多因素不确定条件下的间歇生产调度优化

doi:10.11949/0438-1157.20191507

摘要/Abstract

摘要：

不确定条件下的间歇生产调度优化是生产调度问题研究中具有挑战性的课题。提出了一种基于混合整数线性规划(MILP)的鲁棒优化模型，来优化不确定条件下的生产调度决策。考虑到生产过程中的操作成本和原料成本，建立了以净利润最大为调度目标的确定性数学模型。然后考虑需求、处理时间、市场价格三种不确定因素，建立可调整保守程度的鲁棒优化模型并转换成鲁棒对应模型。实例结果表明，鲁棒优化的间歇生产调度模型较确定性模型利润减少，但生产任务数量增加，设备空闲时间缩短，从而增强了调度方案的可靠性，实现了不确定条件下生产操作性和经济性的综合优化。

关键词: 间歇过程, 生产调度, 不确定, 鲁棒优化

Abstract:

The optimization of batch chemical production scheduling under uncertainty is a challenging topic in the study of production scheduling problems. A robust optimization model based on mixed integer linear programming (MILP) is proposed to optimize production scheduling decisions under uncertain conditions. Considering the operating costs and raw material costs in the production process, a deterministic mathematical model with the target of net profit maximization was constructed. Then three uncertainties, demand, processing time, and market price were considered. The robust optimization model which could adjust the degree of conservatism was established and transformed into a robust counterpart model. The example results showed that the robust optimized batch production scheduling model had lower profit than the deterministic one, but the reliability of the scheduling scheme was enhanced with more production tasks and less equipment idle time, which achieved production operational and economic optimization under uncertainty.

Key words: batch process, production scheduling, uncertain, robust optimization

中图分类号:

TQ 021.8

郑必鸣, 史彬, 鄢烈祥. 多因素不确定条件下的间歇生产调度优化[J]. 化工学报, 2020, 71(3): 1246-1253.

Biming ZHENG, Bin SHI, Liexiang YAN. Optimization of batch production scheduling under multi-factor uncertain conditions[J]. CIESC Journal, 2020, 71(3): 1246-1253.

图/表 11

图1 本例中状态任务网络图描述的间歇生产过程

Fig.1 State task network for production process instance

表1 案例中与任务相关的工艺和成本数据

Table 1 Process and cost data related to tasks in the case

Task	Label(i)	Unit	Label(j)	$α_{i, j}$ /h	$β_{i, j}$ /(h·kg^-1)	$B_{i, j}^{m a x}$ /kg	$B_{i, j}^{m i n}$ /kg	fixc_i/USD	varc_i/(USD·kg^-1)
heating	H	heater	HR	0.667	0.00667	100	—	150	1
reaction 1	R1	reactor 1	RR1	1.334	0.02664	50	—	100	0.5
reaction 1	R1	reactor 2	RR2	1.334	0.01665	80	—	100	0.5
reaction 2	R2	reactor 1	RR1	1.334	0.02664	50	—	100	0.5
reaction 2	R2	reactor 2	RR2	1.334	0.01665	80	—	100	0.5
reaction 3	R3	reactor 1	RR1	0.667	0.01332	50	—	100	0.5
reaction 3	R3	reactor 2	RR2	0.667	0.008325	80	—	100	0.5
separation	S	separator	SR	1.3342	0.00666	200	—	150	1

表1 案例中与任务相关的工艺和成本数据

Table 1 Process and cost data related to tasks in the case

Task	Label(i)	Unit	Label(j)	$α_{i, j}$ /h	$β_{i, j}$ /(h·kg^-1)	$B_{i, j}^{m a x}$ /kg	$B_{i, j}^{m i n}$ /kg	fixc_i/USD	varc_i/(USD·kg^-1)
heating	H	heater	HR	0.667	0.00667	100	—	150	1
reaction 1	R1	reactor 1	RR1	1.334	0.02664	50	—	100	0.5
reaction 1	R1	reactor 2	RR2	1.334	0.01665	80	—	100	0.5
reaction 2	R2	reactor 1	RR1	1.334	0.02664	50	—	100	0.5
reaction 2	R2	reactor 2	RR2	1.334	0.01665	80	—	100	0.5
reaction 3	R3	reactor 1	RR1	0.667	0.01332	50	—	100	0.5
reaction 3	R3	reactor 2	RR2	0.667	0.008325	80	—	100	0.5
separation	S	separator	SR	1.3342	0.00666	200	—	150	1

表2 案例中的物料的库存、初始量、价格和需求量数据

Table 2 Inventory, initial amounts, price, and demand data for materials in the case

Material	$V_{s}^{m a x}$ /kg	Sti_s/kg	pri_s/(USD·kg^-1)	dem_s/kg
S1	UL	AA	1.5	0
S2	UL	AA	1.5	0
S3	UL	AA	1.5	0
S4	100	0	0	0
S5	200	0	0	0
S6	150	0	0	0
S7	200	0	0	0
S8	UL	0	15	80
S9	UL	0	15	100

表2 案例中的物料的库存、初始量、价格和需求量数据

Table 2 Inventory, initial amounts, price, and demand data for materials in the case

Material	$V_{s}^{m a x}$ /kg	Sti_s/kg	pri_s/(USD·kg^-1)	dem_s/kg
S1	UL	AA	1.5	0
S2	UL	AA	1.5	0
S3	UL	AA	1.5	0
S4	100	0	0	0
S5	200	0	0	0
S6	150	0	0	0
S7	200	0	0	0
S8	UL	0	15	80
S9	UL	0	15	100

表3 三种不确定因素的波动范围和预算参数取值范围

Table 3 Range of fluctuations for three uncertain factors and budget parameters

Item	Demand uncertainty		Process time uncertainty		Price uncertainty
Item	$σ^{d}$	$Γ^{d}$	$σ^{t}$	$Γ^{t}$	$σ^{p}$	$Γ^{p}$
range	±30%	[0,1]	±25%	[0,1]	±5%	[0,5]

表3 三种不确定因素的波动范围和预算参数取值范围

Table 3 Range of fluctuations for three uncertain factors and budget parameters

Item	Demand uncertainty		Process time uncertainty		Price uncertainty
Item	$σ^{d}$	$Γ^{d}$	$σ^{t}$	$Γ^{t}$	$σ^{p}$	$Γ^{p}$
range	±30%	[0,1]	±25%	[0,1]	±5%	[0,5]

图2 考虑单一不确定因素的求解结果

Fig.2 Solution results with single uncertainty

表4 同时考虑三种不确定因素的求解结果

Table 4 Solution results with all uncertainties

Item	Budget parameter( $Γ^{d}$ , $Γ^{t}$ , $Γ^{p}$ )
Item	(0,0,0)	(0.1,0.1,0.5)	(0.2,0.2,1)	(0.3,0.3,1.5)	(0.4,0.4,2)	(0.5,0.5,2.5)	(0.6,0.6,3)	(0.7,0.7,3.5)
profit/USD	1435.75	1382.59	1288.46	1192.24	1100.94	1032.97	849.39	/
CPU time/s	0.31	0.38	0.38	0.53	0.59	0.64	0.78	0.77

表4 同时考虑三种不确定因素的求解结果

Table 4 Solution results with all uncertainties

Item	Budget parameter( $Γ^{d}$ , $Γ^{t}$ , $Γ^{p}$ )
Item	(0,0,0)	(0.1,0.1,0.5)	(0.2,0.2,1)	(0.3,0.3,1.5)	(0.4,0.4,2)	(0.5,0.5,2.5)	(0.6,0.6,3)	(0.7,0.7,3.5)
profit/USD	1435.75	1382.59	1288.46	1192.24	1100.94	1032.97	849.39	/
CPU time/s	0.31	0.38	0.38	0.53	0.59	0.64	0.78	0.77

图3 不确定条件下的最优调度方案 (Γ d=0.3, Γ t =0.3, Γ p =1.5)

Fig.3 Optimal scheduling scheme under uncertain conditions(Γ d =0.3, Γ t =0.3, Γ p =1.5)

图4 不确定条件下的最优调度方案(Γ d =0.6, Γ t =0.6, Γ p =3)

Fig.4 Optimal scheduling scheme under uncertain conditions(Γ d =0.6, Γ t =0.6, Γ p =3)

图5 确定条件下的最优调度方案

Fig.5 Optimal scheduling scheme under certain conditions

图6 三种情况下结果的比较

Fig.6 Comparison of results in three cases

图7 三种情况下的销售收入构成分析

Fig.7 Analysis of sales revenue composition in three cases

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