# A Trade-off Analysis of Economic and Environmental Aspects of a Disruption Based Closed-Loop Supply Chain Network

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Closed-Loop Supply Chain

_{2}emission, fuel consumption and social concerns of a new job opening. Mohammed et al. [16] analyzed the environmental impact and total cost by proposing a multi-period and multi-product based CLSC. A trade-off was proposed between CO

_{2}emission and the cost of a supply chain network. Although an adequate amount of research has been offered towards the establishment of an efficient CLSC, there still is a dearth of literature to address the environmental concerns of CLSC, emission, etc. [17]. A detailed procedure was adopted to extensively analyze the concerned literature and it is discussed below.

- The embedded factors include re-manufacturing, energy extraction and disposal.
- The selected choices of objective functions contain cost, environmental/social aspects and time.
- The selected articles were scrutinized against the solution approaches of heuristics, multi-heuristics and hybrid heuristics approaches.
- The additional set of aspects comprised the analysis of vehicle speed and disruption.
- The target markets were identified at three levels i.e., primary, secondary and tertiary market.
- The analysis results are presented in Figure 2. These are further discussed in the following sections.

#### 2.2. Embedded Factors and Market Levels

#### 2.3. Choice of Objective Functions and Additional Aspects

#### 2.4. Solution Approaches

- A multi-objective analysis is presented to analyze the multiple levels of a closed-loop supply chain. The considered objectives are: the total cost, the total time and the carbon emissions.
- A consolidated analysis is presented by integrating the factors of re-manufacturing, energy extraction and disposal. Also, three market levels are considered for minimizing the level of waste.
- We examine the impact of machine disruption on the performance of CLSC. Also, the impact of vehicle speed on the transportation performance of a CLSC problem is presented.
- The solution is attained using multi-heuristics and hybrid approaches. Furthermore, three performance evaluation metrics are used to evaluate the solution efficiency of the considered approaches.
- The objective is to analyze the trade-off behavior of cost, time and emissions. In other words, how these decisions can be controlled while fulfilling customer demand. Secondly, in the presence of machine disruption, which production facility can help accomplishing an overall optimal solution.

## 3. Problem Statement

_{j}. However, due to inadequate maintenance, it starts disruption defined by probability value ${\lambda}_{j}$. Due to disruption, the state of the machine can be divided into “in-control” and “out-of-control” states. The production in the control state results in optimal quality products while the out-of-control state produces moderate quality products and failed products due to machine disruption. The failed units are discarded while the moderate quality products are re-worked to make them conforming. Since the production capacity is fixed, we select the minimum number of appropriate machines j to meet the demand quantity after discarding the failed units.

Indices | ||

i | set of suppliers | i = {1,2,…, I} |

j | set of production machines | j = {1,2,…, J} |

k | set of cross-docking points | k = {1,2,…, K} |

l | set of distribution points | l = {1,2,…, L} |

m | set of customer locations | m = {1,2,…, M} |

n | set of repository for product return | n = {1,2,…, N} |

o | set of secondary markets | o = {1,2,…, O} |

p | set of tertiary markets | p = {1,2,…, P} |

Parameters | ||

${q}_{j}$ | quantity of raw materials fed to production machine j | |

${c}_{j}$ | cost of manufacturing per unit product on machine j | |

$c{e}_{j}$ | cost of exploiting machine j | |

$t{p}_{j}$ | per unit production time at j | |

${e}_{j}$ | per unit production energy used at j | |

$d{x}_{jk}$ | distance between machine facility j and cross-dock point k | |

$c{e}_{m}$ | carbon emitted during production per unit product | |

${c}_{tv}$ | carbon emitted during transportation per kilometer | |

$t{r}_{c}$ | transportation cost per kilometer distance travelled | |

$Fc{a}_{j}$ | feasible production capacity of machine j | |

$Nc{a}_{j}$ | non-feasible production capacity of machine j | |

${\lambda}_{j}$ | probability of machine disruption | |

$d{y}_{kl}$ | distance between cross-dock point k and disruption point l | |

$r{w}_{j}$ | cost of re-work at machine facility j | |

$c{w}_{j}$ | failed product cost per unit due to machine disruption | |

$c{p}_{p}$ | penalty cost of discarded product at tertiary market | |

$d{z}_{lm}$ | distance between distribution point l and customer location m | |

$d{d}_{mn}$ | distance between customer location m and respiratory n | |

$d{f}_{nj}$ | distance between respiratory n and production facility j | |

$\Psi $ | fraction of conforming products at n | |

$1-\Psi $ | fraction of non-conforming products at n | |

$f$ | fraction of non-conforming products used for energy extraction | |

$1-f$ | fraction of non-conforming products discarded as waste | |

$d$ | required level of demand | |

$V$ | vehicle speed in kilometer per hour | |

$c{r}_{m}$ | cost of re-manufacturing per unit | |

$ee$ | energy extracted per unit product at tertiary market | |

$t{t}_{j}$ | re-work time per unit product at production facility j | |

$tr{m}_{j}$ | remanufacturing time per unit product at production facility j | |

$ew$ | energy wasted due to carbon emission at tertiary market | |

$Z$ | A big number | |

Decision variables | ||

${M}_{j}$ | 1, if machine facility j is used for production, else 0 | |

${X}_{jk}$ | 1, if products are shipped between j and k, else 0 | |

${Y}_{kl}$ | 1, if products are transported between k and l, else 0 | |

${Z}_{lm}$ | 1, if products are transported between l and m, else 0 | |

${L}_{mn}$ | 1, if m is used to transport products to n, else 0 | |

${S}_{jo}$ | 1, if products are launched into secondary market o, else 0 | |

${N}_{np}$ | 1, if products are sent to tertiary market, else 0 | |

$NM$ | number of machines required for production | |

${F}_{nj}$ | 1, if conforming products are sent from n to j, else 0 | |

$MN{M}_{j}$ | Auxiliary variable | |

$XN{M}_{j}$ | Auxiliary variable |

#### 3.1. Minimize Total Cost (TC)

#### 3.1.1. Production Cost (PC)

#### 3.1.2. Transportation Cost (TRC)

#### 3.1.3. Failed Units Cost (FC)

#### 3.1.4. Re-work Cost (RC)

#### 3.2. Minimize Total Time (TT)

#### 3.2.1. Production Time (PT)

#### 3.2.2. Transportation Time (TRT)

#### 3.2.3. Lost Production Time (LT)

#### 3.2.4. Re-Work Time (RT)

#### 3.3. Minimize Carbon Emission (CE)

#### 3.3.1. Carbon Emission during Production (CP)

#### 3.3.2. Carbon Emission during Transportation (CTR)

#### 3.3.3. Carbon Emitted Due to Waste (CW)

#### 3.3.4. Useful Energy Extraction (UE)

- A deterministic model is used where demand is met in the current period and back ordering is not allowed.
- The delivery locations of customers are known in advance. All of the delivered products d are sent back at the completion of the useful life of products.
- The problem considers a single supplier, single product, single cross-dock, single repository for return, single secondary market and single tertiary market.
- There are multiple machines available to produce the same product. Also, since the capacity of each machine is pre-defined, a number of copies of the selected machine can be used to fulfil the required level of demand. Each machine has a different production capacity. The distribution of capacity into the control and out of control states is different for different machines. Similarly, the production, remanufacturing, rework costs varies between the available machines.
- The probability of machine disruption has the same value for every machine. There is no cost of inspection. The capacity at return repository is unlimited.
- The distances might vary but travelling cost per km is same for every two selected levels. The transportation costs, emission and distances are known in advance.

## 4. Solution Approaches

#### 4.1. The $\mathsf{\epsilon}$-Constraint Approach

- Implement the model in CPLEX to identify the upper and lower bounds of TT and CE.
- Using (34) and (36), adjust the values of ${\epsilon}_{1}$ and ${\epsilon}_{2}$ between the respective upper and lower bounds.
- Solve the problem using basic version of genetic algorithm (GA) to acquire the non-dominated solutions of mono-objective TC.
- Reduce the values of ${\epsilon}_{1}$ and ${\epsilon}_{2}$ by an amount ${\epsilon}_{1}={\epsilon}_{1}^{\xb0}-\Delta TT$ and ${\epsilon}_{2}={\epsilon}_{2}^{\xb0}-\Delta CE$, where ${\epsilon}_{1}^{\xb0}>$ ${\epsilon}_{1}$ and ${\epsilon}_{2}^{\xb0}>$ ${\epsilon}_{2}$.
- If respectively ${\epsilon}_{1}$ and ${\epsilon}_{2}$ are less than TT and CE then stop the procedure, otherwise re-run step 3.

#### 4.2. Multi-Heuristic Approaches

#### 4.2.1. Ant Colony Optimization

#### 4.2.2. Whale Optimization Algorithm

#### 4.3. Hybrid NSGA-II and MOPSO

^{2}) where N is the number of objectives and P represents the population size. It uses the following five operators: initializing, sorting, crossover, mutation and elitist comparison.

#### 4.4. Parameter Tuning

## 5. Data analysis and Results

#### 5.1. Case Study

#### 5.2. Results

_{sol}= value obtained by the algorithm, M

_{sol}= max. value of performance measure, Min

_{sol}= minimum value of performance measure, B

_{sol}= best solution among the algorithms. The DI was calculated using the interval plot in Minitab V 19.2 and respective results are provided in Figure 9. It can be observed that in all sub-figures (Figure 9a–d), there is no statistical difference in the performance of NSGA-II and MOPSO. The hybrid approach is more robust in terms of DEA, MID and CPU. Also, compared to ACO, WOA performs well in terms of DEA, MID and CPU matrices. Lastly, an increasing shift of deviation is observed in all approaches when problem size is increased from medium to large scale.

#### Sensitivity Analysis

#### 5.3. Managerial Implications

## 6. Conclusions and Suggestions for Future Research

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

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**Figure 2.**Distribution of literature according to (

**a**) Embedded Factors, (

**b**) Objective functions, (

**c**) Solution approaches and (

**d**) Market levels.

**Figure 14.**The objective function values of (

**a**) Total Cost (TC), (

**b**) Total Time (TT) and (

**c**) Carbon Emissions (CE) for different set of machines (Problem 7).

Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|

Nu. of ants (m) | 200 | 150 | 100 |

Nu. of iterations (NI) | 200 | 300 | 400 |

Control parameter (Q) | 100,000 | 200,000 | 300,000 |

Evaporation Rate (p) | 0.3 | 0.5 | 0.7 |

Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|

Number of whales (W) | 100 | 200 | 300 |

Max. number of iterations (MI) | 300 | 500 | 700 |

Probability of movement (pe) | 0.4 | 0.5 | 0.6 |

Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|

Population size (pop size) | 60 | 80 | 100 |

Number of iterations (Max. It) | 600 | 800 | 1000 |

Crossover probability (pc) | 0.2 | 0.4 | 0.6 |

Mutation probability (pm) | 0.7 | 0.5 | 0.3 |

Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|

Swarm size (P) | 60 | 80 | 100 |

Maximum intertia (max. I) | 0.9 | 0.7 | 0.5 |

Minimum inertia (min. I) | 0.4 | 0.3 | 0.2 |

Maximum iterations (max. It) | 600 | 800 | 1000 |

Algorithm | Set of Input Parameters | Optimal Values |
---|---|---|

ACO | (m, NI, Q, p) | (100, 400, 100,000, 0.5) |

WOA | (W, MI, pe) | (300, 500, 0.6) |

NSGA-II | (pop size, Max. it, pm, pc) | (100, 800, 0.4, 0.3) |

MOPSO | (P, max. I, min. I, max. It ) | (100, 0.9, 0.4, 1000) |

Problem Size | Test Problem | Machine Facilities | Distributors | Customers |
---|---|---|---|---|

Small | 1 | 2 | 2 | 4 |

2 | 4 | 4 | 6 | |

3 | 5 | 5 | 8 | |

Medium | 4 | 10 | 8 | 10 |

5 | 15 | 8 | 15 | |

6 | 20 | 10 | 20 | |

Large | 7 | 40 | 12 | 30 |

8 | 50 | 14 | 40 | |

9 | 60 | 16 | 45 | |

10 | 70 | 20 | 55 |

Machine | Capacity | Cost | Time | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Fac_{j} | Nca_{j} | ce_{j} | c_{j} | cw_{j} | rw_{j} | tp_{j} | tt_{j} | trm_{j} | ||

Test Problem 4 | M_{1} | 75 | 25 | 500 | 165 | 180 | 45 | 25 | 12 | 18 |

M_{2} | 60 | 40 | 400 | 150 | 200 | 38 | 22 | 11 | 16 | |

M_{3} | 80 | 20 | 575 | 180 | 325 | 55 | 29 | 14 | 18 | |

M_{4} | 68 | 32 | 365 | 155 | 145 | 35 | 24 | 12 | 15 | |

M_{5} | 72 | 28 | 460 | 170 | 170 | 48 | 27 | 13 | 15 | |

M_{6} | 70 | 30 | 445 | 165 | 185 | 50 | 32 | 17 | 16 | |

M_{7} | 65 | 35 | 400 | 130 | 135 | 45 | 23 | 14 | 15 | |

M_{8} | 62 | 38 | 430 | 145 | 130 | 55 | 20 | 12 | 13 | |

M_{9} | 75 | 25 | 485 | 160 | 190 | 65 | 32 | 18 | 15 | |

M_{10} | 83 | 17 | 600 | 195 | 345 | 65 | 38 | 20 | 17 |

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## Share and Cite

**MDPI and ACS Style**

Khan, A.S.; Pruncu, C.I.; Khan, R.; Naeem, K.; Ghaffar, A.; Ashraf, P.; Room, S.
A Trade-off Analysis of Economic and Environmental Aspects of a Disruption Based Closed-Loop Supply Chain Network. *Sustainability* **2020**, *12*, 7056.
https://doi.org/10.3390/su12177056

**AMA Style**

Khan AS, Pruncu CI, Khan R, Naeem K, Ghaffar A, Ashraf P, Room S.
A Trade-off Analysis of Economic and Environmental Aspects of a Disruption Based Closed-Loop Supply Chain Network. *Sustainability*. 2020; 12(17):7056.
https://doi.org/10.3390/su12177056

**Chicago/Turabian Style**

Khan, Abdul Salam, Catalin Iulian Pruncu, Razaullah Khan, Khawar Naeem, Abdul Ghaffar, Pakeeza Ashraf, and Shah Room.
2020. "A Trade-off Analysis of Economic and Environmental Aspects of a Disruption Based Closed-Loop Supply Chain Network" *Sustainability* 12, no. 17: 7056.
https://doi.org/10.3390/su12177056