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  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 & 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.  Google Scholar

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G. AssadipourG. 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

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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

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Y. Y. KangR. 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

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R. R. LiY. LeungB. 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

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N. MuseeL. 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

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R. PradhanangaE. 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

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R. PradhanangaE. TaniguchiT. 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

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M. RabbaniR. 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

[16]

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[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. Google Scholar

[18]

M. TaslimiR. 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

[19]

R. TunalıoğluÇ. 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

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J. J. WuM. H. LiuH. J. SunT. F. LiZ. 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

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.  Google Scholar

[2]

E. ArdjmandG. WeckmanN. ParkP. 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

[3]

G. AssadipourG. 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

[4]

L. BiancoM. 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

[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.  Google Scholar

[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.  Google Scholar

[7]

T. J. FanW. 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

[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.   Google Scholar

[9]

Y. Y. KangR. 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

[10]

R. R. LiY. LeungB. 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

[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.  Google Scholar

[12]

N. MuseeL. 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

[13]

R. PradhanangaE. 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

[14]

R. PradhanangaE. TaniguchiT. 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

[15]

M. RabbaniR. 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

[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.  Google Scholar

[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. Google Scholar

[18]

M. TaslimiR. 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

[19]

R. TunalıoğluÇ. 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

[20]

J. J. WuM. H. LiuH. J. SunT. F. LiZ. 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

Figure 1.  The results of period 1
Figure 2.  The influence of $ \lambda_3 $
Figure 3.  The influence of $ W $
Table 1.  The weight of hazardous wastes generated by each factory in each period (Tons)
PeriodFactory
1234567
128192124322022
219272316251114
312201510141317
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
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 $$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 5 $
Period 1Period 2Period 3Period 1Period 2Period 3
No. of vehicles644555
Transportation cost($)6373527847045399.85134.75445
Penalty fee($)0001415.712500
Transportation risk (Pop)2442227917261971.71971.71955
Total cost($)1635518645.2
Total transportation risk (Pop)64475898.4
$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 0 $$ \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
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