Abstract
Remanufacturing and recycling industry has developed rapidly in recent years due to its benefits in reducing waste and protecting the environment. However, the uncertain environment and excessive emission during production become two main obstacles for its further development. In this paper, a green-oriented bi-objective disassembly line balancing problem with stochastic task processing times is studied. The objectives are to minimize the total line configuration cost respecting the given budget, and minimize the total contaminant emission, respectively. To depict stochastic processing times, their mean, standard deviation and change-rate upper bound are assumed to be known since it may be difficult to obtain the complete historical data. For the problem, a bi-objective model with chance constraints is first formulated, which is further approximated into a linear distribution-free one. To solve the second model, an efficient \(\varepsilon \)-constraint method is proposed based on problem analysis. Finally, a fuzzy-logic-based approach is applied to recommend preferred solutions for managers according to their perspectives. The solution methods are first examined by a case study, then by 247 benchmark-based instances and randomly generated instances. Experimental results indicate the efficiency and effectiveness of the proposed methods for solving the green-oriented bi-objective problem.
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References
Altekin, F. T. (2016). A piecewise linear model for stochastic disassembly line balancing. IFAC-PapersOnLine, 49(12), 932–937.
Altekin, F. T. (2017). A comparison of piecewise linear programming formulations for stochastic disassembly line balancing. International Journal of Production Research, 55(24), 7412–7434.
Aydemir-Karadag, A., & Turkbey, O. (2013). Multi-objective optimization of stochastic disassembly line balancing with station paralleling. Computers & Industrial Engineering, 65(3), 413–425.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2013a). Chance constrained programming model for stochastic profit-oriented disassembly line balancing in the presence of hazardous parts. In V. Prabhu, M. Taisch, & D. Kiritsis (Eds.), Advances in production management systems, sustainable production and service supply chains (pp. 414–421). Berlin: Springer.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2013b). A decomposition method for stochastic partial disassembly line balancing with profit maximization. In Proceedings of the IEEE international conference on automation science (pp. 404–409). Madison, WI.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2013c). L-shaped algorithm for stochastic disassembly line balancing problem. In Proceedings of the 7th IFAC conference on manufacturing modeling, management, and control (pp. 407–411). Saint Petersburg.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2013d). A stochastic formulation of the disassembly line balancing problem. In Advances in production management systems competitive manufacturing for innovative products and services (pp. 397–404). Berlin: Springer.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2014a). A sample average approximation method for disassembly line balancing problem under uncertainty. Computers & Operations Research, 51, 111–122.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2015a). An exact solution approach for disassembly line balancing problem under uncertainty of the task processing times. International Journal of Production Research, 53(6), 1807–1818.
Bentaha, M. L., Battaïa, O., & Dolgui, A. (2015b). Second order conic approximation for disassembly line design with joint probabilistic constraints. European Journal of Operational Research, 247(3), 957–967.
Bentaha, M. L., Battaïa, O., Dolgui, A., & Hu, J. (2014b). Dealing with uncertainty in disassembly line design. CIRP Annals, 63, 21–24.
Bentaha, M. L., Dolgui, A., Battaïa, O., & Hu, J. (2018). Profit-oriented partial disassembly line design: dealing with hazardous parts and task processing times uncertainty. International Journal of Production Research,. https://doi.org/10.1080/00207543.2017.1418987.
Bérubé, J. F., Gendreau, M., & Potvin, J. Y. (2009). An exact-constraint method for bi-objective combinatorial optimization problems: Application to the traveling salesman problem with Profits. European Journal of Operational Research, 194(1), 39–50.
Esmaili, M., Shayanfar, H. A., & Amjady, N. (2009). Multi-objective congestion management incorporating voltage and transient stabilities. Energy, 34(9), 1401–1412.
Feng, J., Che, A., & Wang, N. (2014). Bi-objective cyclic scheduling in a robotic cell with processing time windows and non-euclidean travel times. International Journal of Production Research, 52(9), 2505–2518.
Grandinetti, L., Guerriero, F., Laganá, D., & Pisacane, O. (2012). An optimization-based heuristic for the multi-objective undirected capacitated arc routing problem. Computers & Operations Research, 39(10), 2300–2309.
Güngör, A., & Gupta, S. M. (1999). Disassembly Line Balancing. In Proceedings of the Annual Meeting of the Northeast Decision Science Institute (pp. 193–195). Newport, RI.
Gurevsky, E., Battaïa, O., & Dolgui, A. (2012). Balancing of simple assembly lines under variations of task processing times. Annals of Operations Research, 201(1), 265–286.
Igarashi, K., Yamada, T., Gupta, S. M., Inoue, M., & Itsubo, N. (2016). Disassembly system modeling and design with parts selection for cost, recycling and CO\(_2\) saving rates using multi criteria optimization. Journal of Manufacturing Systems, 38, 151–164.
Igarashi, K., Yamada, T., & Inoue, M. (2013). Disassembly system design with environmental and economic parts selection using the recyclability evaluation method. Journal of Japan Industrial Management Association, 64(2E), 293–302.
Igarashi, K., Yamada, T., & Inoue, M. (2014). 2-Stage optimal design and analysis for dis-assembly system with environmental and economic parts selection using therecyclability evaluation method. International Journal of Industrial Engineering & Management Systems, 13(1), 52–66.
Ilgın, M. A., & Gupta, S. M. (2010). Environmentally conscious manufacturing and product recovery (ECMPRO): A review of the state of the art. Journal of Environmental Management, 91(3), 563–591.
Kalayci, C. B., Hancilar, A., Güngör, A., & Gupta, S. M. (2015). Multi-objective fuzzy disassembly line balancing using a hybrid discrete artificial bee colony algorithm. Journal of Manufacturing Systems, 37, 672–682.
Kalayci, C. B., Polat, O., & Gupta, S. M. (2016). A hybrid genetic algorithm for sequence-dependent disassembly line balancing problem. Annals of Operations Research, 242(2), 321–354.
Kazancoglu, Y., & Ozturkoglu, Y. (2018). Integrated framework of disassembly line balancing with green and business objectives using a mixed MCDM. Journal of Cleaner Production, 191, 179–191.
Koc, A., Sabuncuoglu, I., & Erel, E. (2009). Two exact formulations for disassembly line balancing problems with task precedence diagram construction using an AND/OR graph. LIE Transactions, 41(10), 866–881.
Kwak, M. J., Hong, Y. S., & Cho, N. W. (2009). Eco-architecture analysis for end-of-life decision making. International Journal of Production Research, 47(22), 6233–6259.
Lambert, A. J. D. (1999). Linear programming in disassembly/clustering sequence generation. Computers & Industrial Engineering, 36(4), 723–738.
Lo, C. K., Yeung, A. C., & Cheng, T. C. E. (2012). The impact of environmental management systems on financial performance in fashion and textiles industries. International Journal of Production Economics, 135(2), 561–567.
Ma, Y. S., Jun, H. B., Kim, H. W., & Lee, D. H. (2011). Disassembly process planning algorithms for end-of-life product recovery and environmentally conscious disposal. International Journal of Production Research, 49(23), 7007–7027.
Maxwell, D., & Van Der Vorst, R. (2003). Developing sustainable products and services. Journal of Cleaner Production, 11(8), 883–895.
Miettnen, K. (1999). Nonlinear multiobjective optimization. Boston, MA: Kluwer.
Movilla, N. A., Zwolinski, P., Dewulf, J., & Mathieux, F. (2016). A method for manual disassembly analysis to support the eco-design of electronic displays. Resources, Conservation and Recycling, 114, 42–58.
Ng, M. W. (2014). Distribution-free vessel deployment for liner shipping. European Journal of Operational Research, 238, 858–862.
Özceylan, E., Kalayci, C. B., Güngör, A., & Gupta, S. M. (2019). Disassembly line balancing problem: A review of the state of the art and future directions. International Journal of Production Research, 57(15–16), 4805–4827.
Ren, Y., Zhang, C., Zhao, F., Tian, G., Lin, W., Meng, L., et al. (2018). Disassembly line balancing problem using interdependent weights-based multi-criteria decision making and 2-optimal algorithm. Journal of Cleaner Production, 174, 1475–1486.
Saif, U., Guan, Z., Liu, W., Zhang, C., & Wang, B. (2014). Pareto based artificial bee colony algorithm for multi-objective single model assembly line balancing with uncertain task times. Computers & Industrial Engineering, 76(C), 1–15.
Schoenherr, T. (2012). The role of environmental management in sustainable business development: A multi-country investigation. International Journal of Production Economics, 140(1), 116–128.
Seidi, M., & Saghari, S. (2016). The balancing of disassembly line of automobile engine using genetic algorithm (GA) in fuzzy environment. Industrial Engineering & Management Systems, 15(4), 364–373.
Smith, S. S., & Chen, W. H. (2011). Rule-based recursive selective disassembly sequence planning for green design. Advanced Engineering Informatics, 25(1), 77–87.
Tang, Y., Zhou, M., & Zussman, E. (2002). Disassembly modeling, planning, and application. Journal of Manufacturing Systems, 21(3), 200–217.
Tao, Y., Meng, K., Lou, P., Peng, X., & Qian, X. (2019). Joint decision-making on automated disassembly system scheme selection and recovery route assignment using multi-objective meta-heuristic algorithm. International Journal of Production Research, 57(1), 124–142.
Wagner, M., & Schaltegger, S. (2004). The effect of corporate environmental strategy choice and environmental performance on competitiveness and economic performance: an empirical analysis of EU manufacturing. European Management Journal, 22(5), 557–572.
Wu, P., Che, A., Chu, F., & Zhou, M. (2015). An improved exact \(\varepsilon \)-constraint and cut-and-solve combined method for biobjective robust lane reservation. IEEE Transactions on Intelligent Transportation Systems, 16(3), 1479–1492.
Yu, S., Zheng, S., Gao, S., & Yang, J. (2017). A multi-objective decision model for investment in energy savings and emission reductions in coal mining. European Journal of Operational Research, 260(1), 335–347.
Zhang, Z., Wang, K., Zhu, L., & Wang, Y. (2017). A Pareto improved artificial fish swarm algorithm for solving a multi-objective fuzzy disassembly line balancing problem. Expert Systems with Applications, 86, 165–176.
Zheng, F., He, J., Chu, F., & Liu, M. (2018). A new distribution-free model for disassembly line balancing problem with stochastic task processing times. International Journal of Production Research, 56(24), 7341–7353.
Zhu, L., Zhang, Z., & Wang, Y. (2018). A Pareto firefly algorithm for multi-objective disassembly line balancing problems with hazard evaluation. International Journal of Production Research, 56(24), 7354–7374.
Acknowledgements
This work was partly supported by the National Natural Science Foundation of China (Grant Nos. 71832001, 71771048, 71571134).
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Appendices
Appendix 1
The proof of Lemma 1
Proof
Since \(t_j={\mathbb {E}}[p_j]\) and \(p_j=t_j(1+d_j)\), then we have \({\mathbb {E}}[d_j]=0\). Using the well-known Taylor series expansion \(e^x=\sum \nolimits _{n=1}^{\infty } \frac{x^n}{n!}\), we have \({\mathbb {E}}[e^{\lambda d_j}]=1+\sum \nolimits _{n=2}^{\infty } \frac{\lambda ^n {\mathbb {E}}[d_j^2d_j^{n-2}]}{n!}\). Because that \(Pr (d_i \le b_i)=1\), the following formulas satisfy:
It completes the proof. \(\square \)
Appendix 2
The proof of Proposition 1
Proof
Knowing that \(\Pr \left( \sum \nolimits _{j \in J} p_j \cdot x_{j,m}> CT \right) = \Pr \left( \sum \nolimits _{j \in J} t_j(1+d_j) \cdot x_{j,m} > CT \right) \). If \(\sum \nolimits _{j \in J} t_j(1+d_j) \cdot x_{j,m} > CT\), then it must follow that \(t_j d_j > \mu _j\) since \(x_{j,m}\) is a feasible solution to model P2. Hence, the following formula can be established:
Let the right side of the above inequality equal \(\beta _m\), it completes the proof. \(\square \)
Appendix 3
The related information of the used instance.
The DCG of the instance is shown in Fig. 6, and the input information is collected in Table 6.
The DCG of this instance (Zheng et al. 2018)
Appendix 4
The proof of Theorem 1
Proof
For model \(\mathbf{P} _E(\varepsilon _i)\), the minimum unit of the total line cost C depends on \(\sum \nolimits _{m \in M} c_m \cdot y_m\) and \(h \cdot \sum \nolimits _{j \in H} \sum \nolimits _{m \in M} x_{j,m}\) in the \(\varepsilon \)-constraint. Since the latter is a constant independent of decision variables due to assumption (viii), therefore, it can be removed when deciding the step length. Then, the minimum unit of C is determined by the former part. Consider that at least one workstation should be opened and each candidate workstation has a cost \(c_m\), thus the minimum unit of C should be the Greatest Common Divisor among the cost of candidate workstations, i.e., \(\bigtriangleup _c = GCD(c_m)\). Finally, according to the first theorem in Wu et al. (2015), the Pareto front for the studied problem can be obtained by exactly solving model \(\mathbf{P} _E(\varepsilon _i)\) with step length \(GCD(c_m)\). \(\square \)
Appendix 5
The complementary input information for the used instance
The complementary input of the instance introduced in Appendix 3 is shown as follows:
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The regular budget RB: 20
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The invest cost of each workstation \(c_m\): [6, 5, 4, 6, 5]
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The contaminant emission of task j generated by machine m, i.e., \(e_{j,m}\):
$$\begin{aligned} \left[ \begin{matrix} 6 &{}\quad 8 &{}\quad 10 &{}\quad 6 &{}\quad 8 \\ 9 &{}\quad 11 &{}\quad 13 &{}\quad 9 &{}\quad 11 \\ 4 &{}\quad 6 &{}\quad 8 &{} \quad 4 &{} \quad 6 \\ 6 &{}\quad 8 &{}\quad 10 &{}\quad 6 &{}\quad 8 \\ 5 &{}\quad 7 &{} \quad 9 &{} \quad 5 &{} \quad 7 \\ 4 &{}\quad 6 &{} \quad 8 &{}\quad 4 &{} \quad 6 \\ 5 &{}\quad 7 &{} \quad 9 &{}\quad 5 &{} \quad 7 \\ 6 &{} \quad 8 &{} \quad 10 &{}\quad 6 &{} \quad 8 \\ 6 &{}\quad 8 &{} \quad 10 &{}\quad 6 &{} \quad 8 \\ 7 &{} \quad 9 &{} \quad 11 &{} \quad 7 &{} \quad 9 \end{matrix} \right] \end{aligned}$$
Appendix 6
The detailed computational results in Sect. 5.3.
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He, J., Chu, F., Zheng, F. et al. A green-oriented bi-objective disassembly line balancing problem with stochastic task processing times. Ann Oper Res 296, 71–93 (2021). https://doi.org/10.1007/s10479-020-03558-z
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DOI: https://doi.org/10.1007/s10479-020-03558-z