An interval joint-probabilistic programming method for solid waste management: a case study for the city of Tianjin, China

doi:10.1007/s11783-013-0536-x

Front Envir Sci Eng

2014, Vol. 8

Issue (2) : 239-255 https://doi.org/10.1007/s11783-013-0536-x

RESEARCH ARTICLE

An interval joint-probabilistic programming method for solid waste management: a case study for the city of Tianjin, China

Yi XU, Shunze WU(

), Hongkuan ZANG, Guiguang HOU

Key Laboratory of Environmental Planning and Policy Simulation, Chinese Academy for Environmental Planning, Beijing 100012, China

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Abstract

Currently, environmental protection and resources conservation continue to be challenges faced by solid-waste managers in China. These challenges are being further compounded by rapid socioeconomic development and population growth associated with increased waste generation rates and decreased waste disposal capacities. In response to these challenges, an interval joint-probabilistic mixed-integer programming (IJMP) method is developed for supporting long-term planning of waste management activities in the city of Tianjin, which is one of the largest municipalities in the northern part of China. In the IJMP, joint probabilistic constraints are introduced into an interval-parameter mixed-integer programming framework, such that uncertainties presented in terms of interval values and random variables can be reflected. Moreover, a number of violation levels for the waste-management-capacity constraints are examined, which can facilitate in-depth analyses of tradeoffs among economic objective and system-failure risk. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment of the city’s existing waste-management practices and the long-term planning of the city’s waste-management facilities.

Keywords interval analysis mixed integer joint probabilistic constraint planning uncertainty waste management

Corresponding Author(s): WU Shunze,Email:wusz@caep.org.cn

Issue Date: 01 April 2014

Cite this article:

Yi XU,Shunze WU,Hongkuan ZANG, et al. An interval joint-probabilistic programming method for solid waste management: a case study for the city of Tianjin, China[J]. Front Envir Sci Eng, 2014, 8(2): 239-255.

URL:

https://academic.hep.com.cn/fese/EN/10.1007/s11783-013-0536-x
https://academic.hep.com.cn/fese/EN/Y2014/V8/I2/239

Fig.1 Study area. (Symbols “A” denotes the “Hongqiao District,” “B” denotes the “Hebei District,” “C” denotes the “Nankai District,” “D” denotes the “Heping District,” “E” denotes the “Hedong District,” “F” denotes the “Hexi District”)

Tab.1 Waste generation amount in different districts

Fig.2 Waste flow in the city of Tianjin

Tab.2 Operating costs and revenues of facilities

Tab.3 Capacity expansion options and costs

Tab.4 Joint probability under different cases

Tab.5 Capacities of landfills and incinerators

Fig.3 Expansion schemes for the landfills: (a) lower bound and (b) upper bound

Fig.4 Expansion schemes for the incinerators: (a) lower bound and (b) upper bound

case	period	facility	waste flows /(tonne·d^-1)
1	1	landfill 1	[2451.2, 2611.7]
	1	landfill 2	[1157.1, 1364.1]
	1	incinerator 1	[613.2, 683.5]
	1	incinerator 2	[1522.0, 1618.5]
	1	incinerator 3	[929.9, 1023.5]
	2	landfill 1	[2555.6, 2745. 8]
	2	landfill 2	[1541.4, 1811.0
	2	incinerator 1	[855.8, 938.5]
	2	incinerator 2	[1757.9, 1873.5]
	2	incinerator 3	[1589.3, 1703.5]
	3	landfill 1	[3503.4, 3712.7]
	3	landfill 2	[1984.5, 2294.9]
	3	incinerator 1	[806.8, 904.7]
	3	incinerator 2	[1904.6, 2043.5]
	3	incinerator 3	[1819.2, 1958.5]
2	1	landfill 1	[2440.0, 2603.3]
	1	landfill 2	[1133.1, 1339.6]
	1	incinerator 1	[620.8, 699.1]
	1	incinerator 2	[1545.8, 1634.1]
	1	incinerator 3	[945.5, 1039.1]
	2	landfill 1	[2528.2, 2719.2]
	2	landfill 2	[1533.6, 1804.8]
	2	incinerator 1	[871.4, 954.1]
	2	incinerator 2	[1773.5, 1889.1]
	2	incinerator 3	[1604.9, 1719.1]
	3	landfill 1	[3566.3, 3777.8]
	3	landfill 2	[2056.7, 2355.8]
	3	incinerator 1	[850.4, 948.3]
	3	incinerator 2	[1750.2, 1889.1]
	3	incinerator 3	[1749.9, 1889.1]
3	1	landfill 1	[2430.3, 2594.4]
	1	landfill 2	[1114.5, 1321.9]
	1	incinerator 1	[632.2, 711.7]
	1	incinerator 2	[1559.6, 1646.7]
	1	incinerator 3	[958.1, 1051.7]
	2	landfill 1	[2506.1, 2697.7]
	2	landfill 2	[1527.3, 1799.8]
	2	incinerator 1	[884.0, 966.7]
	2	incinerator 2	[1786.1, 1901.7]
	2	incinerator 3	[1617.6, 1731.7]
	3	landfill 1	[3586.0, 3794.4]
	3	landfill 2	[2064.4, 2364.8]
	3	incinerator 1	[788.7, 886.6]
	3	incinerator 2	[1762.8, 1901.7]
	3	incinerator 3	[1762.5, 1901.7]
4	1	landfill 1	[2433.9, 2597.9]
1	landfill 2	[1121.9, 1328.8]
1	incinerator 1	[627.3, 706.8]
1	incinerator 2	[1554.7, 1641.8]
1	incinerator 3	[953.2, 1046.8]
2	landfill 1	[2578.5, 2765.6]
2	landfill 2	[1529.8, 1801.7]
2	incinerator 1	[794.1, 876.8]
2	incinerator 2	[1781.2, 1896.8]
2	incinerator 3	[1612.6, 1726.8]
3	landfill 1	[3545.4, 3751.6]
3	landfill 2	[2080.4, 2384.5]
3	incinerator 1	[746.4, 844.4]
3	incinerator 2	[1757.9, 1896.8]
3	incinerator 3	[1842.6, 1981.8]
5	1	landfill 1	[2440.0, 2603.3]
1	landfill 2	[1133.1, 1339.6]
1	incinerator 1	[620.8, 699.1]
1	incinerator 2	[1545.8, 1634.1]
1	incinerator 3	[945.5, 1039.1]
2	landfill 1	[2591.9, 2778.7]
2	landfill 2	[1533.6, 1804.8]
2	incinerator 1	[786.4, 869.1]
2	incinerator 2	[1773.5, 1889.1]
2	incinerator 3	[1604.9, 1719.1]
3	landfill 1	[3538.8, 3746.3]
3	landfill 2	[2080.6, 2384.0]
3	incinerator 1	[770.2, 868.2]
3	incinerator 2	[1750.2, 1889.1]
3	incinerator 3	[1834.9, 1974.1]
6	1	landfill 1	[2371.4, 2530.6]
1	landfill 2	[1188.9, 1398.7]
1	incinerator 1	[620.8, 693.2]
1	incinerator 2	[1550.3, 1646.7]
1	incinerator 3	[958.1, 1051.7]
2	landfill 1	[2506.1, 2697.7]
2	landfill 2	[1527.3, 1799.8]
2	incinerator 1	[884.0, 966.7]
2	incinerator 2	[1786.1, 1901.7]
2	incinerator 3	[1617.6, 1731.7]
3	landfill 1	[3683.6, 3896.5]
3	landfill 2	[2034.2, 2326.1]
3	incinerator 1	[868.8, 966.7]
3	incinerator 2	[1762.8, 1901.7]
3	incinerator 3	[1592.5, 1731.7]

Tab.6 Solutions of waste-flow allocation under different cases

Fig.5 Waste flows to different facilities (Symbols “WTI” and “WTL” denote the total amount of waste flows to incinerators and landfills, respectively): (a) period 1, (b) period 2 and (c) period 3

Tab.7 Solutions for costs under different cases

Fig.6 Transportation, operation and expansion costs under different cases

Fig.7 The total expanded capacity for the three incinerators under the two scenarios

Fig.8 Costs and revenues under the two scenarios. (“TC” denotes the “transportation cost,” “OC” denotes the “operation cost,” “EC” denotes the “expansion cost,” “RE” denotes the “revenue of all the facilities,” “SC” denotes the “system cost”)

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