# A Green Quality Management Decision Model with Carbon Tax and Capacity Expansion under Activity-Based Costing (ABC)—A Case Study in the Tire Manufacturing Industry

## Abstract

**:**

## 1. Introduction

## 2. Green Quality Management in the Tire Manufacturing Industry

#### 2.1. Green Quality Cost Management

#### 2.2. Production Flow in the Tire Industry

- (1)
- Mixing and Component preparation: First, natural rubber, processed oil, carbon black, and other chemicals are mixed into a compound using a Banbury mixer, which is then squeezed into a thin sheet using extruders. Other components include fabric calendar transferred from textiles and fabric, and wire calendar, steel calendar, bead, and belt transferred from steel.
- (2)
- Tire building: The tire building machine pre-shapes radial tires into a form very close to their final dimensions to make sure the many components are in their proper positions before the tire goes into the mold.
- (3)
- Curing press: The curing press is where tires attain their final shape and tread pattern. Hot molds shape and vulcanize the tire. The molds are then engraved with the tread pattern and sidewall marking.
- (4)
- Tire inspection: Trained inspectors perform a visual inspection to check the tire surfaces. A balance inspection and force variation are then carried out to check uniformity. Finally, some tires are sampled from the production line and X-rayed to detect any hidden weaknesses or internal failures. In addition, quality control engineers regularly perform cut sections and study details of the tire construction that affect performance, ride, or safety [22].

#### 2.3. Shop Flow Control and ABC Costing with the Help of Industry 4.0

#### 2.3.1. Origin and Meaning of Industry 4.0

#### 2.3.2. Collecting Data for ABC Costing Using Industry 4.0 Techniques

## 3. Research Method

#### 3.1. TOC and Capacity Expansion

#### 3.2. Green Quality Cost Measurement under ABC

#### 3.3. Carbon Tax Functions

## 4. Model Formulation

#### 4.1. Assumptions

#### 4.2. Green Quality Management Decision Model under ABC

#### 4.2.1. Notations

_{k}: Total machine cost when the machine hour is expanded to kth level of machine resource, MA

_{K}

_{K}: The machine hour when the machine hour is expanded to kth level of machine resource

#### 4.2.2. The Objective Function

#### 4.2.3. Total Direct Material Cost

_{r}], (TD

_{r},W

_{r}], and (W

_{r},X

_{r}], in which the unit costs are L

_{r}, Ld

_{r}, and Ldd

_{r}, respectively, and ${L}_{r}<L{d}_{r}<Ld{d}_{r}$. The constraints associated with the material cost are shown in Equations (2)–(10).

_{r}, MD

_{r}, and Mdd

_{r}represent the variables of the material purchase quantity in the three ranges of Figure 5. In addition, $N{D}_{r}+S{D}_{r}+O{D}_{r}=1$, and $N{D}_{r},S{D}_{r},O{D}_{r}$ are 0–1 indicator variables which are used to indicate which range the material purchase quantity is in for the optimal solution. For example, if $N{D}_{r}=1$, then $S{D}_{r}=O{D}_{r}=0$ from Equation (10), which indicates the material purchase quantity is in first range of Figure 5. Then, $0\le {M}_{r}\le T{D}_{r}$ from Equations (4) and (5), $M{d}_{r}=Md{d}_{r}=0$ from Equations (6)–(9), and $\sum _{i=1}^{n}{d}_{ir}}{q}_{i}\le {M}_{r$ from Equation (3). Therefore, the total material cost is ${L}_{r}{M}_{r}$ for the material with a purchase discount.

#### 4.2.4. Total Direct Labor Cost

_{1}, with the fixed cost WC

_{1}used no matter how many labor hours the company uses. The labor resources can be expanded to WH

_{2}and WH

_{3}with two different higher wage rates. The total additional labor costs are represented by $(W{C}_{2}-W{C}_{1}){\alpha}_{1}+(W{C}_{3}-W{C}_{1}){\alpha}_{2}$, and the associated constraints are shown in Equations (11)–(16).

#### 4.2.5. Total Rework Cost

#### 4.2.6. Total Maintenance Cost

#### 4.2.7. Total Inspection Cost

#### 4.2.8. Total Waste Disposal Cost

#### 4.2.9. Carbon Tax Expenditure

_{1}< T

_{2}< T

_{3}. In Equation (29), the company’s total carbon emission quantity is $TCQ={\displaystyle \sum _{i=1}^{n}T{A}_{i}}{q}_{i}$ where $T{A}_{i}$ is the carbon emission quantity per unit of product i; and ${A}_{t}{,B}_{t}{,C}_{t}{,D}_{t}$ are the variables of TCQ when it falls within the first, second, third, and fourth range of carbon emission quantity shown in Figure 4, respectively. Also, ${B}_{t},{C}_{t},{D}_{t}$ are the variables of TCQ when it falls within the first, second, and third taxable range of carbon emission quantity whose carbon tax rates are ${T}_{1}$, ${T}_{2}$, and ${T}_{3}$, respectively. In Equation (37), $({G}_{1},{G}_{2},{G}_{3},{G}_{4})$ is an SOS1 set of 0–1 variables, within which exactly one variable must be one, which is a set of 0–1 indicator variables. If ${G}_{1}=1$, then ${G}_{2}={G}_{3}={G}_{4}=0$ from Equation (37), $0\le {A}_{t}\le {G}_{1}{Q}_{1}$ from Equations (30) and (31), and ${B}_{t}={C}_{t}={D}_{t}=0$ from Equations (32)–(36). Thus, TCQ falls within the first range of Figure 4, in which the carbon tax is zero. Similarly, TCQ falls within the second, third, or fourth range of carbon emission quantities in Figure 4 when ${G}_{2}=1$, ${G}_{3}=1$, or ${G}_{4}=1$.

#### 4.2.10. Total Machine Cost

_{0}under the current capacity of MA

_{i}

_{0}machine hours. If tire production requires an expansion of machine hours to MA

_{i}

_{1}, MA

_{i}

_{2}, …, or MA

_{ik}, the total machine cost will increase to MC

_{i}

_{1}, M

_{i}

_{2}, …, or MC

_{ik}, respectively. According to the assumption, the term $\sum _{k=0}^{t}M{C}_{ik}{\theta}_{ik}$ in Equation (1) represents the total machine costs, and the associated constraints are shown in Equations (38) and (39). $({\theta}_{i1},{\theta}_{i2},\dots ,{\theta}_{ik})$ is an SOS1 set of 0–1 variables, within which exactly one variable must be one, which is a set of 0–1 indicator variables. If ${\theta}_{ik}=1$, then the machine hours will be expanded to $M{A}_{ik}{\theta}_{ik}$, i.e., ${H}_{i}{q}_{i}\le M{A}_{k}{\theta}_{k}$, where ${H}_{i}$ is the carbon emission quantity for one unit of product i. Thus, the machine cost will be $M{C}_{ik}{\theta}_{ik}$.

#### 4.2.11. The Complete Model

- Scenario 1: Current Capacity without Carbon Tax. The complete model for Scenario 1 included the objective function, Equation (1), and 28 constraints, Equations (2)–(28), and Equation (38), in which Equation (38) is ${H}_{i}{q}_{i}\le M{A}_{i0}$.
- Scenario 2: Capacity Expansion without Carbon Tax. The complete model for Scenario 2 included the objective function, Equation (1), and Equation (29) constraints, Equations (2)–(28), and Equations (38) and (39).
- Scenario 3: Current Capacity with Carbon Tax. The complete model for Scenario 3 included the objective function, Equation (1), and Equation (37) constraints, Equations (2)–(38), in which Equation (38) is ${H}_{i}{q}_{i}\le M{A}_{i0}$.
- Scenario 4: Capacity Expansion with Carbon Tax. The complete model for Scenario 4 included the objective function, Equation (1), and Equation (38) constraints, Equations (2)–(39).

## 5. Numerical Illustration

#### 5.1. Data and Description of a Numerical Example

#### 5.2. Four Scenario Analyses

#### 5.2.1. Scenario 1: Current Capacity without Carbon Tax

#### 5.2.2. Scenario 2: Capacity Expansion without Carbon Tax

#### 5.2.3. Scenario 3: Current Capacity with Carbon Tax

#### 5.2.4. Scenario 4: Capacity Expansion with Carbon Tax

## 6. Discussion of Results

## 7. Conclusions

- It uses mathematical programming to simultaneously consider material purchase discounts, capacity expansions, capacity constraints, waste disposal, and carbon tax expenditures in order to determine an optimal product-mix decision.
- It uses Activity-Based Costing to consider various levels of activities in order to accurately measure the cost of activities, identify the costs of quality, and identify the costs of value-added and non-value-added activities, which can indicate the possible benefits of improving or eliminating non-value-added activities.
- It successfully formulates the various cost functions in the mathematical programming, such as material quantity discounts, the labor cost with high overtime rates, the piecewise linear waste disposal cost function, the machine cost with capacity expansion, and the carbon tax with full progressive tax rates and a threshold (used in the illustration). In such a way, companies can incorporate various resource expansions into the mathematical programming model to alleviate the workload of post-optimal analysis.

- First, it can provide decision-makers in tire production with the decisions and actions needed to respond to carbon tax policies, and it can provide environmental policy-makers with strategic thinking in policy making.
- Second, it can help enterprises plan new practices for emission reduction and energy saving by combining Activity-based Costing Method and adopting Mathematical Programming Model analysis to create a win-win production method for environmental protection and enterprise profit.

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**The quality management decision model for current capacity without carbon tax (Scenario 1).

$\begin{array}{ll}Max\text{}\pi & =4000\times {q}_{1}+6000\times {q}_{2}+7500\times {q}_{3}-50\times {M}_{r1}-40\times M{d}_{r1}-30\times Md{d}_{r1}-40\times {M}_{r2}-600,000-500,000\times {\alpha}_{1}-1,800,000\times {\alpha}_{2}\\ & -15\times 400\times (B{A}_{1}+B{A}_{2}+B{A}_{3})\xf760\text{}-400\times (50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3})\xf760-300\times (50\times {\delta}_{1}+50\times {\delta}_{2}+50\times {\delta}_{3})\xf760-300\times (8\times {q}_{1}+8\times {q}_{2}+8\times {q}_{3})\xf760\\ & -702.5\times (150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3})\text{}-400,000\times {\beta}_{1}-900,000\times {\beta}_{2}+200,000\times {\beta}_{3}-200,000-300,000-720,000-200,000\end{array}$ | |

Subject to—Direct Material $\begin{array}{l}6\times {q}_{1}+8\times {q}_{2}+10\times {q}_{3}-{M}_{r1}-M{d}_{r1}-Md{d}_{r1}\le 0\\ 2.5\times {q}_{1}+3\times {q}_{2}+4\times {q}_{3}-{M}_{r2}\le 0\\ ND+SD+OD=1\hspace{1em}{M}_{r2}\le 10,000\hspace{1em}{M}_{r2}\ge 0\\ {M}_{r1}\le 10,000\times ND\hspace{1em}M{d}_{r1}\le 20,000\times SD\hspace{1em}Md{d}_{r1}\le 30,000\times OD\\ M{d}_{r1}\ge 10,000\times SD\hspace{1em}Md{d}_{r1}\ge 20,000\times OD\end{array}$ | Subject to—Direct Labour $\begin{array}{l}2\times {q}_{1}+2\times {q}_{2}+3.5\times {q}_{3}-3000-2000\times {\alpha}_{1}-5000\times {\alpha}_{2}\le 0\\ {\alpha}_{0}-{\eta}_{1}\le 0\hspace{1em}{\alpha}_{1}-{\eta}_{1}-{\eta}_{2}\le 0\hspace{1em}{\alpha}_{2}-{\eta}_{2}\le 0\\ {\eta}_{1}+{\eta}_{2}=1\hspace{1em}{\alpha}_{0}+{\alpha}_{1}+{\alpha}_{2}=1\end{array}$ Subject to—Machine Hour $2\times {q}_{1}-2000\le 0\hspace{1em}2\times {q}_{2}-3000\le 0\hspace{1em}3\times {q}_{3}-6000\le 0$ |

Subject to—Inspection $\begin{array}{l}150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3}\le 1000\\ {q}_{1}\le 7000\times {\tau}_{1}\hspace{1em}{q}_{2}\le 4000\times {\tau}_{2}\hspace{1em}{q}_{3}\le 5000\times {\tau}_{3}\end{array}$ Subject to—Waste Disposal $\begin{array}{l}2\times {q}_{1}+3\times {q}_{2}+3\times {q}_{3}-2000{\beta}_{1}-3000\times {\beta}_{2}-5000\times {\beta}_{3}\le 0\\ {\beta}_{0}-{\mu}_{1}\le 0\hspace{1em}{\beta}_{1}-{\mu}_{1}-{\mu}_{2}\le 0\hspace{1em}{\beta}_{2}-{\mu}_{2}-{\mu}_{3}\le 0\hspace{1em}{\beta}_{3}-{\mu}_{3}\le 0\\ {\beta}_{0}+{\beta}_{1}+{\beta}_{2}+{\beta}_{3}=1\hspace{1em}{\mu}_{1}+{\mu}_{2}+{\mu}_{3}=1\end{array}$ | Subject to—Rework $\begin{array}{l}15\times B{A}_{1}+15\times B{A}_{2}+15\times B{A}_{3}+50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3}\le 250\times 60\\ {q}_{1}=B{A}_{1}\times 10\hspace{1em}{q}_{2}=B{A}_{2}\times 4\hspace{1em}{q}_{3}=B{A}_{3}\times 4\end{array}$ Subject to—Maintenance $\begin{array}{l}50{\delta}_{1}+50{\delta}_{2}+50{\delta}_{3}+8{q}_{1}+8{q}_{2}+8{q}_{3}\le 4100\times 60\\ {q}_{1}=5\times {\delta}_{1}\hspace{1em}{q}_{2}=2\times {\delta}_{2}\hspace{1em}{q}_{3}=2\times {\delta}_{3}\end{array}$ |

**Table A2.**The quality management decision model for capacity expansion without carbon tax (Scenario 2).

$\begin{array}{ll}Max\text{}\pi & =4000\times {q}_{1}+6000\times {q}_{2}+7500\times {q}_{3}-50\times {M}_{r1}-40\times M{d}_{r1}-30\times Md{d}_{r1}-40\times {M}_{r2}-600,000-500,000\times {\alpha}_{1}-1,800,000\times {\alpha}_{2}\\ & -15\times 400\times (B{A}_{1}+B{A}_{2}+B{A}_{3})\xf760\text{}-400\times (50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3})\xf760-300\times (50\times {\delta}_{1}+50\times {\delta}_{2}+50\times {\delta}_{3})\xf760-300\times (8\times {q}_{1}+8\times {q}_{2}+8\times {q}_{3})\xf760\\ & -702.5\times (150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3})-400,000\times {\beta}_{1}-900,000\times {\beta}_{2}+200,000\times {\beta}_{3}\\ & -200,000\times {\theta}_{10}-300,000\times {\theta}_{20}-720,000\times {\theta}_{30}-450,000\times {\theta}_{11}-600,000\times {\theta}_{21}-1,200,000\times {\theta}_{31}-1,000,000\times {\theta}_{12}-1,200,000\times {\theta}_{22}-1,800,000\times {\theta}_{32}-200,000\end{array}$ | |

Subject to—Direct Material $\begin{array}{l}6\times {q}_{1}+8\times {q}_{2}+10\times {q}_{3}-{M}_{r1}-M{d}_{r1}-Md{d}_{r1}\le 0\\ 2.5\times {q}_{1}+3\times {q}_{2}+4\times {q}_{3}-{M}_{r2}\le 0\\ ND+SD+OD=1\hspace{1em}{M}_{r2}\le 10,000\hspace{1em}{M}_{r2}\ge 0\\ {M}_{r1}\le 10,000\times ND\hspace{1em}M{d}_{r1}\le 20,000\times SD\hspace{1em}Md{d}_{r1}\le 30,000\times OD\\ M{d}_{r1}\ge 10,000\times SD\hspace{1em}Md{d}_{r1}\ge 20,000\times OD\end{array}$ | Subject to—Direct Labour $\begin{array}{l}2\times {q}_{1}+2\times {q}_{2}+3.5\times {q}_{3}-3000-2000\times {\alpha}_{1}-5000\times {\alpha}_{2}\le 0\\ {\alpha}_{0}-{\eta}_{1}\le 0\hspace{1em}{\alpha}_{1}-{\eta}_{1}-{\eta}_{2}\le 0\hspace{1em}{\alpha}_{2}-{\eta}_{2}\le 0\\ {\eta}_{1}+{\eta}_{2}=1\hspace{1em}{\alpha}_{0}+{\alpha}_{1}+{\alpha}_{2}=1\end{array}$ Subject to—Rework $\begin{array}{l}15\times B{A}_{1}+15\times B{A}_{2}+15\times B{A}_{3}+50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3}\le 250\times 60\\ {q}_{1}=B{A}_{1}\times 10\hspace{1em}{q}_{2}=B{A}_{2}\times 4\hspace{1em}{q}_{3}=B{A}_{3}\times 4\end{array}$ |

Subject to—Inspection $\begin{array}{l}150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3}\le 1000\\ {q}_{1}\le 7000\times {\tau}_{1}\hspace{1em}{q}_{2}\le 4000\times {\tau}_{2}\hspace{1em}{q}_{3}\le 5000\times {\tau}_{3}\end{array}$ Subject to—Waste Disposal $\begin{array}{l}2\times {q}_{1}+3\times {q}_{2}+3\times {q}_{3}-2000{\beta}_{1}-3000\times {\beta}_{2}-5000\times {\beta}_{3}\le 0\\ {\beta}_{0}-{\mu}_{1}\le 0\hspace{1em}{\beta}_{1}-{\mu}_{1}-{\mu}_{2}\le 0\hspace{1em}{\beta}_{2}-{\mu}_{2}-{\mu}_{3}\le 0\hspace{1em}{\beta}_{3}-{\mu}_{3}\le 0\\ {\beta}_{0}+{\beta}_{1}+{\beta}_{2}+{\beta}_{3}=1\hspace{1em}{\mu}_{1}+{\mu}_{2}+{\mu}_{3}=1\end{array}$ | Subject to—Stepwise Machine Hour $\begin{array}{l}2\times {q}_{1}-2000\times {\theta}_{10}-3000\times {\theta}_{11}-5000\times {\theta}_{12}\le 0\hspace{1em}{\theta}_{10}+{\theta}_{11}+{\theta}_{12}=1\\ 2\times {q}_{2}-3000\times {\theta}_{20}-4000\times {\theta}_{21}-6000\times {\theta}_{22}\le 0\hspace{1em}{\theta}_{20}+{\theta}_{21}+{\theta}_{22}=1\\ 3\times {q}_{3}-6000\times {\theta}_{30}-8000\times {\theta}_{31}-9000\times {\theta}_{32}\le 0\hspace{1em}{\theta}_{30}+{\theta}_{31}+{\theta}_{32}=1\end{array}$ Subject to—Maintenance $\begin{array}{l}50{\delta}_{1}+50{\delta}_{2}+50{\delta}_{3}+8{q}_{1}+8{q}_{2}+8{q}_{3}\le 4100\times 60\\ {q}_{1}=5\times {\delta}_{1}\hspace{1em}{q}_{2}=2\times {\delta}_{2}\hspace{1em}{q}_{3}=2\times {\delta}_{3}\end{array}$ |

$\begin{array}{ll}Max\text{}\pi & =4000\times {q}_{1}+6000\times {q}_{2}+7500\times {q}_{3}-50\times {M}_{r1}-40\times M{d}_{r1}-30\times Md{d}_{r1}-40\times {M}_{r2}-600,000-500,000\times {\alpha}_{1}-1,800,000\times {\alpha}_{2}\\ & -15\times 400\times (B{A}_{1}+B{A}_{2}+B{A}_{3})\xf760\text{}-400\times (50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3})\xf760\text{}-300\times (50\times {\delta}_{1}+50\times {\delta}_{2}+50\times {\delta}_{3})\xf760-300\times (8\times {q}_{1}+8\times {q}_{2}+8\times {q}_{3})\xf760\\ & -702.5\times (150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3})-400,000\times {\beta}_{1}-900,000\times {\beta}_{2}+200,000\times {\beta}_{3}-40\times (Bt-10,000)-50\times (Ct-10,000)-60\times (Dt-10,000)\\ & -200,000-300,000-720,000-200,000\end{array}$ | |

Subject to—Direct Material $\begin{array}{l}6\times {q}_{1}+8\times {q}_{2}+10\times {q}_{3}-{M}_{r1}-M{d}_{r1}-Md{d}_{r1}\le 0\\ 2.5\times {q}_{1}+3\times {q}_{2}+4\times {q}_{3}-{M}_{r2}\le 0\\ ND+SD+OD=1\hspace{1em}{M}_{r2}\le 10,000\hspace{1em}{M}_{r2}\ge 0\\ {M}_{r1}\le 10,000\times ND\hspace{1em}M{d}_{r1}\le 20,000\times SD\hspace{1em}Md{d}_{r1}\le 30,000\times OD\\ M{d}_{r1}\ge 10,000\times SD\hspace{1em}Md{d}_{r1}\ge 20,000\times OD\end{array}$ | Subject to—Direct Labour $\begin{array}{l}2\times {q}_{1}+2\times {q}_{2}+3.5\times {q}_{3}-3000-2000\times {\alpha}_{1}-5000\times {\alpha}_{2}\le 0\\ {\alpha}_{0}-{\eta}_{1}\le 0\hspace{1em}{\alpha}_{1}-{\eta}_{1}-{\eta}_{2}\le 0\hspace{1em}{\alpha}_{2}-{\eta}_{2}\le 0\\ {\eta}_{1}+{\eta}_{2}=1\hspace{1em}{\alpha}_{0}+{\alpha}_{1}+{\alpha}_{2}=1\end{array}$ Subject to—Machine hour $2\times {q}_{1}-2000\le 0\hspace{1em}2\times {q}_{2}-3000\le 0\hspace{1em}3\times {q}_{3}-6000\le 0$ |

Subject to—Waste Disposal $\begin{array}{l}2\times {q}_{1}+3\times {q}_{2}+3\times {q}_{3}-2000{\beta}_{1}-3000\times {\beta}_{2}-5000\times {\beta}_{3}\le 0\\ {\beta}_{0}-{\mu}_{1}\le 0\hspace{1em}{\beta}_{1}-{\mu}_{1}-{\mu}_{2}\le 0\hspace{1em}{\beta}_{2}-{\mu}_{2}-{\mu}_{3}\le 0\hspace{1em}{\beta}_{3}-{\mu}_{3}\le 0\\ {\beta}_{0}+{\beta}_{1}+{\beta}_{2}+{\beta}_{3}=1\hspace{1em}{\mu}_{1}+{\mu}_{2}+{\mu}_{3}=1\end{array}$ Subject to—Carbon Tax $\begin{array}{l}20\times {q}_{1}+40\times {q}_{2}+50\times {q}_{3}\le At+Bt+Ct+Dt\\ At\ge 0\hspace{1em}At\le {G}_{1}\times 10,000\hspace{1em}Bt\ge {G}_{2}\times 10,000\hspace{1em}Bt\le {G}_{2}\times 12,000\\ Ct\ge {G}_{3}\times 12,000\hspace{1em}Ct\le {G}_{3}\times 15,000\hspace{1em}Dt\ge {G}_{4}\times 15,000\\ {G}_{1}+{G}_{2}+{G}_{3}+{G}_{4}=1\end{array}$ | Subject to—Rework $\begin{array}{l}15\times B{A}_{1}+15\times B{A}_{2}+15\times B{A}_{3}+50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3}\le 250\times 60\\ {q}_{1}=B{A}_{1}\times 10\hspace{1em}{q}_{2}=B{A}_{2}\times 4\hspace{1em}{q}_{3}=B{A}_{3}\times 4\end{array}$ Subject to—Maintenance $\begin{array}{l}50{\delta}_{1}+50{\delta}_{2}+50{\delta}_{3}+8{q}_{1}+8{q}_{2}+8{q}_{3}\le 4100\times 60\\ {q}_{1}=5\times {\delta}_{1}\hspace{1em}{q}_{2}=2\times {\delta}_{2}\hspace{1em}{q}_{3}=2\times {\delta}_{3}\end{array}$ Subject to—Inspection $\begin{array}{l}150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3}\le 1000\\ {q}_{1}\le 7000\times {\tau}_{1}\hspace{1em}{q}_{2}\le 4000\times {\tau}_{2}\hspace{1em}{q}_{3}\le 5000\times {\tau}_{3}\end{array}$ |

**Table A4.**The quality management decision model for capacity expansion with carbon tax (Scenario 4).

$\begin{array}{ll}Max\text{}\pi & =4000\times {q}_{1}+6000\times {q}_{2}+7500\times {q}_{3}-50\times {M}_{r1}-40\times M{d}_{r1}-30\times Md{d}_{r1}-40\times {M}_{r2}-600,000-500,000\times {\alpha}_{1}-1,800,000\times {\alpha}_{2}-15\times 400\times (B{A}_{1}+B{A}_{2}+B{A}_{3})\xf760\\ & -400\times (50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3})\xf760-300\times (50\times {\delta}_{1}+50\times {\delta}_{2}+50\times {\delta}_{3})\xf760-300\times (8\times {q}_{1}+8\times {q}_{2}+8\times {q}_{3})\xf760\text{}-702.5\times (150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3})\\ & -400,000\times {\beta}_{1}-900,000\times {\beta}_{2}-200,000{\beta}_{3}\text{}-40\times (Bt-10,000)-50\times (Ct-10,000)-60\times (Dt-10,000)-200,000\times {\theta}_{10}-300,000\times {\theta}_{20}-720,000\times {\theta}_{30}\\ & -450,000\times {\theta}_{11}-600,000\times {\theta}_{21}-1,200,000\times {\theta}_{31}-1,000,000\times {\theta}_{12}-1,200,000\times {\theta}_{22}-1,800,000\times {\theta}_{32}-200,000\end{array}$ | |

Subject to—Direct Material $\begin{array}{l}6\times {q}_{1}+8\times {q}_{2}+10\times {q}_{3}-{M}_{r1}-M{d}_{r1}-Md{d}_{r1}\le 0\\ 2.5\times {q}_{1}+3\times {q}_{2}+4\times {q}_{3}-{M}_{r2}\le 0\\ ND+SD+OD=1\hspace{1em}{M}_{r2}\le 10,000\hspace{1em}{M}_{r2}\ge 0\\ {M}_{r1}\le 10,000\times ND\hspace{1em}M{d}_{r1}\le 20,000\times SD\hspace{1em}Md{d}_{r1}\le 30,000\times OD\\ M{d}_{r1}\ge 10,000\times SD\hspace{1em}Md{d}_{r1}\ge 20,000\times OD\end{array}$ | Subject to—Direct Labour $\begin{array}{l}2\times {q}_{1}+2\times {q}_{2}+3.5\times {q}_{3}-3000-2000\times {\alpha}_{1}-5000\times {\alpha}_{2}\le 0\\ {\alpha}_{0}-{\eta}_{1}\le 0\hspace{1em}{\alpha}_{1}-{\eta}_{1}-{\eta}_{2}\le 0\hspace{1em}{\alpha}_{2}-{\eta}_{2}\le 0\\ {\eta}_{1}+{\eta}_{2}=1\hspace{1em}{\alpha}_{0}+{\alpha}_{1}+{\alpha}_{2}=1\end{array}$ Subject to—Rework $\begin{array}{l}15\times B{A}_{1}+15\times B{A}_{2}+15\times B{A}_{3}+50\times B{A}_{1}+55\times B{A}_{2}+60\times B{A}_{3}\le 250\times 60\\ {q}_{1}=B{A}_{1}\times 10\hspace{1em}{q}_{2}=B{A}_{2}\times 4\hspace{1em}{q}_{3}=B{A}_{3}\times 4\end{array}$ |

Subject to—Inspection $\begin{array}{l}150\times {\tau}_{1}+300\times {\tau}_{2}+250\times {\tau}_{3}\le 1000\\ {q}_{1}\le 7000\times {\tau}_{1}\hspace{1em}{q}_{2}\le 4000\times {\tau}_{2}\hspace{1em}{q}_{3}\le 5000\times {\tau}_{3}\end{array}$ Subject to—Waste disposal $\begin{array}{l}2\times {q}_{1}+3\times {q}_{2}+3\times {q}_{3}-2000{\beta}_{1}-3000\times {\beta}_{2}-5000\times {\beta}_{3}\le 0\\ {\beta}_{0}-{\mu}_{1}\le 0\hspace{1em}{\beta}_{1}-{\mu}_{1}-{\mu}_{2}\le 0\hspace{1em}{\beta}_{2}-{\mu}_{2}-{\mu}_{3}\le 0\hspace{1em}{\beta}_{3}-{\mu}_{3}\le 0\\ {\beta}_{0}+{\beta}_{1}+{\beta}_{2}+{\beta}_{3}=1\hspace{1em}{\mu}_{1}+{\mu}_{2}+{\mu}_{3}=1\end{array}$ Subject to—Shipping $\begin{array}{l}50{\delta}_{1}+50{\delta}_{2}+50{\delta}_{3}+8{q}_{1}+8{q}_{2}+8{q}_{3}\le 4100\times 60\\ {q}_{1}=5\times {\delta}_{1}\hspace{1em}{q}_{2}=2\times {\delta}_{2}\hspace{1em}{q}_{3}=2\times {\delta}_{3}\end{array}$ | Subject to—Stepwise Machine Hour $\begin{array}{l}2\times {q}_{1}-2000\times {\theta}_{10}-3000\times {\theta}_{11}-5000\times {\theta}_{12}\le 0\hspace{1em}{\theta}_{10}+{\theta}_{11}+{\theta}_{12}=1\\ 2\times {q}_{2}-3000\times {\theta}_{20}-4000\times {\theta}_{21}-6000\times {\theta}_{22}\le 0\hspace{1em}{\theta}_{20}+{\theta}_{21}+{\theta}_{22}=1\\ 3\times {q}_{3}-6000\times {\theta}_{30}-8000\times {\theta}_{31}-9000\times {\theta}_{32}\le 0\hspace{1em}{\theta}_{30}+{\theta}_{31}+{\theta}_{32}=1\end{array}$ Subject to—Carbon Tax $\begin{array}{l}20\times {q}_{1}+40\times {q}_{2}+50\times {q}_{3}\le At+Bt+Ct+Dt\\ At\ge 0\hspace{1em}At\le {G}_{1}\times 10,000\hspace{1em}Bt\ge {G}_{2}\times 10,000\hspace{1em}Bt\le {G}_{2}\times 12,000\\ Ct\ge {G}_{3}\times 12,000\hspace{1em}Ct\le {G}_{3}\times 15,000\hspace{1em}Dt\ge {G}_{4}\times 15,000\\ {G}_{1}+{G}_{2}+{G}_{3}+{G}_{4}=1\end{array}$ |

## References

- Report of the Conference of the Parties on Its Twenty-First Session. 2015. Available online: http://unfccc.int/resource/docs/2015/cop21/eng/10a01.pdf. (accessed on 11 July 2018).
- Hunter, D. Implications of the Copenhagen Accord for Global Climate Governance. Sustain. Dev. Law Policy
**2010**, 10, 4–15, 56–57. [Google Scholar] - Abas, N.; Kalair, A.R.; Khan, N.; Haider, A.; Saleem, Z.; Saleem, M.S. Natural and synthetic refrigerants, global warming: A review. Renew. Sustain. Energy Rev.
**2018**, 90, 557–569. [Google Scholar] [CrossRef] - Douiri, L.; Jabri, A.; El Barkany, A. Models for optimization of supply chain network design integrating the cost of quality: A literature review. Am. J. Ind. Bus. Manag.
**2016**, 6, 860–876. [Google Scholar] [CrossRef] - García-Pastor, A.; Guirao, B.; López-Lambas, M.E. Quality cost in bus operations based on activity-based costing. Proc. Inst. Civ. Eng. Transp.
**2016**, 169, 107–117. [Google Scholar] [CrossRef] [Green Version] - Ittner, C.D. Activity-based costing concepts for quality improvement. Eur. Manag. J.
**1999**, 17, 492–500. [Google Scholar] [CrossRef] - Khataie, A.H.; Bulgak, A.A. A cost of quality decision support model for lean manufacturing: Activity-based costing application. Int. J. Qual. Reliab. Manag.
**2013**, 30, 751–764. [Google Scholar] [CrossRef] - Özkan, S.; Karaibrahimoǧlu, Y.Z. Activity-based costing approach in the measurement of cost of quality in SMEs: A case study. Total Qual. Manag. Bus. Excell.
**2013**, 24, 420–431. [Google Scholar] [CrossRef] - Tsai, W.-H. Quality cost measurement under activity-based costing. Int. J. Qual. Reliab. Manag.
**1998**, 15, 719–752. [Google Scholar] [CrossRef] - Turney, P.B.B. Common Cents: The ABC Performance Breakthrough—How to Succeed with Activity-Based Costing; McGraw-Hill Education: New York, NY, USA, 2005. [Google Scholar]
- Goldratt, E.M.; Cox, J. The Goal: Excellence in Manufacturing; North River Press: Great Barrington, MA, USA, 1984. [Google Scholar]
- Yi, Y.; Li, J. Cost-Sharing Contracts for Energy Saving and Emissions Reduction of a Supply Chain under the Conditions of Government Subsidies and a Carbon Tax. Sustainability
**2018**, 10, 895. [Google Scholar] - Baranzini, A.; Carattini, S. Effectiveness, earmarking and labeling: testing the acceptability of carbon taxes with survey data. Environ. Econ. Policy Stud.
**2017**, 19, 197–227. [Google Scholar] [CrossRef] [Green Version] - Bhupendra, K.V.; Sangle, S. Pollution Prevention Strategy: A Study of Indian Firms. J. Clean. Prod.
**2016**, 133, 795–802. [Google Scholar] [CrossRef] - Tsai, W.-H.; Yang, C.-H.; Huang, C.-T.; Wu, Y.-Y. The Impact of the Carbon Tax Policy on Green Building Strategy. J. Environ. Plan. Manag.
**2017**, 60, 1412–1438. [Google Scholar] [CrossRef] - Tsai, W.-H.; Chang, J.-C.; Hsieh, C.-L.; Tsaur, T.-S.; Wang, C.-W. Sustainability Concept in Decision-Making: Carbon Tax Consideration for Joint Product Mix Decision. Sustainability
**2016**, 8, 1232. [Google Scholar] [CrossRef] - Revoredo-Giha, C.; Chalmers, N.; Akaichi, F. Simulating the Impact of Carbon Taxes on Greenhouse Gas Emission and Nutrition in the UK. Sustainability
**2018**, 10, 134. [Google Scholar] [CrossRef] - Chopra, A.; Garg, D. Behavior patterns of quality cost categories. TQM J.
**2011**, 23, 510–515. [Google Scholar] [CrossRef] - Chopra, S.; Wu, P.-J. Eco-activities and operating performance in the computer and electronics industry. Eur. J. Oper. Res.
**2016**, 248, 971–981. [Google Scholar] [CrossRef] - Grottke, M.; Schleich, B. Cost Optimality in Testing and Rejuvenation. In Proceedings of the 23rd IEEE International Symposium on Software Reliability Engineering Workshops, Dallas, TX, USA, 27–30 November 2012; pp. 259–264. [Google Scholar]
- Tye, L.H.; Halim, H.A.; Ramayah, T. An exploratory study on cost of quality implementation in Malaysia: The case of Penang manufacturing firms. Total Qual. Manag. Bus. Excell.
**2011**, 22, 1299–1315. [Google Scholar] [CrossRef] - Trongkaew, P.; Utistham, T.; Reubroycharoen, P.; Hinchiranan, N. Photocatalytic Desulfurization of Waste Tire Pyrolysis Oil. Energies
**2011**, 4, 1880–1896. [Google Scholar] [CrossRef] [Green Version] - Yu, H.; Solvang, W.D. Enhancing the Competitiveness of manufacturers through Small-scale Intelligent Manufacturing System (SIMS): A Supply Chain Perspective. In Proceedings of the 6th International Conference on Industrial Technology and Management (ICITM), Cambridge, UK, 7–10 March 2017. [Google Scholar] [CrossRef]
- Blanchet, M.; Rinn, T.; Thaden, G.V.; Thieulloy, G.D. INDUSTRY 4.0 The New Industrial Revolution: How Europe Will Succeed. Available online: http://www.iberglobal.com/files/Roland_Berger_Industry.pdf (accessed on 11 July 2018).
- Erol, S.; Schumacher, A.; Sihn, W. Strategic guidance towards Industry 4.0—A three-stage process model. In Proceedings of the International Conference on Competitive Manufacturing, Stellenbosch, South Africa, 27–29 January 2016. [Google Scholar]
- Zhong, R.Y.; Xu, X.; Klotz, E.; Newman, S.T. Intelligent Manufacturing in the Context of Industry 4.0: A Review. Engineering
**2017**, 3, 616–630. [Google Scholar] [CrossRef] - Liu, Y.; Xu, X. Industry 4.0 and cloud manufacturing: A comparative analysis. J. Manuf. Sci. Eng.
**2016**, 139. [Google Scholar] [CrossRef] - Talkhestani, B.A.; Jazdi, N.; Schlögl, W.; Weyrich, M. A concept in synchronization of virtual production system with real factory based on anchor-point method. Procedia CIRP
**2018**, 67, 13–17. [Google Scholar] [CrossRef] - Oviroh, P.; Jen, T.-C. The Energy Cost Analysis of Hybrid Systems and Diesel Generators in Powering Selected Base Transceiver Station Locations in Nigeria. Energies
**2018**, 11, 687. [Google Scholar] [CrossRef] - Wan, J.; Tang, S.; Shu, Z.; Li, D.; Wang, S.; Imran, M.; Vasilakos, A.V. Software-Defined Industrial Internet of Things in the Context of Industry 4.0. IEEE Sensors J.
**2016**, 16, 7373–7380. [Google Scholar] [CrossRef] - Yang, Y.; Li, X.; Yang, Z.; Wei, Q.; Wang, N.; Wang, L. The Application of Cyber Physical System for Thermal Power Plants: Data-Driven Modeling. Energies
**2018**, 11, 690. [Google Scholar] [CrossRef] - Paraskevopoulos, D.; Karakitsos, E.; Rustem, B. Robust capacity planning under uncertainty. Manag. Sci.
**1991**, 37, 787–800. [Google Scholar] [CrossRef] - Aghezzaf, B.; Hachimi, M. Generalized invexity and duality in multiobjective programming problems. J. Glob. Optim.
**2000**, 18, 91–101. [Google Scholar] [CrossRef] - De Kok, T.G. Capacity allocation and outsourcing in a process industry. Int. J. Prod. Econ.
**2000**, 68, 229–239. [Google Scholar] [CrossRef] - Kaplan, R.S. Cost and Effect: Using Integrated Cost Systems to Drive Profitability and Performance; Harvard Business School Press: Boston, MA, USA, 1998. [Google Scholar]
- Huang, S.-Y.; Chen, H.-J.; Chiu, A.-A.; Chen, C.-P. The application of the theory of constraints and activity-based costing to business excellence: The case of automotive electronics manufacture firms. Total Qual. Manag. Bus. Excell.
**2014**, 25, 532–545. [Google Scholar] [CrossRef] - Tsai, W.-H.; Hsu, J.-L.; Chen, C.-H.; Chou, Y.-W.; Lin, S.-J.; Lin, W.-R. Application of ABC in hot spring country inn. Int. J. Manag. Enterp. Dev.
**2010**, 8, 152–174. [Google Scholar] [CrossRef] - Oh, S.-C.; Hildreth, A.J. Decisions on Energy Demand Response Option Contracts in Smart Grids Based on Activity-Based Costing and Stochastic Programming. Energies
**2013**, 6, 425–443. [Google Scholar] [CrossRef] [Green Version] - Nordhaus, W.D. Carbon taxes to move toward fiscal sustainability. The Economists’ Voice 2.0: The Financial Crisis, Health Care Reform, and More; Edlin, A.S., Stiglitz, J.E., Eds.; Columbia University Press: New York, NY, USA, 2012; pp. 208–214. [Google Scholar]
- Carbon Tax vs Cap-and-Trade: Which Is Better? Available online: https://www.theguardian.com/environment/2013/jan/31/carbon-tax-cap-and-trade. (accessed on 11 July 2018).
- Descateaux, P.; Astudillo, M.F.; Amor, M.B. Assessing the life cycle environmental benefits of renewable distributed generation in a context of carbon taxes: The case of the Northeastern American market. Renew. Sustain. Energy Rev.
**2016**, 53, 1178–1189. [Google Scholar] [CrossRef] - Ouchida, Y.; Goto, D. Environmental research joint ventures and time-consistent emission tax: Endogenous choice of R&D formation. Econ. Model.
**2016**, 55, 179–188. [Google Scholar] - Lambertini, L.; Poyago-Theotoky, J.; Tampieri, A. Cournot competition and “green” innovation: An inverted-U relationship. Energy Econ.
**2017**, 68, 116–123. [Google Scholar] [CrossRef] [Green Version] - Lee, S.H.; Xu, L. Endogenous timing in private and mixed duopolies with emission taxes. J. Econ.
**2018**, 124, 175–201. [Google Scholar] [CrossRef] - The Difference between a Carbon Tax and an Emissions Tax. Available online: https://www.emissionstax.org/what/carbon-tax/ (accessed on 14 July 2018).
- Wang, M.; Liu, K.; Choi, T.-M.; Yue, X. Effects of carbon emission taxes on transportation mode selections and social welfare. IEEE Trans. Syst. Man Cybern.
**2015**, 45, 1413–1423. [Google Scholar] [CrossRef] - Wang, X.; Zhu, Y.; Sun, H.; Jia, F. Production decisions of new and remanufactured products: Implications for low carbon emission economy. J. Clean. Prod.
**2018**, 171, 1225–1243. [Google Scholar] [CrossRef] - Yang, L.; Hu, X.; Fang, L. Carbon emissions tax policy of urban road traffic and its application in Panjin, China. PLoS ONE
**2018**, 13, e0196762. [Google Scholar] [CrossRef] [PubMed] - Liu, Y.; Xing, J.; Li, Y.; Wang, Y.; Wang, L.; Zheng, B.; Tao, D. Effect of carbon equivalent on thermal and mechanical properties of compacted graphite cast iron. Int. J. Mater. Res.
**2016**, 31, 2516–2523. [Google Scholar] [CrossRef] - Wu, B.; Huang, W.; Liu, P. Carbon reduction strategies based on an NW small-world network with a progressive carbon tax. Sustainability
**2017**, 9, 1747. [Google Scholar] [CrossRef] - Böhringer, C. Carbon taxes with exemptions in an open economy: A general equilibrium analysis of the German tax initiative. J. Econ. Manag.
**1997**, 32, 189–203. [Google Scholar] [CrossRef] - Zheng, J.; Qiao, H.; Wang, S. The Effect of Carbon Tax in Aviation Industry on the Multilateral Simulation Game. Sustainability
**2017**, 9, 1247. [Google Scholar] [CrossRef] - Pereira, V.; Costa, H.G. A literature review on lot size with quantity discounts: 1995–2013. J. Model. Manag.
**2015**, 10, 341–359. [Google Scholar] [CrossRef] - Alfares, H.K.; Ghaithan, A.M. Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Comput. Ind. Eng.
**2016**, 94, 170–177. [Google Scholar] [CrossRef] - Rezaee, M.J.; Yousefi, S.; Hayati, J. A multi-objective model for closed-loop supply chain optimization and efficient supplier selection in a competitive environment considering quantity discount policy. J. Ind. Eng. Int.
**2017**, 13, 199–213. [Google Scholar] [CrossRef] - Shahsavar, A.; Zoraghi, N.; Abbasi, B. Integration of resource investment problem with quantity discount problem in material ordering for minimizing resource costs of projects. Oper. Res.
**2018**, 18, 1–28. [Google Scholar] [CrossRef] - Demeere, N.; Stouthuysen, K.; Roodhooft, F. Time-driven activity-based costing in an outpatient clinic environment: development, relevance and managerial impact. Health Policy
**2009**, 92, 296–304. [Google Scholar] [CrossRef] [PubMed] - Szychta, A. Time-driven activity-based costing in service industries. Social Sci.
**2010**, 1, 49–60. [Google Scholar] - Öker, F.; Adıgüzel, H. Time-driven activity-based costing: An implementation in a manufacturing company. J. Corp. Acc. Financ.
**2016**, 27, 39–56. [Google Scholar] [CrossRef]

Activities | Activity Drivers | ABC Categories | COQ Scheme |
---|---|---|---|

Direct labor | Labor hours | VA | - |

Machine 1 | Machine hours | VA | - |

Machine 2 | Machine hours | VA | - |

Machine 3 | Machine hours | VA | - |

Marketing, Plant guard & management | Labor hours | VA | - |

Waste disposal | Number of disposal | NVA | Internal failure |

Carbon emission | Carbon emission quantities | NVA | External failure |

Rework | Labor hours | NVA | Internal failure |

Inspection | Inspection hours | VA | Appraisal |

Maintenance | Machine hours | VA | Prevention |

Panel A: Production Information | Product 1 | Product 2 | Product 3 | Available Capacity | |||||
---|---|---|---|---|---|---|---|---|---|

Maximum Demand | 70,000 | 40,000 | 50,000 | - | |||||

Selling Price | $4000 | $6000 | $7500 | - | |||||

Quantity of Batch | BA_{i} | 10 | 4 | 4 | - | ||||

Quantity of Maintenance | s_{i} | 5 | 2 | 2 | - | ||||

Direct Material Constraint | |||||||||

Cost/Unit | L_{1} = $50/unit | Ld_{1} = $40/unit | Ldd_{1} = $30/unit | 6 | 8 | 10 | X_{1} = 30,000 | ||

L_{2} = $40/unit | - | - | 2.5 | 3 | 4 | X_{2} = 10,000 | |||

Material Quantities | TD_{1} = 10,000 | W_{1} = 20,000 | - | - | - | - | - | ||

Direct Labour Constraint | |||||||||

Cost | WC_{1} = $600,000 | WC_{2} = $1,100,000 | WC_{3} = $2,400,000 | - | - | - | - | ||

Labour Hours | WH_{1} = 3000 | WH_{2} = 5000 | WH_{3} = 8000 | 2 | 2 | 3.5 | WH_{3} = 8000 | ||

Wage Rate | WR_{1} = $200/h | WR_{2} = $250/h | WR_{3} = $300/h | - | - | - | - | ||

Waste Disposal Constraint | |||||||||

Cost | WA_{1} = $400,000 | WA_{2} = $900,000 | WA_{2} = $2,000,000 | - | - | - | - | ||

Disposal Quantity | WQ_{1} = 2000 | WQ_{2} = 3000 | WQ_{3} = 5000 | 2 | 3 | 3 | WQ_{3} = 5000 | ||

Disposal Rate | DR_{1} = $200/h | DR_{2} = $300/h | DR_{3} = $400/h | - | - | - | - | ||

Time Driver | |||||||||

Inspection Hours | ${t}_{\tau i}$ | 150 | 300 | 250 | - | ||||

Machine Hours | ${H}_{i}$ | 2 | 2 | 3 | |||||

Carbon Emission Constraint | |||||||||

Cost/Unit | T_{1} = $40/unit | T_{2} = $50/unit | T_{3} = $60/unit | - | - | - | - | ||

Upper Limit of Carbon Emission Quantity | Q_{1} = 10,000 | Q_{2} = 12,000 | Q_{3} = 15,000 | 20 | 40 | 50 | Q_{3} = 15,000 | ||

Process-level activity | Machine 1 | Machine 2 | Machine 3 | ||||||

Current capacity | |||||||||

Cost | MC_{10} = $200,000 | MC_{20} = $300,000 | MC_{30} = $720,000 | ||||||

Machine hours | MA_{10} = 2000 | MA_{20} = 3000 | MA_{30} = 6000 | ||||||

Capacity expansion 1 | |||||||||

Cost | MC_{11} = $450,000 | MC_{21} = $600,000 | MC_{31} = $1,200,000 | ||||||

Machine hours | MA_{11} = 3000 | MA_{21} = 4000 | MA_{31} = 8000 | ||||||

Capacity expansion 2 | |||||||||

Cost | MC_{12} = $1,000,000 | MC_{22} = $1,200,000 | MC_{32} = $1,800,000 | ||||||

Machine hours | MA_{12} = 5000 | MA_{22} = 6000 | MA_{32} = 9000 | ||||||

Panel B: Resources consumed | |||||||||

Rework | Maintenance | Inspection | |||||||

Resources | $100,000 | $1,230,000 | $702,500 | ||||||

Capacity (hours) | ${\sigma}_{o}$ = 250 | ${\sigma}_{\delta}$ = 4100 | ${\sigma}_{\tau}$ = 1000 | ||||||

Per hour/rate | ${k}_{0}$ = $400/h | ${k}_{\delta}$= $300/h | ${k}_{\tau}$= $702.5/h |

Optimal Product Mix Solution for Current Capacity without Carbon Tax (Scenario 1) |
---|

$\begin{array}{l}{q}_{1}=580\hspace{1em}{q}_{2}=204\hspace{1em}{q}_{3}=408\hspace{1em}{M}_{r1}=0\hspace{1em}M{d}_{r1}=10,000\hspace{1em}Md{d}_{r1}=0\hspace{1em}{M}_{r2}=3694\hspace{1em}{\alpha}_{0}=1\hspace{1em}{\alpha}_{1}=0\hspace{1em}{\alpha}_{2}=0\hspace{1em}{\beta}_{0}=0\hspace{1em}{\beta}_{1}=0\\ {\beta}_{2}=1\hspace{1em}{\beta}_{3}=0\hspace{1em}B{A}_{1}=58\hspace{1em}B{A}_{2}=51\hspace{1em}B{A}_{3}=102\hspace{1em}{\delta}_{1}=116\hspace{1em}{\delta}_{2}=102\hspace{1em}{\delta}_{3}=204\hspace{1em}{\tau}_{1}=1\hspace{1em}{\tau}_{2}=1\hspace{1em}{\tau}_{3}=1\hspace{1em}ND=0\hspace{1em}SD=1\hspace{1em}OD=0\\ {\eta}_{1}=1\hspace{1em}{\eta}_{2}=0\hspace{1em}{\mu}_{1}=0\hspace{1em}{\mu}_{2}=1\hspace{1em}{\mu}_{3}=0\end{array}$ |

Optimal Product Mix Solution for Capacity Expansion without Carbon Tax (Scenario 2) |
---|

$\begin{array}{l}{q}_{1}=2300\hspace{1em}{q}_{2}=0\hspace{1em}{q}_{3}=0\hspace{1em}{M}_{r1}=0\hspace{1em}M{d}_{r1}=13,800\hspace{1em}Md{d}_{r1}=0\hspace{1em}{M}_{r2}=5750\hspace{1em}{\alpha}_{0}=0\hspace{1em}{\alpha}_{1}=1\hspace{1em}{\alpha}_{2}=0\hspace{1em}{\beta}_{0}=0\hspace{1em}{\beta}_{1}=0\hspace{1em}{\beta}_{2}=0\hspace{1em}{\beta}_{3}=1\hspace{1em}B{A}_{1}=230\hspace{1em}B{A}_{2}=0\hspace{1em}B{A}_{3}=0\\ {\delta}_{1}=460\hspace{1em}{\delta}_{2}=0\hspace{1em}{\delta}_{3}=0\hspace{1em}{\tau}_{1}=1\hspace{1em}{\tau}_{2}=0\hspace{1em}{\tau}_{3}=0\hspace{1em}ND=0\hspace{1em}SD=1\hspace{1em}OD=0\hspace{1em}{\eta}_{1}=0\hspace{1em}{\eta}_{2}=1\hspace{1em}{\mu}_{1}=0\hspace{1em}{\mu}_{2}=0\hspace{1em}{\mu}_{3}=1\hspace{1em}{\theta}_{10}=0\hspace{1em}{\theta}_{11}=0\hspace{1em}{\theta}_{12}=1\hspace{1em}{\theta}_{20}=1\hspace{1em}{\theta}_{21}=0\hspace{1em}{\theta}_{22}=0\\ {\theta}_{30}=1\hspace{1em}{\theta}_{31}=0\hspace{1em}{\theta}_{32}=0\end{array}$ |

Optimal Product Mix Solution for Current Capacity with Carbon Tax (Scenario 3) |
---|

$\begin{array}{l}{q}_{1}=1000\hspace{1em}{q}_{2}=0\hspace{1em}{q}_{3}=284\hspace{1em}{M}_{r1}=0\hspace{1em}M{d}_{r1}=10,000\hspace{1em}Md{d}_{r1}=0\hspace{1em}{M}_{r2}=3636\hspace{1em}{\alpha}_{0}=1\hspace{1em}{\alpha}_{1}=0\hspace{1em}{\alpha}_{2}=0\hspace{1em}{\beta}_{0}=0\hspace{1em}{\beta}_{1}=0\hspace{1em}{\beta}_{2}=1\hspace{1em}{\beta}_{3}=0\hspace{1em}B{A}_{1}=100\hspace{1em}B{A}_{2}=0\hspace{1em}B{A}_{3}=71\\ {\delta}_{1}=200\hspace{1em}{\delta}_{2}=0\hspace{1em}{\delta}_{3}=142\hspace{1em}{\tau}_{1}=1\hspace{1em}{\tau}_{2}=0\hspace{1em}{\tau}_{3}=1\hspace{1em}ND=0\hspace{1em}SD=1\hspace{1em}OD=0\hspace{1em}{\eta}_{1}=1\hspace{1em}{\eta}_{2}=0\hspace{1em}{\mu}_{1}=0\hspace{1em}{\mu}_{2}=1\hspace{1em}{\mu}_{3}=0\hspace{1em}At=0\hspace{1em}Bt=0\hspace{1em}Ct=0\hspace{1em}Dt=34,200\\ {G}_{1}=0\hspace{1em}{G}_{2}=0\hspace{1em}{G}_{3}=0\hspace{1em}{G}_{4}=1\end{array}$ |

Optimal Product Mix Solution for Capacity Expansion with Carbon Tax (Scenario 4) |
---|

$\begin{array}{l}{q}_{1}=1500\hspace{1em}{q}_{2}=0\hspace{1em}{q}_{3}=0\hspace{1em}{M}_{r1}=0\hspace{1em}M{d}_{r1}=10,000\hspace{1em}Md{d}_{r1}=0\hspace{1em}{M}_{r2}=3750\hspace{1em}{\alpha}_{0}=1\hspace{1em}{\alpha}_{1}=0\hspace{1em}{\alpha}_{2}=0\hspace{1em}{\beta}_{0}=0\hspace{1em}{\beta}_{1}=0\hspace{1em}{\beta}_{2}=1\hspace{1em}{\beta}_{3}=0\hspace{1em}B{A}_{1}=150\hspace{1em}B{A}_{2}=0\hspace{1em}B{A}_{3}=0\\ {\delta}_{1}=300\hspace{1em}{\delta}_{2}=0\hspace{1em}{\delta}_{3}=0\hspace{1em}{\tau}_{1}=1\hspace{1em}{\tau}_{2}=0\hspace{1em}{\tau}_{3}=0\hspace{1em}ND=0\hspace{1em}SD=1\hspace{1em}OD=0\hspace{1em}{\eta}_{1}=1\hspace{1em}{\eta}_{2}=0\hspace{1em}{\mu}_{1}=0\hspace{1em}{\mu}_{2}=1\hspace{1em}{\mu}_{3}=0\hspace{1em}{\theta}_{10}=0\hspace{1em}{\theta}_{11}=1\hspace{1em}{\theta}_{12}=0\hspace{1em}{\theta}_{20}=1\hspace{1em}{\theta}_{21}=0\hspace{1em}{\theta}_{22}=0\\ {\theta}_{30}=1\hspace{1em}{\theta}_{31}=0\hspace{1em}{\theta}_{32}=0\hspace{1em}At=0\hspace{1em}Bt=0\hspace{1em}Ct=0\hspace{1em}Dt=30,000\hspace{1em}{G}_{1}=0\hspace{1em}{G}_{2}=0\hspace{1em}{G}_{3}=0\hspace{1em}{G}_{4}=1\end{array}$ |

Current Capacity | Capacity Expansion | ||||
---|---|---|---|---|---|

Without Carbon Tax (Scenario 1) | With Carbon Tax (Scenario 2) | Without Carbon Tax (Scenario 3) | With Carbon Tax (Scenario 4) | ||

Panel A: Production-mix | Product A1 | 580 | 1000 | 2300 | 1500 |

Product A2 | 204 | 0 | 0 | 0 | |

Product A3 | 408 | 284 | 0 | 0 | |

Panel B: Resources Consumed | Direct material 1 | 10,000 | 10,000 | 13,800 | 10,000 |

Direct material 2 | 3694 | 3636 | 5750 | 3750 | |

Direct labor hours | 2996 | 2994 | 4600 | 3000 | |

Machine 1 (hours) | 1160 | 2000 | 4600 | 3000 | |

Machine 2 (hours) | 408 | 0 | 0 | 0 | |

Machine 3 (hours) | 1224 | 852 | 0 | 0 | |

Waste disposal | 2996 | 2852 | 4600 | 3000 | |

Carbon emission | - | 34,200 | - | 30,000 | |

Rework | 250 | 197 | 249 | 163 | |

Inspection | 700 | 450 | 150 | 150 | |

Maintenance | 511 | 456 | 690 | 450 | |

Panel C: Profit | Revenue | 6,604,000 | 6,130,000 | 9,200,000 | 6,000,000 |

Direct material 1 | 400,000 | 400,000 | 552,000 | 400,000 | |

Direct material 2 | 147,760 | 145,440 | 230,000 | 150,000 | |

Direct labor (VA) | 600,000 | 600,000 | 1,100,000 | 600,000 | |

Machine 1 (VA) | 200,000 | 200,000 | 1,000,000 | 450,000 | |

Machine 2 (VA) | 300,000 | 300,000 | 300,000 | 300,000 | |

Machine 3 (VA) | 720,000 | 720,000 | 720,000 | 720,000 | |

Waste disposal cost (NVA, Internal failure) | 900,000 | 900,000 | 2,000,000 | 900,000 | |

Carbon tax (NVA, External failure) | - | 1,452,000 | - | 1,200,000 | |

Rework cost (NVA, Internal failure) | 99,933 | 78,833 | 99,667 | 65,000 | |

Inspection cost (VA, Appraisal) | 491,750 | 281,000 | 105,375 | 105,375 | |

Maintenance cost (VA, Prevention) | 153,180 | 136,860 | 207,000 | 135,000 | |

Marketing, Plant guard & management (VA) | 200,000 | 200,000 | 200,000 | 200,000 | |

Income based on resources consumed | 2,391,377 | 715,867 | 2,685,958 | 774,625 | |

Panel D: COQ Report | Total product cost | 4,012,623 | 5,214,133 | 6,314,042 | 5,025,375 |

Total activity cost | 3,664,863 | 4,868,693 | 5,732,042 | 4,675,375 | |

Total VA cost | 2,664,930 | 2,437,860 | 3,632,375 | 2,510,375 | |

Total NVA cost | 999,933 | 2,430,833 | 2,099,667 | 2,165,000 | |

Total COQ cost | 1,644,863 | 2,848,693 | 2,412,042 | 2,405,375 | |

Data Sources | Table 3 | Table 5 | Table 4 | Table 6 |

© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tsai, W.-H.
A Green Quality Management Decision Model with Carbon Tax and Capacity Expansion under Activity-Based Costing (ABC)—A Case Study in the Tire Manufacturing Industry. *Energies* **2018**, *11*, 1858.
https://doi.org/10.3390/en11071858

**AMA Style**

Tsai W-H.
A Green Quality Management Decision Model with Carbon Tax and Capacity Expansion under Activity-Based Costing (ABC)—A Case Study in the Tire Manufacturing Industry. *Energies*. 2018; 11(7):1858.
https://doi.org/10.3390/en11071858

**Chicago/Turabian Style**

Tsai, Wen-Hsien.
2018. "A Green Quality Management Decision Model with Carbon Tax and Capacity Expansion under Activity-Based Costing (ABC)—A Case Study in the Tire Manufacturing Industry" *Energies* 11, no. 7: 1858.
https://doi.org/10.3390/en11071858