Integrated optimization of process planning and scheduling for reducing carbon emissions

Qiong Liu; Jialiang Liu; Zhaorui Dong; Mengmeng Zhan; Zhen Mei; Baosheng Ying; Xinyu Shao

doi:10.3934/jimo.2020010

Article Contents

2021, Volume 17, Issue 3: 1025-1055. Doi: 10.3934/jimo.2020010

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Integrated optimization of process planning and scheduling for reducing carbon emissions

1.
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
2.
School of Automobile and Traffic Engineering, Wuhan University of Science and Technology, Wuhan 430081, China

^* Corresponding author: Qiong Liu
^* Corresponding author: Qiong Liu

Received: October 2018

Revised: June 2019

Early access: January 2020

Published: May 2021

The first author is supported by NSFC grant No.51675206 and No.51561125002 and FRFCU HUST:2016YXMS275

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Abstract

In order to reduce environment impacts of manufacturing processes and fill in research gaps that most previous separated optimization of process planning and scheduling ignored influences of process planning on scheduling, a multi-objective integrated optimization model of process planning and scheduling for reducing carbon emissions in manufacturing processes is proposed. The model aims at minimizing makespan and carbon emissions in manufacturing processes by integrated optimizing machining methods for all machining features of workpieces, machine allocations of processes, process routes and machining sequence of workpieces. Because there are many parameters in the proposed model needed to be optimized and they are interactional, a four segment encoding method is designed and a Non-dominated Sorting Genetic Algorithm II is adopted to solve the proposed model. A case study including three workpieces with twenty-three machining features to be processed by turning, milling, drilling, boring and grinding is used to verify the proposed integrated model and algorithm. Results show that the proposed integrated optimization method can further reduce carbon emissions and makespan in manufacturing processes compared with conventional separated optimization of process planning and scheduling. The proposed integrated optimization method is validated.

Keywords:

Low carbon manufacturing,
integrated optimization of process planning and scheduling,
scheduling,
process planning.

Mathematics Subject Classification: Primary: 90B35, 90C10, 90C59, 90C29.

Citation:

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Figure 1. Flow chart of NSGA-II

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Figure 2. Four segment encoding

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Figure 3. Crossover of genes in machining method and machine allocation codes

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Figure 4. Crossover of genes in process route code

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Figure 5. Crossover of genes in machining sequence code

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Figure 6. Mutation of genes in machining method and machine allocation code

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Figure 7. Mutation of process route code

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Figure 8. Mutation of machine allocation code

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Figure 9. Mutation of machining sequence code

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Figure 10. The workpiece 1 of sleeve

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Figure 11. The workpiece 2 of hinge

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Figure 12. The workpiece 3 of flange

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Figure 13. The Gantt chart of solution 1

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Figure 14. The Gantt chart of solution 29

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Figure 15. The relationship of two objectives

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Figure 16. Components of carbon emissions in each solution in the Pareto set

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Figure 17. Gantt chart of solution 1 for scheduling after process planning

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Table 1. Literatures on IPPS

IPPS	Publication	Optimization Objectives	Decision Variables	Optimization method
Integrated Optimization of Cutting Parameters and Scheduling	Fang et al.(2011)	1. Makespan 2. Peak total power consumptions 3. Carbon footprints of machines	1. Schedule plans	Schedule under limited sets of cutting speed
	Lin et al. [20]	1. Makespan 2. Carbon footprints caused by energy consumption of machines in machining and idling states and material consumption of cutting tools	1. Cutting parameters 2. Schedule plans	Optimization of cutting parameters before scheduling
	Zhang et al. [45]	1. Completion time 2. Carbon emissions caused by energy consumption of machines in machining and idling states, and material consumption of cutting tools and cutting fluid	1. Cutting parameters 2. Schedule plans	Real integrated optimization
Integrated Optimization of Process Planning	Chaudhry and Usman [6]	1. Makespan	1. Process routes 2.Schedule plans	Select one process route for each workpiece from a predetermined process route set before scheduling
	Qiao and Lv [31]	1. Makespan 2. Mean flow time	1. Process routes 2. Machining methods	Optimization of process plan before scheduling
	Bettwyet al. [4]	1. Makespan	1. Process routes 2. Schedule plans	Integrated optimization, but transportation time and setup time were ignored
	Li et al. [19]	1. Makespan 2. Machine utilization 3. Energy consumption of machines in powered on, idling, preheated, machining and powered off states	1. Machining sequence of workpieces 2. Machine allocation 3. Cutting tool selection 4. Cutting tool approaching direction	Scheduling based on generated process plans of workpieces
	Zhang et al. [46]	1. Energy consumptions of machines in machining and idling states	1. Process plans 2. scheduling plans	Scheduling under the process plans selected from candidates
	Wang et al. [37]	1. Makespan 2. Energy consumptions of machines in machining, idling, setup and tool changing states	1. Cutting parameters 2. Process routes 3. Scheduling	Integrated optimization of process routes and scheduling using the optimized cutting parameters

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Table 2. Parameters and variables

N=(1, 2, ...n)	set of workpieces	M=(1, 2, ..., m)	set of machines
i	workpiece i $ \in $ N	k	machine k$ \in $ M
$ f_{ir} $	the r-th machining feature of workpiece i, r$ \in $ (1, 2, ..., $ F_{i} $)	(1, 2, ...$ N_{fir} $)	set of candidate machining methods for machining feature $ f_{ir} $
$ o_{ij} $	the j-th process of workpiece i, j$ \in $J, J=(1, 2, ..., $ n_{i} $)	$ M_{ij} $	set of candidate machines for the j-th process of workpiece i
$ C_{p} $	carbon emissions in manufacturing processes
$ C_{Me} $	carbon emissions caused by energy consumption of machines in machining state
$ C_{Ie} $	carbon emissions caused by energy consumption of machines in idling state
$ C_{Ae} $	carbon emissions caused by energy consumption of machines in setup state
$ C_{c} $	carbon emissions caused by consumption of coolant
$ C_{l} $	carbon emissions caused by consumption of lubricant
$ C_{t} $	carbon emissions caused by energy consumption of electric fork lifts
$ \alpha_{e} $	carbon emission factor of electric energy
$ P_{ijk} $	power of machine k to machine the j-th process of workpiece i
$ t_{ijk} $	power of machine to machine the j-th process of workpiece i on machine k
$ P_{idle, k} $	idling power of machine k
$ S_{ijk} $, $ C_{ijk} $	start time and completion time of the j-th process of workpiece i on the machine k
$ C_{hlk} $	completion time of the l-th process of the immediate preceding processing workpiece h of workpiece i on machine k, $ S_{ijk} $=$ C_{hlk} $ if the j-th process of workpiece i is the first process on machine k
$ S_{fok} $	start time of the o-th process of the immediate succeeding processing workpiece h of workpiece i on machine k, $ S_{fok} $=$ C_{ijk} $ if the j-th process of workpiece i is the last process on machine k
$ P_{hik} $, $ t_{hik} $	setup power and time of machine k from processing the immediate preceding processing workpiece h to workpiece i
$ E_{k} $	energy consumption of machine in state of power on, preheating and power off
$ T_{ck} $	effective duration of coolant in machine k
$ L_{ck} $	recycling coolants in machine k
$ \alpha_{ck} $	carbon emission factor of coolant
$ T_{open, k} $, $ T_{dose, k} $	power on time and power off time of machine k; $ T_{open, k} $-$ T_{dose, k} $: operation time of machine k.
$ T_{lk} $	effective duration of lubricant in machine k
$ L_{lk} $	lubricant consumptions in machine k
$ \alpha_{l} $	carbon emission factor of lubricant
$ P_{tij} $	power of electric forklift to handle workpiece i from machine k' for the (j-1)-th process of workpiece i to machine k for the j-th process of workpiece
$ T_{lk} $	effective duration of lubricant in machine k
$ t_{tij} $	transmission time needed to move workpiece i from machine k' for the (j-1)-th process of workpiece i to machine k for the j-th process of workpiece i
$ C_{time} $	makespan in manufacturing processes
$ X_{fir} $	the selected machining method for machining feature $ f_{ir} $ of workpiece i
$ l_{z} $	the l-th flexible process section of type $ T_{z} $
$ O_{iplz} $	process p in the l-th flexible process section of type $ T_{z} $ of workpiece i
$ X_{ijk} $	decision variable

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Table 3. Machining features, processing constraint, machining methods and machine types of workpieces

Workpiece	Machining features	Processing constraints on machining feature	Candidate machining methods	Process re-coding	Machine types
Workpiece 1	$ f_{1} $		Method 1:Rough turning a(200s)-Finish turning b(160s) Method 2:Rough milling a (180s)-Finish milling b(150s)	Rough turning 1- Finish turning 9 Rough milling 1- Finish milling 9	Turning lathe- Turning lathe Milling machine- Milling machine
	$ f_{2} $		Method 1:Rough turning c (120s)- Finish turning d(60s)-Grinding e(100s)	Rough turning 2- Finish turning 10- Grinding 16	Turning lathe - Turning lathe -Grinding machine
	$ f_{3} $		Method 1:Rough turning f (130s)- Finish turning g (50s)- Grinding h (120s) Method 2:Rough milling f(100s)-Finish milling g(40s)- Grinding h (120s)	Rough turning 4-Finish turning12-Grinding 18 Rough milling 4-Finish milling 12 -Grinding 18	Turning lathe - Turning lathe -Grinding machine Milling machine - Milling machine -Grinding machine
	$ f_{4} $		Method 1:Rough turning i (150s)- Finish turning j (60s)- Grinding k (120s)	Rough turning3-Finish turning11 -Grinding 17	Turning lathe - Turning lathe -Grinding machine
	$ f_{5} $		Method 1:Rough turning l (150s)- Finish turning m(100s) Method 2:Rough milling l (130s)-Finish milling m(90s)	Rough turning 5- Finish turning 13 Rough milling 5-Finish milling 13	Turning lathe - Turning lathe Milling machine - Milling machine
	$ f_{6} $	After $ f_{1} $-$ f_{5} $	Method :Drilling n (120s)-Counterboring o (80s) -Reaming p (60s)	Drilling 6-Counterboring 7-Reaming14	Drilling machine-Drilling machine -Drilling machine
	$ f_{7} $	After $ f_{1} $-$ f_{5} $	Method 1:Drilling q (200s)-Counterboring r (150s)	Drilling 8-Counterboring 15	Drilling machine-Drilling machine
Workpiece 2	$ f_{1} $		Method1:Rough milling a (120s)-Semi finish milling b (50s)-Finish milling c (60s)	Rough milling 1-Semi finish milling 2-Finish milling 9	Milling machine - Milling machine - Milling machine
	$ f_{2} $		Method 1:Milling d (110s)	Milling 3	Milling machine
	$ f_{3} $	After $ f_{1} $, $ f_{2} $, $ f_{5} $	Method 1:Rough boring e (60s)-Semi boring f (50s) -Finish boring g (60s)-h (0s) Method 2:Drilling e (50s)-Counterboring f (40s) -Rough reaming g (50s)-Finish reaming h (60s)	Rough boring 5-Semi boring 7-Finish boring 10-12 Drilling5-Counterboring 7-Rough reaming 10-Finish reaming 12	Boring machine-Boring machine -Boring machine-0 Drilling machine-Drilling machine -Drilling machine -Drilling machine
	$ f_{4} $	After $ f_{1} $, $ f_{2} $, $ f_{5} $	Method 1:Rough boring i (60s)-Semi boring j(50s) -Finish boring k(60s)-l(0s) Method 2:Drilling i(50s)-Counterboring j(40s) -Rough reaming k(50s)-Finish reaming l(60s)	Rough boring 6-Semi boring 8 -Finish boring 11-13 Drilling 6-Counterboring 8-Rough reaming 11-Finish reaming 13	Boring machine-Boring machine-Boring machine-0 Drilling machine-Drilling machine-Drilling machine-Drilling machine
	$ f_{5} $		Method 1:Milling m(110s)	Milling 4	Milling machine
Workpiece 3	$ f_{1} $		Method 1:Milling a(120s)	Milling 1	Milling machine
	$ f_{2} $		Method 1:Rough milling b(100s)- Semi finish milling c(80s)	Rough milling 2-Semi finish milling 15	Milling machine-Milling machine
	$ f_{3} $	After $ f_{1} $, $ f_{2} $	Method 1;Rough milling d(150s)- Semi finish milling e(130s)	Rough milling 3-Semi finish milling 16	Milling machine - Milling machine
	$ f_{4} $	After $ f_{1} $, $ f_{2} $	Method 1:Rough turning f(150s)- Semi finish turning g(100s) Method 2;Rough milling f(130s)- Semi finish milling g(100s)	Rough turning 4-Semi finish turning17	Turning lathe - Turning lathe
	$ f_{5} $	After $ f_{1} $, $ f_{2} $	Method 1;Rough turning h(180s)- Semi finish turning i(100s)- Finish turning j(110s)	Rough turning 5-Semi finish turning 6- Finish turning 18	Turning lathe - Turning lathe-Turning lathe
	$ f_{6} $	After $ f_{1} $, $ f_{2} $	Method 1:Turning k(100s)	Turning 7	Turning lathe
	$ f_{7} $	After $ f_{1} $, $ f_{2} $	Method 1:Rough milling l(120s)- Semi finish milling m(100s)-Finish milling n(50s)	Rough milling 8-Semi finish milling 9-Finish milling 19	Milling machine - Milling machine - Milling machine
	$ f_{8} $	After $ f_{3} $-$ f_{6} $	Method 1;Rough boring o(100s)-Semi boring p(60s)-Finish boring q(110s) Method 2:Rough turning o(120s)-Semi finish turning p(110s)- Finish turning q(80s)	Rough boring 10-Semi boring 11-Finish boring 20 Rough turning 10-Semi finish turning 11- Finish turning 20	Boring machine-Boring machine-Boring machine Turning lathe - Turning lathe - Turning lathe
	$ f_{9} $	After $ f_{3} $-$ f_{6} $	Method 1:Rough milling r(130s)- Semi finish milling s(90s) Method 2:Rough turning r(150s)- Semi finish turning s(110s) Method 3:Rough boring r(120s)-Semi boring s(70s)	Rough milling12-Semi finish milling21 Rough turning 12-Semi finish turning 21	Milling machine- Milling machine Turning lathe- Turning lathe
	$ f_{10} $	After $ f_{8} $, $ f_{9} $	Method 1:Drilling t(100s)-Counterboring u(50s)	Drilling 13-Counterboring 22	Drilling machine-Drilling machine
	$ f_{11} $	After $ f_{8} $, $ f_{9} $	Method 1:Drilling v(120s)-Counterboring w(60s)	Drilling 14-Counterboring 23	Drilling machine-Drilling machine

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Table 4. Time needed to move a workpiece from one machine to another (/s)

Process/machine		Turning			Milling		Drilling		Boring	Grinding
		M1	M2	M3	M4	M5	M6	M7	M8	M9
Turning	M1	0	10	19	40	42	60	62	70	80
	M2	10	0	10	40	40	60	60	70	78
	M3	19	10	0	40	40	60	60	70	72
Milling	M4	40	40	40	0	12	30	30	40	50
Milling	M5	42	40	40	12	0	30	30	40	53
Drilling	M6	60	60	60	30	30	0	12	20	28
Drilling	M7	62	60	60	30	30	12	0	20	26
Boring	M8	70	70	70	40	40	20	20	0	18
Grinding	M9	80	78	72	50	53	28	26	18	0

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Table 5. The identifiers of clamping method for machining features of workpieces

Workpiece		Workpiece 1					Workpiece 2			Workpiece 3
Machining features		$ f_{1} $	$ f_{2} $	$ f_{3} $	$ f_{4} $	$ f_{5} $	$ f_{1} $	$ f_{2} $	$ f_{5} $	$ f_{1} $	$ f_{2} $	$ f_{3} $	$ f_{4} $	$ f_{5} $	$ f_{6} $	$ f_{7} $	$ f_{8} $	$ f_{9} $
Machining	Turning	1	1	2	2	2	-	-	-	-	-	-	10	10	10	-	11	11
Machining	Milling	3	-	4	-	4	7	8	9	12	12	13	13	-	-	13	-	14
methods	Grinding	-	5	6	5	-	-	-	-	-	-	-	-	-	-	-	-	-

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Table 6. Setup times for processing different workpieces on the same machine and times needed to change clamping types (/s)

Workpiece		1	2	3	1	2	3	1	2	3
Machine		M1			M2			M3
Workpiece	1	(26)	28	32	(20)	26	30	(20)	26	30
	2	30	(0)	40	30	(0)	26	30	(0)	26
	3	40	50	(29)	35	30	(22)	35	30	(22)
		M4			M5			M6
	1	(26)	26	30	(21)	21	30	(0)	58	31
	2	30	(22)	26	25	(22)	26	55	(0)	60
	3	35	30	(30)	35	30	(30)	25	50	(0)
		M7			M8			M9
	1	(0)	58	24	(0)	32	40	(18)	29	45
	2	55	(0)	60	35	(0)	90	25	(15)	30
	3	20	50	(0)	30	80	(28)	40	25	(20)

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Table 7. Powers of machines, usages of coolant and lubricant

			Machine
			M1	M2	M3	M4	M5	M6	M7	M8	M9
Power (/$ 10^{3}w $)	Workpiece	1	9.5	7.6	8	8.5	11.5	12	9.5	9.25	15
		2	13.5	9	9.5	9.25	10.6	11.5	10	9.9	15.5
		3	9.5	7.5	12	10	9.25	9	9.1	8	15
	Idling		1.1	1.4	1.25	0.75	0.9	2.75	2.1	2	2.5
	Setup		2.1	2.5	2.3	1.9	2.1	3.8	3.2	3.1	3.6
Coolant	Usage(/$ 10^{-3} $$ m^{3} $)		350	360	350	210	200	410	400	300	300
Coolant	Use cycle(/$ 10^{4}s $)		86	86	86	120	120	90	90	130	100
Lubricant	Usage(/$ 10^{-3} $$ m^{3} $)		0.3	0.31	0.33	0.28	0.3	0.33	0.35	0.29	0.32
Lubricant	Use cycle(/$ 10^{4}s $)		41	41	41	46	46	54	54	50	58

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Table 8. Carbon emission factors

Resource	Carbon emission factor
Electrical energy	1.8742x$ 10^{-7} $ $ kgCO_{2}/J $
Lubricant	2,850 $ kgCO_{2}/ $$ m^{3} $
coolant	3,050$ kgCO_{2}/ $ $ m^{3} $

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Table 9. A Pareto set of the proposed integrated method of process planning and scheduling

The number of Pareto solutions	$ C_{Me} $ $ (kgCO_{2}) $	$ C_{Ie} $ $ (kgCO_{2}) $	$ C_{Ae} $ $ (kgCO_{2}) $	$ C_{t} $ $ (kgCO_{2}) $	$ C_{c} $ $ (kgCO_{2}) $	$ C_{l} $ $ (kgCO_{2}) $	$ C_{p} $ $ (kgCO_{2}) $	$ C_{time} $ (s)
1	8.7531	3.7681	0.095985	0.45655	0.10306	0.19883	13.376	2,796
2	9.0407	3.8443	0.11121	0.52739	0.10387	0.19315	13.821	2,780
3	9.108	3.7814	0.12769	0.53395	0.10151	0.18059	13.833	2,735
...	...	...	...	...	...	...	...	...
27	8.9757	6.1699	0.14854	0.62382	0.10072	0.25358	16.272	2,536
28	8.8894	6.3467	0.2138	0.53723	0.10252	0.22544	16.315	2,530
29	8.8997	6.281	0.27783	0.54117	0.10202	0.22421	16.326	2,525

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Table 10. Pareto solutions of scheduling after process planning

The number of Pareto solutions	$ C_{Me} $ $ (kgCO_{2}) $	$ C_{Ie} $ $ (kgCO_{2}) $	$ C_{Ae} $ $ (kgCO_{2}) $	$ C_{t} $ $ (kgCO_{2}) $	$ C_{c} $ $ (kgCO_{2}) $	$ C_{l} $ $ (kgCO_{2}) $	$ C_{p} $ $ (kgCO_{2}) $	$ C_{time} $ (s)
1	8.5521	4.5633	0.12961	0.4408	0.09917	0.20544	13.966	3,082
2	8.994	4.2145	0.13048	0.44605	0.10144	0.18311	14.169	2,941
3	8.9908	4.4446	0.13095	0.53526	0.1023	0.22189	14.426	2,616
...	...	...	...	...	...	...	...	...
11	9.1172	5.7343	0.072699	0.53526	0.10447	0.21548	15.779	2,545
12	8.9459	6.0728	0.12725	0.47951	0.10216	0.21728	15.945	2,535
13	9.3706	6.1467	0.1115	0.5392	0.10312	0.25379	16.525	2,530

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