Reducing Carbon Emission by two Dispatching Rules for Multi-Objective Flexible Job Shops

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 250-259

J. Environ. Treat. Tech.

ISSN: 2309-1185

Journal web link: http://www.jett.dormaj.com

Reducing Carbon Emission by two Dispatching

Rules for Multi-Objective Flexible Job Shops

Arash Gholamkhasi, Syed Helmi Bin Syed Hassan, Aini Zuhra bt Abdul kadir

Department of Mechanical Engineering, University Technology Malaysia, Johor Bahru, 81310, Malaysia

Received: 16/02/2019

Accepted: 05/06/2019

Published: 30/09/2019

Abstract

Manufacturing direct or indirect is accountable for almost one-third of carbon emission. Carbon eventually has trapped in the

atmosphere in the shape of Co2; the dangerous gas that causes climate change and threatens human life. On the other hand, albeit

the significant share of flexible job shops in manufacturing systems; few studies have been executed to overcome the carbon

emission issue. Thus two fast algorithms called MCT and MCE have been introduced to reduce carbon emission along C-max

and total machine workload. Then the results have been examined alongside some well-known meta-heuristic algorithms.

Investigating results have shown a reasonable standard deviation; which proves a proper balance in production lines.

Furthermore, for most instances, a minimum workload has been reported. Moreover, the completion times were acceptable, as

well. Then reported data guaranteed the quality of the offered algorithm regarding time and accuracy. Furthermore, implementing

a random operator or hybridizing these methods with meta-heuristics might enhance the performance.

Keywords: Environment, Carbon emission, Flexible job shop, Dispatching rules, Multi-objective, Makespan

obvious. Some had clustered carbon emissions declining

Introduction

approaches in three fields: 1- strategic; as pre-production

decisions consist of supply chain planning and structural

layout decisions. 2- Tactical during manufacturing and

distribution phases; like changing the cutting tools, the turn

on/off policy, and speed-level of machines. 3-operational;

that decision makers concentrate on scheduling and

planning more than anything else. Nonetheless, previous

studies significantly have been directed on the first two

perspectives and production focus strategies like scheduling

have been neglected [1,2,8]. That was the reason Piroozfard

et al. have described carbon footprint problems as an

inventory control problem [6]. For instance, a turn on/off

policy on scheduling model has been initiated by Mouzon

et al. Albeit their objective was to lessen the energy costs,

diminishing emitted carbon will be guaranteed [9]. Fang et

al. offered another tactical strategy regarding the speed-

level of machining. They have reported the higher speed

level implies a lower machining time, but the higher energy

utilization [10]. Lin et al. have used mentioned strategies

along with a delay policy. To apply this, all operations but

the last of each job have delayed as much as possible to

reduce the machine pauses [8].

Eventually, human has apprehended that protecting the

environment guarantees a better life for the next generation.

From1980 to 2010, carbon emission (CE) rate increased by

2% notwithstanding a 3% decline in the emission

intensity; this outlines a serious greenhouse impact matter

called the global climate change. Anthropogenic events

such as coal-fired electricity have increased the carbon

dioxide (CO

gas that traps heat and threatens the environment [1]. Some

have anticipated that the emitted CO resultant from energy

) concentration in the atmosphere; a dangerous

consumption in 2035 possibly increases by 43% higher

than the 2007 reported data [2]. Some others believe that

keep pumping emitted carbon to the atmosphere at the

current rate may increase the global temperature by 1.9 C in

the year 2100; that means a 3.8m higher level of water in

the sea [3]. Thus, as a universal matter, any activity leads to

it needs to be monitored consciously [4]. On the other hand,

circulated reports have emphasized the manufacturing is

accountable for 29% of the total emitted CO2 directly. The

aforementioned incites the manufacturers to consider

diminishing strategies regarding carbon emission [5–7].

Researches indicated on manufacturing regarding

sustainable manufacturing have existed; however, the lack

of efficient strategies adopted by literature remained

The aforementioned besides turn on/off policy eliminate

most of the wasted energy during the machine pauses.

Speed and feed rate of machining was the other considered

policy that they had studied. Jiang et al. also employ a

speed scaling strategy to minimize total completion time

Corresponding author: Arash Gholamkhasi, Department

of Mechanical Engineering, University Technology

Malaysia, Johor Bahru, 81310, Malaysia.

(

C-max) and carbon emission (CE) on a distributed

permutation flow-shop [11]. Furthermore, Chen et al. and

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Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 250-259

Lu and Jiang assumed a multi-speed strategy to control

energy consumption [12,13]. Wu and Sun relatively have

practiced a multi-speed model with a turn on/off switcher;

which an excessive number of switching could damage the

machines [14]. Despite the importance of these contributed

approaches, some believed strategic and tactical methods

which concern machine tools, were barely applicable and

may harm the machine and job; especially for small and

medium enterprises (SMEs) with no multi-speed machines

and the exceeding cost of updates [12–16].

The literature on sustainable manufacturing significantly

has been focused on managing energy. Albeit, reducing

energy utilization leads to higher beneficial aspects, and

may satisfy manufacturers economically; involving energy

expenses, planning, inventory, maintenance, machines life

cycle, and other associated prices. Still, another crucial

environmental issue, carbon emission, has been neglected

entirely [5,8]. Adversely the classics in modern systems,

the new high-performance machines are multi-task; this

leads manufacturers to flexibility besides more

complications regarding energy utilization and carbon

colony (ABC), Tabu search (TS), Annealing simulation

(SA), particle swarm optimization (PSO), and etc. [17–

23,27].

As mentioned above, meta-heuristics have been applied

to FJSP to save time while other objectives almost

neglected. In other words, environment-oriented papers

mostly have reviewed flow shops, JSP, and other

manufacturing. Moreover, despite some studies on energy

consumption, carbon emission rarely has been targeted in

FJSP [6,14,21,26,28,29]. Zheng and Wang studied project

scheduling with limited resources using an estimation

distribution algorithm (EDA) aimed to minimize C-max

and carbon emission [1]. Moreover, some considered

carbon emission dealing multi-objective flow-shops

scheduling problems [10,11,30]. Another research has been

done by Lin et al. to reduce the carbon footprint in flow-

shops [8]. They employed three methods named: 1-

postponing; by reducing the gap between completion of

operation o_i_,_jand commence ofo_i_,_j₊₁in ꢀ job, 2-setup

concerned; by turn on/off the machines on their idle time,

beside 3-parameter concerned; adjusting tools at proper

processing parameters. Regarding job shops, Yi et al.

simultaneously targeted minimizing carbon footprint and

C-max [15]. Lei and Gao, likewise, executed their novel

method on a dual-resource constraint job shop [5].

Furthermore, Seng et al. tried to reduce carbon footprint

and total completion time on a job shop equipped by multi-

speed machines using an NSGA-II [31].

To the best of the author’s knowledge, few papers have

been concerned emitted carbon as the central objective. The

most related works in this area were a low-carbon pattern

that has been studied by Zhang et al. to diminish C-max,

the total workload and the emitted carbon [2]. and a

different multi-objective Genetic Algorithm (MOGA)

suggested by Piroozfard et al. to decrease total work and

carbon footprint concurrently [6]. They claimed there was

no low-carbon FJSP regarding job routing and sequencing.

Following that Yin et al. had investigated the emitted

carbon from different points of view includes productivity,

energy consumption, and noise [28]. At the same time, a

fruit fly optimization algorithm (FOA) has been offered by

Liu et al. to decrease the makespan and carbon footprint

considering 1-plant inputs, 2-material inputs, 3-process

energy inputs and 4-transportation [21].

emission control. For instance,

a flexible job shop

represents the job shop with the advantage of multitasking

machines [17].

Recently flexible job shop scheduling problem (FJSP)

has studied by many researchers due to broadly applicable

fields. FJSP being NP-hard problem seems obvious since

traditional job shop scheduling problem (JSP) had

classified as one. Augmenting flexibility by using more

than one capable machine modifies the job shop scheduling

problem (JSP) to a flexible one [6,17–19]. Although the

foremost scheduled FJSP has practiced by Bruker and

Schlie at 1990; still, researchers keep seeking novel

approaches to optimize complex FJSPs [20,21].

The FJSP mainly presents two difficulties. To assign

every operation to a machine out of a set of fit machines

and to determine the sequence of indicated operations,

respectively. The aforementioned has created two

flexibilities regarding the machine selection and process

plan [20,22–24]. In reality, multiple objectives may cause

trade-offs. Hence the Single-objective FJSP further

investigated in the literature; due to some papers [25]. The

contributed approaches to deal with the multi-objective

flexible job shop scheduling (MO-FJSP) roughly have been

categorized to the weighting approach and the Pareto-based

ones. Turn the problem to a single objective using

coefficients is what the weighting approach does. On the

other hand, the Pareto face considers all objectives

simultaneity and generates a set of optimums [2,26].

Due to the complexity of FJSP, the exact approaches and

JSP solvers have been emphasized inapplicable or time-

consuming. Thus heuristic methods have been applied to

find the best possible solution close enough to the global

optimum. Thus heuristic methods have been applied to find

the best possible solution close enough to the global

optimum. Thus heuristic methods have been applied to find

the best possible solution close enough to the global

optimum. Other than these heuristics, the new generation of

iterative algorithms, called meta-heuristics, have been

offered to tackle FJSP cases; includes Genetic algorithm

Kacem et al. believe the efficiency of an approach

depends on how intelligently it seeks the solution area; to

spend the precious time on valuable paths and nothing else

[

17]. On the other hand, meta-heuristics methods generally

take a lot of time and energy, especially for big problems

30,32]. Therefore, in this study, an innovative approach

[

with the original minimum completion time (MCT) by

Maheswaran et al. has been investigated. MCT is one of the

dispatching rules algorithms that discover the nearest

completion time among the sets of capable machines [32].

Nevertheless, the second provided method is not time

concerned and has revised the MCT method to a carbon

emission based attempting to hit the minimum possible

emitted carbon in each iteration. Furthermore, to the best of

the author’s knowledge, this is the first study that has been

used the carbon emission criteria to select operations per

iteration; All other methods focused on time while carbon

(

GA), Ant colony optimization (ACO), Artificial bee

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Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 250-259

emission assumed as the second objective. Section 2

describes the methodology and offered methods. Results

have given in section 3 following by discussion and

conclusion in section 4 and 5. Moreover, some potential

future works have been declared succeeding.

study, equations 1-3 presents how these objectives have

fulfilled.

푘

ꢂꢃ1

푚푖푛 푍퐶퐸 = 훼 ∗ { ꢂꢃ1

∑

푃표푤 ^∗^푙^표^푎^푑ꢂ ꢄ ∑ 푃표푤_푖푑푙푒 ∗ 푀

}

ꢅꢆꢇꢈꢂ

ꢁꢂ

ꢂ

(ꢉ)

(2)

(3)

푚푖푛 푍퐶−ꢊꢋ푥 = 푀푎ꢌ(푙표푎푑ꢂ )

푚푖푛 푍_ꢁ_ꢍ_푟_푘_ꢇ_ꢍ_ꢋ_ꢆ= ∑^푘푙표푎푑_ꢂ

ꢂꢃ1

.2 The procedure of MCT algorithm

The original MCT algorithm comprises these steps. First,

process-times have imported from “EXCEL”; using the

XLSREAD” function. Then, four different instances

Proposed methods

This paper investigates a multi-objective flexible job

shop scheduling. The availability of more than one nominee

machine to process each operation modifies a flexible job

shop as a more complicated Np-Hard scheduling problem.

Thus two main sub-problems have been described to be

tackled regarding time, cost, and resource barriers. The

operations sequence of each job and the design of allocated

machines to the operations define those two difficulties.

Technically, the FJSP represents by 푛 jobs meant to

process on 푚 machines. Every job includes 푗 sequenced

operations; independent from other job's. These jobs have

released at time zero; besides, in particular cases,

cancelation or the arrival of new orders at an expected or

random time have affected the scheduling. On the other

hand, if all machines were able to perform any operations,

flexibility is total; otherwise, partial. Assuming the

following limitations may ease simulating carbon emission

FJSP. 1- Jobs and machines are available from time zero. 2-

The sequencing between the operations of each job shall

consider. 3- Machines are independent, and always are

available with full capacity and power. 4- Each machine

can only process one operation per time. 5- Operations are

not authorized to run on more than a device simultaneously.

“

including: “4X4”, “8X8”, “10X10”, and “15X10” have

been extracted from literature [35]. The first number in the

mentioned instances (nXk) represents the number of jobs

(

n), while the second one refers to the number of machines

k). Along the process times, power consumption data had

extracted too the process times, power consumption data is

extracted too [6]. In step2 some indexes, parameters, and

variables of a general FJSP were introduced; which have

listed below:



Indexes

operation index (1, 2, . . ., mn)

Job index (1, 2, . . ., n)

Machine index (1, 2, . . ., k)

 Parameters

Maximum no. of operation of all jobs

Total number of jobs

mn:

Total number of operation

6- Pre-emption is not allowed; interruption or pause is

Total number of machines

impossible after an operation initiated on a machine. 7-

There is no buffer limit. 8- Transportation time and setup

time have neglected; assumed as part of defined process

time. 9-Machines are simple; mono-speed with no turn

on/off switcher at the idle time. 10- The emitted carbon per

kilowatt power utilization is constant [17,18,22,27].

d (i,l,j):

Pow_w (j):

Pow_idl (j):

α :

Process time for op. i of job 푙 on machine j

Power consumption of machine j at working time

Power consumption of the ꢎthmachin at idle time

Quantity of emitted carbon per kilowatt hour

Assumed as a big number

2.1 Minimum completion time (MCT) algorithm

BigM :

One of the simplest methods among scheduling



Variables

heuristics is Dispatching rules (DR). Their mechanism is

like when a machine is free, the DR ranks jobs based on

their characteristics or system circumstances, to determine

which job should run succeeding. Fast reacting to dynamics

is DR's strength; which led them to obtain high-quality

answers in a much better execution time comparing

metaheuristic methods. Nonetheless, the proposed DRs

rarely have studied different scheduling cases [33,34].

In this paper a minimum completion time (MCT)

heuristic has performed; a fast greedy method introduced

by Maheswaran et al. MCT is an immediate mode

heuristics which works indicating every job to a machine

aim to achieve the closest completion time. In "immediate"

models, jobs rapidly allot to machines at the arrival. Job

selection per iteration is conditional and temporary; it

means the second priority in this iteration may not

preceding at the next round [32].

Start time of job l on the ꢎ^t^hmachin

Finish time of job l the ꢎ^t^hmachin

st (l,j):

ct (l,j):

Availability of the ꢎ^t^hmachin

M_avlbl (j):

M_idle (j):

load (j):

Cmax:

_D_u_r_a_t_i_o_n_o_f_t_h_e_i_d_l_e_s_t_a_t_e_f_o_r_t_h_e_ꢎthmachin

Total workload on the ꢎ^t^hmachine

Total makespan (C-max)

Carbon_E:

kdd(i):

Total emitted carbon footprint of the solution

Priority index (0,1)

t(l):

Completion time of job l

 Variables of Results

X (i,1):

X (i,2):

X (i,3):

X (i,4):

Chromosome place

Finally, the mathematical model regarding the objectives

produces the answers. Since minimizing carbon emission

and C-max along with total workload has targeted in this

Operation number

Process time

Machine number

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2019, Volume 7, Issue 3, Pages: 250-259

X (i,5):

X (i,6):

X (i,7):

Power consumption

Start time of operation

Completion time of operation

The only priority here was the sequencing among

operations of every single job. Then, through each

iteration 푛 candidates (kdd) processes. In the first iteration,

for example, the first operation of any job will be picked.

Equation 4 declares how a simple m-steps counter in the

range of [ꢉ 푚푛] can handle difficulty.

ꢏ푑푑(ꢉ: 푚: 푚푛) = ꢉ;

(4)

Following step3 that has explained, in step4 a “SORT”

function was applied regarding the objective criterion.

Since only prior operations of each job have “kdd” with

value 1 and others were 0, and then sorting function sorts

these 푛 candidates. Here the iterations start using an index 푖

in the range[ꢉ 푚푛]. At each run or iteration, the result

variables will produce and save. The result variables will

produce and save. Next, in step5, the algorithm updates the

variable, and after 푚푛 iterations the counter stops. Figure 1

illustrates the update phase of the presented algorithm.

At first, the algorithm checks if the operation was real or

dummy. In the case of being dummy (branch1), there will

be some updates following with another conditional

statement that asks if this operation was the last of its job. If

there were some unallocated operation in this job yet

Figure 1: MCT algorithm – updating per iteration

^ꢐ^ꢑꢁ

(

ꢂ⁾⁼^푃^표^푤

ꢁ

(

ꢂ⁾^∗^ꢒ^푐^푡⁽^푙^,^푗⁾^ꢓ^푠^푡⁽^푙^,^푗⁾^ꢔ^;

(5)

(6)

^ꢐ^ꢑꢅꢆꢇ

(

ꢂ⁾⁼^ꢐ^ꢑ

ꢅꢆꢇ

(

ꢂ⁾^ꢄ^ꢕ^푃^표^푤

ꢅꢆꢇ

(

푟⁾^∗^ꢒ^푐^푡⁽^푙^,^푗⁾^ꢓ^푀푟⁾^ꢔ^ꢖ^;

ꢋ푣ꢇ푏ꢇ

(

branch4), the priority shifts to the next one; oppositely

branch3), priority doesn't change, except its process time

alters to a 퐵푖푔푀 later to prevent reselection. And left of

updates applies at the end.

On the other hand, if the operation was not dummy

3 Results

Four instances have extracted from literature and results

for the proposed algorithms have been revealed; three total

flexible job shop (4X5, 10X10, and 15X10 respectively)

and a partial (8X8). Later these results have been compared

with reported results of some quality methods offered by

[17,35]. In “Total 4X5” to ease the simulation, one dummy

operation has been allocated to jobs 1 and 2, while two

dummies completed job 4.

(

branch2), the same question regarding the possibility of

being the last operation will be examined. Updates and

adjusting퐵푖푔푀, as the processing time, follows the yes

scenario (branch5). Oppositely, changing candidates, and

updating the variables before moving to the next possible

iteration happens.

Steps3 to 5 repeats for 푚푛 iteration and finally when푖 =

푚푛, step6 commences. At this step, the results to the

objective will count.

2.3 Minimum carbon emission (MCE) algorithm

The MCE algorithm, on the other hand, almost follows

the same steps. First importing data, then indexes and

variables have addressed in the second step; similar to

section 2-2. Later in step3 and step4, the candidate

operations have been selected. The only contrast here was

the criteria; the original method was time oriented while in

this algorithm, carbon emission was the criterion. Per

iteration, a compare between candidates declares the best

operation to assign with the lowest amount of power

consumption (or carbon emission). Devices at a production

line are busy, or in the idle mode; with adverse power

utilization [6][8]. Utilizing a machine alters others to idle

mode. Hence two equations of power consumption have

been calculated; operating using of machine j (equation 5)

along with the idle consumption of others (equation 6).

Figure 2: Gant chart of result for MCT algorithm (Total emitted

carbon=278.198, C-max=12)

Figure 3: Gant chart of result for MCE algorithm (Total emitted

carbon=266.585, C-max=13)

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2019, Volume 7, Issue 3, Pages: 250-259

In this “Partial 8X8” dummy operation has been applied

on every job except the second, fifth, and eighth. On the

other hand, instead of infinite, a constant (BigM=1000) has

been employed to present the incapability of machines

regarding the allocation.

Table 2: Processing times of instance “Partial 8X8”

Jobs 8X8

1000

Table 1: Processing times of instance “Total 4X5”

Jobs 4X5

1000

o10

1000

o11

1000

o12

o13

o14

o10

o15

o11

o16

o17

o18

1000

o12

o13

o14

1000

o19

1000

o15

o20

o21

1000

o16

1000

o22

o23

1000

o24

o25

1000

o26

1000

o27

o28

o29

1000

Figure 4: Gant chart of result for MCT algorithm (Total emitted

carbon=766.2548, C-max=18)

1000

o30

1000

o31

o32

1000

In this “Total 10X10”, there was no dummy, nor a

BigM”. Moreover, all machines were capable of being

“

assigned to every operation.

In the "Total 15X10", sixth and seventh jobs were the

exceptions; which two dummies have been attached to

preserve the unity of operation numbers.

Figure 5: Gant chart of result for MCE algorithm (Total emitted

carbon=752.476, C-max=17)

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2019, Volume 7, Issue 3, Pages: 250-259

Table 3: Processing times of instance “Total 10X10”

Table 4: Processing times of instance “Total 15X10”

Jobs 10X10 M1 M2 M3 M4 M5 M6

M9 M10

Jobs 15X10 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10

o10

o11

o12

o13

o14

o15

o16

o17

o18

o19

o20

o21

o22

o23

o24

o25

o26

o27

o28

o29

o30

o31

o32

o33

o34

o35

o36

o37

o38

o39

o40

o41

o42

o43

o44

o45

o46

o47

o48

o49

o50

o51

o52

o53

o54

o55

o56

o57

o58

o59

o60

o10

o11

o12

o13

o14

o15

o16

o17

o18

o19

o20

o21

o22

o23

o24

o25

o26

o27

o28

o29

o30

22 44

12 15

Figure 6: Gant chart of result for MCT algorithm (Total emitted

carbon=465.2415, C-max=9)

Figure 7: Gant chart of result for MCE algorithm (Total emitted

carbon=439.8576, C-max=10)

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2019, Volume 7, Issue 3, Pages: 250-259

Table 6.

Figure 10: Gant chart of result for [35] (Total emitted

carbon=278.198, C-max=12)

Figure 8: Gant chart of result for MCT algorithm (Total emitted

carbon=932.8696, C-max=14)

Table 6: Reported emitted carbon for [35]–Total 4X5

time

energy cons.

idle work

Machine1

Machine2

Machine3

Machine4

Machine5

14.46 56.84

17.99 49.74

13.65

16.5

7.38

74.4

49.98

79.8

Sum:

Total energy cons:

69.98 310.8

380.74

results:

Emitted Carbon:

289.3624

Figure 9: Gant chart of result for MCE algorithm (Total emitted

carbon=940.9864, C-max=17)

-2 Instance “Partial 8X8”

A partial flexible job shop, with six or more machines

for every operation, has been studied here. Other than

second, fifth, and eighth jobs, all others have received a

dummy. In addition, a big constant has been performed to

code the incapability of some machines; by forcing the

algorithm to neglect to assign this machine to the current

operation.

Discussions

-1 Instance “Total 4X5”

All machines in this total flexible system were capable

of processing all operations; there were five options for

each. As it has shown in figures 1 and 2, completion times

were 12 and 13, respectively. The fifth machine, because of

its smaller power usage, was completely idle for both

models. Despite reducing workloads was not the prior

objective, still has been calculated for both algorithms

Figures 4 and 5 demonstrated that the seventh machine

has the lowest workload among all. Completion times were

18 and 17, and the carbon emissions have been calculated

as 766.3 and 752.5, respectively. Further, for evaluating the

carbon emission, the power consumption index has been

shown in Table7.

(

MCT: M1=12, M2=6, M3=11, M4=4, M5=0 and MCE:

M1=10, M2=11, M3=6, M4=6, M5=0).

Machines idle-time has been calculated by reducing

machine workloads from C-max (MCT: M1=0, M2=6,

M3=1, M4=8, M5=12 and MCE: M1=3, M2=2, M3=7,

M4=7, M5=13). The power consuming indexes (Table 5)

were extracted from literature and multiplied by 0.76 to

find the carbon emission per kilowatt [6]; which were 278.2

and 266.6 respectively.

Some standard instances have been taken from [35] to

verify the quality of the solution. They have suggested a

hybrid Genetic Algorithm to tackle the FJSP. Later their

results have been compared to the collected answers of

proposed algorithms.

Table 7: Power consumption indexes for “Partial 8X8”

8X8

7.45

1.38

17.81

2.61

15.5

1.94

12.98

2.44

11.57

1.12

7.82 11.05

2.4 2.98

work

idle

5.7

2.99

Despite the proper balance of workloads, the total

workload of all machines (83) was 10 minutes more than

both offered algorithms. Predicting more energy

consumption and carbon emission as well resulted by a

higher total workload was not that surprising. Then a 55-

kilowatt idle-consumption plus a 950.8-kilowatt processing

consumption results in

a 764.38 carbon emission.

Table 5: Power consumption indexes for “Total 4X5”

Comparing MCT and MCE with the presented GA has

confirmed that MCE produced a better schedule regarding

emission reduction. As mentioned before, MCT has a time-

concerned nature while MCE focused on carbon emission;

and this has justified 766.3 emitted carbon in MCT and

8.12

2.41

8.29

2.57

12.4

1.95

7.14

2.75

11.4

1.23

work

idle

The calculations on data extracted from [35] revealed a

higher carbon emission comparing both MCT and MCE

methods (carbon=278.198 and C-max=12); which proves

the quality of the proposed algorithms. Figure 10 clarified

the final schedule, and all calculations have displayed in

52.5 for MCE. Table 8 exposes the details of calculating

carbon emission for "Partial 8X8" using [17].

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Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 250-259

Table 8: Reported emitted carbon for [17]– “Partial 8X8”

however, refer to methods investigated by [17].

Furthermore, the last row, has been addressed a PSO

algorithm offered by [36].

time

energy cons.

idle

work

idle

13.8

7.76

12.2

4.48

4.8

11.92

54.96

work

29.8

249.34

155

116.82

115.7

79.8

93.84

110.5

950.8

Machine1

Machine2

Machine3

Machine4

Machine5

Machine6

Machine7

Machine8

Table 11: Data on Makespan and Maximum Workload

MAKESPAN

CRITICAL MWL

METHODS

4X5

8X8

10X10 15X10 4X5

8X8

10X10 15X10

solution1 MCT

solution2 MCE

Solution1

Sum:

results:

total energy cons:

1005.76

764.3776

Emitted Carbon:

Solution2

A1: ‘Temporal

Decomposition

-3 Instance “Total 10X10”

In the first method, the eighth machine was completely

A2: ‘Classic’ GA

A3: Approach by

Localization

idle; on the other hand, in the second method, it has been

processed only one minute. Then, C-max and carbon

emission were 9 and 465.2 for MCT vs. 10 and 439.9 for

MCE. Table 8 has presented the detailed data needed to

find the reported carbon emission for the GA algorithm.

And Table 9 has elicited the multipliers for power

consumption.

A4: ‘AL+CGA’

A6: ‘PSO+SA’

16 14/15/16

11 15/16/14

24/23 10

14/13/13

10 12/13/2012

11/11

According to Table 11, the reported makespan was

acceptable in most cases. However, the critical machine

workload, which did not consider as a primary objective,

was not promising.

On the other hand, in Table 12, the results for total

machine workload have presented; that is crucial regarding

power consuming. Investigating machine workloads reveals

that the results were proper and better than most of the

reviewed meta-heuristics. Furthermore, the standard

deviation, which refers to line balancing, has been

calculated for studied methods.

Table 9: Power consumption indexes for “Total 10X10”

0X10 M1

work 7.45 17.81

idle 1.38 2.61

15.5

1.94

12.98 11.57

2.44 1.12

7.82

2.4

11.05 11.05 11.05

2.98 2.98 2.98

M10

5.7

2.99

-4 Instance “Total 15X10”

All machines in this total flexible system have been

available for all operations. Then C-max has been counted

and 10 for both models in order. Despite neglecting the

machine workloads, yet MCT showed balanced

Table 12: Data on Total Workload and Standard Deviation

TOTAL MWL

Standard Deviation

METHODS

8X8

10X10 15X10 4X5

8X8

0.033

0.044

0.023

10X10 15X10

allocation, except the 52nd (the last operation of the 13th

job) in MCE, has been placed on the second machine

behind an enormous gap. This extended C-max and idle-

time, so the emitted carbon increases from 932.9 in MCT to

100

0.131

0.151

0.017

0.051 0.0247

0.05 0.0226

0.029 0.0217

solution1 MCT

solution2 MCE

Solution1

41.0 in MCE. The reason for this failure could be a wrong

Solution2

selection among two candidates with a similar value of

selecting criterion. A random selection of the candidate in

these circumstances may work. Table 10 illustrates the

power consumption indexes regarding this instance.

A1: ‘Temporal

Decomposition

A2: ‘Classic’

A3: Approach

by Localization

0.018

0.015

A4: ‘AL+CGA’ 34 83/79/75

A6: ‘PSO+SA’ 32 75/73/77

91/95

0.038/-/-

0.101/0.103 0.029 0.0173

Table 10: Power consumption indexes for Total 15X10

5X10 M1

work

idle

M10

As illustrated in Table12, albeit machine workload and

line balancing were not the priority of the proposed

method, still results were in an acceptable range.

Considering solutions created by proposed algorithms have

been founded less than a minute, while results of these

meta-heuristics collected due 100, 1000, or even more

iterations, significantly assures the quality of MCT and

MCE algorithms.

The mentioned instances have been investigated

precisely along with some well-known meta-heuristics.

Then the results have been compared with the proposed

algorithms. Tables 11 and 12 had summarized all

comparisons.

The stated meta-heuristics had focused on makespan and

machine workloads. Therefore using available data on idle-

times and workloads, the emitted carbon of each model, has

been calculated subsequently. Data mostly has been

extracted from [35]; then solution 1 and 2 (3rd and 4th raw)

refers to their recommended solutions. Fifth to eighth rows,

Conclusions and future recommendations

Two fast algorithms, called MCT and MCE, have been

proposed, to reduce carbon emission along C-max and total

machine workload. Results had compared with some well-

257

Journal of Environmental Treatment Techniques

2019, Volume 7, Issue 3, Pages: 250-259

known meta-heuristics. The original MCT was a time

concern dispatching rules, while MCE is a novel method

that has contributed to reducing carbon emissions. This

method was significantly faster than meta-heuristics, while

results comparing to most of them were better. For

instance, the total machine workload in the "Partial 8X8"

instance (72 and 73) was the best among all investigated

approaches. And the emitted carbon was lower than both

methods for minimization of energy consumption of

manufacturing equipment. Int J Prod Res, 2007.45(18–

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approach to scheduling in manufacturing for power

consumption and carbon footprint reduction. J Manuf

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for each instance has proven that machine workloads

balance were satisfying. Thus, this MCE method strongly

suggested for carbon emission minimization problems in

FJSP due to its quick performance and accuracy.

However, as future work, a random operator in the phase

of selection can improve the performance of the proposed

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heuristic or applying it as an initializer also seems

promising. On the other hand, dynamic environment is

another challenging field to examine the efficiency of these

algorithms.

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