission of procurement and the decreasing of transportation carbon emission. Third analysis is related to manufacturing and distribution process. The change of recovery rate does not have any impact on the selection of supplier, manufacturing technology, distribution center, and vehicle, so manufacturing cost and carbon emission, distribution cost, and carbon emission are constant. With regard to the total operating cost, before recovery rate reaches 80%, if recovery rate increases, the increasing of recovery cost is less than the decreasing of procurement cost, so total operating cost will decrease. As recovery rate reaches 80%, if recovery rate increases, the increasing of recovery cost is gradually over reduced in procurement cost, so the total operating cost will increase. Based on the above analysis, when the recovery rate increases, total operating cost decreases first and then increases. With the recovery rate increase, total carbon emission increases constantly.


## 6.1. The Impact of Carbon Emission Price

Table10 summarizes the decisions of supply chain network with different carbon emission prices. Figures 6(a)–6(c) show the impact of carbon price on (a) the total operating and procurement cost, (b) manufacturing, distribution, and recovery cost, and (c) total carbon footprint and carbon emission of procurement, manufacturing, distribution, and recycling, respectively. We can see that if the increasing of carbon price is between 1 and 5 times of the original price, the original price is 40 yuan and the operating cost and carbon emission remain constant. When the increase reaches 6 times, the total operation and distribution cost increase and the total carbon emission of supply chain and the distribution carbon emission decrease, but the other costs and carbon emission do not change. When the increasing reaches 10 times, the total operation and procurement cost increase and the total carbon emission of supply chain and procurement carbon emission decrease, but the other costs and carbon emission remain unchanged. When the increase is between 10 and 12 times of the original price, all are the same as 10 times of original value.Table 10
Decisions of supply chain network with different carbon price.
Carbon price
1,2,…,5 times
6,7,…,9 times
10,11,…,12 times
Supplier of PET chip
Jiangsu
Jiangsu
Xiamen
Manufacturing technology
Technology 5
Technology 5
Technology 5
Distribution center
Quanzhou
Quanzhou
Quanzhou
Recycling center
Xiamen
Xiamen
Xiamen
Vehicle selection
truck
van
van
The percentage of recovery PET chip
6.44%
6.44%
6.44%Figure 6
Impact of carbon price on supply chain network design.
(a)
Total operating cost and procurement cost of the supply chain
(b)
Manufacturing cost, distribution cost, and recovery cost
(c)
Total carbon footprint and the carbon emissions of procurement, manufacturing, distribution, and recyclingManagement Analysis. If the increasing of carbon emission price is between 1 and 5 times, marginal cost of reducing carbon emissions in any part of supply chain is much higher than the expense. Hence, the corporation needs not to change the strategy of current supply chain design. One to 5 times increasing in carbon price will only increase the cost of carbon emission, but have no impact on the total operating cost and carbon emission. If the increasing of carbon price reaches 6 times, the savings in carbon emission cost of using van are more than the savings in transportation cost of using truck. So, under this condition, van should be selected. Distribution process is affected the most because the transportation volume and distance of product in distribution process is very large, and the change of vehicle increases the unit transportation cost and reduces unit carbon emission, so the cost increases and the carbon emission in distribution process decreases greatly. Although the change of vehicle has some impact on procurement and recycling process, lower purchase volume leads to lower transportation volume of raw materials in procurement process, and lower recovery rate leads to lower transportation volume of recovery material for recycling process. Furthermore, since recycling center, corporation, and markets are in the same region, the distance between each other is small. So the proportion of transportation cost of procurement process in total procurement cost, the proportion of transportation carbon emission of procurement process in total procurement carbon emission, the transportation cost of recycling process in total recovery cost, and the transportation emission of the recycling process in total recovery carbon emission are relatively small. Therefore, procurement cost and carbon footprint, recovery cost, and carbon footprint are hardly affected. In addition, the increasing of carbon price 6 times does not change other decisions, so manufacturing cost and carbon emission do not change. Therefore, the total operating cost will increase with the increasing of distribution cost and the total carbon footprint will decrease with the decreasing of distribution carbon emission. When the increasing of carbon price reaches 10 times, the advantage on price of foreign supplier cannot make up higher initial carbon footprint of product, higher procurement cost, and higher transportation carbon emission cost. At this time, the corporation should give up foreign supplier and choose the local supplier. Because the price of raw material from local suppliers is higher and the initial carbon footprint is lower, procurement cost will increase and procurement carbon emission will decrease if the purchase amount does not change. In additional, the 10 times increasing of carbon price does not change in other decisions except procurement. So, the total operating cost will increase with the increasing of procurement cost and the total carbon footprint will decrease with the decreasing of procurement carbon emission.


## 6.2. The Impact of Recovery Rate

Table11 summarizes the decisions of supply chain network with different recovery rates. Figures 7(a) and 7(b) show the impact of recovery rate. As shown, recovery cost increases and procurement cost decreases, but manufacturing cost and distribution costs do not change with the increasing of recovery rate. Moreover, total operating cost first decreases and then increases, total carbon footprint and recycling carbon emission increases, and procurement carbon emission decreases, but the carbon emissions of manufacturing and distribution do not change with the increasing of recovery rate.Table 11
Decisions of supply chain network design with different recovery rates.
Recovery rate
30%
50%
80%
100%
Supplier of PET chip
Jiangsu
Jiangsu
Jiangsu
Jiangsu
Manufacturing technology
Technology 5
Technology 5
Technology 5
Technology 5
Distribution center
Quanzhou
Quanzhou
Quanzhou
Quanzhou
Recycling center
Xiamen
Xiamen
Xiamen
Xiamen
Vehicle selection
truck
truck
truck
truck
The percentage of recovery PET chip
6.44%
12.80%
22.37%
26.26%Figure 7
Impact of recovery rate.
(a)
Total operating cost, procurement cost, manufacturing cost, distribution cost, and recovery cost of the supply chain
(b)
The total carbon footprint and carbon emissions of procurement, manufacturing, distribution, and recyclingManagement Analysis. The first analysis is related to the recycling process. When the demand of product is constant, if the recovery rate increases, the quantity of returned products will increase constantly from market to recycling center which can increase the transportation cost and transportation carbon emission. The saving cost of purchasing recovery material is more than the carbon footprint cost saving of purchasing raw material. Its results show that the demand of recovery material is more than that of raw material. Therefore, the recycling center will change the arrangements of recycling. It is recommended to expand the scale of reprocessing returned products and recovering material in order to satisfy the demand. Expanded recycling and reprocessing lead recovery cost and carbon emission to increase constantly. At last, the cost of recycling process increases constantly with the impact of recovery cost, reprocessing cost, and transportation cost in recycling process. The total carbon emission in recycling process also increases constantly with the impact of the recovery carbon emission, reprocessing carbon emission and transportation carbon emission of returned products. Second analysis is related to procurement process. With recovery material deliverability increasing, corporation will change the procurement proportion between raw material and recovery material. It causes more and more recovery materials to be purchased and relatively less raw materials to be purchased. So this causes purchasing cost of materials to decrease constantly, and the decreasing in the procurement quantity of raw materials leads to a reduction of initial carbon footprint of procurement. On the other hand, the distance between recycling center and corporation is less than the distance between the supplier of raw material and corporation, so this decision causes the transportation cost and transportation of carbon emission decreasing. At last, the total cost in procurement process continuously reduces with the impact of the decreasing of purchasing materials cost and transportation cost. The total carbon emission in procurement process reduces with the increasing of recovery rate under the impact of the decreasing of the initial carbon emission of procurement and the decreasing of transportation carbon emission. Third analysis is related to manufacturing and distribution process. The change of recovery rate does not have any impact on the selection of supplier, manufacturing technology, distribution center, and vehicle, so manufacturing cost and carbon emission, distribution cost, and carbon emission are constant. With regard to the total operating cost, before recovery rate reaches 80%, if recovery rate increases, the increasing of recovery cost is less than the decreasing of procurement cost, so total operating cost will decrease. As recovery rate reaches 80%, if recovery rate increases, the increasing of recovery cost is gradually over reduced in procurement cost, so the total operating cost will increase. Based on the above analysis, when the recovery rate increases, total operating cost decreases first and then increases. With the recovery rate increase, total carbon emission increases constantly.


## 7. Conclusions and Future Research

This paper addressed the design of SSC network with consideration of carbon footprint and proposed a MILP model for optimizing decisions of partner selection, technology selection, vehicle selection, supplies of raw materials, and recovery materials. In general, the SSC design may be influenced by many factors; two key factors are selected, which are the price of carbon emissions and recovery rate. By conducting a sensitivity analysis, we obtained the following insights.A small increasing in carbon price has little impact on SSC network design. When the increasing of carbon price reaches a certain level, the total operating cost, carbon footprint, and decisions of a sustainable supply chain will be greatly affected. So the corporation does not need to make adjustments in the original design of SSC with the modest increase in carbon price. Among all the supply chain design decisions, vehicle selection is the most sensitive to carbon price, followed by the supplier selection decision, whilst the other decisions are not very sensitive. So the corporation should adjust the decision of vehicle selection and supplier selection in time and select a supplier and vehicle with lower carbon emission.With the increasing of recovery rate, the procurement and recycling process are largely affected, whilst manufacturing and distribution process are a little affected. With the increasing of recovery rate, the total operating cost will first increase and then decrease; the total carbon footprint will increase constantly; the total cost will increase first and then decrease considering the two aspects. So when the recovery rate reaches a particular value, the total cost is the least, so recovery rate is not the higher the better. Government should introduce a reasonable recovery policy, and the corporation should develop a suitable recovery rate. The total carbon footprint and carbon emission in recycling process are affected by the increasing of recovery rate. In order to face the risk of carbon emission cost increasing, the recycling center should use more environmentally friendly recycling and reprocessing technology.In the future, we will focus on several issues. Firstly, the external control mechanism should be considered in our model, such as cap-and-trade control for carbon. Secondly, carbon emission in consuming process is not considered in our paper, but carbon emission in consuming process is also very large in some cases, so the impact of carbon emissions in consuming process on SSC design can be further analyzed. Thirdly, we consider only the situation with determinate market demand; further effort is required for SSC design under uncertain demand and return.



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*Source: 3162471-2019-07-04.xml*