Procedia CIRP 29 ( 2015 ) 185 – 190

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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 scientifi c committee of The 22nd CIRP conference on Life Cycle Engineeringdoi: 10.1016/j.procir.2015.01.041

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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 energy-efficient, demand-responsive, and cost-effective manufacturing processes. © 2015 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the International Scientific Committee of the Conference “22nd CIRP conference on Life Cycle Engineering.

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.

© 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 scientifi c committee of The 22nd CIRP conference on Life Cycle Engineering

186 Xu Gong et al. / Procedia CIRP 29 ( 2015 ) 185 – 190

Nomenclature

Ci electricity cost for the ith scheduled job, i ϵ I CRi electricity cost for the machine to stay at Ready state

after the completion of the ith job, i ϵ [1, 2, …, NJ-1] CSDi electricity cost for the machine to be shut down after

the completion of the ith job, i ϵ [1, 2, …, NJ-1] D time duration of one pricing slot Ds 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

DT due time for all jobs in the concerned work shifts EPts electricity price during the tsth time slot ETi end time for the ith scheduled job, i ϵ I ETSi end time in slots for the ith scheduled job, i ϵ I I set of job scheduling positions [1, 2, …, NJ] J set of job IDs [1, 2, …, NJ] NJ total number of jobs in the concerned work shifts Ns total number of machine states Ps 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)

S set of machine states [1, 2, …, Ns] STi start time for the ith scheduled job, i ϵ I STSi start time in slots for the ith scheduled job, i ϵ I Ts start time of the concerned work shifts TO time duration for the machine to stay off TR default time duration for the machine to stay ready TSD time duration to shut down the machine TSU time duration to start up the machine s machine state, s ϵ S t time in δt, t ϵ [Ts, Ts+ δt …, DT- δt, DT] δt defined time step for energy consumption estimation ts time in priced slots, ts ϵ [1, 2, …, ceil(DT/D)] αi machine operation indicator, i ϵ [1, 2, …, NJ-1] βts 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 shut-down 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) meta-heuristic 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 shut-down, 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 real-time 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.

3. Scheduling model for energy cost minimization

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.

Table 1 Numeration for machine states

Machine state s Index Off Startup Ready Production Shutdown Others

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

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.

1

, 1 1min (1 )J JN N

s t i i i i ii iC CR CSD (1)

Subject to:

1,i i s

i i

ETS ET N ti ts ts sts STS t ST s

C EP P t i I (2) 1 1

3 , 1,2,..., 1i i

i i

STS STi ts ts Jts ETS t ET

CR EP P t i N (3)

3 3

3 5 3 5

3 3

1 1

1 2 1 2

( ) /3

/5/

/2/

,

1,2,...,

i s i

i i

i s i

i s i

i s i

i s i

ET D T D ET Di ts tsts ETS t ET

ET D D T D ET D Dts tsts ET D T D t ET D

ST T D STts tsts ST D T D t ST D

CSD EP P t

EP P t

EP P t

i 1JN

(4)

1 3 5 21, ( ) ( ),

0,

1,2,..., 1

i i i ii

J

if ST ET D D D or CR CSDotherwise

i N (5)

1, [ , ( 1) )0,ts

if t ts D ts Dotherwise

(6)

11 1 ,jET ST TSU TR D j J (7)

, 2,3,..., 1 ,ii i j JET ST TR D i N j J (8)

,J

J J

NN N jET ST TR D TR TSD j J (9)

! : ,i I i j j J (10)

1, , , ,..., ,sNt t

s s k s skP P P s S t T T t DT t DT (11)

/ , , - ,, ss sts t T t T T t DT t DTD ò (12)

1 3 5 2

1 3 5 2

0,,

( ),

1,2,..., 1

i i

i i

J

if ST ET D D DTO

ST ET D D D otherwise

i N (13)

1, , 1,2,..., 1i i i i JST ET ET TR ST i N (14)

JNET TR TSD DT (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-

188 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)

Average power (kW)

Cycle duration (s)

Startup 3.55 652 Ready 5.93 25 (default) Grinding 9.49 25 Dressing 6.72 125 Shutdown 1.00 362

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 “day-ahead 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 Number of steel workpieces

Required production time (grinding + dressing)

1 100 3375s (56m15s) 2 200 6750s (1h52m30s) 3 300 10125 (2h48m45s) 4 400 13500 (3h45m) 5 500 16875 (4h41m15s)

Table 4 Genetic algorithm (GA) configuration

Parameter Value Explanation population size 80 Each generation has 80 individuals.

elitism rate 15% The top 15% of individuals are retained from one generation to the next.

mutation rate 3% Two random genes in a chromosome will change each other’s position at a rate of 3%.

crossover rate 95% Two chromosomes in one population will swap each other’s genes at a random point along the chromosome at a rate of 95%.

maximum iteration 100 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).

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 on-peak period. Moreover, all the jobs are scheduled to be bunched together for energy saving, because either staying

Time (in hour, from 8am March-3-2014 to 8am March-4-2014)

Figure 1 RTP and the optimal production schedule

189 Xu Gong et al. / Procedia CIRP 29 ( 2015 ) 185 – 190

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),

Table 5 Cost and makespan comparison between the optimal schedule and classic schedule under different electricity tariffs

Case Cost (€)

Makespan (seconds)

As early as possible schedule under RTP 6.49 51789 Optimal schedule under RTP 5.05 84612 As early as possible schedule under ToUP 7.35 51789 Optimal schedule under ToUP 5.90 80589 As early as possible schedule under CPP 19.13 51789 Optimal schedule under CPP 5.95 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

schedule leads to 69% electricity cost saving (see Table 5).

4.4. Trade-off between electricity cost and 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

Figure 2 ToUP and the optimal production schedule

Figure 4 Pareto frontiers together with the solution regions indicating the trade-off between the electricity cost saving and the makespan

Figure 3 CPP and the optimal production schedule

190 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-of-use 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 RMP. 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.

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