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International Journal of Production Research

ISSN: 0020-7543 (Print) 1366-588X (Online) Journal homepage: http://www.tandfonline.com/loi/tprs20

Modelling and simulation of energy consumptionof ceramic production chains with mixed flowsusing hybrid Petri nets

Hongcheng Li, Haidong Yang, Bixia Yang, Chengjiu Zhu & Sihua Yin

To cite this article: Hongcheng Li, Haidong Yang, Bixia Yang, Chengjiu Zhu & Sihua Yin (2018)Modelling and simulation of energy consumption of ceramic production chains with mixed flowsusing hybrid Petri nets, International Journal of Production Research, 56:8, 3007-3024, DOI:10.1080/00207543.2017.1391415

To link to this article: https://doi.org/10.1080/00207543.2017.1391415

Published online: 23 Oct 2017.

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Modelling and simulation of energy consumption of ceramic production chains with mixedflows using hybrid Petri nets

Hongcheng Lia,b*, Haidong Yanga, Bixia Yanga, Chengjiu Zhua and Sihua Yina

aGuangdong CIMS Key Laboratory, Guangdong University of Technology, Guangzhou, China; bSchool of Advanced ManufacturingEngineering, Chongqing University of Posts and Telecommunications, Chongqing, China

(Received 10 August 2016; accepted 26 September 2017)

Ceramic production chain consisting of discrete flow and continuous flow energy-intensive processes consumessubstantial amounts of energy. This study aims to evaluate energy consumption performance and energy-saving potentialsof the ceramic production chain. According to the energy consumption characteristics of manufacturing processes andprocess interaction constraints in a ceramic production chain, an approach integrating the first-order hybrid Petri net(FOHPN) model, an objective linear programming model and a sensitivity analysis is proposed. The FOHPN model willsimulate the energy consumption patterns of the ceramic production chain. Meanwhile, multi-objective linear program-ming model and sensitivity analysis will suggest the optimal specific energy consumption (SEC) of the production chainand identify the influences of input parameters (i.e. production rate of a process) on the SEC in the optimal productionscheme. Finally, a real case study from bathroom ceramic plant validates the approach. It provides a tool for modellingand simulation of energy consumption of ceramic production chains with mixed flows and helps operators to performenergy-saving actions in the ceramic enterprise.

Keywords: ceramic production chain; specific energy consumption; sensitivity analysis; first-order hybrid Petri net;linear programming

1. Introduction

Revolution in industry has moved from pure cost to quality and production efficiency and is in the transition towardsproduction sustainability (May et al. 2015; May, Stahl, and Taisch 2016). With increasing focus on environmental con-siderations, energy efficiency is widely viewed as a lever for business competitiveness and technology innovation inmanufacturing industry. Currently, the industrial sector in China consumes 2911.31 million tonnes of standard coal,which has almost doubled over the past decades, accounting for approximately 69.8% of the total energy consumptionin 2013 (National Bureau of Statistics of China 2016). Consequently, energy efficiency has been one of the majorfocuses of policy-makers and decision-makers. ‘Made in China 2025,’ issued by the State Council of China, requiresthat energy consumption per unit value added by large-scale industry be reduced by 22% in 2020 and 40% in 2025compared with 2015.

The improvement of energy efficiency at the machine level (Guo et al. 2015; Yoon et al. 2015; Zhou et al. 2016),process level (Göschel, Schieck, and Schönherr 2012; Madan et al. 2015; Spiering et al. 2015) or system level (Duflouet al. 2012; Javied, Rackow, and Franke 2015; Wahren, Siegert, and Bauernhansl 2015) has attracted extensive attention.These studies indicated that a significant energy-saving potential lies in production processes. A deeper insight intoenergy consumption patterns from an individual process to entire production chain is a prerequisite of improving energyefficiency. It means that an integrated production chain modelling is needed to capture energy consumption patterns.Uluer et al. (2016) proposed an integrated framework for energy consumption reduction in process chains, from partdesign and process planning to process chain simulation. They indicated that dynamic aspects of a process chain mustbe captured to predict energy consumption at operational level and evaluate the influence of operational decisions.Schönherr (2013) developed a simulation-based energy consumption model of a production chain, which includes per-ception, interpretation, analysis, structuring, formalisation, balancing and evaluation. Herrmann and Thiede (2009) pre-sented a process chain simulation approach that allows the integrated evaluation of technical, ecological and economiccriteria at a production system layer. Subsequently, they investigated the combined application of the proposed approach

*Corresponding author. Email: cqulhc@163.com

© 2017 Informa UK Limited, trading as Taylor & Francis Group

International Journal of Production Research, 2018Vol. 56, No. 8, 3007–3024, https://doi.org/10.1080/00207543.2017.1391415

in an aluminium die casting industry (Herrmann, Heinemann, and Thiede 2011). These studies provide useful tools toprofile the required energy of a discrete production chain.

The ceramic production chain consists of continuous flow and discrete flow energy-intensive manufacturing pro-cesses. In a ceramic production chain, interactions between two types of processes increase the complexity of modellingand evaluating energy consumption performance (Valentin and Ladet 1993; Engell et al. 2000). Unlike a continuousflow process, the equipment of a discrete flow process can be individually started or stopped and run at varying produc-tion rates, in which the final product may be produced out of single or multiple inputs. Asynchronous process interac-tions that are caused by events such as machine idling and unfilled work of a continuous process will result in energywaste of the entire production chain. Ensuring the synchronisation of production flows helps achieving energy-efficientmanufacturing in the ceramic industry. The state-based technique (Dietmair and Verl 2009; Verl et al. 2011; He et al.2012) has been widely used to simulate energy consumption behaviour of discrete processes such as machining. Thistechnique offers the possibility to model overall energy usage of an individual process, which can be employed as ahigh-level model to connect accurate energy models of individual operations (Peng and Xu 2014). However, processessuch as sintering in a ceramic production chain usually operate 24 h per day, seven days per week without shutdowns.The equipment of a continuous flow process will persistently stay in the ‘ON’ state until maintenance, and several pro-cessing stages (i.e. sintering includes preheating, heating and cooling) may be needed in the ‘ON’ state. Thus, it is a bigchallenge to profile the required energy of a ceramic production chain due to the mixed flows.

A hybrid Petri net, which integrates the Petri net model and fluid model, has the capability to capture the time-dri-ven and event-driven dynamics of energy consumption of an individual process and to provide an aggregate formulationto address the complex interactions of mixed production flows. The hybrid Petri net has been widely used in the mod-elling and simulation of complex manufacturing systems. For example, Balduzzi, Giua, and Seatzu (2001) provided aframework of the first-order Petri net model, and then a flexible manufacturing system was simulated using thisapproach. Dotoli et al. (2008) represented the concurrent activities of distributed manufacturing systems using first-orderhybrid Petri nets (FOHPNs), and some optimisation problems were solved via the corresponding numerical simulation.Thus, the hybrid Petri net model is a potential tool to capture energy consumption patterns of a ceramic productionchain.

Even though capturing complicated dynamics will improve energy consumption visibility and awareness, it still doesnot suggest when it is in an optimal operation scenario and how the optimal energy efficiency improvements of a pro-duction chain depend on its input parameters. In fact, a hybrid Petri net has an advantage for the analysis and control ofcomplex manufacturing systems. Namely, it allows performance optimisation and sensitivity analysis.

In this paper, an improved FOHPN will be used for the simulation of energy consumption patterns of a ceramic pro-duction chain. To further benchmark the energy consumption performance of the production chain and detect the influ-ences of input parameters, a multi-objective linear programming model which suggests the optimal specific energyconsumption (SEC) will be integrated with the FOHPN model. Additionally, the sensitivity analysis of multi-objectivelinear programming is implemented to identify how the optimal solution changes with the changes of input parameters(i.e. production rate of an individual process).

The remainder of this paper is outlined as follows. A methodology framework consisting of four steps is proposedin Section 2. Energy consumption characteristic of the individual process and process interaction constraints of a cera-mic production chain are analysed in Section 3. The modelling and simulation of energy consumption patterns of a cera-mic production chain using an FOHPN is proposed in Section 4. A multi-objective linear programming model and itssensitivity analysis are presented in Section 5. Then, a case study is implemented in Section 6. Finally, this paper con-cludes with remarks and an outlook for future work.

2. Methodology framework

A ceramic production chain consists of discrete flow and continuous flow processes. Here, a process can refer to a pieceof equipment or a set of multiple interconnected pieces of equipment. As shown in Figure 1, an integrated approachconsisting of four steps is proposed for reducing the specific energy of the ceramic production chain through operationalcontrol.

Step 1: Characterisation of the ceramic production chain. The energy consumption characteristics of the individualprocess and process interaction constraints of the ceramic production chain will be analysed in this step.Step 2: Prediction of energy consumption patterns. According to the energy consumption characteristics of the indi-vidual process and process interaction constraints, an improved FOHPN model is established to predict the energyconsumption patterns of the ceramic production chain.

3008 H. Li et al.

Step 3: Determining the optimal operation scheme. In this step, a linear programming model will be integrated withFOHPN model to suggest the optimal operation scheme and the corresponding input parameters.Step 4: Identifying the influence of input parameters. The sensitivity analysis of the linear programming model willbe implemented for identifying the influence of input parameters on SEC of the production chain in the optimaloperation scheme.

3. Characterisation of the ceramic production chain

3.1 Formulation of synchronisation constraints of the ceramic production chain

In ceramic manufacturing industry, continuous flow processes, such as sintering, usually operate 24 h per day, sevendays per week with infrequent maintenance shutdowns. Furthermore, the equipment of a continuous flow process, suchas a tunnel kiln, whose production cannot be interrupted even if the plan changes, always demands higher investmentand start-up costs. To ensure the stability of synchronisation, interactions between the discrete flow and continuous flowprocesses must be controlled. Two types of process interactions must be considered in a ceramic production chain: (1)continuous process upstream of the discrete process; (2) continuous process downstream of the discrete process. Inaccordance with (Valentin and Ladet 1993), four types of flow converters exist in both scenarios, as shown in Figure 2:(1) Conversion of a continuous flow into a discrete flow; (2) Conversion of a discrete flow into a continuous flow; (3)Conversion of pieces arriving in discrete flow through the use of materials delivered in continuous flow; (4) Conversionof a material arriving in continuous flow through the use of pieces delivered in discrete flow.

In this paper, the synchronisation constraints of a ceramic production chain will be formulated according to both ofthe above-mentioned interaction scenarios.

3.1.1 Continuous process downstream of discrete process

In the first interaction scenario, the feeding shortage of the upstream discrete process will reduce the production effi-ciency of a continuous process. However, a fixed energy input is required in a continuous flow process to maintainstable production conditions (i.e. temperature, pressure and humidity). Thus, any non-continuity in a first interaction sce-nario will result in indirect energy waste or an increase in energy intensity. Sufficient feeding of the upstream discreteprocess is the prerequisite of stable synchronisation. In this scenario, the synchronisation constraints can be expressed asEquations (1)–(3).

BDðk � 1Þ �Z tk

0vðtÞ[ 0 (1)

Figure 1. Modelling methodology framework of production chain for energy efficiency improvement.

International Journal of Production Research 3009

Subject to:

BDðk � 1Þ ¼ BDðk � 2Þ þ rðk � 1Þ �Z tk�1

0vðtÞ (2)

VminI � vðtÞ�Vmax

I (3)

where BD(k) denotes the output buffer level of the discrete process in the kth production cycle, v(t) is the input velocityof a continuous process with a minimum velocity Vmin and a maximum velocity Vmax, r(k) is the production rate of thediscrete process in the kth production cycle, and tk is the production time in the kth production cycle.

3.1.2 Continuous process upstream of discrete process

If a continuous process is upstream of a discrete process, the discrete process can be flexibly controlled through theactions. For example, energy-efficient scheduling can avoid energy waste that is caused by idle operation or discreteprocess waiting (Gahm et al. 2016; Mansouri, Aktas, and Besikci 2016). However, the buffer capacity of the continuousprocess and the utility of discrete process equipment must be constrained. In this case, the synchronisation constraintscan be expressed as Equations (4)–(6).

BCðk � 1Þ � R tk0 rmin � 0

BCðkÞ�BCcapcity

�(4)

Subject to:

BCðkÞ ¼Z tk

0vðkÞ �

Z tk

0rðkÞ þ BCðk � 1Þ (5)

VminI � vðtÞ�Vmax

Irmin � rðkÞ� rmax

�(6)

where BC(k) denotes the output buffer level of continuous process, r(k) with a minimum rate rmin and a maximum ratermax is the production rate of the discrete process in the kth production cycle.

Figure 2. Four types of production flow converters (Valentin and Ladet 1993).

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3.2 Energy consumption characteristics of the individual process

Discrete flow and continuous flow processes in a ceramic production chain show different energy consumption charac-teristics, as illustrated in Table 1.

Equipment of a discrete process always has several operation states, and each state has a specific power and timeperiod. Energy consumption is driven by state transition (discrete event) and continuous time. Taking a ball mill as anexample, a production cycle includes three operation states: first feeding, stop and the second feeding. The energy con-sumption of the ball mill in a production cycle can then be estimated based on the energy input rate and time period ofeach operation state. Furthermore, each state has an energy profile that is influenced by different operational parameters,as shown in Table 1.

In a continuous flow process, the materials that are being processed are continuously in motion, undergoing chemi-cal reactions or subject to mechanical or heat treatment. Thus, equipment of a continuous flow process generally hastwo operational states, ON and OFF. To maintain stable production conditions (i.e. temperature, pressure and humidity)in the ON state, a fixed energy input is required in a continuous flow process. In practice, a continuous flow processcan be divided into several stages that are controlled by different operational parameters. For example, sintering can bedivided into three stages (preheating, heating and cooling) based on temperature control requirement. Thus, the energyconsumption of a continuous flow process can be estimated based on the comprehensive energy input rate and time per-iod in each stage. Furthermore, each stage has an energy profile that is controlled by different operational parameters, asshown in Table 1.

4. Prediction of energy consumption patterns

A FOHPN model is used for the simulation of energy consumption patterns of a ceramic production chain. A FOHPNmodel is defined as a structure HPN = (P, T, Pre, Post, D, C) (Balduzzi, Giua, and Seatzu 2001; Dotoli et al. 2008). P isthe set of places that include a set of discrete places Pd and a set of continuous places Pc. T = Td + Tc is a finite set oftransitions, where Td and Tc are the finite sets of discrete and continuous transitions, respectively. Furthermore, discretetransitions are divided into a set of immediate, deterministically timed and stochastically timed transitions. The functionD:Td → R+ specifies the timing of discrete transitions, and R+ specifies positive real numbers. The functionC:Tc ! Rþ

0 � Rþ1 defines the firing speed of each continuous transition, and Rþ

a denotes Rþ [ af g. For any continuous

Table 1. Energy consumption characteristics comparison between discrete flow and continuous flow processes.

Items Discrete process Continuous process

Drivers Equipment of discrete process always has several states andeach state has a specific power and time period. The energyconsumption is driven by state transition and continuoustime

Equipment of continuous process stays in the ‘On’ stateuntil infrequent maintenance shutdowns. A continuousprocess always consists of several stages that arecontrolled by different operation parameters

Energy estimation Energy ¼ PNi¼1 E � Poweri � Timei

Energy ¼ PMi¼1 E � Powerj � Timej

i = index of machine states j = index of process sub-stageE − Poweri = energy flow rate of the ith state E − Powerj = energy flow rate of the jth stage

ModellingTool

i.e. State-based technique i.e. Differential equations or transfer functions

Profile

International Journal of Production Research 3011

transition, its firing speed is defined as V 0j � vj �Vj, where V 0

j denotes the minimum firing speed (mfs) and Vj representsthe maximum firing speed (MFS).

4.1 The FOHPN model of an individual process

The FOHPN model of an individual process forms the basic element of the energy consumption model of a ceramicproduction chain. The FOHPN model of an individual process will be established according to the energy consumptioncharacteristics of the discrete flow and continuous flow processes, respectively.

In a discrete flow process, the production continuous transition (PCT) tp and energy consumption continuous transi-tion (CCT) tM,E are defined for simulating production and energy consumption dynamics, respectively, as shown in Fig-ure 3. The operation states are controlled by discrete places PM,S, PM,I and PM,I’. The energy consumption of a discreteflow process is recorded by continuous place PE. Discrete transitions tM,IS, tM,SI and tM,I’S decide either how long theequipment stays at each operation state or under which circumstances the equipment can switch from one operation stateto another. Furthermore, the discrete transition tM,SI is enabled via the continuous place PB through a control valve. Thesimulation algorithm for predicting the energy consumption patterns of a discrete process in each production cycle isdescribed in Table A1 in Appendix 1.

In a continuous flow process, the production flow is divided into two stages that are modelled via the transition tP-s1and transition tP-s2, and both transitions have the same firing speed. Two operation states, ON and OFF, exist in eachstage. Energy flow transitions are controlled by these operation states. For example, if the operation stays in the ONstate in the first production stage, the energy flow transitions tP-s1,E will be enabled. In addition, the continuous place PB

is used to simulate the buffer level of production chain, while the accumulated energy consumption is recorded via thecontinuous place PE. Discrete transitions tP-s1,SW and tP-s2,SW are accordingly enabled via the continuous place PP-s1 andPP-s2 through the corresponding control valve. The simulation algorithm for predicting the energy consumption patternsof a continuous process in each production cycle is described in Table A2 in Appendix 1.

4.2 Forming a feasible FOHPN model of the ceramic production chain

Once the individual process model is established, the FOHPN model of a ceramic production chain can be formedthrough constraining process interactions. In the FOHPN model of the ceramic production chain, process interactionsare described by synchronisation constraints of production transition velocity. Because instantaneous firing speeds (IFSs)of continuous transitions are the control variables in the FOHPN model, the feasible FOHPN model of the ceramic pro-duction chain can be formed by linear constraint inequalities, as shown by Equations (7)–(11).

Figure 3. The FOHPN model of an individual process in ceramic production chain.

3012 H. Li et al.

Vj � vj � 0 8tj 2 TenðmÞ (7)

vj � V 0j � 0 8tj 2 TenðmÞ (8)

vj ¼ 0 8tj 2 TnðmÞ (9)

Xtj2Ten

Cðp; tjÞ � vj � 0 8p 2 PenðmÞ (10)

vj � p� pcapacity 8p 2 PbðmÞ (11)

where Ten(m) ⊂ Tc(Tn(m) ⊂ Tc) is the subset of continuous transitions enabled (not enabled) at m,Pen ¼ p 2 Pc mp ¼ 0

��� �is the subset of empty continuous places, and Pb ¼ p 2 Pc pjf g is the buffer place followed by

production transition. Equations (7) and (8) are the constraints of any enabled continuous transitions IFS that should bewithin the limits of mfs and MFS. It is worth noting that the constraint of Equation (8), which is associated with tj,reduces to a non-negative constraint on vj if V 0

j ¼ 0. Equation (9) indicates that the IFS of the non-enabled continuoustransition is zero. Equation (10) indicates that if a continuous place is empty, then its fluid content cannot decrease.Equation (11) gives the synchronisation constraints, as shown in Section 3.

4.3 Capturing energy consumption dynamics of the ceramic production chain

In the FOHPN model of a ceramic production chain, energy consumption dynamics are simulated through the enablingand firing of transitions. Let τk−1 and τk be the occurrence times of consecutive macro-events, and the interval of time[τk−1, τk] is defined as the macro-period whose length is represented as Δk = τk − τk−1. The enabling and firing rules aredefined based on a previous study (Balduzzi, Giua, and Seatzu 2001), where the enabling of a discrete transitiondepends on the marking of all its input places, while the continuous transition is enabled only by the marking of itsinput discrete places: (1) a discrete transition t is enabled at m(τ) at time instant τ if for all pj ∊ •t:mj(τ) ≥ I(pj, t), where•t denotes all of the input places of discrete transition t; (2) a continuous transition t is enabled at m(τ) at time instant τif for all pj ∊ •dt, mj(τ) ≥ I(pj, t), where •dt represents all of the input discrete places of the transition t; an enabled con-tinuous transition t ∊ Tc is strongly enabled at m(τ) for all places pj ∊ •ct:mj(τ) > 0; an enabled continuous transitiont ∊ Tc is weakly enabled at m(τ) for some places pj ∊ •ct:mj(τ) = 0. Furthermore, a macro-event occurs when either a dis-crete transition fires, thus changing the discrete marking or enabling/disabling a continuous transition, or a continuousplace becomes empty, thus changing the enabling state of a continuous transition from strong to weak.

Let I rt be the set of indices of the enabled PCTs, and let Iet be the set of indices of the enabled CCTs. Assuming theIFS of a PCT at time τ is vrj ðsÞ and the IFS of a CCT at time τ is vej ðsÞ, the evolution of the buffer level and energy con-sumption level of an individual process can be described by Equation (12).

dmepðsÞds ¼ P

Cðp; tjÞ � vej ðsÞ j 2 Ietdmr

pðsÞds ¼ P

Cðp; tjÞ � vej ðsÞ j 2 I rt

8<: (12)

where no discrete transition is fired at time τ, and all firing speeds vj(τ) are continuous. Let τk(k > 0) be the occurringinstants of macro-events with the initial time τ0, and v(τ) is the corresponding IFS vector during the macro-period lengthΔk. Assuming that the IFS of continuous transitions are constant during a macro-period, the discrete marking and theIFS vector define a macro-state. In this macro-state, the dynamic characteristics of the FOHPN model can be describedby Equation (13). Here, the production and the corresponding energy consumption dynamics are separately describedthrough the production incidence matrix Ce

cc and energy consumption incidence matrix Crcc.

mepðsÞ ¼ me

pðskÞ þ CeccvðskÞðs� skÞ

mrpðsÞ ¼ mr

pðskÞ þ CrccvðskÞðs� skÞ

�(13)

where Ccc ¼ Cecc [ Cr

cc. The production synchronisation and energy consumption behaviour are controlled by the discretetransition (i.e. state transition). Assuming that ϕ(τk−1) ∊ Nn is the discrete firing vector representing the number of times,the discrete transition tdi is fired up to the current time τk−1, and the control mechanism can be described bymcðskÞ ¼ mcðs�k Þ þ Ccd � uðsk�1Þ.

International Journal of Production Research 3013

5. Determining the optimal operation scheme

5.1 Energy efficiency

To measure the energy consumption performance of a ceramic production chain, SEC indicator is used. Specific energy,which is the energy per unit mass, is estimated by Equation (14) based on (Giacone and Mancò 2012). In this paper,the SEC is a time-dependent evaluation indicator. It provides a real-time monitoring capability for the balance trendsbetween production loads and energy consumption.

Specific energy ¼ energy

mass¼ energy

time�mass

time¼ energy input rateðMJ=unit timeÞ

production rate (kg/unit time)(14)

In the FOHPN model, the SEC of the entire production chain and individual process can be estimated by Equations(15) and (16), respectively. The energy input rate of the entire production chain is the sum of instantaneous firing veloc-ities of all energy continuous transitions, while its production rate equals the instantaneous firing velocity of the last pro-cess. The energy input rate of an individual process equals the instantaneous firing velocity of its energy CCT, whilethe production rate equals the IFS of its PCT.

SECchain ¼

Pj2I et

vej

vrlast�process

(15)

SECprocess ¼vej ð8j 2 Iet Þvrj ð8j 2 I rt Þ

(16)

where SECchain is the SEC of the entire production chain, SECprocess is the SEC of the jth individual process, vej is thecomprehensive energy flow input rate of the jth individual process, vrj is the production rate of the jth individual pro-cess, Iej is the set of indices of the energy continuous transitions in FOHPN model, I rj is the set of indices of the PCTsin FOHPN model, and vrlast�process is the instantaneous firing velocity of the PCT that denotes the last process.

5.2 Determining the optimal operation scheme

According to Equation (15), the optimal operation scheme of the production chain should achieve maximum productiv-ity with the least amount of energy. Let I rt ¼ a1; . . .; akf g be the set of indices of the enabled PCT, andI rt ¼ a2kþ1; . . .; alf g is the set of indices of the empty PCT. A multi-objective linear programming model will be estab-lished for determining the optimal operation scheme. As shown by Equations (17) and (18), the model aims to optimisethe energy efficiency of the entire production chain, namely, by maximising the production rate of the last processvrlast�process and minimising the energy flow input rate of the production chain

Pj2I et v

ej . The energy consumption of the

entire production chain is determined by its configuration, process synchronisation, technical features of individual pro-cesses, etc. Santos et al. (2011) has shown that the energy consumption of an individual process linearly increases withits throughput. In this model, the velocity of CCT is further designed as the linear function of the velocity of the corre-sponding PCT. Furthermore, the linear coefficient of CCT–PCT is defined as cj. Thus, to minimise the energy flow inputrate

Pj2Iet v

ej can be replaced by minimising the function

Pj2I rt cjv

rj . In Equation (17), the coefficient cj is determined by

the velocity of the corresponding CCT.

Max: vrlast�processMin:

Pj2I rt cjv

rj

(17)

s.t.

va1 þ s1 ¼ Va1� � �vak þ sk ¼ Vakva1 � skþ1 ¼ V 0

a1� � �vak � s2k ¼ V 0

akPj2I rt

Cðpa2kþ1 ; tjÞvj � s2kþ1 ¼ 0

� � �Pj2I rt

Cðpal ; tjÞvj � sl ¼ 0

8>>>>>>>>>>>>>><>>>>>>>>>>>>>>:

sj � 0; j ¼ 1; 2; . . .; l (18)

3014 H. Li et al.

Let x ¼ ½va1 � � � vak s1 � � � sl�T ; then, Equations (17) and (18) can be expressed as the standard model of the multi-objectivelinear programming, as shown by Equation (19).

maxx

cT x Ax ¼ b; x� 0j� �(19)

where c is the coefficient vector of the objective function, A is the l × (l + k) matrix of constraints and b denotes the lvector of the resource coefficients, which are determined by the minimal firing speed (mfs) and MFS of continuous tran-sitions.

5.3 Sensitivity analysis of input parameters in the optimal operation scheme

A sensitivity analysis will be implemented based on the perturbation analysis theory of the linear programming model.In theory, a sensitivity analysis refers to the study of how optimal solutions change with the changes of the given linearprograming terms of the coefficients of the matrix, the right-hand side and the objective function (Ignizio and Cavalier1994). Assuming q = [q0 ⋯ qp]

T is the uncertain parameter vector in a ceramic production chain, the optimal solution ofEquation (19) (using the simplex method) can be written as Equation (20) for a given value of q. The correspondingoptimal basis B is a set of l variables, and the optimal basis matrix AB can be obtained by taking only those columns ofA whose corresponding variables are in B. The variables in B are the basic variables, while the others are called non-ba-sic (their set is denoted as N). It is worth noting that the optimal solution in Equation (20) is degenerate because manybases are associated with it.

x0ðqÞ ¼ xBðqÞxN ðqÞ

� �¼ A�1

B ðqÞbðqÞ0

� �(20)

In this paper, a sensitivity analysis will be developed with respect to CCT–PCT coefficients and the design parame-ters by assuming changes in the right-hand side vector and in the matrix coefficients, respectively. If an optimal solutionin �q is computed, the corresponding optimal basis is B. Then, the sensitivity of basic variable xBð�qÞ with respect to qican be computed using Equation (21) by taking partial derivatives.

@xBð�qÞ@qi

¼ A�1B ð�qÞ @bð�qÞ

@qi� @ABð�qÞ

@qixBð�qÞ

� (21)

Equation (21) shows the effect of a small change of qi on the optimal solution while the non-basic variables xN ð�qÞ donot change. Only the first-order differentiability of ABð�qÞ and bð�qÞ with respect to qi is required. Furthermore, if theoptimal solution is not degenerate, the obtained sensitivity is unique (Renegar 1994; Kato 1995).

6. Case study

6.1 Background

The production chain from a bathroom ceramic plant will be investigated to validate the proposed approach. This plantyearly consumes more than 25 million kWh of electricity, 14 million cubic metres of natural gas, 280 ton of diesel and350,000 tonnes of water. Its production chain mainly consists of ball-milling, slip-casting, glazing and sintering. Someassumptions are made in this case study: (1) the experimental period is designed as 30 shifts (240 h), and the corre-sponding production data are collected from its energy management system, as shown in Figure 4; (2) Energy includesthe electricity, natural gas and energy-consumed medium such as industrial water and compressed air; (3) the processes,such as inspection and grading, are not considered due to their slight contribution to energy consumption of productionchain; (4) ten parallel slip casting lines are used for the same type of products, while in the FOHPN model, these linesare abstracted as one line with 10-fold yields and energy consumption; (5) sintering is viewed as a continuous flow pro-cess divided into pre-heating, heating and cooling stage, and two states, ON and OFF, are used to control the transitionof each stage; and (6) waste heat of the tunnel kiln will be recovered.

6.2 Simulation of the ceramic production chain

The FOHPN model of the ceramic production chain is shown in Figure 5, and the corresponding description is as fol-lows.

International Journal of Production Research 3015

(1) The velocity of continuous transitions tR1-1 (v 2 0:478 0:524½ �) and tR1-2 (v 2 2:353 2:581½ �) denote the produc-tion rate (unit: ton/hour) of an 8-ton ball mill and a 40-ton ball mill, respectively. Each ball mill has three opera-tion states (first feeding PR1,I, second feeding PR1,I’ and stop PR1,S) that control production and energy flowdynamics.

(2) Continuous transition tR2 is the filter process of the slurry, which has a MFS (v = 3.5ton/hour). The place PB3

has sufficient store capacity which is infinite in the FOHPN model.(3) Continuous transition tR3 (v 2 2:4 3:1½ �, unit: ton/hour) denotes the slip casting process. The defective rate β of

this process is 0.7%.(4) Continuous transition tR4 (v 2 2:6 3:0½ �, unit: ton/hour) denotes the glazing process whose energy consumption

place is PE4. The reworking rate α of this process is 1.2%.(5) In the sintering process, the pre-heating, heating and cooling stages are represented by transitions tR5-1, tR5-2 and

tR5-3, respectively. Furthermore, these transitions have the same firing speed, with a minimum firing speed of 2.6ton/hour and a MFS of 3.1 ton/hour.

(6) CCT–PCT coefficients are assumed to be constant: cR1-1 = 363 MJ/ton, cR1-2 = 225 MJ/ton, cR2 = 0,cR3 = 156 MJ/ton, cR4 = 43 MJ/ton, cR1-1 = 3943 MJ/ton.

Finally, the FOHPN model is run according to the improved algorithm in MATLAB [Version 7.11.0 (R2010b)]. Theinitial macro-state of the FOHPN model and the constraints of linear programming in this state are presented in Appen-dix 2. It is worth noting that the firing speed of all production transitions will be zero if their upstream places are empty.Furthermore, the functions in MATLAB, such as LINPROG and FMINCON, are used to implement the sensitivity anal-ysis. The total input energy is measured by comprehensive energy consumption represented with energy equivalents byapplying the energy equivalent coefficients (GB/T 2589-2008 2008).

6.3 Simulation results and SEC benchmarking

According to Equation (17) and (18), the optimal solution is as follows: SEC* = 4.4119 MJ/kg with vR1-1 = 0.478 ton/hour, vR1-2 = 2.353 ton/hour, vR2 = 3.32 ton/hour, vR3 = 2.6385 ton/hour, vR4 = 2.6519 ton/hour, vR5-1 = vR5-2 = vR5-3 = 2.62 ton/hour. The above firing speeds of production transitions define an optimal operation scheme. In this scheme,assuming the optimal solution is the baseline of SEC of the production chain, the gap between the real-time SEC and

Figure 4. Energy management centre for energy consumption data collection.

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SEC* can be predicted, as shown in Figure 6. Thus, the model provides an alarm function. As shown in Figure 6, thealarm value is designed as 1.5-fold of the optimal SEC and energy consumption abnormality occurs in approximatelythe 38th hour. In practice, the alarm value must be determined according to the operational management requirement.

6.4 Sensitivity analysis for input parameters of the process chain

6.4.1 Impact of synchronisation constraint parameters

Section 2 indicates that the synchronisation constraints of the production chain are determined by the velocity of pro-duction transition. To analyse the impact of synchronisation constraints on SEC, how the optimal solutions change withthe changes of the given linear programing in terms of the right-hand side is implemented. Let biðk0Þ ¼ bi þ k0 inEquation (18); the optimal SEC will change with the parameter k0 in the range of [0, 0.2]. This means that the optimalSEC will change with the increase in firing speed of a production transition whose increasing amplitude is designed as[0, 20%]. As shown in Figure 7, the increase in firing speed of transitions tR1-1, tR1-2 and tR3 will result in the increasein optimal SEC of the production chain. The main reason is that the increasing firing speed of these transitions requiresmore energy consumption according to the assumptions in Section 5.2. The increase of firing speed of transitions tR2

Figure 5. Modelling and simulation of energy consumption of the ceramic production chain.

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and tR5 lead to a small change of the optimal SEC, while a significant reduction of the optimal SEC can be achieved byincreasing the firing speed of transition tR4. This shows that glazing represents the bottleneck of the system. If themaximum production rate of the glazing is improved, the value of the optimal SEC proportionally increases.

6.4.2 Impact of the CCT–PCT coefficients

Coefficient cj in Equation (17) can be viewed as the value coefficient of objective function in the linear programmingmodel. In the FOHPN model, the coefficient also represents the energy efficiency of the jth individual process. Asshown in Table 2, the optimal SEC of the production chain will reduce with the reduction of the CCT–PCT coefficientof a process. In particular, the coefficient of the sintering process has an obvious influence on the optimal SEC of theproduction chain. The optimal SEC of the production chain can be reduced by approximately 19.01% when the SEC ofsintering is improved with a 20% reduction. Therefore, more attention should be paid to energy consumption monitoringand optimisation of the sintering.

6.4.3 Impact of reworking rate α or defective rate β

Figure 4 shows that the defective rate of slip casting is β, and the reworking rate of glazing is α. Assumingaðk1Þ ¼ aþ k1 and bðk2Þ ¼ bþ k2, the perturbation of both parameters will cause the change of constraint Equations(A16) and (A17) in Appendix 2. This means that the constraint of the coefficient matrix of the linear programmingmodel is changed. Therefore, the objective function SEC and the optimal basic solution v(λ) vary linearly with theparameter λ as long as it remains within the allowable range [−0.5%, 0.5%]. As shown in Table 2, the improvement ofthe defective rate of slip casting and the reworking rate of glazing results in a small reduction of the optimal SEC. Thismeans that they should not be the focus for improving the SEC of the production chain.

6.4.4 Action suggestions based on sensitivity analysis

According to the results of the sensitivity analysis, the following actions are suggested to improve the energy efficiencyof the entire production chain. (1) Keeping the synchronisation between the discrete flow and continuous flow processesreduces energy waste caused by unwanted waiting. As shown in Figure 7, glazing as the pre-process of sintering (con-tinuous flow process) is the bottleneck of the production chain. Therefore, a decision-maker should stabilise the produc-tion rate of glazing for a safe semi-product input of sintering. (2) Table 2 shows that the value coefficient of sinteringhas a significant influence on the optimal SEC of the production chain. This means that both approaches, improving the

Figure 6. Real-time SEC compared with the optimal SEC.

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heat utilisation efficiency and the production rate of sintering, can be adopted. For example, the recovery of waste heatfrom the cooling zones, which offers substantial efficiency improvement of heat utilisation, can be used for pre-heatingof the combustion air. If the pre-heating temperature can be raised, more energy can be saved. On the other hand,

Figure 7. Sensitivity of the PCT firing speed.

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high-speed burners that improve heat transfer can be used during the design stage of the ceramic production chain.High-speed burners will allow significant energy savings compared with conventional burners. (3) Further optimisationof the reworking rate or defective rate is not suggested for reducing the SEC of the production chain. As shown inTable 3, changing the reworking rate or defective rate has a small effect on the SEC of the production chain. Rather, afurther decrease in the reworking or defective rates will require greater efforts such as upgrading production machines.

6.5 Discussion

A production chain is a combination of different production processes, with various machines for processing or trans-porting, as well as personnel (Herrmann and Thiede 2009). When manufacturing processes are investigated and opti-mised in an isolated manner, one may neglect possible energy-intensive pre- and post-processes and thus may miss anoverall optimum (Mose and Weinert 2015). Capturing the energy profile of a production chain is a prerequisite for opti-mising energy efficiency, while the manifold interdependencies and necessary consideration of different consumptionprofiles of the production chain result in a dynamic and complex planning problem. In the ceramic manufacturing indus-try, mixed flow processes further increase the complexity of this problem because energy consumption dynamics of aceramic production chain dynamically depend on two fundamental aspects: process interactions and the operational stateof machinery (Sproedt et al. 2015; Yoon et al. 2015). The proposed approach, which is based on the FOHPN, can cap-ture real-time energy efficiency performance of a production chain and also help a decision-maker understand the energyconsumption dynamics of production processes. This paper assumes that the energy input rate of a process has a linearrelationship with its production velocity. In practice, the energy consumption and throughput of a process are a separatefunction of process parameters (Neugebauer et al. 2012). Furthermore, the selection of process conditions will result ina different linear relationship coefficient (Diaz et al. 2009; Yoon et al. 2015).

In practice, capturing an energy profile is insufficient to help a decision-maker to improve energy efficiency. In theceramic manufacturing industry, the energy consumption benchmarking of the production chain is fundamental for esti-mating its energy efficiency and energy conservation potential (Yang, Liu, and Liu 2016). An optimal operationalscheme of a production chain is used to establish a baseline for improving energy efficiency. Meanwhile, the influenceof corresponding input parameters can be identified based on a sensitivity analysis. This will help decision-makers toestimate the energy consumption patterns and develop strategies for energy efficiency improvements.

7. Conclusions

In this paper, an approach that integrates the FOHPN model, a linear programming model, and a sensitivity analysis hasbeen proposed to evaluate the energy efficiency and energy-saving potential of a ceramic production chain. Althoughthe method focuses on the ceramic production chain, it is actually generic enough to extend to other sectors, such as analuminium production chain with mixed processes.

Table 2. Sensitivity of the CCT–PCT coefficient.

Variation range

−20% (MJ/kg) −15% (MJ/kg) −10% (MJ/kg) −5% (MJ/kg)

c1 4.3987 4.4020 4.4053 4.4086c2 4.3715 4.3816 4.3917 4.4022c3 4.3805 4.3883 4.3962 4.4041c4 4.4032 4.4054 4.4075 4.4098c5 3.622 3.8197 4.0171 4.2145

Table 3. Sensitivity of reworking rate α and defective rate β.

Reworking rate or defective rate

Variation range

−0.5% (MJ/kg) 0.5% (MJ/kg)

β = 0.7% 4.4111 4.4127α = 1.2% 4.4116 4.4122

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A ceramic production chain consists of discrete flow and continuous flow processes. The existing approach for adiscrete production system cannot be used to model the energy consumption patterns of a ceramic production chain dueto the more complex energy consumption characteristics and process interactions. The contributions of this paper can beillustrated as follows.

(1) An improved FOHPN model simulates the energy consumption patterns from an individual process to the entireceramic production chain. It not only relates equipment energy data with corresponding machine states orprocessing stages at the process level, but also demonstrates the process interaction dynamics. The model willprovide useful functions for the energy management system of the ceramic production chain, visualising theenergy flow dynamics and the transition mechanisms of energy drivers and identifying the influences of processinteractions on energy efficiency.

(2) The objective linear programming and sensitivity analysis models suggest the optimal SEC of a production chainand detect the influences of various input parameters on SEC. They will provide a benchmark for energyefficiency improvement of a ceramic production chain and identify the critical parameters affecting the energyefficiency. Then, they provide a function helping the operator to perform the energy-saving actions.

The proposed approach mainly focuses on the direct energy consumption of the production chain. To improve theapproach, indirect energy consumption should be considered in future studies. Furthermore, the system boundary of themodel can be extended, which will include more auxiliary processes such as mould making. In future studies, the pro-posed approach also can be integrated into the enterprise energy management system to help a decision-maker withreal-time energy efficiency improvement.

Disclosure statementNo potential conflict of interest was reported by the authors.

FundingThis work was supported by the National Natural Science Foundation of China (NSFC) [grant number 51475096]; the NSFC-Guang-dong Collaborative Fund [grant number U1501248]; the Guangdong CIMS Key Laboratory Open Fund [grant number CIM-SOF2016011].

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Appendix 1Table A1. Simulation algorithm for predicting the energy consumption patterns of a discrete process in each production cycle.

Table A2. Simulation algorithm for predicting the energy consumption patterns of a continuous process in each production cycle.

Simulation Algorithm for a discrete process

1: if the markings of a continuous place PB m(PB) > 0 then2: the state transition tM,SI and production continuous transition tp are enabled;3: the marking of discrete place PM,I m(PM,I) = 1 and energy consumption continuous transition tM,E are enabled.4: do τ = τ + Δτ5: The marking of continuous place PE m(PE) = m(PE) + vM,E

6: Until τ equals the period of state PM,I

7: the state transition tM,IS is enabled, and the marking of discrete place PM,S’ m(PM,S’) = 18: if the state transition tM,SI’ is enabled then

the discrete place PM,I’ m(PM,I’) = 1 and energy consumption continuous transition tM,E are enabled9: do τ’ = τ’ + Δτ’10: The marking of a continuous place PE m(PE) = m(PE) + v’M,E

11: Until τ’ equals the period of state PM,I’

12: the state transition tM,I’S is enabled, and the marking of a discrete place PM,S m(PM,S) = 113: end if14: end if

Simulation Algorithm for a continuous process

1: if the markings of a continuous place PP-s1 m(PP-s1) > 0;2: the discrete transition tP-s1,SW is enabled and the marking of a discrete place PP-s1,W m(PP-s1,W) = 1 and the marking of a discrete

place PP-s1,S m(PP-s1,S) = 0;3:tP-s1 is enabled and tP-s1,E is enabled;4: if the markings of a continuous place PP-s2 m(PP-s2) > 05: the discrete transition tP-s2,SW is enabled and the marking of discrete place PP-s2,W m(PP-s2,W) = 1 and the marking of discrete

place PP-s2,S m(PP-s2,S) = 0;6: end if;7: tP-s2 is enabled and tP-s2,E is enabled;8: the markings of a continuous place PP-s2 m(PP-s2) = m(PP-s2) + vP-s1 − vP-s2;9: The markings of energy consumption continuous place PE m(PE) = m(PE) + vP-s1,E + vP-s2,E;10: end if

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Appendix 2The initial marking in the model represents an initial macro-state in which all machines are operational and all buffers are empty.Such a marking has a discrete component:

mdðs0Þ ¼ pR1�1;I ; pR1�1;I 0 ; pR1�1;S ; pR1�2;I ; pR1�2;I 0 ; pR1�2;S ; pR2;I ; pR2;W ; pR3;I ;pR3;W ; pR3;S ; pR4;I ; pR4;W ; pR5�1;W ; pR5�2;W ; pR5�3;W

� �T¼ 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1½ �T (A1)

And a continuous component:

mcðs0Þ ¼ pB1�1; pB1�2; pB2; pB3; pB40 ; pB5; pE1; pE2; pE3; pE4; pE5; pE6½ �T¼ 0 0 0 0 0 0 0 0 0 0 0 0½ �T (A2)

For this initial macro-state, the following set of constraints can be associated with a standard form (no negativity constraints areomitted):

S0 :

vR1�1 þ s1 ¼ 0:524 (A3)vR1�1 � s2 ¼ 0:478 (A4)vR1�2 þ s3 ¼ 2:581 (A5)vR1�2 � s4 ¼ 2:353 (A6)vR2 þ s7 ¼ 3:5 (A7)vR3 þ s8 ¼ 3:1 (A8)vR3 � s9 ¼ 2:4 (A9)vR4 þ s10 ¼ 3:0 (A10)vR5 � s11 ¼ 2:6 (A11)vR5�1 þ s10 ¼ 3:1 (A12)vR5�1 � s11 ¼ 2:6 (A13)

vR1�1 þ vR1�2 � vR2 þ s12 ¼ 0 (A14)vR3 � vR2 þ s13 ¼ 0 (A15)

vR4 � ð1� bÞ � vR3 � a � vR4 þ s14 ¼ 0 (A16)vR5�1 � ð1� aÞ � vR4 þ s15 ¼ 0 (A17)

vR5�1 ¼ vR5�2 ¼ vR5�3 (A18)

8>>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>>:

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