Optimization of batch production scheduling under multi-factor uncertain conditions

doi:10.11949/0438-1157.20191507

Abstract

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

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

CLC Number:

TQ 021.8

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

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.

Figures/Tables 11

Fig.1 State task network for production process instance

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

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

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

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

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]

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]

Fig.2 Solution results with single uncertainty

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

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

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

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

Fig.5 Optimal scheduling scheme under certain conditions

Fig.6 Comparison of results in three cases

Fig.7 Analysis of sales revenue composition in three cases

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