A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

doi:10.1007/s11705-019-1858-4

Frontiers of Chemical Science and Engineering

2019, Vol. 13

Issue (4): 784-802 https://doi.org/10.1007/s11705-019-1858-4

本期目录

A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

Nikolaos Rakovitis¹, Nan Zhang¹, Jie Li¹(

), Liping Zhang²

¹. Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester, M13 9PL, UK
². Department of Industrial Engineering, School of Machinery and Automation, Wuhan University of Science and Technology, Wuhan 430081, China

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Abstract：

The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.

Key words： scheduling multipurpose batch processes simultaneous transfer mixed-integer linear programming

收稿日期: 2018-12-01 出版日期: 2019-12-04

Corresponding Author(s): Jie Li

引用本文:

. [J]. Frontiers of Chemical Science and Engineering, 2019, 13(4): 784-802.
Nikolaos Rakovitis, Nan Zhang, Jie Li, Liping Zhang. A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy. Front. Chem. Sci. Eng., 2019, 13(4): 784-802.

链接本文:

https://academic.hep.com.cn/fcse/CN/10.1007/s11705-019-1858-4
https://academic.hep.com.cn/fcse/CN/Y2019/V13/I4/784

Fig.1

Fig.2

Unit	Maximum capacity /mu	Minimum capacity /mu	$α i$ /h	$β i$ /h
J1	100	0	3	0.02
J2	100	0	2	0.01

Tab.1

Fig.3

Fig.4

Fig.5

Tab.2

Fig.6

Fig.7

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	1.333	0.01333	100
2	2	1.333	0.01333	150
3	3	1.000	0.00500	200
4	4	0.667	0.00445	150
5	5	0.667	0.00445	150

Tab.3

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	0.667	0.00667	100
2	2	1.334	0.02664	50
3	3	1.334	0.01665	80
4	2	1.334	0.02664	50
5	3	1.334	0.01665	80
6	2	0.667	0.01332	50
7	3	0.667	0.008325	80
8	4	1.334	0.00666	200

Tab.4

Fig.8

Task	Processing unit	$α i$	$β i$	$B i min$	$B i max$
1	1	0.667	0.00667	0	100
2	1	1.000	0.01000	0	100
3	2	1.333	0.01333	0	100
4	3	1.333	0.00889	0	150
5	2	0.667	0.00667	0	100
6	3	0.667	0.00445	0	150
7	2	1.333	0.01330	0	100
8	3	1.333	0.00889	0	150
9	4	2.000	0.00667	0	300
10	5	1.333	0.00667	20	200
11	6	1.333	0.00667	20	200

Tab.5

Fig.9

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	1.333	0.01333	100
2	2	1.333	0.01333	150
3	3	1.000	0.00500	200
4	4	0.667	0.00445	150
5	5	0.667	0.00445	150
6	6	1.000	0.00500	200

Tab.6

Fig.10

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	1.333	0.01333	100
2	2	1.333	0.01333	150
3	3	1.000	0.00500	200
4	4	0.667	0.00445	150
5	5	0.667	0.00445	150
6	6	1.000	0.00500	200
7	7	1.333	0.01333	100
8	8	1.333	0.01333	150

Tab.7

Fig.11

Task	Processing unit	$α i$	$β i$	$B i max$
1?3	1	1.333	0.01333	100
4?6	2	1.333	0.01333	150
7?9	3	1.000	0.00500	200
10?12	4	0.667	0.00445	150
13?15	5	0.667	0.00445	150
16?18	6	1.000	0.00500	200
19?21	7	1.333	0.01333	100
22?24	8	1.333	0.01333	150

Tab.8

Fig.12

Task	Processing unit	$α i$	$B i max$
1	1	6.000	200
2	2	5.000	100
3	3	9.000	100
4	4	2.000	50
5	5	3.000	50
6	6	4.000	50
7	7	2.000	100

Tab.9

Fig.13

Task	Processing unit	$α i$	$B i max$
1	1	1.000	10
2	2	3.000	4
3	3	1.000	2
4	4	2.000	10

Tab.10

Fig.14

Task	Processing unit	$α i$	$B i max$
1	1	1.500	150
2	2	4.500	60
3	3	1.500	30
4	4	1.500	30
5	5	3.000	150

Tab.11

Fig.15

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	17.333	0.866	20
2	2	2.667	0.133	20
3	3	2.667	0.133	20
4	4	4.000	0.200	20
5	5	5.333	0.266	20
6	6	5.333	0.266	20

Tab.12

Fig.16

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	1.666	0.03335	40
2	2	2.333	0.08335	20
3	3	0.667	0.06600	5
4	4	2.667	0.008325	40

Tab.13

Task	Processing unit	$α i$	$β i$	$B i max$
1	1	1.666	0.03335	40
2	2	2.333	0.08335	20
3	3	0.333	0.06800	2.5
4	4	2.667	0.008325	40

Tab.14

Tab.15

Tab.16

Tab.17

Tab.18

Tab.19

Example	Model	Event points	CPU time /s	RMILP /h	MILP /h	Discrete variables	Continuous variables	Constraints
1a (H= 50 h)	SF	14	11.45	24.24	27.88	70	268	394
$D s 4$ =2000	M2	12	5.30	25.36	27.88	60	230	342
	M1	12	6.96	24.24	27.88	60	254	383
1b (H= 100 h)	SF	23	7.50	48.47	52.07	115	439	646
$D s 4$ =4000	M2	21	5.70	50.06	52.07	105	401	594
	M1	21	4.81	48.47	52.07	105	443	671
2a(H= 50 h)	SF	9	96.00	10.78	19.34	72	301	515
$D s 8$ =200	M2	9	28.78	10.78	19.34	72	301	515
$D s 9$ =200	M1	9	46.58	18.68	19.34	72	265	425
2b(H= 100 h)	SF	19	3600^a)	45.57	46.31	152	631	1105
$D s 8$ =500	M2	19	3600^b)	45.57	46.31	152	631	1107
$D s 9$ =400	M1	19	3600^c)	45.57	46.31	152	555	905
3a (H= 50 h)	SF	7	0.187	11.07	13.37	77	327	572
$D s 12$ =100	M2	7	0.250	11.07	13.37	77	327	572
$D s 13$ =200	M1	7	0.374	11.25	13.37	77	306	501
3b (H= 50 h)	SF	10	0.515	12.50	17.03	110	465	827
$D s 12$ =250	M2	10	0.374	12.76	17.03	110	465	827
$D s 13$ =250	M1	10	0.359	14.27	17.03	110	435	723

Tab.20

Fig.17

Fig.18

Tab.21

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