# American Institute of Mathematical Sciences

January  2021, 17(1): 393-408. doi: 10.3934/jimo.2019117

## Multi-period hazardous waste collection planning with consideration of risk stability

 School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China

* Corresponding author: Xiang Li

Received  January 2019 Revised  March 2019 Published  January 2021 Early access  September 2019

Hazardous wastes are likely to cause danger to humans and the environment. In this paper, a new mathematical optimization model is developed for the multi-period hazardous waste collection planning problem. The hazardous wastes generated by each source are time-varying in weight and allow incomplete and delayed collection. The aim of the model is to help decision makers determine the weight of hazardous wastes to collect from each source and the transportation routes of vehicles in each period. In the developed model, three objectives are considered simultaneously: (1) minimisation of total cost over all periods, which includes start-up fee of vehicles, transportation cost of hazardous wastes, and penalty fee for the delayed collection; (2) minimisation of total transportation risk posing to the surrounding of routes over all periods; and (3) even distribution of transportation risk among all periods, also called risk stability. The developed multi-objective model is transformed into a single-objective one based on the weighted sums method, which is finally equated to a mixed 0-1 linear programming by introducing a set of auxiliary variables and constraints. Numerical experiments are computed with CPLEX software to find the optimal solutions. The computational results and parameters analysis demonstrate the applicability and validity of the developed model. It is found that the consideration of the risk stability can reduce the total transportation risk, the uneven distribution of the transportation risk among all periods, and the maximum number of vehicles used, though increasing the total cost to some extent.

Citation: Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial and Management Optimization, 2021, 17 (1) : 393-408. doi: 10.3934/jimo.2019117
##### References:
 [1] K. N. Androutsopoulos and K. G. Zografos, Solving the bicriterion routing and scheduling problem for hazardous materials distribution, Transportation Research Part C: Emerging Technologies, 18 (2010), 713-726.  doi: 10.1016/j.trc.2009.12.002. [2] E. Ardjmand, G. Weckman, N. Park, P. Taherkhani and M. Singh, Applying genetic algorithm to a new location and routing model of hazardous materials, International Journal of Production Research, 53 (2015), 916-928. [3] G. Assadipour, G. Y. Ke and M. Verma, Planning and managing intermodal transportation of hazardous materials with capacity selection and congestion, Transportation Research Part E: Logistics and Transportation Review, 76 (2015), 45-57.  doi: 10.1016/j.tre.2015.02.003. [4] L. Bianco, M. Caramia and S. Giordani, A bilevel flow model for hazmat transportation network design, Transportation Research Part C: Emerging Technologies, 17 (2009), 175-196.  doi: 10.1016/j.trc.2008.10.001. [5] S. W. Chiou, A traffic-responsive signal control to enhance road network resilience with hazmat transportation in multiple periods, Reliability Engineering & System Safety, 175 (2018), 105-118.  doi: 10.1016/j.ress.2018.03.016. [6] J. Current and S. Ratick, A model to assess risk, equity and efficiency in facility location and transportation of hazardous materials, Location Science, 3 (1995), 187-201.  doi: 10.1016/0966-8349(95)00013-5. [7] T. J. Fan, W. C. Chiang and R. Russell, Modeling urban hazmat transportation with road closure consideration, Transportation Research Part D: Transport and Environment, 35 (2015), 104-115.  doi: 10.1016/j.trd.2014.11.009. [8] H. Jin and R. Batta, Objectives derived from viewing hazmat shipments as a sequence of independent Bernoulli trials, Transportation Science, 31 (1997), 252-261. [9] Y. Y. Kang, R. Batta and C. Y. Kwon, Generalized route planning model for hazardous material transportation with VaR and equity considerations, Computers & Operations Research, 43 (2014), 237-247.  doi: 10.1016/j.cor.2013.09.015. [10] R. R. Li, Y. Leung, B. Huang and H. Lin, A genetic algorithm for multiobjective dangerous goods route planning, International Journal of Geographical Information Science, 27 (2013), 1073-1089.  doi: 10.1080/13658816.2012.737921. [11] G. List and P. Mirchandani, An integrated network/planar multiobjective model for routing and siting for hazardous materials and wastes, Transportation Science, 25 (1991), 99-174.  doi: 10.1287/trsc.25.2.146. [12] N. Musee, L. Lorenzen and C. Aldrich, An aggregate fuzzy hazardous index for composite wastes, Journal of Hazardous Materials, 137 (2006), 723-733.  doi: 10.1016/j.jhazmat.2006.03.060. [13] R. Pradhananga, E. Taniguchi and T. Yamada, Ant colony system based routing and scheduling for hazardous material transportation, Procedia-Social and Behavioral Sciences, 2 (2010), 6097-6108.  doi: 10.1016/j.sbspro.2010.04.022. [14] R. Pradhananga, E. Taniguchi, T. Yamada and A. G. Qureshi, Bi-objective decision support system for routing and scheduling of hazardous materials, Socio-Economic Planning Sciences, 48 (2014), 135-148.  doi: 10.1016/j.seps.2014.02.003. [15] M. Rabbani, R. Heidari and R. Yazdanparast, A stochastic multi-period industrial hazardous waste location-routing problem: Integrating NSGA-Ⅱ and Monte Carlo simulation, European Journal of Operational Research, 272 (2019), 945-961.  doi: 10.1016/j.ejor.2018.07.024. [16] F. Samanlioglu, A multi-objective mathematical model for the industrial hazardous waste location-routing problem, European Journal of Operational Research, 226 (2013), 332-340.  doi: 10.1016/j.ejor.2012.11.019. [17] D. E. Shobrys, A Model for the Selection of Shipping Routes and Storage Locations for a Hazardous Substance, Ph. D thesis, Johns Hopkins University, 1981. [18] M. Taslimi, R. Batta and C. Kwon, A comprehensive modeling framework for hazmat network design, hazmat response team location, and equity of risk, Computers & Operations Research, 79 (2017), 119-130.  doi: 10.1016/j.cor.2016.10.005. [19] R. Tunalıoğlu, Ç. Koç and T. Bektaș, A multiperiod location-routing problem arising in the collection of Olive Oil Mill Wastewater, Journal of the Operational Research Society, 67 (2016), 1012-1024. [20] J. J. Wu, M. H. Liu, H. J. Sun, T. F. Li, Z. Y. Gao and D. Z. W. Wang, Equity-based timetable synchronization optimization in urban subway network, Transportation Research Part C: Emerging Technologies, 51 (2015), 1-18.  doi: 10.1016/j.trc.2014.11.001.

show all references

##### References:
 [1] K. N. Androutsopoulos and K. G. Zografos, Solving the bicriterion routing and scheduling problem for hazardous materials distribution, Transportation Research Part C: Emerging Technologies, 18 (2010), 713-726.  doi: 10.1016/j.trc.2009.12.002. [2] E. Ardjmand, G. Weckman, N. Park, P. Taherkhani and M. Singh, Applying genetic algorithm to a new location and routing model of hazardous materials, International Journal of Production Research, 53 (2015), 916-928. [3] G. Assadipour, G. Y. Ke and M. Verma, Planning and managing intermodal transportation of hazardous materials with capacity selection and congestion, Transportation Research Part E: Logistics and Transportation Review, 76 (2015), 45-57.  doi: 10.1016/j.tre.2015.02.003. [4] L. Bianco, M. Caramia and S. Giordani, A bilevel flow model for hazmat transportation network design, Transportation Research Part C: Emerging Technologies, 17 (2009), 175-196.  doi: 10.1016/j.trc.2008.10.001. [5] S. W. Chiou, A traffic-responsive signal control to enhance road network resilience with hazmat transportation in multiple periods, Reliability Engineering & System Safety, 175 (2018), 105-118.  doi: 10.1016/j.ress.2018.03.016. [6] J. Current and S. Ratick, A model to assess risk, equity and efficiency in facility location and transportation of hazardous materials, Location Science, 3 (1995), 187-201.  doi: 10.1016/0966-8349(95)00013-5. [7] T. J. Fan, W. C. Chiang and R. Russell, Modeling urban hazmat transportation with road closure consideration, Transportation Research Part D: Transport and Environment, 35 (2015), 104-115.  doi: 10.1016/j.trd.2014.11.009. [8] H. Jin and R. Batta, Objectives derived from viewing hazmat shipments as a sequence of independent Bernoulli trials, Transportation Science, 31 (1997), 252-261. [9] Y. Y. Kang, R. Batta and C. Y. Kwon, Generalized route planning model for hazardous material transportation with VaR and equity considerations, Computers & Operations Research, 43 (2014), 237-247.  doi: 10.1016/j.cor.2013.09.015. [10] R. R. Li, Y. Leung, B. Huang and H. Lin, A genetic algorithm for multiobjective dangerous goods route planning, International Journal of Geographical Information Science, 27 (2013), 1073-1089.  doi: 10.1080/13658816.2012.737921. [11] G. List and P. Mirchandani, An integrated network/planar multiobjective model for routing and siting for hazardous materials and wastes, Transportation Science, 25 (1991), 99-174.  doi: 10.1287/trsc.25.2.146. [12] N. Musee, L. Lorenzen and C. Aldrich, An aggregate fuzzy hazardous index for composite wastes, Journal of Hazardous Materials, 137 (2006), 723-733.  doi: 10.1016/j.jhazmat.2006.03.060. [13] R. Pradhananga, E. Taniguchi and T. Yamada, Ant colony system based routing and scheduling for hazardous material transportation, Procedia-Social and Behavioral Sciences, 2 (2010), 6097-6108.  doi: 10.1016/j.sbspro.2010.04.022. [14] R. Pradhananga, E. Taniguchi, T. Yamada and A. G. Qureshi, Bi-objective decision support system for routing and scheduling of hazardous materials, Socio-Economic Planning Sciences, 48 (2014), 135-148.  doi: 10.1016/j.seps.2014.02.003. [15] M. Rabbani, R. Heidari and R. Yazdanparast, A stochastic multi-period industrial hazardous waste location-routing problem: Integrating NSGA-Ⅱ and Monte Carlo simulation, European Journal of Operational Research, 272 (2019), 945-961.  doi: 10.1016/j.ejor.2018.07.024. [16] F. Samanlioglu, A multi-objective mathematical model for the industrial hazardous waste location-routing problem, European Journal of Operational Research, 226 (2013), 332-340.  doi: 10.1016/j.ejor.2012.11.019. [17] D. E. Shobrys, A Model for the Selection of Shipping Routes and Storage Locations for a Hazardous Substance, Ph. D thesis, Johns Hopkins University, 1981. [18] M. Taslimi, R. Batta and C. Kwon, A comprehensive modeling framework for hazmat network design, hazmat response team location, and equity of risk, Computers & Operations Research, 79 (2017), 119-130.  doi: 10.1016/j.cor.2016.10.005. [19] R. Tunalıoğlu, Ç. Koç and T. Bektaș, A multiperiod location-routing problem arising in the collection of Olive Oil Mill Wastewater, Journal of the Operational Research Society, 67 (2016), 1012-1024. [20] J. J. Wu, M. H. Liu, H. J. Sun, T. F. Li, Z. Y. Gao and D. Z. W. Wang, Equity-based timetable synchronization optimization in urban subway network, Transportation Research Part C: Emerging Technologies, 51 (2015), 1-18.  doi: 10.1016/j.trc.2014.11.001.
The results of period 1
The influence of $\lambda_3$
The influence of $W$
The weight of hazardous wastes generated by each factory in each period (Tons)
 Period Factory 1 2 3 4 5 6 7 1 28 19 21 24 32 20 22 2 19 27 23 16 25 11 14 3 12 20 15 10 14 13 17
 Period Factory 1 2 3 4 5 6 7 1 28 19 21 24 32 20 22 2 19 27 23 16 25 11 14 3 12 20 15 10 14 13 17
The transportation cost (＄/Ton) and the number of population exposed (Pop/Ton) of transporting a unit weight of hazardous wastes from one node to another
 Node 0 1 2 3 4 5 6 7 0 0/0 8/7 10/10 11/3 6/11 11/13 8/4 10/14 1 0/0 17/9 17/6 7/8 14/11 3/11 11/17 2 0/0 2/7 16/2 9/4 16/12 12/10 3 0/0 17/8 7/11 15/6 10/13 4 0/0 17/3 9/13 15/12 5 0/0 11/16 4/12 6 0/0 8/13 7 0/0
 Node 0 1 2 3 4 5 6 7 0 0/0 8/7 10/10 11/3 6/11 11/13 8/4 10/14 1 0/0 17/9 17/6 7/8 14/11 3/11 11/17 2 0/0 2/7 16/2 9/4 16/12 12/10 3 0/0 17/8 7/11 15/6 10/13 4 0/0 17/3 9/13 15/12 5 0/0 11/16 4/12 6 0/0 8/13 7 0/0
The computational results
 $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 0$ $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 5$ Period 1 Period 2 Period 3 Period 1 Period 2 Period 3 No. of vehicles 6 4 4 5 5 5 Transportation cost(＄) 6373 5278 4704 5399.8 5134.7 5445 Penalty fee(＄) 0 0 0 1415.7 1250 0 Transportation risk (Pop) 2442 2279 1726 1971.7 1971.7 1955 Total cost(＄) 16355 18645.2 Total transportation risk (Pop) 6447 5898.4
 $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 0$ $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 5$ Period 1 Period 2 Period 3 Period 1 Period 2 Period 3 No. of vehicles 6 4 4 5 5 5 Transportation cost(＄) 6373 5278 4704 5399.8 5134.7 5445 Penalty fee(＄) 0 0 0 1415.7 1250 0 Transportation risk (Pop) 2442 2279 1726 1971.7 1971.7 1955 Total cost(＄) 16355 18645.2 Total transportation risk (Pop) 6447 5898.4
 [1] Xiliang Sun, Wanjie Hu, Xiaolong Xue, Jianjun Dong. Multi-objective optimization model for planning metro-based underground logistics system network: Nanjing case study. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021179 [2] Jian Xiong, Zhongbao Zhou, Ke Tian, Tianjun Liao, Jianmai Shi. A multi-objective approach for weapon selection and planning problems in dynamic environments. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068 [3] Tien-Fu Liang, Hung-Wen Cheng. Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial and Management Optimization, 2011, 7 (2) : 365-383. doi: 10.3934/jimo.2011.7.365 [4] Zongmin Li, Jiuping Xu, Wenjing Shen, Benjamin Lev, Xiao Lei. Bilevel multi-objective construction site security planning with twofold random phenomenon. Journal of Industrial and Management Optimization, 2015, 11 (2) : 595-617. doi: 10.3934/jimo.2015.11.595 [5] Ya Liu, Zhaojin Li. Dynamic-programming-based heuristic for multi-objective operating theater planning. Journal of Industrial and Management Optimization, 2022, 18 (1) : 111-135. doi: 10.3934/jimo.2020145 [6] Han Yang, Jia Yue, Nan-jing Huang. Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration. Journal of Industrial and Management Optimization, 2020, 16 (2) : 759-775. doi: 10.3934/jimo.2018177 [7] Tone-Yau Huang, Tamaki Tanaka. Optimality and duality for complex multi-objective programming. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 121-134. doi: 10.3934/naco.2021055 [8] Maedeh Agahgolnezhad Gerdrodbari, Fatemeh Harsej, Mahboubeh Sadeghpour, Mohammad Molani Aghdam. A robust multi-objective model for managing the distribution of perishable products within a green closed-loop supply chain. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021107 [9] Alireza Eydi, Rozhin Saedi. A multi-objective decision-making model for supplier selection considering transport discounts and supplier capacity constraints. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3581-3602. doi: 10.3934/jimo.2020134 [10] Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial and Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130 [11] Zhongqiang Wu, Zongkui Xie. A multi-objective lion swarm optimization based on multi-agent. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022001 [12] Masoud Mohammadzadeh, Alireza Arshadi Khamseh, Mohammad Mohammadi. A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels. Journal of Industrial and Management Optimization, 2017, 13 (2) : 1041-1064. doi: 10.3934/jimo.2016061 [13] Dušan M. Stipanović, Claire J. Tomlin, George Leitmann. A note on monotone approximations of minimum and maximum functions and multi-objective problems. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 487-493. doi: 10.3934/naco.2011.1.487 [14] Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial and Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747 [15] Yuan-mei Xia, Xin-min Yang, Ke-quan Zhao. A combined scalarization method for multi-objective optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2669-2683. doi: 10.3934/jimo.2020088 [16] Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095 [17] Shungen Luo, Xiuping Guo. Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021208 [18] Adriel Cheng, Cheng-Chew Lim. Optimizing system-on-chip verifications with multi-objective genetic evolutionary algorithms. Journal of Industrial and Management Optimization, 2014, 10 (2) : 383-396. doi: 10.3934/jimo.2014.10.383 [19] Qiang Long, Xue Wu, Changzhi Wu. Non-dominated sorting methods for multi-objective optimization: Review and numerical comparison. Journal of Industrial and Management Optimization, 2021, 17 (2) : 1001-1023. doi: 10.3934/jimo.2020009 [20] Min Zhang, Gang Li. Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1413-1426. doi: 10.3934/dcdss.2019097

2020 Impact Factor: 1.801