American Institute of Mathematical Sciences

Advanced
doi: 10.3934/jimo.2019117

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

Hongguang Ma and  Xiang Li ,

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

* Corresponding author: Xiang Li

Received  January 2019 Revised  March 2019 Published  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.

Keywords: Hazardous waste collection, planning, multiple periods, multi-objective model, risk stability.
Mathematics Subject Classification: Primary: 90B06, 90B50; Secondary: 90C30.
Citation: Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019117
References:
[1]

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.  Google Scholar

[2]

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.  Google Scholar

[3]

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. Google Scholar

[4]

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.  Google Scholar

[5]

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.  Google Scholar

[6]

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.  Google Scholar

[7]

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.  Google Scholar

[8]

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.  Google Scholar

[9]

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.  Google Scholar

[10]

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.  Google Scholar

[11]

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.   Google Scholar

[12]

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.  Google Scholar

[13]

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.  Google Scholar

[14]

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.  Google Scholar

[15]

H. Jin and R. Batta, Objectives derived from viewing hazmat shipments as a sequence of independent Bernoulli trials, Transportation Science, 31 (1997), 252-261.   Google Scholar

[16]

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.  Google Scholar

[17]

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.  Google Scholar

[18]

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.  Google Scholar

[19]

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.  Google Scholar

[20]

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.   Google Scholar

show all references

References:
[1]

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.  Google Scholar

[2]

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.  Google Scholar

[3]

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. Google Scholar

[4]

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.  Google Scholar

[5]

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.  Google Scholar

[6]

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.  Google Scholar

[7]

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.  Google Scholar

[8]

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.  Google Scholar

[9]

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.  Google Scholar

[10]

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.  Google Scholar

[11]

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.   Google Scholar

[12]

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.  Google Scholar

[13]

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.  Google Scholar

[14]

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.  Google Scholar

[15]

H. Jin and R. Batta, Objectives derived from viewing hazmat shipments as a sequence of independent Bernoulli trials, Transportation Science, 31 (1997), 252-261.   Google Scholar

[16]

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.  Google Scholar

[17]

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.  Google Scholar

[18]

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.  Google Scholar

[19]

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.  Google Scholar

[20]

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.   Google Scholar

Figure 1.  The results of period 1
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  The influence of $ \lambda_3 $
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  The influence of $ W $
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  The weight of hazardous wastes generated by each factory in each period (Tons)
PeriodFactory
1234567
128192124322022
219272316251114
312201510141317
Table Options

Download as excel

PeriodFactory
1234567
128192124322022
219272316251114
312201510141317
Table 2.  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
Node01234567
00/08/710/1011/36/1111/138/410/14
10/017/917/67/814/113/1111/17
20/02/716/29/416/1212/10
30/017/87/1115/610/13
40/017/39/1315/12
50/011/164/12
60/08/13
70/0
Table Options

Download as excel

Node01234567
00/08/710/1011/36/1111/138/410/14
10/017/917/67/814/113/1111/17
20/02/716/29/416/1212/10
30/017/87/1115/610/13
40/017/39/1315/12
50/011/164/12
60/08/13
70/0
Table 3.  The computational results
$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 0 $$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 5 $
Period 1Period 2Period 3Period 1Period 2Period 3
No. of vehicles644555
Transportation cost(＄)6373527847045399.85134.75445
Penalty fee(＄)0001415.712500
Transportation risk (Pop)2442227917261971.71971.71955
Total cost(＄)1635518645.2
Total transportation risk (Pop)64475898.4
Table Options

Download as excel

$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 0 $$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 5 $
Period 1Period 2Period 3Period 1Period 2Period 3
No. of vehicles644555
Transportation cost(＄)6373527847045399.85134.75445
Penalty fee(＄)0001415.712500
Transportation risk (Pop)2442227917261971.71971.71955
Total cost(＄)1635518645.2
Total transportation risk (Pop)64475898.4
[1]

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 & Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068
[2]

Tien-Fu Liang, Hung-Wen Cheng. Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial & Management Optimization, 2011, 7 (2) : 365-383. doi: 10.3934/jimo.2011.7.365
[3]

Zongmin Li, Jiuping Xu, Wenjing Shen, Benjamin Lev, Xiao Lei. Bilevel multi-objective construction site security planning with twofold random phenomenon. Journal of Industrial & Management Optimization, 2015, 11 (2) : 595-617. doi: 10.3934/jimo.2015.11.595
[4]

Han Yang, Jia Yue, Nan-jing Huang. Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2018177
[5]

Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019130
[6]

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 & Management Optimization, 2017, 13 (2) : 1041-1064. doi: 10.3934/jimo.2016061
[7]

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 & Optimization, 2011, 1 (3) : 487-493. doi: 10.3934/naco.2011.1.487
[8]

Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial & Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747
[9]

Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095
[10]

Adriel Cheng, Cheng-Chew Lim. Optimizing system-on-chip verifications with multi-objective genetic evolutionary algorithms. Journal of Industrial & Management Optimization, 2014, 10 (2) : 383-396. doi: 10.3934/jimo.2014.10.383
[11]

Liwei Zhang, Jihong Zhang, Yule Zhang. Second-order optimality conditions for cone constrained multi-objective optimization. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1041-1054. doi: 10.3934/jimo.2017089
[12]

Danthai Thongphiew, Vira Chankong, Fang-Fang Yin, Q. Jackie Wu. An on-line adaptive radiation therapy system for intensity modulated radiation therapy: An application of multi-objective optimization. Journal of Industrial & Management Optimization, 2008, 4 (3) : 453-475. doi: 10.3934/jimo.2008.4.453
[13]

Min Zhang, Gang Li. Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1413-1426. doi: 10.3934/dcdss.2019097
[14]

Lorena Rodríguez-Gallego, Antonella Barletta Carolina Cabrera, Carla Kruk, Mariana Nin, Antonio Mauttone. Establishing limits to agriculture and afforestation: A GIS based multi-objective approach to prevent algal blooms in a coastal lagoon. Journal of Dynamics & Games, 2019, 6 (2) : 159-178. doi: 10.3934/jdg.2019012
[15]

Henri Bonnel, Ngoc Sang Pham. Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions. Journal of Industrial & Management Optimization, 2011, 7 (4) : 789-809. doi: 10.3934/jimo.2011.7.789
[16]

Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (2) : 855-879. doi: 10.3934/jimo.2018074
[17]

Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi. Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences & Engineering, 2012, 9 (2) : 297-312. doi: 10.3934/mbe.2012.9.297
[18]

Ábel Garab, Veronika Kovács, Tibor Krisztin. Global stability of a price model with multiple delays. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6855-6871. doi: 10.3934/dcds.2016098
[19]

Lou Caccetta, Elham Mardaneh. Joint pricing and production planning for fixed priced multiple products with backorders. Journal of Industrial & Management Optimization, 2010, 6 (1) : 123-147. doi: 10.3934/jimo.2010.6.123
[20]

Yanqin Bai, Chuanhao Guo. Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (2) : 543-556. doi: 10.3934/jimo.2014.10.543

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (15)
  • HTML views (81)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences