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Procedia CIRP 29 (2015) 185 – 190
The 22nd CIRP conference on Life Cycle Engineering
An energy-cost-aware scheduling methodology for sustainable
manufacturing
Xu Gong*, Toon De Pessemier, Wout Joseph, Luc Martens
Department of Information Technology, Ghent University/iMinds, Gaston Crommenlaan 8 box 201, 9050 Ghent, Belgium
* Corresponding author. Tel.: +32 9 33 14908; fax: +32 9 33 14899. E-mail address: xu.gong@intec.ugent.be
Abstract
With the rising energy price and the ever-increasing consciousness of environmental friendliness, it is becoming practically helpful for
manufacturers to have a clear view on how the energy is consumed at their shop floors, what the corresponding energy cost is, and how to
reduce the energy consumption or the energy cost. However, there is currently limited literature investigating the energy cost minimization in
manufacturing through production scheduling under volatile energy prices. This paper proposes a generic mixed-integer linear programming
model to enable the job scheduling on a single machine for the purpose of minimizing the necessary energy cost without exceeding the due
date. The results given by a case study on a surface grinding machine demonstrate this scheduling methodology effectively contributes to the
reduction of greenhouse gas emissions during peak time periods by shifting the production load to off-peak periods, and leads to energyefficient, demand-responsive, and cost-effective manufacturing processes.
© 2015
2015 The
The Authors.
Authors. Published
Published by
by Elsevier
Elsevier B.V.
B.V.This is an open access article under the CC BY-NC-ND license
©
Peer-review under responsibility of the International Scientific Committee of the Conference “22nd CIRP conference on Life Cycle
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Engineering.under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering
Peer-review
Keywords: Sustainable production scheduling; Energy efficiency; Demand response; Energy cost minimization; Volatile energy price
1. Introduction
Industry is a sector of high energy consumption all over
the world. For example, in Belgium, industry took up 36%
of the total energy consumption and 47% of the total
electricity consumed in 2012 [1]. The industrial electric
demand is often quite dynamic with some peaks which are
evidently higher than the normal demand [2]. Peak power
generations are usually called on to meet these sharply
rising demands. Since the thermal plants can be started up
anytime in comparison to the renewable energy sources of
which the power generation usually depends on the
weather, those peak power generators are traditionally
thermal power plants with high emissions of greenhouse
gas (GHG). As a consequence, the power grid stability was
jeopardized and the environment was seriously polluted [3].
Against this background, the demand response (DR), an
electric load shifting program, is proposed within the
framework of demand side management (DSM) [4]. For
industrial users, this can be interpreted as spontaneously
shifting their electric load demand from peak to off-peak
time without exceeding the production due date. These DR
efforts not only help to stabilize the power grid and to
decrease the GHG emissions, but also contribute to the
electric cost reduction for factories.
In the existing literature, a limited number of
production schedulers take volatile electricity prices into
account. Dynamic electricity prices are implicitly taken into
account by several existing schedulers. In the production
planning control (PPC) software developed by Pechmann et
al. [5], peak power reduction was newly introduced as one
of the multiple scheduling objectives. Without explicitly
considering energy prices, an energy cost reduction was
simply claimed to be brought by a decrease of peak
consumption. In the multi-machine scheduler proposed by
Fang and Lin [6], the power consumption was integrated
with tardiness. Particle swarm optimization (PSO) was
carried out to search for the minimization solution.
Nevertheless, neither the energy consumption nor the
energy cost was clearly described. A trade-off was simply
assumed between the machine speed and the energy
consumption: a higher machine speed would bring a shorter
job makespan, while the corresponding energy consumption
and energy cost would increase.
2212-8271 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the scientific committee of The 22nd CIRP conference on Life Cycle Engineering
doi:10.1016/j.procir.2015.01.041
186
Xu Gong et al. / Procedia CIRP 29 (2015) 185 – 190
Nomenclature
Ci
CRi
CSDi
D
Ds
‫ܦ‬௝௜
DT
EPts
ETi
ETSi
I
J
NJ
Ns
Ps
ܲ௦௧
S
STi
STSi
Ts
TO
TR
TSD
TSU
s
t
δt
ts
αi
βts
electricity cost for the ith scheduled job, i ϵ I
electricity cost for the machine to stay at Ready state
after the completion of the ith job, i ϵ [1, 2, …, NJ-1]
electricity cost for the machine to be shut down after
the completion of the ith job, i ϵ [1, 2, …, NJ-1]
time duration of one pricing slot
time duration for machine state s, s ϵ S
processing duration for the job with ID j at the ith
scheduling position, i ϵ I, j ϵ J
due time for all jobs in the concerned work shifts
electricity price during the tsth time slot
end time for the ith scheduled job, i ϵ I
end time in slots for the ith scheduled job, i ϵ I
set of job scheduling positions [1, 2, …, NJ]
set of job IDs [1, 2, …, NJ]
total number of jobs in the concerned work shifts
total number of machine states
power consumption of the machine state s
power consumption of the machine state s at time t
(It equals to Ps when the machine state at t is s;
otherwise zero)
set of machine states [1, 2, …, Ns]
start time for the ith scheduled job, i ϵ I
start time in slots for the ith scheduled job, i ϵ I
start time of the concerned work shifts
time duration for the machine to stay off
default time duration for the machine to stay ready
time duration to shut down the machine
time duration to start up the machine
machine state, s ϵ S
time in δt, t ϵ [Ts, Ts+ δt …, DT- δt, DT]
defined time step for energy consumption estimation
time in priced slots, ts ϵ [1, 2, …, ceil(DT/D)]
machine operation indicator, i ϵ [1, 2, …, NJ-1]
time slot indicator
The time-dependent electricity prices are further
explicitly considered by some other scheduling models. In
the multi-process scheduler built up by Küster et al. [7], a
multi-agent based distributed evolutionary algorithm was
used to explore the potential for rearranging process steps
by shifting loads to electric pricing valleys so as to obtain
an optimal energy cost. However, machine operational
states are ignored, e.g., the actual machine start-up or shutdown operation correlated with time when encountering
idle periods. The hybrid flow shop scheduler of Luo et al.
[8] used a new ant colony optimization (MOACO) metaheuristic to simultaneously minimize the makespan and
electric cost. The time-of-use (TOU) pricing mechanism
and different machine processing speeds were considered.
Nonetheless, both the TOU price and machine power
consumption were randomly generated; only two machine
states were assumed, i.e., processing and standby; the time
aspect of the scheduling result was unclearly described
either. The PSO based scheduling approach proposed by
Wang and Li [9] minimized respectively the electric
consumption and the electric cost of manufacturing systems
while respecting the production target. The effects of the
summer and winter TOU pricing profiles on the scheduling
results were also investigated. However, machine transition
states between off and producing, i.e., start-up and shutdown, were ignored, and the power consumption was
assumed theoretically. The TOU tariff was also adopted in
the scheduling of Zhang et al. [10] to minimize the electric
cost while keeping trade-offs with production throughput
and CO2 emission, respectively. Whereas, only machine on
and off modes are concerned in the energy modelling; both
the power and electricity price were theoretically assumed.
The hourly volatile electricity price was used in the single
machine scheduler built by Shrouf et al. [11]. But the
scheduler only focused on determining when a job would
start without reordering the job sequence. Furthermore, a
limited number of machine states, and only presumed
power and price values are involved. Consequently, the
above limitations caused a gap between the academia and
the industry in regard to energy-cost-aware production
scheduling.
Based on these identified constraints, this paper presents
a novel energy-cost-aware production scheduling
methodology. It assigns the job sequence on a single
machine according to volatile electricity prices such that
cost-effective and environment friendly manufacturing unit
processes are promoted. A case study on a surface grinding
machine under three DR electricity tariff structures is
conducted, in order to demonstrate the economical and
environmental potential of this methodology.
2. Background on energy-cost-aware scheduling
Production planning and scheduling lay at two crucial
and distinguishable decision layers in production
management of a manufacturing enterprise [12]. There is
typically a sequential relationship between them. The
planning model first takes customer order demands as its
input, partitions the time horizon in a set of planning
periods, and determines the production quantities for each
period. Because multiple products can be allocated into the
same period, the scheduling model then gets the production
quantities and types as its input, and schedules production
sequences to different machines within a time horizon that
is equal to the corresponding planning period. Briefly,
production planning is located higher at the enterprise
tactical level, while production scheduling is situated lower
at the shop floor operational level [13]. This clear
separation thus enables an individual deep research into
production scheduling.
In the conventional production scheduling, the
commonly existing objectives for optimization include
makespan [14], completion time [15], job flow time [16],
and tardiness-earliness penalties [17]. Some novel
objectives are further considered to be integrated into
scheduling, e.g., decreasing energy consumption [18],
reducing carbon footprint [19], and improving robustness
[20]. However, production systems are currently faced with
a new turbulence from the energy market [21]. Energy
prices are becoming more volatile, depending on the realtime energy demand and generation from various energy
sources, e.g., coal, wind, solar, and tide. This volatility can
187
Xu Gong et al. / Procedia CIRP 29 (2015) 185 – 190
be found in a variety of price-based DR programs. For
example, in real time
pricing (RTP), the electricity price
varies every hour within a day; in time-of-use pricing
(ToUP or TOU), the electricity rate differs by time periods
of a day, but remains constant within one period [22]; in
critical peak pricing (CPP), a pre-specified extra high rate is
triggered by the utility, and is in effect for a limited number
of hours. As large electricity consumers (see Section 1),
industry will certainly adapt its electricity consumption
behavior to a specific implemented DR program, so as to
minimize its corresponding electricity cost. As a result, this
industrial interaction and responsiveness will determine
short-term impacts on the electricity market, through
helping reduce peak power generation and GHG emissions.
Furthermore, by enhancing the power grid’s stability, this
peak demand reduction, in the long term, postpones the
need for network upgrades and decreases overall plant cost
investments. Therefore, the novel production scheduling,
which is sensitive to volatile energy prices, will contribute
to both economic and environmental benefits for either the
industry or the utility.
to receive and load its next operation), cost for shutting
down, and cost for starting up just before the next job starts.
Eq. (5) determines the machine to stay Ready or off when
the current job is completed. Eq. (6) judges whether the
current time is within the tsth (ts: time in priced slot, see the
nomenclature) electricity priced slot.
Eq. (7) - (9) define the duration of each job according to
its scheduled position. Eq. (10) guarantees each job is
scheduled only once and thus all the jobs can be scheduled.
Eq. (11) limits the machine to have only one state at a time
point, and also enables a constant power value is associated
with each state. Eq. (12) uses the flooring function to decide
at which priced slot the current discrete time is located.
Eq. (13) calculates the duration for staying off between two
jobs. Constraint (14) makes sure that only one job is
executed at one time on respecting the scheduled job
sequence, and pre-emption is prohibited. Constraint (15)
shows the requirement that all the jobs should be fulfilled
before the due time, and finally the machine is set off.
min s ,t
^¦
Ci ¦i
N J 1
NJ
i 1
1
>Di ˜ CRi (1 Di ) ˜ CSDi @`
(1)
Subject to:
3. Scheduling model for energy cost minimization
Ci
A mixed integer linear programming model is
formulated for this problem. The inputs of this novel
scheduling model are volatile electricity prices, job IDs and
durations, a pre-fixed due time, and the possible electricity
consumption machine states. The outputs include the job
sequence, the start time and end time of each job, and the
corresponding machine energy consumption states.
The concerned parameters are introduced in the
nomenclature box (see the second page of this paper). The
objective function is given below, followed by a bunch of
relations or constraints closely correlated with machine
energy consumption states. For the sake of conciseness,
each machine state is assigned a unique integer index. As
shown in Table 1, the last item “others” is retained for any
case study that needs to extend the generic machine states.
CRi
¦
¦
ETi
STSi 1
ts ETSi
¦
CSDi
EPts ˜ Ets ˜ ¦t
ETSi
ts STSi
¦
EPts ˜ Ets ˜ ¦t
ts ETSi
¬« STi 1 D2 Ts
ETi
Ns
s 1
Pst ˜ t , i  I
P3 ˜ t , i  >1,2,..., N J 1@
EPts ˜ Ets ˜ ¦ t
ETi D3
«¬ ETi D3 D5 Ts / D »¼
ts ¬« ETi D3 Ts / D ¼»
« STi 1 Ts / D ¼»
Di
¦
STi 1
«¬( ETi D3 Ts ) / D »¼
¦ ts¬
STi
ETi
EPts ˜ Ets ˜ ¦ t
ETi D3
STi 1
¼
(3)
P3 ˜ t
ETi D3 D5
EPts ˜ Ets ˜ ¦ t
/ D»
(2)
STi 1 D2
P5 ˜ t
(4)
P2 ˜ t ,
i  >1, 2,..., N J 1@
­1, if ( STi 1 ETi ) d ( D3 D5 D2 ) or CRi d CSDi
,
®
¯0, otherwise
(5)
i  >1,2,..., N J 1@
Ets
­1, if t  [ts ˜ D, (ts 1) ˜ D)
®
¯0, otherwise
(6)
ET1
ST1 TSU TR D1j , j  J
(7)
Table 1 Numeration for machine states
ETi
STi TR D , i  > 2,3,..., N J 1@, j  J
(8)
Machine state s
Off
Startup
Ready
Production
Shutdown
Others
ETNJ
STNJ TR D jNJ TR TSD, j  J
Index
1
2
3
4
5
…
Eq. (1) is the objective function. It assigns the job
sequence, which is correlated with machine state based
energy consumption estimation, along time such that the
total electricity cost within the concerned work shifts is
minimal. Eq. (2) calculates the electricity cost for
completing a job. By convention, the cost for powering on
in the beginning and powering off at the end of production
is automatically included in the first and last scheduled
jobs, respectively. Eq. (3)-(4) calculate the electricity cost
for the machine to stay Ready and Off between two jobs,
respectively. The cost concerned in Eq. (4) comprises three
parts: cost for staying Ready during a default duration
(which is considered as a necessary period for the machine
i
j
!i  I : i
Pst
Ps
j, j  J
¦
(9)
(10)
P , s  S , t  >Ts ,Ts G t ,..., DT G t , DT @ (11)
Ns
t
k 1 k
«¬ t Ts / D»¼ , t ò >Ts ,Ts G t }, DT -G t, DT @
­0, if STi 1 ETi d D3 D5 D2
TO ®
,
¯ STi 1 ( ETi D3 D5 D2 ), otherwise
ts
(12)
(13)
i  >1,2,..., N J 1@
STi
ETi , ETi TR d STi 1, i  >1,2,..., N J 1@
ETNJ TR TSD d DT
(14)
(15)
4. Case study: scheduling on a surface grinder
The generic energy-cost-aware production scheduling
methodology was applied to a surface grinding machine
(Paragon RC-18CNC). To obtain its energy consumption
states, a power measurement was performed with a clamp-
Xu Gong et al. / Procedia CIRP 29 (2015) 185 – 190
on power meter (Yokogawa CW240). Connected between
the power supply and the grinder, the power meter records
the grinder’s overall power consumption every second.
Based on the measurement data, five states were identified
by using the time study in the in-depth approach proposed
by Kellens et al. [23], as presented by Table 2. The job
scheduling for this grinder was then performed with diverse
DS programs as discussed in the following sub-sections.
Table 2 Energy consumption states of the surface grinder
Machine state
(one cycle)
Startup
Ready
Grinding
Dressing
Shutdown
Average power
(kW)
3.55
5.93
9.49
6.72
1.00
Cycle duration
(s)
652
25 (default)
25
125
362
4.1. Real time pricing
The RTP data was taken from Belpex, the Belgian
electricity spot market [24], where the hourly dynamic
electricity price is known one day in advance (called “dayahead market" price). A number of assumptions were first
made. (1) The concerned production lasts from 8 AM
of 3 March 2014 to 8 AM of 4 March 2014. (2) The
involved steel workpieces are of the same type as those in
the measurement. (3) The grinder runs the same numerical
control (NC) program, which means it keeps the same
energy consumption behavior as that identified in the
measurement. (4) After consecutively grinding 14
workpieces (which was identified from the peaks in the
measured power data), the machine passes from Grinding to
Dressing to ensure a high-quality of the grinder surface. But
if the machine grinds less than 14 workpieces before it
fulfills the current job, it will grind another 14 for the next
job before it carries out another dressing operation. We
denote this as “non-memory dressing”. (5) If the grinder
stays idle or off before the start of one job, the start time of
this job is always set at the very start of a certain hour, e.g.,
9 AM and 11 PM. (6) The grinding jobs are pre-designed in
Table 3.
Table 3 Grinding jobs for scheduling
Job ID
1
2
3
4
5
Number of steel
workpieces
100
200
300
400
500
Required production time
(grinding + dressing)
3375s (56m15s)
6750s (1h52m30s)
10125 (2h48m45s)
13500 (3h45m)
16875 (4h41m15s)
Table 4 Genetic algorithm (GA) configuration
Parameter
Value
population size
80
elitism rate
15%
mutation rate
3%
crossover rate
95%
maximum
iteration
100
Explanation
Each generation has 80 individuals.
The top 15% of individuals are retained
from one generation to the next.
Two random genes in a chromosome will
change each other’s position at a rate of 3%.
Two chromosomes in one population will
swap each other’s genes at a random point
along the chromosome at a rate of 95%.
The maximum number of generation
revolution is 100.
The scheduling model was implemented in Java, and a
genetic algorithm (GA) was further developed for the
optimization. Each scheduling solution is represented by a
chromosome. A chromosome contains a chain of genes.
Each gene stands for a job, and has its own ID
corresponding to the job ID. The gene position in a
chromosome represents the actual job order. The related
GA configuration is listed in Table 4.
The automatically obtained optimal scheduling solution
is presented in Figure 1, which evidently demonstrates its
effectiveness for electricity cost saving. The hourly
dynamic electricity price has its peak from 7 PM to 9 PM
on 3 March, while having its lowest valley from 2 AM to 7
AM on 4 March. This optimal scheduling solution can not
only effectively avoid the pricing peak, but also allocate the
jobs to low-priced periods, e.g., the aforementioned valley
and the period from 4 PM to 7 PM on 3 March. Besides,
this optimization will not jeopardize the normal production
since the last job3 will be completed before the pre-defined
due time which is 8 AM of 4 March 2014 (see Figure 1).
(OHFWULFLW\SULFH
-RE
-RE
-RE
-RE
-RE
(OHFWULFLW\SULFH 噉P:K
188
Time (in hour, from 8am March-3-2014 to 8am March-4-2014)
Figure 1 RTP and the optimal production schedule
Table 5 demonstrates the performance of the proposed
scheduling methodology for the concerned case studies.
The “as early as possible” schedule is taken for comparison,
in which all the jobs are carried out consecutively from the
very beginning. In contrast to this classic schedule which
costs 6.49 €, the optimal schedule, at the cost of 5.05 €, is
demonstrated to gain an electricity cost saving ratio of 22%
for performing the same jobs before the due time. The
trade-off between the electricity cost and makespan (which
is the total time duration of a production schedule) in
Table 5 will be discussed in sub-Section 4.4.
4.2. Time-of-use pricing
The ToUP tariff data was taken from the electricity bill
of a Belgian plastic bottle manufacturer. All the
assumptions and GA configurations are the same as those in
the RTP case. As shown in Figure 2, this price structure has
two levels: on-peak and off-peak, at 61.1 €/mWh and 39.6
€/mWh, respectively. The off-peak period lasts from 9 PM
to 6 AM the next day, which has only nine hours within a
day. Therefore, the electricity cost oriented optimal
schedule makes full use of this period. As the whole
schedule lasts longer than nice hours, job1, job2, a part of
job3 and a part of job5 have to be performed within the onpeak period. Moreover, all the jobs are scheduled to be
bunched together for energy saving, because either staying
189
Xu Gong et al. / Procedia CIRP 29 (2015) 185 – 190
(OHFWULFLW\SULFH 噉P:K
(OHFWULFLW\SULFH
-RE
-RE
-RE
-RE
-RE
(OHFWULFLW\SULFH 噉P:K
idle between batches or powering off followed by powering
on later will surely cause more non-productive energy
consumption. Last but not the least, the job execution
sequence exactly corresponds to the natural job ID
sequence
(see
Figure
2),
(OHFWULFLW\SULFH
-RE
-RE
-RE
-RE
-RE
7LPH LQKRXUIURPDP0DUFKWRDP0DUFK
Figure 3 CPP and the optimal production schedule
schedule leads to 69% electricity cost saving (see Table 5).
7LPH LQKRXUIURPDP0DUFKWRDP0DUFK
4.4. Trade-off between electricity cost and makespan
Figure 2 ToUP and the optimal production schedule
Table 5 Cost and makespan comparison between the optimal schedule and
classic schedule under different electricity tariffs
Case
As early as possible schedule under RTP
Optimal schedule under RTP
As early as possible schedule under ToUP
Optimal schedule under ToUP
As early as possible schedule under CPP
Optimal schedule under CPP
Cost
(€)
6.49
5.05
7.35
5.90
19.13
5.95
Makespan
(seconds)
51789
84612
51789
80589
51789
83962
which is only a coincidence brought by the GA. As
summarized by Table 5, this optimal schedule is able to
reach an electricity cost saving rate of 20% under ToUP
compared to the classic schedule.
4.3. Critical peak pricing
In CPP, the maximum number and length of critical
peak periods are agreed upon between the utility and
customers in advance. In the long term, the exact moments
when critical peaks occur cannot be determined beforehand,
since they actually depend on the market and weather
conditions. However, CPP event days are called only from
Monday to Friday, excluding holidays. Moreover, in the
short term, CPP event days are usually determined based on
a day-ahead maximum temperature forecast at specific
locations, since peak demands usually occur in a hot
summer or a cold winter. The utility notifies its customers
by 3 PM, on a day-ahead basis if a CPP day is to take place
the next day. There are a high price and a moderate price
during a CPP period [25]. The high price can be five times
as high as the on-peak price of a normal ToUP tariff, and
the moderate price can be almost three times as high as the
off-peak price. A CPP period often lasts from the noon to
the early evening.
In this case study, the CPP tariff structure was assumed
based on the above identified charging rules and the ToUP
values in sub-Section 4.2. As presented in Figure 3, the
moderate price lasts from 11 AM to 2 PM of 3 March, and
the high price has a period from 2 PM to 6 PM on the same
day. The optimal scheduling result assigns the job sequence
such that all the jobs are effectively executed outside both
the moderate and high peak periods, and the priced valleys
are fully made use of. Compared to the classic one, this
Figure 4 Pareto frontiers together with the solution regions indicating the
trade-off between the electricity cost saving and the makespan
As revealed by Table 5, there exists a trade-off between
the electricity cost and the makespan: a saving in the
electricity cost will always cause a longer makespan. For
example, in the case of RTP (see Table 5), the optimal
schedule contributes to an electricity cost saving rate of
22% compared to the classic schedule, while its makespan
becomes 1.63 times longer, or has a prolongation rate of
63%. This is reasonable because the electricity cost saving
is realized by shifting the grinding load to low-priced
periods, and consequently leads to a delay of performing
out some jobs even though all the jobs are completed before
the due date.
Three Pareto frontiers (which is respectively a set of
optimal solutions) are further drawn by running one million
random schedules under each of the above three electricity
tariff structures and with the same assumptions. The
obtained trade-off between the electricity cost saving rate
(RECS) and the makespan prolongation rate (RMP) is clearly
illustrated by Figure 4. Among the three Pareto frontiers,
the one under CPP is relatively steadier and covers an
obviously larger range of RECS (0.6%-69%), because of its
two significantly higher priced levels during its predefined
critical period. However, the other two Pareto frontiers
under RTP and ToUP, which have more or less the same
slope and the same coverage, slightly include a negative
interval on the horizontal axis. This demonstrates that there
are a few schedules even more expensive than the classic
schedule, or the classic schedule is already within the set of
the most expensive schedules. In CPP, the classic schedule
is uniquely the most costly one, since starting at 8 PM of 3
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Xu Gong et al. / Procedia CIRP 29 (2015) 185 – 190
March, it already covers the entire critical period by ending
at 10:16:42 PM on the same day (see Figure 3). Vertically,
the RMP ranges of the three Pareto frontiers vary between 0
and 70%. There is no negative rate, as the classic schedule
already has the shortest makespan.
5. Conclusion
To promote sustainability in unit manufacturing
processes, this paper proposes a mix-integer linear
programming model to perform energy-cost-aware
production scheduling for a single machine. Coupled with a
genetic algorithm, the scheduling model was further applied
to allocating jobs to a surface grinding process. The case
study under three demand response (DR) programs
demonstrated its effectiveness to avoid high-priced periods,
and to shift production loads to low-priced periods, while
respecting the predefined due date. Compared to the classic
“as early as possible” schedule, the optimal job schedule
achieved an electricity cost saving rate of 22%, 20%, and
69% respectively under real time pricing (RTP), time-ofuse pricing (ToUP), and critical peak pricing (CPP). This
automatic adaptation to DR can not only save electricity
expenditure for the industry, but also spontaneously reduce
peak power demand to the power grid and decrease
greenhouse gas (GHG) emissions (or carbon foot prints).
Moreover, a trade-off was found between electricity cost
saving and makespan in a general sense: the higher the
electricity cost saving rate (RECS) is, the longer the
makespan tends to be; or the longer the makespan is, the
larger chance the RECS will have to be great. This is further
studied and proved by means of Pareto frontier analysis
together with the solution region. The RECS turns out to vary
between -1% and 22%, -1% and 20%, and 1% and 69%,
under RTP, ToUP, and CPP, respectively; while the
makespan prolongation rate (RMP) fluctuates between 2%
and 67% for all the DR programs. A high electricity cost
saving rate only corresponds to the set of high RMP, while a
low RECS corresponds to a wide range of R MP. Last but not
the least, this analysis reveals a critical condition for
performing the energy-cost-aware scheduling: there should
exist some idle time in a certain process, which thus enables
a flexible load shift.
Concerning the outlook, several further extensions of the
described work are identified: (1) multi-objective
scheduling with one explicit objective of minimizing the
energy cost, (2) scheduling which considers more costs
related to the production load shift, e.g., a higher personnel
cost for the night shift. All the extensions try to integrate
energy cost awareness into the existing production
scheduling models as an important and feasible roadmap
towards sustainable manufacturing.
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
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