- Email: [email protected]
An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops
Journal of Cleaner Production xxx (2014) 1e10
Contents lists available at ScienceDirect
Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro
An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops Yan He a, b, *, Yufeng Li a, Tao Wu c, John W. Sutherland b a
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China Environmental and Ecological Engineering, Purdue University, West Lafayette, IN, USA c Business Analytics and Optimization, Apollo Group Inc., Phoenix, AZ 85040, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 May 2014 Received in revised form 17 August 2014 Accepted 3 October 2014 Available online xxx
The environmental burden caused by energy consumption during the use phase of machine tool systems is widely acknowledged and hence ways must be found to use energy more efficiently. There is potentially a significant amount of energy savings that could be realized by selecting alternative machine tools and reducing the idle energy consumption through better scheduling. This paper proposes an energy-saving optimization method that considers machine tool selection and operation sequence for flexible job shops. The former seeks to reduce the energy consumption for machining operations, and the latter aims to reduce the idle energy consumption of machine tools. A mathematical model is formulated using mixed integer programming and the energy consumption objective is combined with a classical objective, the makespan. A Nested Partitions algorithm, which has proved to be robust for NP-hard problems, is utilized to solve the model. The proposed method is evaluated in a test case by two scenarios with different energy optimization schemes as well as the classical makespan objective. The results show that the proposed method is effective at realizing energy-savings for a flexible machining job shop. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Energy saving Machine tool selection Operation sequence Flexible job shops Nested partitions
1. Introduction The global manufacturing industry sector is responsible for 31% of primary energy consumption and 36% of CO2 emissions (Bruzzone et al., 2012). In manufacturing, machine tools consume an enormous amount of energy as they physically transform raw materials into finished products. Reducing the energy consumed by machine tool systems has been identified as one of the strategies to improve sustainability in manufacturing (Pusavec et al., 2010). The environmental impact of the use phase of a machine tool is more important than that of the other life cycle stages of a machine tool and resides mainly in the amount of energy consumed (Dahmus and Gutowski, 2004). With approximately 83% of the total impact, the use stage systematically is considered as the dominant contributor to the total life cycle environmental impact of machine tools (Duflou et al., 2012). Against the background, energy consumption during the use phase of machine tools has received much research attention, and * Corresponding author. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China. E-mail address: [email protected] (Y. He).
significant energy waste has been observed. The energy breakdown of machine tools has shown that only 10% of energy is used for actual material removal (Dahmus and Gutowski, 2004; Drake et al., 2006), and the rest of the energy is consumed by the auxiliary functions and components of machine tools. Moreover, substantial energy waste is associated with the idle phase of machine tool operation. At Toyota, it was reported that 85.2% of the energy was used for operations not directly related to the production of parts (Gutowski et al., 2005). Bladh (2009) also reported that the energy savings potential was 10e25% through the reduction of the time used waiting or in the start-up mode. To reduce these energy wastes, some energy-focused optimizing methods have been proposed for production operation of machine tool systems. For a single machine system, energy-focused optimizing methodologies have been proposed to reduce idle energy or energy during peak periods. Mouzon et al. (2007) investigated the problem of scheduling a single machine to minimize the idle energy consumption using several dispatching rules. They also proposed a framework to incorporate energy consumption into consideration while making scheduling decisions to optimize objectives such as total tardiness. According to previous investigations, proposed optimization methods were used to reduce
http://dx.doi.org/10.1016/j.jclepro.2014.10.006 0959-6526/© 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
2
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
idle energy consumption for a single machine. Liu et al. (2014a) focused on a single machine system and the consumed energy of the machine when it stays idle. An optimization model was proposed to minimize the carbon dioxide emissions based on the arrival time and the processing time of each product. Moreover, energy cost optimization was modeled by Fadi et al. (2014) for single machine production scheduling during production processes. Based on the model, the reduction in energy costs is achieved by avoiding high-energy price periods. Some studies have been carried out to address on energy optimization for production operation of flow shops. Herrmann and Thiede (2009) proposed process chain simulation to foster energy efficiency in manufacturing. Using the method, energy efficiency can be improved by the combination of quantity allocation and lot size of parts across two production lines. Some researchers focus on energy-efficient scheduling problems in flow shops, and presented mixed integer programming models for different energy-related objectives. Bruzzone et al. (2012) introduced a mixed integer programming model to minimize the shop floor power's peak. Fang et al. (2011a) and Dai et al. (2013) proposed a multi-objective optimization model considering both productivity (i.e., makespan) and energy (i.e., peak load, unload and carbon footprint). Besides these, Chen et al. (2013) studied specifically on productivity and energy performance in Bernoulli serial lines with machine startup and shutdown, and they utilized Markovian analysis method to discuss the effect of machine startup and shutdown schedule on system performance. These energy-focused methods for flow shops are not efficient for energy reduction in flexible job shops where significant flexibility involving both process routings and alternative machine tools exist for jobs. Only a few methods for energy optimization in flexible job shops have been reported in the literature. Weinert et al. (2011) proposed the EnergyBlocks methodology for integrated energyefficiency criteria with evaluation and decision processes during production system planning and scheduling in job shops, the limit of which is that the evaluated job planning or scheduling is known a priori. He and Liu (2010) introduced an energy conscious method for machine tool selection for machining jobs. They assumed each job required only one operation and the idle energy waste of machine tools was not considered during the investigation. Fang et al. (2011b) proposed a scheduling model that considered energy consumption for machining operations of jobs; however, no attempt was made to reduce the idling portion of machine tool operation. Furthermore, Liu et al. (2014b) developed a multiobjective scheduling method with reducing energy consumption as one of the objectives. The model focused on non-processing electricity consumption which only includes the idle power consumption of machine tools. This paper proposes a method for optimizing energy efficiency that integrates machine tool selection and operation sequence selection for flexible job shops. To reduce idle time/energy, the mentioned method seeks to reduce the energy for machining operations through optimized selection of machine tools, and the choice of operation sequence. The rest of the paper is organized as follows: The problem for the energy-aware machine tool selection and operation sequence in flexible machining job shops is described and a simple example to demonstrate the problem is shown in Section 2. In Section 3, the mathematical model which considers energy consumption as well as the classical objectives makespan is formulated. In Section 4, the Nested Partitions algorithm for solving the mathematical model is presented. Also, a test case to evaluate the proposed method using two scenarios with different energy optimization objectives as well as the classical makespan objective is demonstrated in Section 5 and finally concluding remarks are presented.
2. Description of the problem It was reported by Dahmus and Gutowski (2004) that energy consumption depends on specific machine tools utilized, even for machining the same job. They reported that when machining steel on four different milling machines, the specific cutting energy may be as high as 60 kJ/cm3 or as low as 10 kJ/cm3. Even for the same machine tool type and size, the specific energy can vary by 50% which was also reported by He and Liu (2010). Different machine tools performing the same job with identical process parameters, may consume different amounts of energy. Fig. 1 presents an energy comparison for machining the same job with the same process parameters. And two different lathes which were made by Chongqing No. 2 Machine Tool Works company. There is 42% energy savings by selecting the C2-6136HK NC lathe to machine the job instead of the C2-6132HK/1 NC lathe. Accordingly, from a production operation perspective, energy consumption can be optimized by selecting the best available machine tool to perform a job. Energy wasted through excessive machine idling energy waste can also be reduced. Mouzon and Yildirim (2008) observed that there is massive idle energy waste of machine tools in production operations. Great energy-savings can be realized by reducing the idle time, especially for machine tools with a high running power. This idling can be reduced by optimizing the operation sequences of jobs. Based on the above observations, this paper proposes an optimization method for improving energy efficiency that integrates machine selection and job operation sequence (EMS/OS) in flexible machining job shops. Here, we present a simple example with two jobs and two machines to explicitly describe the EMS/OS problem. Table 1 shows the processing time and energy consumption for the jobs on different machines. The idle power of machine M1 and machine M2 are respectively 650W and 950W. The operation precedence constraints and the machine tool alternatives are shown in Fig. 2. For job 2, operation O21 is the predecessor of operation O22 (Oij refers to the jth operation for the ith job). Suppose that the release time of both jobs is zero; two feasible schedules are shown in Fig. 2. The makespans of both solutions are equal to 10 min while the total energy consumption of the first solution is 14.4% less than the energy required for the second solution. As shown in this example, the objective of the EMS/OS problem is to determine an optimal schedule with machine tool selection
Fig. 1. Energy consumption comparison for two machine tools.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
For multiple-function machine tools, energy consumption in switching time tg is also considered as shown in Eq. (4):
Table 1 Operation data for the machines and jobs (Time/Energy). Processing time (min)/energy consumption (kW$h)
Job i Job 1
Es ¼ Po $ts þ Po $tg
Job 2
M1 M2
(4)
O11
O21
O22
The cutting energy, Ec, is modeled as shown in Eq. (5) (Gutowski et al., 2006):
5/0.09 6/0.15
7/0.144 7/0.18
e 3/0.06
, Ec ¼ Po þ kv $tc
Operation Oij
Machine Mk
3
(5)
,
and operation sequence for all the jobs. Therefore, the EMS/OS problem can be described as: It is desired to process a set of N independent jobs, where the kth job consists of Jk operations. Operation precedence constraints exist and the jobs are to be completed by a set of machine tools M. The objective is to find the optimum schedule for use of the machine tools for the jobs. Optimal condition in this case refers to minimizing the total energy consumption as well as the classical optimization objective, makespan.
, E ¼ Po $tw þ Po $ts þ Po $tg þ Po þ kv $tc , ¼ Po $ tw þ ts þ tg þ tc þ kv$tc
3. The EMS/OS optimization model 3.1. Energy criterion for the problem In the EMS/OS problem, the energy-related criterion E consists of both Em, the machining energy of the operations, and Ew, the non-machining idle energy of the machine tools. The criterion is shown in Eq. (1).
E ¼ Ew þ Em
(1)
The non-machining (idle) energy of machine tools Ew is the energy consumed by machine tools when they are not machining, for example, waiting to process next jobs. According to the research by Mouzon et al. (2007), on average, a machine in the wait phase consumes 13% of the energy consumed in an 8-h shift. This energy is obtained by multiplying the machine idle power, Po, by the idle (wait) time for the next operation, tw, as shown in Eq. (2), which is specific on machining process:
Ew ¼ Po $tw
(2)
Take Fig. 2 as an example, tw is the idle time between operation O11 and operation O22 in the machine tool M2. The machining energy, Em, consists of two components: i) idle energy during job setup (Es), and ii) cutting energy (Ec). Eq. (3) shows the relation for the machining energy:
Em ¼ Es þ Ec
where v is the material removal rate [mm3/s]. tc is the cutting time (s). As shown in Table 1, the processing time is equal to the sum of tc, ts, and tg. k is the specific cutting energy [W$s/mm3], which is closely related to the work piece hardness and the specifics of the cutting mechanics (Gutowski et al., 2006). Since the cutting conditions are fixed prior to schedule optimization, the values of coefficient “k” can be identified at the outset. The specific values can be obtained by cutting experiments or handbook with empirical data for different materials. Substituting Eqs. (2)e(5) into Eq. (1) produces Eq. (6) for the model energy criterion.
(3)
The setup energy Es is evaluated by multiplying the idle power Po by the time for tool and workpiece setup (Rajemi et al., 2010), ts.
(6)
Note that the proposed method is specific on machining process.
3.2. Mathematical model of the problem To formulate the model more precisely, the following assumptions have been made: All the jobs arrive simultaneously without priority; jobs are available in the analyzed cycle, and jobs in the next cycle are not considered in the proposed model. Moreover, all the machines are available in the analyzed cycle; it is not allowed to interrupt the processing of an operation at any point in time. The following notations are used to formulate the model. Indices i,k Index for job, i,k ¼ 1,...,N, where N is the number of jobs (k is the second index that may also be used to refer to a job. Note that the decision variable yijmkln is required to denote the sequence of two operations for scheduling schemes, so two indices for the jobs are used to distinguish the two jobs for the decision variable.) j,l Index for operation number, j,l ¼ 1,...,Ji, where Ji is the number of all operations for job i(l is the second index which is similar with k index for jobs.) m,n Index for machine, m,n ¼ 1,...,M, where M is the number of machines.
Fig. 2. Example for the EMS/OS problem.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
4
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
Parameters
M X
Oij Operation j on job i tijm Processing time of operation Oij on machine Mm, tijm ¼ ts,ijm þ tc,ijm tw,m Idle time tw on machine Mm Eijm Energy consumption of operation Oij on machine Mm, , Eijm ¼ Po;m $ts;ijm þ Po;m $tg;ijm þ ðPo;m þ ki vij Þ$tc;ijm Po,m Idle power Po of machine Mm Ri Release (arrival) time of job i cijm End time of operation Oij on machine Mm LAn arbitrarily large positive number Qi ¼ {(j,l)}iNo operation precedence constraints between operation j and operation l for job i PRi ¼ {(j,l)}iOperation j is the predecessor of operation l for job i Decision variables:
xijm ¼
1 0
yijmkln ¼
if operation Oij on machine Mm otherwise
1 0
xijm ¼ 1
ci; j
(17)
m¼1
xijm 2f0; 1g; ci; j; m
(18)
yijklm 2f0; 1g; ci; j; k; l; m
(19)
Constraint (9) ensures that the operations of each job are processed according to the required precedence constraint. Constraints (10) and (11) require that both two operations belonging to the same job cannot be processed simultaneously. Constraints (12) and (13) ensure the feasible operation sequence. Constraints (14) and (15) guarantee that a machine cannot simultaneously process more than one operation. Constraint (16) forces the operation to be done after the release time and Constraint (17) ensures that one operation cannot be processed on more than one machine. Constraints (18) and (19) require that the indicated variables are binary.
if operation Oij on machine Mm precedes operation Okl on machine Mn otherwise
The mathematical model is formulated using mixed integer programming (MIP) as follows. Objective function:
min
f1 ¼ C ¼ max cijm
min
f2 ¼ E ¼
(7)
ci;j;m
Ji X N X M X
M X Po;m tw;m Eijm xijm þ
i¼1 j¼1 m¼1
(8)
m¼1
Constraints:
cilm cijn þ L 2 xilm xijn tilm ciln cijm þ L 1 yijmiln tiln
c j; l 2PRi ; i
c j; l 2Qi ; i; m; n
(9) (10)
cijm ciln þ Lyijmiln þ L 2 xijm xiln tijm c j; l 2Qi ; i; m; n
(11)
yijmijn ¼ 0; ci; j; m; n
(12)
yijmkln þ yklnijm ¼ 1; ci; j; k; l; m
(13)
cklm cijm þ L 1 yijmklm tklm
ci; j; k; l
cijm cklm þ Lyijmklm þ L 2 xijm xklm tijm
(14)
j ¼ 1; ci; m
The optimization problems of EMS/OS which are larger-scale discrete optimization problems which including operation precedence constraints, machine tool selection for each operation, and selection of an operation sequence, and is a large-scale discrete optimization problem. The Nested Partitions (NP) for optimization has been proven to be a useful approach for effectively solving large-scale discrete optimization problems (Shi, 2000). The NP method is a partitioning- and sampling-based strategy that focuses computational effort on the most promising region of the solution space while maintaining a global perspective. In each iteration, the entire solution space is divided into a promising region and a surrounding region. The algorithm partitions, the current most promising region into several sub-regions and aggregates surrounding regions into one region. A good partitioning strategy would cluster most of the good solutions together in the promising sub-regions so that the algorithm quickly converges by concentrating the search on these sub-regions. The next step of the algorithm is to select samples randomly from each of the sub-regions and from the aggregated surrounding region. Once each region has been sampled, the next step is to use the sample points to calculate a “promising index” for each region, where a variety of local search heuristics can be used to construct the promising index. If one of the sub-regions has the best promising index, the algorithm moves to this region and considers it to be the most promising region for the next iteration. Furthermore, if the surrounding region has the best promising index, the algorithm backtracks (Yau and Shi, 2009;Wu et al., 2010).
ci; j; k; l (15)
cijm tijm þ L 1 xijm Ri
4. Solution approach
(16)
4.1. Partitioning Partitioning is the first key step for the NP approach. It divides the current most promising region into smaller sub-regions by
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
fixing different operations at a particular position on a machine and the remaining regions are aggregated into the surrounding regions. Note that, at the first iteration of the algorithm, the current most promising region is considered as the entire feasible region. There are two partitioning schemes including machine preference and position preference (Yau and Shi, 2009). Since the solution of the EMS/OS problem greatly depends on the position of each operation, the vertical partitioning based on position preference is used in this phase. It firstly fixes an operation on position Po of all machines, and then switches to position Po þ 1 as shown in Fig. 3. 4.2. Random sampling
maxðtÞ
fq
5
n o maxðt1Þ ¼ max fq ; fq Sr jr ¼ 1; 2; :::; NUM k
maxðtÞ
(21)
minðtÞ
wherefq and fq are the maximum and minimum value of the qth objective function, Sr and NUM are the rth sampling point and number of sampling points on current iteration, respectively. The value for evaluating the promising index function is calculated as follows:
Obj Sr ¼
ðtÞ
maxðtÞ
f1
ðtÞ
minðtÞ
f1 f1
þ minðtÞ
f1
minðtÞ
f2 f2 maxðtÞ
f2
minðtÞ
f2
(22)
Random sampling is a key step to determine the most promising region in the NP approach. The random sampling scheme for the EMS/OS model is shown in Fig. 4. As seen in the stepwise procedure, for each iteration, the algorithm updates the free operation set U and then randomly selects one operation from set U to be scheduled. Since the prefixed operations determined in the partitioning phase are also required to be included in the sampling processes, Fm is defined with the position of the first none free fixed operation. For each machine m, if all of the prefixed operations are free, then Fm is set to 1 Fm ) 1. Jl is the alternative machine set for operation l. 4.3. Calculation of promising index Once each region has been sampled, the next step is to use the sample point to estimate the promising index for each region. The promising index function is defined based on the objectives of the model. In each iteration, the region with the best promising index is identified; this region then serves as the promising region for the next iteration. In this paper, the adapted weighted sum method is used to construct the promising index function. Considering the mathematical model in Section 3.2, makespan (f1) and energy (f2) are not incompatible objective functions. Hence, the two objective functions f1 and f2 are combined into a single objective function, and this function is then used to evaluate each sample and determine the most promising region. An explanation of how the promising index function is constructed as provided below: The promising index function is based on specific function evaluations for each objective. At the tth iteration, choose the sampling points which contain the minimum f1min (or f2min ) and maximum f1max (or f2max ) corresponding to each objective function, then compare with the stored sampling points at the previous iteration and select the best points. minðtÞ
fq
n o minðt1Þ ¼ min fq ; fq Sr jr ¼ 1; 2; :::; NUM k
Fig. 3. Partitioning scheme of position preference.
(20)
Fig. 4. Random sampling algorithm scheme.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
6
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
promising region happens to be the surrounding region, backtrack to the root region and start from the beginning. Either reaching the bottom region or finding no better solution is the stop criterion. 4.5. NP approach scheme Based on the above procedures, the detailed NP approach employed in this paper is shown in Fig. 5. Before proceeding, several important parameters must be defined. G is the set of all the unfixed operations used for the stop criterion. Pm and Gm are the set of the fixed operation sequence and the unfixed operations on machine m, which is used to form subregions in each iteration. oij is defined with the fixed operation in the most promising subregion 00 Q . 5. Model evaluation and discussion To evaluate the energy-saving potential of the proposed method, a test case was employed. For this test case (Scenario 1), the energy consumption was examined for different machine tools, operation sequence, and for both machine tools and operation sequence. While Scenario 1 only considers energy, Scenario 2 considers both energy consumption and makespan. The detailed information of the test case is presented as below. A machining job shop with five machine tools was used to test the proposed method. Four jobs were considered, and the precedence relations for the operations associated with each job are shown in Fig. 6. Table 2 gives the idle power of each machine tool. The setup (ts) and processing (tc) times for the operations on the different machines is shown in Table 3. Based on the above power and time parameters, the energy consumption of the operations during setup and cutting phases can be calculated according to Eq. (6) as shown in Table 4. 5.1. Scenario 1: energy consumption optimization
Fig. 5. Nested partitions scheme for the model.
4.4. Backtracking Basing on the promising index function, the most promising region in each iteration can be determined. But, if the most
First, the mathematical model presented previously was optimized by minimizing the total energy consumption, including the cutting energy and idle energy. The optimized schedule was obtained using the proposed NP approach, and the result is shown in Table 5. For this energy-optimized schedule, the total energy consumption of the jobs was 1668.72 W h, where about 96.7% of the total was associated with machining and only 3.3% was spent on machine idling. Fig. 7 shows the detailed energy breakdown on each machine and each job. Job 4 consumed the largest energy for the operations, while the largest percentage of idle energy was for M4. The energy optimization by only machine tool selection and only operation sequence are respectively scheduled to make a comparison with the total energy optimization. Table 6 and Fig. 8
Fig. 6. Operation constraints of four jobs.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
7
Table 2 Idle power of machine tools. Machine Mm
M1
M2
M3
M4
M5
Idle power (W)
995
1485
1910
600
430
Table 3 Setup and cutting times for the operations on the different machine tools. ts/tc (min) Job 1
Job 2
Job 3
Job 4
O11 O12 O13 O21 O22 O23 O24 O31 O32 O33 O34 O35 O41 O42 O43
M1
M2
M3
M4
M5
1.5/5.6 e 2.0/4.4 e e 1.0/0.2 e 1.5/1.3 1.5/0.9 e 2.5/0.8 2.0/3.5 e 3.0/12.3 e
1.5/5.6 e 2.0/4.4 e e 1.5/0.2 e 1.0/1.3 1.0/0.9 e 2.5/0.8 2.0/3.5 e 4.0/12.3 e
2.0/6.3 e 2.5/5.0 e e 2.5/0.5 e 1.5/1.8 1.5/1.2 e 4.0/1.2 3.0/4.0 e 5.5/14.0 e
e 3.0/3.7 e 1.0/0.3 1.0/0.8 e 3.0/1.6 e e 2.5/3.0 e e 3.0/9.6 e 5.0/2.4
e 3.0/4.1 e 1.5/0.5 2.5/1.2 e 4.0/2.3 e e 3.5/3.4 e e 4.0/11.0 e 6.5/3.0
Table 4 Energy consumption during setup and cutting for operations on different machines. Energy consumption (10e3 kW h)
M1
M2
M3
M4
M5
Job 1
170.7 e 138.0 e e 21.9 e 60.4 49.8 e 62.9 100.3 e 367.9 e
228.7 e 205.9 e e 44.1 e 70.9 57.0 e 89.7 149.7 e 517.4 e
317.2 e 310.4 e e 97.5 e 119.1 96.0 e 173.5 245.1 e 734.8 e
e 97.2 e 15.6 20.7 e 50.6 e e 66.0 e e 195.3 e 99.9
e 80.9 e 17.3 29.5 e 50.2 e e 60.5 e e 176.5 e 94.1
Job 2
Job 3
Job 4
O11 O12 O13 O21 O22 O23 O24 O31 O32 O33 O34 O35 O41 O42 O43
shows the comparison of the scheduling results where Scheduling I, Scheduling II and Scheduling III are correspondingly the optimized scheduling with only machine tool selection, only operation sequence, and both of them, respectively. Comparing the three scheduling results, although the minimum machining energy is obtained for Scheduling I and the minimum idle energy is found for Scheduling II, the total energy consumption is minimal for Scheduling III. By considering both machine tool selection and operation sequence, there are respectively 33.6% and 48.2% energy savings comparing to considering only one of them.
Fig. 7. Energy breakdown of the optimal schedule.
5.2. Scenario 2: energy consumption optimization as well as makespan In most cases, energy optimization cannot be the only scheduling objective, and makespan as an essential objective has to be optimized for jobs' production. Fig. 9 shows the approximation Pareto Front for this scenario consisting of the set of solutions. It can be seen that a tradeoff between energy consumption and makespan exists for the jobs although it is well known that energy consumption is proportional to time for only one job or machine. For producing the same batch of jobs, the energy consumption variation ranges from 2137.95 W h to 1672.02 W h. Namely, if the largest makespan 40.1 min can be tolerated in production, there would be 21.8% energy savings for these jobs. One the other hand, if time is the dominant consideration, makspan of these jobs can be optimized to 35.3 min while the energy consumption is the largest one. According to the Eq. (22), the optimum solution for this scenario is shown in form of Gant chart in Fig. 10. The total energy consumption of the optimum solution is 1672.0 W h and the makespan is 40.1min. Table 7 presents the comparison results among the optimum scheduling solution (denoted with Solution 1), the solution with minimal energy (denoted with Solution 2), and the solution with minimal makespan (denoted with Solution 3). Solution 2 has the minimal total energy consumption but the longest makspan, while Solution 3 has the minimal makespan but the largest total energy consumption. Also, the values of energy and makespan for Solution 1 are in between. Comparing the energy of the three solution, it can be seen that reducing jobs on the machine M3 which of power is larger than others can decrease the total energy consumption, but enables loads of machine tools imbalance. Comparing the time of the three solution, it is observed that cutting down idle time can also reduce energy consumption, but increase makespan of jobs. However, only reducing idle time of machine does not always decrease total energy consumption. For example, the idle time of
Table 5 Optimum schedule of the minimal total energy. Machine Mm
Operation Oij (start time-finishing time) min
M1 M2 M3 M4 M5
O31(0e2.8) O11(0e7.1) e O21(0e1.3) O22(1.3e5)
O42(2.8e18.1) O23(7.1e8.8) e O33(2.8e8.3) e
O13(18.1e24.5) O32(8.8e10.7) e O12(8.3e15) e
O34(24.5e27.8) e e O41(18.1e30.7) e
O35(27.8e33.3) e e O43(30.7e38.1) e
e e e O24(38.1e42.7) e
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
8
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
Table 6 Energy consumption of the three optimized scheduling.
Machining energy of operations (W h) Idle energy (W h) Total energy (W h)
Scheduling I (only considering machine tool selection)
Scheduling II (only considering operation sequence)
Scheduling III (considering both of them)
1496.9 733.2 2230.1
2450.2 23.65 2473.85
1613.4 55.32 1668.72
Solution 1 is shorter than the one of Solution 2 while the total energy of Solution 1 is larger than the one of Solution 2. Besides, as shown in Table 2, the idle power in each of M1, M2, and M3 in the test case is larger than idle power in M4 and M5. Thus, in Solution3, due to increasing the idle time for M1 and M3, the energy increases
significantly e even though it has the smallest makespan. This suggests that there is an energy saving opportunity if long idle times are avoided on high idle power machines. This may require a tradeoff between makespan and energy.
6. Conclusion
Fig. 8. Comparison of three scheduling results.
Fig. 9. Pareto Front obtained by optimizing energy and makespan.
This paper addresses energy optimization of flexible machining job shops by machine tool selection and operation sequence at the production operational level. The proposed energy-aware optimization is based on the recognition that energy for machining operations of jobs can be optimized by appropriately selecting machine tools and the idle energy of machine tools for nonmachining operations can be reduced by optimizing operation sequence of jobs. The proposed method helps the production manager's making-decision on energy-savings when managing the production operation of machine tool systems. The mathematical model for formulating the optimizing problem is constructed by mixed integer programming. According to the generalized machining cycle, the critical optimization objective of energy consumption in the model is evaluated by the energy during the cutting phase and the energy during the waiting phase and setup phase. The classical optimization objectives at production operating level such as makespan are also integrated in the model. For this NP-hard problem, Nested Partitions algorithm is used to solve the model. The case study with two scenarios is presented to evaluate the energy-saving potentials of the model. The results show that there is more energy savings by integrating machine tool selection and operation sequence compared to considering only one of them. Also, there are more efficient energy optimization by integrating machine tool selection and operation sequence than by considering only one of them. Also, there exist close relations among the total energy consumption, idle energy, machining energy, idle time, and makespan. The potential energy-savings can be achieved as well as the classical criteria are satisfied. The authors of this paper are planning a future study to develop a general framework model integrated the process plan costs and lot size selections in flexible job shop. Besides, considering the unforeseen disturbances in reality, integrating energy consumption
Fig. 10. Optimum scheduling solution for optimizing makespan and energy.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
9
Table 7 Comparison of the three solutions.
Energy consumption (W h) (machining energy/idle energy)
Time (min) (machining time/idle time)
M1 M2 M3 M4 M5 M1 M2 M3 M4 M5
Solution 1 (optimum scheduling solution)
Solution 2 (solution with minimal energy)
Solution 3 (solution with minimal makespan)
740.8/0 228.7/0 119.1/0 524.6/20 29.5/9.32 34.1/0 7.1/0 3.3/0 38.1/2 3.7/1.3
729.5/0 329.8/0 0/0 524.6/46 29.5/9.32 33.3/0 10.7/0 0/0 38.1/4.6 3.7/1.3
606.2/6.63 343.7/0 269.5/248.3 361.2/98 177.9/26.52 27.2/0.4 11.1/0 7.9/7.8 25.5/9.8 19.1/3.7
into dynamic scheduling or real time scheduling problem clearly is a challenging research work. Acknowledgements The authors would like to thank the support from the National Natural Science Foundation of China (Grant No. 51105394) and National High Technology Research and Development Program of China (863) (Grant No. 2014AA041506). The authors also thank Mr. Ehsan Vahidi for his contribution in the paper. Nomenclature cijm E Em Ew Es Ec Eijm Fm fq maxðtÞ
fq
minðtÞ
End time of operation Oij on machine Mm energy criterion (W s) machining energy of the operations (W s) non-machining idle energy of the machine tools (W s) idle energy during job setup (W s) cutting energy (W s) Energy consumption of operation Oij on machine Mm position of the first none free fixed operation qthobjective function maximum value of the qth objective function
fq minimum value of the qth objective function number of operations for the kth job Jk j,l Index for operations k specific cutting energy (W s/mm3) i,k Index for jobs L An arbitrarily large positive number M number of machine tools m,n Index for machine tools Mm mth machine tool N number of jobs NUM number of sampling points on current iteration Oij Operation j on job i Po idle power of machine tools (W) Po positions on machine tools Po,m Idle power Po of machineMm PRi ¼ {(j,l)}i Operation j is the predecessor of operation l for job i Qi ¼ {(j,l)}i No operation precedence constraints between operation j and operation l for job i Ri Release (arrival) time of job i Srrth sampling point tc cutting time(s) tg switching time(s) ts setup time(s) tw idle (wait) time for the next operation (s) tw;m Idle time tw on machine Mm
tijm
Processing time of operation Oij on machine Mm
v
material removal rate (mm3/s) 1 if operation Oij on machine Mm ¼ 0 otherwise 8 < 1 if operation Oij on machine Mm precedes ¼ operation Okl on machine Mn : 0 otherwise free operation set alternative machine set for operation l set of all the unfixed operations used for the stop criterion set of the unfixed operations on machine m set of the fixed operation sequence on machine m root region most promising subregion.
,
xijm yijmkln U Jl G Gm Pm Q Q0
References Bladh, I., 2009. Energy Efficiency in Manufacturing. Berlin, German. Bruzzone, A.A.G., Anghinolfi, D., Paolucci, M., Tonelli, F., 2012. Energy-aware scheduling for improving manufacturing process sustainability: a mathematical model for flexible flow shops. CIRP Annals Manuf. Technol. 61, 459e462. Chen, G.R., Liang, L., Arinez, J., Biller, S., 2013. Energy-efficient production systems through schedule-based operations. IEEE Trans. Automat. Sci. Eng. 10 (1), 27e37. Dahmus, J.B., Gutowski, T.G., 2004. An environmental analysis of machining. In: 2004 ASME International Mechanical Engineering Congress and RD&D Expo, 13e19 November California. ASME, New York, pp. 1e10. Dai, M., Tang, D., Giret, A., Salido, M.A., et al., 2013. Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm. Robotics Comp. Integr. Manuf. 29, 418e442. Duflou, J.R., Sutherland, J.W., Dornfeld, D., Herrmann, C., Jeswiet, J., Kara, S., Hauschild, M., Kellens, K., 2012. Towards energy and resource efficient manufacturing: a processes and systems approach. CIRP Annals Manuf. Technol. 61, 587e609. Drake, R., Yildirim, M.B., Twomey, J., Whitman, L., Ahmad, J., Lodhia, P., 2006. Data collection frame-work on energy consumption in manufacturing. In: Proceedings of 2006 Institute of Industrial Engineering Research Conference, Orlando, Florida, USA. 20e24 May, pp. 1e5. Fadi, S., Joaquin, O., Alvaro, G., Miguel, O., 2014. Optimizing the production scheduling of a single machine to minimize total energy consumption costs. J. Clean. Prod. 67, 197e207. Fang, K., Uhan, N., Zhao, F., Sutherland, J.W., 2011a. A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction. SME J. Manuf. Syst. 30, 234e240. Fang, K., Uhan, N., Zhao, F., Sutherland, J.W., 2011b. A new shop scheduling approach in support of sustainable manufacturing. In: Hesselbach, J., Herrmann, C. (Eds.), Glocalized Solutions for Sustainability in Manufacturing, Proceedings of the 18th CIRP International Conference on Life Cycle Engineering, 2e4 May 2011, Braunschweig, Germany. Spinger-Verlag, Berlin, pp. 305e310. Gutowski, T., Murphy, C., Allen, D., Bauer, D., Bras, B., Piwonka, T., Sheng, P., Sutherland, J., Thurston, D., Wolff, E., 2005. Environmentally benign manufacturing: observations from Japan, Europe and the United States. J. Clean. Prod. 13 (1), 1e17. Gutowski, T., Dahmus, J., Thiriez, A., 2006. Electrical energy requirements for manufacturing processes. In: 13th CIRP International Conference on Life Cycle Engineering, Leuven, Belgium, vol. 5, pp. 560e564. Herrmann, C., Thiede, S., 2009. Process chain simulation to foster energy efficiency in manufacturing. CIRP J. Manuf. Sci. Technol. 1 (4), 221e229.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
10
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
He, Y., Liu, F., 2010. Methods for integrating energy consumption and environmental impact considerations into the production operation of machining processes. Chin. J. Mech. Eng. 23 (4), 428e435. Liu, C., Yang, J., Lian, J., Li, W., Evans, S., Yin, Y., 2014a. Sustainable performance oriented operational decision-making of single machine systems with deterministic product arrival time. J. Clean. Prod. http://dx.doi.org/10.1016/ j.jclepro.2014.07.025. Liu, Y., Dong, H., Lohse, N., Petrovic, S., Gindy, N., 2014b. An investigation into minimising total energy consumption and total weighted tardiness in job shops. J. Clean. Prod. 65, 87e96. Mouzon, G., Yildirim, M.B., Twomey, J., 2007. Operational methods for minimization of energy consumption of manufacturing equipment. Int. J. Prod. Res. 45 (18e19), 4247e4271. Mouzon, G.C., Yildirim, M.B., 2008. A framework to minimize total energy consumption and total tardiness on a single machine. Int. J. Sustain. Eng. 1 (2), 105e116.
Rajemi, M.F., Mativenga, P.T., Aramcharoen, A., 2010. Sustainable machining selection of optimum turning conditions based on minimum energy considerations. J. Clean. Prod. 18 (10), 1059e1065. Shi, L., 2000. Nested partitions method for global optimization. Oper. Res. 48, 390e407. Weinert, N., Chiotellis, S., Seliger, G., 2011. Methodology for planning and operating energy-efficient production systems. CIRP Annals. Manuf. Technol. 60, 41e44. Wu, T., Shi, L., Duffie, N.A., 2010. An HNP-MP approach for the capacitated multiitem lot sizing problem with setup times. IEEE Trans. Autom. Sci. Eng. 7 (3), 500e511. Yau, H., Shi, L., 2009. Nested partitions for the large-scale extended job shop scheduling problem. Ann. Oper. Res. 168 (1), 23e39.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Contents lists available at ScienceDirect
Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro
An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops Yan He a, b, *, Yufeng Li a, Tao Wu c, John W. Sutherland b a
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China Environmental and Ecological Engineering, Purdue University, West Lafayette, IN, USA c Business Analytics and Optimization, Apollo Group Inc., Phoenix, AZ 85040, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 May 2014 Received in revised form 17 August 2014 Accepted 3 October 2014 Available online xxx
The environmental burden caused by energy consumption during the use phase of machine tool systems is widely acknowledged and hence ways must be found to use energy more efficiently. There is potentially a significant amount of energy savings that could be realized by selecting alternative machine tools and reducing the idle energy consumption through better scheduling. This paper proposes an energy-saving optimization method that considers machine tool selection and operation sequence for flexible job shops. The former seeks to reduce the energy consumption for machining operations, and the latter aims to reduce the idle energy consumption of machine tools. A mathematical model is formulated using mixed integer programming and the energy consumption objective is combined with a classical objective, the makespan. A Nested Partitions algorithm, which has proved to be robust for NP-hard problems, is utilized to solve the model. The proposed method is evaluated in a test case by two scenarios with different energy optimization schemes as well as the classical makespan objective. The results show that the proposed method is effective at realizing energy-savings for a flexible machining job shop. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Energy saving Machine tool selection Operation sequence Flexible job shops Nested partitions
1. Introduction The global manufacturing industry sector is responsible for 31% of primary energy consumption and 36% of CO2 emissions (Bruzzone et al., 2012). In manufacturing, machine tools consume an enormous amount of energy as they physically transform raw materials into finished products. Reducing the energy consumed by machine tool systems has been identified as one of the strategies to improve sustainability in manufacturing (Pusavec et al., 2010). The environmental impact of the use phase of a machine tool is more important than that of the other life cycle stages of a machine tool and resides mainly in the amount of energy consumed (Dahmus and Gutowski, 2004). With approximately 83% of the total impact, the use stage systematically is considered as the dominant contributor to the total life cycle environmental impact of machine tools (Duflou et al., 2012). Against the background, energy consumption during the use phase of machine tools has received much research attention, and * Corresponding author. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China. E-mail address: [email protected] (Y. He).
significant energy waste has been observed. The energy breakdown of machine tools has shown that only 10% of energy is used for actual material removal (Dahmus and Gutowski, 2004; Drake et al., 2006), and the rest of the energy is consumed by the auxiliary functions and components of machine tools. Moreover, substantial energy waste is associated with the idle phase of machine tool operation. At Toyota, it was reported that 85.2% of the energy was used for operations not directly related to the production of parts (Gutowski et al., 2005). Bladh (2009) also reported that the energy savings potential was 10e25% through the reduction of the time used waiting or in the start-up mode. To reduce these energy wastes, some energy-focused optimizing methods have been proposed for production operation of machine tool systems. For a single machine system, energy-focused optimizing methodologies have been proposed to reduce idle energy or energy during peak periods. Mouzon et al. (2007) investigated the problem of scheduling a single machine to minimize the idle energy consumption using several dispatching rules. They also proposed a framework to incorporate energy consumption into consideration while making scheduling decisions to optimize objectives such as total tardiness. According to previous investigations, proposed optimization methods were used to reduce
http://dx.doi.org/10.1016/j.jclepro.2014.10.006 0959-6526/© 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
2
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
idle energy consumption for a single machine. Liu et al. (2014a) focused on a single machine system and the consumed energy of the machine when it stays idle. An optimization model was proposed to minimize the carbon dioxide emissions based on the arrival time and the processing time of each product. Moreover, energy cost optimization was modeled by Fadi et al. (2014) for single machine production scheduling during production processes. Based on the model, the reduction in energy costs is achieved by avoiding high-energy price periods. Some studies have been carried out to address on energy optimization for production operation of flow shops. Herrmann and Thiede (2009) proposed process chain simulation to foster energy efficiency in manufacturing. Using the method, energy efficiency can be improved by the combination of quantity allocation and lot size of parts across two production lines. Some researchers focus on energy-efficient scheduling problems in flow shops, and presented mixed integer programming models for different energy-related objectives. Bruzzone et al. (2012) introduced a mixed integer programming model to minimize the shop floor power's peak. Fang et al. (2011a) and Dai et al. (2013) proposed a multi-objective optimization model considering both productivity (i.e., makespan) and energy (i.e., peak load, unload and carbon footprint). Besides these, Chen et al. (2013) studied specifically on productivity and energy performance in Bernoulli serial lines with machine startup and shutdown, and they utilized Markovian analysis method to discuss the effect of machine startup and shutdown schedule on system performance. These energy-focused methods for flow shops are not efficient for energy reduction in flexible job shops where significant flexibility involving both process routings and alternative machine tools exist for jobs. Only a few methods for energy optimization in flexible job shops have been reported in the literature. Weinert et al. (2011) proposed the EnergyBlocks methodology for integrated energyefficiency criteria with evaluation and decision processes during production system planning and scheduling in job shops, the limit of which is that the evaluated job planning or scheduling is known a priori. He and Liu (2010) introduced an energy conscious method for machine tool selection for machining jobs. They assumed each job required only one operation and the idle energy waste of machine tools was not considered during the investigation. Fang et al. (2011b) proposed a scheduling model that considered energy consumption for machining operations of jobs; however, no attempt was made to reduce the idling portion of machine tool operation. Furthermore, Liu et al. (2014b) developed a multiobjective scheduling method with reducing energy consumption as one of the objectives. The model focused on non-processing electricity consumption which only includes the idle power consumption of machine tools. This paper proposes a method for optimizing energy efficiency that integrates machine tool selection and operation sequence selection for flexible job shops. To reduce idle time/energy, the mentioned method seeks to reduce the energy for machining operations through optimized selection of machine tools, and the choice of operation sequence. The rest of the paper is organized as follows: The problem for the energy-aware machine tool selection and operation sequence in flexible machining job shops is described and a simple example to demonstrate the problem is shown in Section 2. In Section 3, the mathematical model which considers energy consumption as well as the classical objectives makespan is formulated. In Section 4, the Nested Partitions algorithm for solving the mathematical model is presented. Also, a test case to evaluate the proposed method using two scenarios with different energy optimization objectives as well as the classical makespan objective is demonstrated in Section 5 and finally concluding remarks are presented.
2. Description of the problem It was reported by Dahmus and Gutowski (2004) that energy consumption depends on specific machine tools utilized, even for machining the same job. They reported that when machining steel on four different milling machines, the specific cutting energy may be as high as 60 kJ/cm3 or as low as 10 kJ/cm3. Even for the same machine tool type and size, the specific energy can vary by 50% which was also reported by He and Liu (2010). Different machine tools performing the same job with identical process parameters, may consume different amounts of energy. Fig. 1 presents an energy comparison for machining the same job with the same process parameters. And two different lathes which were made by Chongqing No. 2 Machine Tool Works company. There is 42% energy savings by selecting the C2-6136HK NC lathe to machine the job instead of the C2-6132HK/1 NC lathe. Accordingly, from a production operation perspective, energy consumption can be optimized by selecting the best available machine tool to perform a job. Energy wasted through excessive machine idling energy waste can also be reduced. Mouzon and Yildirim (2008) observed that there is massive idle energy waste of machine tools in production operations. Great energy-savings can be realized by reducing the idle time, especially for machine tools with a high running power. This idling can be reduced by optimizing the operation sequences of jobs. Based on the above observations, this paper proposes an optimization method for improving energy efficiency that integrates machine selection and job operation sequence (EMS/OS) in flexible machining job shops. Here, we present a simple example with two jobs and two machines to explicitly describe the EMS/OS problem. Table 1 shows the processing time and energy consumption for the jobs on different machines. The idle power of machine M1 and machine M2 are respectively 650W and 950W. The operation precedence constraints and the machine tool alternatives are shown in Fig. 2. For job 2, operation O21 is the predecessor of operation O22 (Oij refers to the jth operation for the ith job). Suppose that the release time of both jobs is zero; two feasible schedules are shown in Fig. 2. The makespans of both solutions are equal to 10 min while the total energy consumption of the first solution is 14.4% less than the energy required for the second solution. As shown in this example, the objective of the EMS/OS problem is to determine an optimal schedule with machine tool selection
Fig. 1. Energy consumption comparison for two machine tools.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
For multiple-function machine tools, energy consumption in switching time tg is also considered as shown in Eq. (4):
Table 1 Operation data for the machines and jobs (Time/Energy). Processing time (min)/energy consumption (kW$h)
Job i Job 1
Es ¼ Po $ts þ Po $tg
Job 2
M1 M2
(4)
O11
O21
O22
The cutting energy, Ec, is modeled as shown in Eq. (5) (Gutowski et al., 2006):
5/0.09 6/0.15
7/0.144 7/0.18
e 3/0.06
, Ec ¼ Po þ kv $tc
Operation Oij
Machine Mk
3
(5)
,
and operation sequence for all the jobs. Therefore, the EMS/OS problem can be described as: It is desired to process a set of N independent jobs, where the kth job consists of Jk operations. Operation precedence constraints exist and the jobs are to be completed by a set of machine tools M. The objective is to find the optimum schedule for use of the machine tools for the jobs. Optimal condition in this case refers to minimizing the total energy consumption as well as the classical optimization objective, makespan.
, E ¼ Po $tw þ Po $ts þ Po $tg þ Po þ kv $tc , ¼ Po $ tw þ ts þ tg þ tc þ kv$tc
3. The EMS/OS optimization model 3.1. Energy criterion for the problem In the EMS/OS problem, the energy-related criterion E consists of both Em, the machining energy of the operations, and Ew, the non-machining idle energy of the machine tools. The criterion is shown in Eq. (1).
E ¼ Ew þ Em
(1)
The non-machining (idle) energy of machine tools Ew is the energy consumed by machine tools when they are not machining, for example, waiting to process next jobs. According to the research by Mouzon et al. (2007), on average, a machine in the wait phase consumes 13% of the energy consumed in an 8-h shift. This energy is obtained by multiplying the machine idle power, Po, by the idle (wait) time for the next operation, tw, as shown in Eq. (2), which is specific on machining process:
Ew ¼ Po $tw
(2)
Take Fig. 2 as an example, tw is the idle time between operation O11 and operation O22 in the machine tool M2. The machining energy, Em, consists of two components: i) idle energy during job setup (Es), and ii) cutting energy (Ec). Eq. (3) shows the relation for the machining energy:
Em ¼ Es þ Ec
where v is the material removal rate [mm3/s]. tc is the cutting time (s). As shown in Table 1, the processing time is equal to the sum of tc, ts, and tg. k is the specific cutting energy [W$s/mm3], which is closely related to the work piece hardness and the specifics of the cutting mechanics (Gutowski et al., 2006). Since the cutting conditions are fixed prior to schedule optimization, the values of coefficient “k” can be identified at the outset. The specific values can be obtained by cutting experiments or handbook with empirical data for different materials. Substituting Eqs. (2)e(5) into Eq. (1) produces Eq. (6) for the model energy criterion.
(3)
The setup energy Es is evaluated by multiplying the idle power Po by the time for tool and workpiece setup (Rajemi et al., 2010), ts.
(6)
Note that the proposed method is specific on machining process.
3.2. Mathematical model of the problem To formulate the model more precisely, the following assumptions have been made: All the jobs arrive simultaneously without priority; jobs are available in the analyzed cycle, and jobs in the next cycle are not considered in the proposed model. Moreover, all the machines are available in the analyzed cycle; it is not allowed to interrupt the processing of an operation at any point in time. The following notations are used to formulate the model. Indices i,k Index for job, i,k ¼ 1,...,N, where N is the number of jobs (k is the second index that may also be used to refer to a job. Note that the decision variable yijmkln is required to denote the sequence of two operations for scheduling schemes, so two indices for the jobs are used to distinguish the two jobs for the decision variable.) j,l Index for operation number, j,l ¼ 1,...,Ji, where Ji is the number of all operations for job i(l is the second index which is similar with k index for jobs.) m,n Index for machine, m,n ¼ 1,...,M, where M is the number of machines.
Fig. 2. Example for the EMS/OS problem.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
4
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
Parameters
M X
Oij Operation j on job i tijm Processing time of operation Oij on machine Mm, tijm ¼ ts,ijm þ tc,ijm tw,m Idle time tw on machine Mm Eijm Energy consumption of operation Oij on machine Mm, , Eijm ¼ Po;m $ts;ijm þ Po;m $tg;ijm þ ðPo;m þ ki vij Þ$tc;ijm Po,m Idle power Po of machine Mm Ri Release (arrival) time of job i cijm End time of operation Oij on machine Mm LAn arbitrarily large positive number Qi ¼ {(j,l)}iNo operation precedence constraints between operation j and operation l for job i PRi ¼ {(j,l)}iOperation j is the predecessor of operation l for job i Decision variables:
xijm ¼
1 0
yijmkln ¼
if operation Oij on machine Mm otherwise
1 0
xijm ¼ 1
ci; j
(17)
m¼1
xijm 2f0; 1g; ci; j; m
(18)
yijklm 2f0; 1g; ci; j; k; l; m
(19)
Constraint (9) ensures that the operations of each job are processed according to the required precedence constraint. Constraints (10) and (11) require that both two operations belonging to the same job cannot be processed simultaneously. Constraints (12) and (13) ensure the feasible operation sequence. Constraints (14) and (15) guarantee that a machine cannot simultaneously process more than one operation. Constraint (16) forces the operation to be done after the release time and Constraint (17) ensures that one operation cannot be processed on more than one machine. Constraints (18) and (19) require that the indicated variables are binary.
if operation Oij on machine Mm precedes operation Okl on machine Mn otherwise
The mathematical model is formulated using mixed integer programming (MIP) as follows. Objective function:
min
f1 ¼ C ¼ max cijm
min
f2 ¼ E ¼
(7)
ci;j;m
Ji X N X M X
M X Po;m tw;m Eijm xijm þ
i¼1 j¼1 m¼1
(8)
m¼1
Constraints:
cilm cijn þ L 2 xilm xijn tilm ciln cijm þ L 1 yijmiln tiln
c j; l 2PRi ; i
c j; l 2Qi ; i; m; n
(9) (10)
cijm ciln þ Lyijmiln þ L 2 xijm xiln tijm c j; l 2Qi ; i; m; n
(11)
yijmijn ¼ 0; ci; j; m; n
(12)
yijmkln þ yklnijm ¼ 1; ci; j; k; l; m
(13)
cklm cijm þ L 1 yijmklm tklm
ci; j; k; l
cijm cklm þ Lyijmklm þ L 2 xijm xklm tijm
(14)
j ¼ 1; ci; m
The optimization problems of EMS/OS which are larger-scale discrete optimization problems which including operation precedence constraints, machine tool selection for each operation, and selection of an operation sequence, and is a large-scale discrete optimization problem. The Nested Partitions (NP) for optimization has been proven to be a useful approach for effectively solving large-scale discrete optimization problems (Shi, 2000). The NP method is a partitioning- and sampling-based strategy that focuses computational effort on the most promising region of the solution space while maintaining a global perspective. In each iteration, the entire solution space is divided into a promising region and a surrounding region. The algorithm partitions, the current most promising region into several sub-regions and aggregates surrounding regions into one region. A good partitioning strategy would cluster most of the good solutions together in the promising sub-regions so that the algorithm quickly converges by concentrating the search on these sub-regions. The next step of the algorithm is to select samples randomly from each of the sub-regions and from the aggregated surrounding region. Once each region has been sampled, the next step is to use the sample points to calculate a “promising index” for each region, where a variety of local search heuristics can be used to construct the promising index. If one of the sub-regions has the best promising index, the algorithm moves to this region and considers it to be the most promising region for the next iteration. Furthermore, if the surrounding region has the best promising index, the algorithm backtracks (Yau and Shi, 2009;Wu et al., 2010).
ci; j; k; l (15)
cijm tijm þ L 1 xijm Ri
4. Solution approach
(16)
4.1. Partitioning Partitioning is the first key step for the NP approach. It divides the current most promising region into smaller sub-regions by
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
fixing different operations at a particular position on a machine and the remaining regions are aggregated into the surrounding regions. Note that, at the first iteration of the algorithm, the current most promising region is considered as the entire feasible region. There are two partitioning schemes including machine preference and position preference (Yau and Shi, 2009). Since the solution of the EMS/OS problem greatly depends on the position of each operation, the vertical partitioning based on position preference is used in this phase. It firstly fixes an operation on position Po of all machines, and then switches to position Po þ 1 as shown in Fig. 3. 4.2. Random sampling
maxðtÞ
fq
5
n o maxðt1Þ ¼ max fq ; fq Sr jr ¼ 1; 2; :::; NUM k
maxðtÞ
(21)
minðtÞ
wherefq and fq are the maximum and minimum value of the qth objective function, Sr and NUM are the rth sampling point and number of sampling points on current iteration, respectively. The value for evaluating the promising index function is calculated as follows:
Obj Sr ¼
ðtÞ
maxðtÞ
f1
ðtÞ
minðtÞ
f1 f1
þ minðtÞ
f1
minðtÞ
f2 f2 maxðtÞ
f2
minðtÞ
f2
(22)
Random sampling is a key step to determine the most promising region in the NP approach. The random sampling scheme for the EMS/OS model is shown in Fig. 4. As seen in the stepwise procedure, for each iteration, the algorithm updates the free operation set U and then randomly selects one operation from set U to be scheduled. Since the prefixed operations determined in the partitioning phase are also required to be included in the sampling processes, Fm is defined with the position of the first none free fixed operation. For each machine m, if all of the prefixed operations are free, then Fm is set to 1 Fm ) 1. Jl is the alternative machine set for operation l. 4.3. Calculation of promising index Once each region has been sampled, the next step is to use the sample point to estimate the promising index for each region. The promising index function is defined based on the objectives of the model. In each iteration, the region with the best promising index is identified; this region then serves as the promising region for the next iteration. In this paper, the adapted weighted sum method is used to construct the promising index function. Considering the mathematical model in Section 3.2, makespan (f1) and energy (f2) are not incompatible objective functions. Hence, the two objective functions f1 and f2 are combined into a single objective function, and this function is then used to evaluate each sample and determine the most promising region. An explanation of how the promising index function is constructed as provided below: The promising index function is based on specific function evaluations for each objective. At the tth iteration, choose the sampling points which contain the minimum f1min (or f2min ) and maximum f1max (or f2max ) corresponding to each objective function, then compare with the stored sampling points at the previous iteration and select the best points. minðtÞ
fq
n o minðt1Þ ¼ min fq ; fq Sr jr ¼ 1; 2; :::; NUM k
Fig. 3. Partitioning scheme of position preference.
(20)
Fig. 4. Random sampling algorithm scheme.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
6
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
promising region happens to be the surrounding region, backtrack to the root region and start from the beginning. Either reaching the bottom region or finding no better solution is the stop criterion. 4.5. NP approach scheme Based on the above procedures, the detailed NP approach employed in this paper is shown in Fig. 5. Before proceeding, several important parameters must be defined. G is the set of all the unfixed operations used for the stop criterion. Pm and Gm are the set of the fixed operation sequence and the unfixed operations on machine m, which is used to form subregions in each iteration. oij is defined with the fixed operation in the most promising subregion 00 Q . 5. Model evaluation and discussion To evaluate the energy-saving potential of the proposed method, a test case was employed. For this test case (Scenario 1), the energy consumption was examined for different machine tools, operation sequence, and for both machine tools and operation sequence. While Scenario 1 only considers energy, Scenario 2 considers both energy consumption and makespan. The detailed information of the test case is presented as below. A machining job shop with five machine tools was used to test the proposed method. Four jobs were considered, and the precedence relations for the operations associated with each job are shown in Fig. 6. Table 2 gives the idle power of each machine tool. The setup (ts) and processing (tc) times for the operations on the different machines is shown in Table 3. Based on the above power and time parameters, the energy consumption of the operations during setup and cutting phases can be calculated according to Eq. (6) as shown in Table 4. 5.1. Scenario 1: energy consumption optimization
Fig. 5. Nested partitions scheme for the model.
4.4. Backtracking Basing on the promising index function, the most promising region in each iteration can be determined. But, if the most
First, the mathematical model presented previously was optimized by minimizing the total energy consumption, including the cutting energy and idle energy. The optimized schedule was obtained using the proposed NP approach, and the result is shown in Table 5. For this energy-optimized schedule, the total energy consumption of the jobs was 1668.72 W h, where about 96.7% of the total was associated with machining and only 3.3% was spent on machine idling. Fig. 7 shows the detailed energy breakdown on each machine and each job. Job 4 consumed the largest energy for the operations, while the largest percentage of idle energy was for M4. The energy optimization by only machine tool selection and only operation sequence are respectively scheduled to make a comparison with the total energy optimization. Table 6 and Fig. 8
Fig. 6. Operation constraints of four jobs.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
7
Table 2 Idle power of machine tools. Machine Mm
M1
M2
M3
M4
M5
Idle power (W)
995
1485
1910
600
430
Table 3 Setup and cutting times for the operations on the different machine tools. ts/tc (min) Job 1
Job 2
Job 3
Job 4
O11 O12 O13 O21 O22 O23 O24 O31 O32 O33 O34 O35 O41 O42 O43
M1
M2
M3
M4
M5
1.5/5.6 e 2.0/4.4 e e 1.0/0.2 e 1.5/1.3 1.5/0.9 e 2.5/0.8 2.0/3.5 e 3.0/12.3 e
1.5/5.6 e 2.0/4.4 e e 1.5/0.2 e 1.0/1.3 1.0/0.9 e 2.5/0.8 2.0/3.5 e 4.0/12.3 e
2.0/6.3 e 2.5/5.0 e e 2.5/0.5 e 1.5/1.8 1.5/1.2 e 4.0/1.2 3.0/4.0 e 5.5/14.0 e
e 3.0/3.7 e 1.0/0.3 1.0/0.8 e 3.0/1.6 e e 2.5/3.0 e e 3.0/9.6 e 5.0/2.4
e 3.0/4.1 e 1.5/0.5 2.5/1.2 e 4.0/2.3 e e 3.5/3.4 e e 4.0/11.0 e 6.5/3.0
Table 4 Energy consumption during setup and cutting for operations on different machines. Energy consumption (10e3 kW h)
M1
M2
M3
M4
M5
Job 1
170.7 e 138.0 e e 21.9 e 60.4 49.8 e 62.9 100.3 e 367.9 e
228.7 e 205.9 e e 44.1 e 70.9 57.0 e 89.7 149.7 e 517.4 e
317.2 e 310.4 e e 97.5 e 119.1 96.0 e 173.5 245.1 e 734.8 e
e 97.2 e 15.6 20.7 e 50.6 e e 66.0 e e 195.3 e 99.9
e 80.9 e 17.3 29.5 e 50.2 e e 60.5 e e 176.5 e 94.1
Job 2
Job 3
Job 4
O11 O12 O13 O21 O22 O23 O24 O31 O32 O33 O34 O35 O41 O42 O43
shows the comparison of the scheduling results where Scheduling I, Scheduling II and Scheduling III are correspondingly the optimized scheduling with only machine tool selection, only operation sequence, and both of them, respectively. Comparing the three scheduling results, although the minimum machining energy is obtained for Scheduling I and the minimum idle energy is found for Scheduling II, the total energy consumption is minimal for Scheduling III. By considering both machine tool selection and operation sequence, there are respectively 33.6% and 48.2% energy savings comparing to considering only one of them.
Fig. 7. Energy breakdown of the optimal schedule.
5.2. Scenario 2: energy consumption optimization as well as makespan In most cases, energy optimization cannot be the only scheduling objective, and makespan as an essential objective has to be optimized for jobs' production. Fig. 9 shows the approximation Pareto Front for this scenario consisting of the set of solutions. It can be seen that a tradeoff between energy consumption and makespan exists for the jobs although it is well known that energy consumption is proportional to time for only one job or machine. For producing the same batch of jobs, the energy consumption variation ranges from 2137.95 W h to 1672.02 W h. Namely, if the largest makespan 40.1 min can be tolerated in production, there would be 21.8% energy savings for these jobs. One the other hand, if time is the dominant consideration, makspan of these jobs can be optimized to 35.3 min while the energy consumption is the largest one. According to the Eq. (22), the optimum solution for this scenario is shown in form of Gant chart in Fig. 10. The total energy consumption of the optimum solution is 1672.0 W h and the makespan is 40.1min. Table 7 presents the comparison results among the optimum scheduling solution (denoted with Solution 1), the solution with minimal energy (denoted with Solution 2), and the solution with minimal makespan (denoted with Solution 3). Solution 2 has the minimal total energy consumption but the longest makspan, while Solution 3 has the minimal makespan but the largest total energy consumption. Also, the values of energy and makespan for Solution 1 are in between. Comparing the energy of the three solution, it can be seen that reducing jobs on the machine M3 which of power is larger than others can decrease the total energy consumption, but enables loads of machine tools imbalance. Comparing the time of the three solution, it is observed that cutting down idle time can also reduce energy consumption, but increase makespan of jobs. However, only reducing idle time of machine does not always decrease total energy consumption. For example, the idle time of
Table 5 Optimum schedule of the minimal total energy. Machine Mm
Operation Oij (start time-finishing time) min
M1 M2 M3 M4 M5
O31(0e2.8) O11(0e7.1) e O21(0e1.3) O22(1.3e5)
O42(2.8e18.1) O23(7.1e8.8) e O33(2.8e8.3) e
O13(18.1e24.5) O32(8.8e10.7) e O12(8.3e15) e
O34(24.5e27.8) e e O41(18.1e30.7) e
O35(27.8e33.3) e e O43(30.7e38.1) e
e e e O24(38.1e42.7) e
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
8
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
Table 6 Energy consumption of the three optimized scheduling.
Machining energy of operations (W h) Idle energy (W h) Total energy (W h)
Scheduling I (only considering machine tool selection)
Scheduling II (only considering operation sequence)
Scheduling III (considering both of them)
1496.9 733.2 2230.1
2450.2 23.65 2473.85
1613.4 55.32 1668.72
Solution 1 is shorter than the one of Solution 2 while the total energy of Solution 1 is larger than the one of Solution 2. Besides, as shown in Table 2, the idle power in each of M1, M2, and M3 in the test case is larger than idle power in M4 and M5. Thus, in Solution3, due to increasing the idle time for M1 and M3, the energy increases
significantly e even though it has the smallest makespan. This suggests that there is an energy saving opportunity if long idle times are avoided on high idle power machines. This may require a tradeoff between makespan and energy.
6. Conclusion
Fig. 8. Comparison of three scheduling results.
Fig. 9. Pareto Front obtained by optimizing energy and makespan.
This paper addresses energy optimization of flexible machining job shops by machine tool selection and operation sequence at the production operational level. The proposed energy-aware optimization is based on the recognition that energy for machining operations of jobs can be optimized by appropriately selecting machine tools and the idle energy of machine tools for nonmachining operations can be reduced by optimizing operation sequence of jobs. The proposed method helps the production manager's making-decision on energy-savings when managing the production operation of machine tool systems. The mathematical model for formulating the optimizing problem is constructed by mixed integer programming. According to the generalized machining cycle, the critical optimization objective of energy consumption in the model is evaluated by the energy during the cutting phase and the energy during the waiting phase and setup phase. The classical optimization objectives at production operating level such as makespan are also integrated in the model. For this NP-hard problem, Nested Partitions algorithm is used to solve the model. The case study with two scenarios is presented to evaluate the energy-saving potentials of the model. The results show that there is more energy savings by integrating machine tool selection and operation sequence compared to considering only one of them. Also, there are more efficient energy optimization by integrating machine tool selection and operation sequence than by considering only one of them. Also, there exist close relations among the total energy consumption, idle energy, machining energy, idle time, and makespan. The potential energy-savings can be achieved as well as the classical criteria are satisfied. The authors of this paper are planning a future study to develop a general framework model integrated the process plan costs and lot size selections in flexible job shop. Besides, considering the unforeseen disturbances in reality, integrating energy consumption
Fig. 10. Optimum scheduling solution for optimizing makespan and energy.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
9
Table 7 Comparison of the three solutions.
Energy consumption (W h) (machining energy/idle energy)
Time (min) (machining time/idle time)
M1 M2 M3 M4 M5 M1 M2 M3 M4 M5
Solution 1 (optimum scheduling solution)
Solution 2 (solution with minimal energy)
Solution 3 (solution with minimal makespan)
740.8/0 228.7/0 119.1/0 524.6/20 29.5/9.32 34.1/0 7.1/0 3.3/0 38.1/2 3.7/1.3
729.5/0 329.8/0 0/0 524.6/46 29.5/9.32 33.3/0 10.7/0 0/0 38.1/4.6 3.7/1.3
606.2/6.63 343.7/0 269.5/248.3 361.2/98 177.9/26.52 27.2/0.4 11.1/0 7.9/7.8 25.5/9.8 19.1/3.7
into dynamic scheduling or real time scheduling problem clearly is a challenging research work. Acknowledgements The authors would like to thank the support from the National Natural Science Foundation of China (Grant No. 51105394) and National High Technology Research and Development Program of China (863) (Grant No. 2014AA041506). The authors also thank Mr. Ehsan Vahidi for his contribution in the paper. Nomenclature cijm E Em Ew Es Ec Eijm Fm fq maxðtÞ
fq
minðtÞ
End time of operation Oij on machine Mm energy criterion (W s) machining energy of the operations (W s) non-machining idle energy of the machine tools (W s) idle energy during job setup (W s) cutting energy (W s) Energy consumption of operation Oij on machine Mm position of the first none free fixed operation qthobjective function maximum value of the qth objective function
fq minimum value of the qth objective function number of operations for the kth job Jk j,l Index for operations k specific cutting energy (W s/mm3) i,k Index for jobs L An arbitrarily large positive number M number of machine tools m,n Index for machine tools Mm mth machine tool N number of jobs NUM number of sampling points on current iteration Oij Operation j on job i Po idle power of machine tools (W) Po positions on machine tools Po,m Idle power Po of machineMm PRi ¼ {(j,l)}i Operation j is the predecessor of operation l for job i Qi ¼ {(j,l)}i No operation precedence constraints between operation j and operation l for job i Ri Release (arrival) time of job i Srrth sampling point tc cutting time(s) tg switching time(s) ts setup time(s) tw idle (wait) time for the next operation (s) tw;m Idle time tw on machine Mm
tijm
Processing time of operation Oij on machine Mm
v
material removal rate (mm3/s) 1 if operation Oij on machine Mm ¼ 0 otherwise 8 < 1 if operation Oij on machine Mm precedes ¼ operation Okl on machine Mn : 0 otherwise free operation set alternative machine set for operation l set of all the unfixed operations used for the stop criterion set of the unfixed operations on machine m set of the fixed operation sequence on machine m root region most promising subregion.
,
xijm yijmkln U Jl G Gm Pm Q Q0
References Bladh, I., 2009. Energy Efficiency in Manufacturing. Berlin, German. Bruzzone, A.A.G., Anghinolfi, D., Paolucci, M., Tonelli, F., 2012. Energy-aware scheduling for improving manufacturing process sustainability: a mathematical model for flexible flow shops. CIRP Annals Manuf. Technol. 61, 459e462. Chen, G.R., Liang, L., Arinez, J., Biller, S., 2013. Energy-efficient production systems through schedule-based operations. IEEE Trans. Automat. Sci. Eng. 10 (1), 27e37. Dahmus, J.B., Gutowski, T.G., 2004. An environmental analysis of machining. In: 2004 ASME International Mechanical Engineering Congress and RD&D Expo, 13e19 November California. ASME, New York, pp. 1e10. Dai, M., Tang, D., Giret, A., Salido, M.A., et al., 2013. Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm. Robotics Comp. Integr. Manuf. 29, 418e442. Duflou, J.R., Sutherland, J.W., Dornfeld, D., Herrmann, C., Jeswiet, J., Kara, S., Hauschild, M., Kellens, K., 2012. Towards energy and resource efficient manufacturing: a processes and systems approach. CIRP Annals Manuf. Technol. 61, 587e609. Drake, R., Yildirim, M.B., Twomey, J., Whitman, L., Ahmad, J., Lodhia, P., 2006. Data collection frame-work on energy consumption in manufacturing. In: Proceedings of 2006 Institute of Industrial Engineering Research Conference, Orlando, Florida, USA. 20e24 May, pp. 1e5. Fadi, S., Joaquin, O., Alvaro, G., Miguel, O., 2014. Optimizing the production scheduling of a single machine to minimize total energy consumption costs. J. Clean. Prod. 67, 197e207. Fang, K., Uhan, N., Zhao, F., Sutherland, J.W., 2011a. A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction. SME J. Manuf. Syst. 30, 234e240. Fang, K., Uhan, N., Zhao, F., Sutherland, J.W., 2011b. A new shop scheduling approach in support of sustainable manufacturing. In: Hesselbach, J., Herrmann, C. (Eds.), Glocalized Solutions for Sustainability in Manufacturing, Proceedings of the 18th CIRP International Conference on Life Cycle Engineering, 2e4 May 2011, Braunschweig, Germany. Spinger-Verlag, Berlin, pp. 305e310. Gutowski, T., Murphy, C., Allen, D., Bauer, D., Bras, B., Piwonka, T., Sheng, P., Sutherland, J., Thurston, D., Wolff, E., 2005. Environmentally benign manufacturing: observations from Japan, Europe and the United States. J. Clean. Prod. 13 (1), 1e17. Gutowski, T., Dahmus, J., Thiriez, A., 2006. Electrical energy requirements for manufacturing processes. In: 13th CIRP International Conference on Life Cycle Engineering, Leuven, Belgium, vol. 5, pp. 560e564. Herrmann, C., Thiede, S., 2009. Process chain simulation to foster energy efficiency in manufacturing. CIRP J. Manuf. Sci. Technol. 1 (4), 221e229.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006
10
Y. He et al. / Journal of Cleaner Production xxx (2014) 1e10
He, Y., Liu, F., 2010. Methods for integrating energy consumption and environmental impact considerations into the production operation of machining processes. Chin. J. Mech. Eng. 23 (4), 428e435. Liu, C., Yang, J., Lian, J., Li, W., Evans, S., Yin, Y., 2014a. Sustainable performance oriented operational decision-making of single machine systems with deterministic product arrival time. J. Clean. Prod. http://dx.doi.org/10.1016/ j.jclepro.2014.07.025. Liu, Y., Dong, H., Lohse, N., Petrovic, S., Gindy, N., 2014b. An investigation into minimising total energy consumption and total weighted tardiness in job shops. J. Clean. Prod. 65, 87e96. Mouzon, G., Yildirim, M.B., Twomey, J., 2007. Operational methods for minimization of energy consumption of manufacturing equipment. Int. J. Prod. Res. 45 (18e19), 4247e4271. Mouzon, G.C., Yildirim, M.B., 2008. A framework to minimize total energy consumption and total tardiness on a single machine. Int. J. Sustain. Eng. 1 (2), 105e116.
Rajemi, M.F., Mativenga, P.T., Aramcharoen, A., 2010. Sustainable machining selection of optimum turning conditions based on minimum energy considerations. J. Clean. Prod. 18 (10), 1059e1065. Shi, L., 2000. Nested partitions method for global optimization. Oper. Res. 48, 390e407. Weinert, N., Chiotellis, S., Seliger, G., 2011. Methodology for planning and operating energy-efficient production systems. CIRP Annals. Manuf. Technol. 60, 41e44. Wu, T., Shi, L., Duffie, N.A., 2010. An HNP-MP approach for the capacitated multiitem lot sizing problem with setup times. IEEE Trans. Autom. Sci. Eng. 7 (3), 500e511. Yau, H., Shi, L., 2009. Nested partitions for the large-scale extended job shop scheduling problem. Ann. Oper. Res. 168 (1), 23e39.
Please cite this article in press as: He, Y., et al., An energy-responsive optimization method for machine tool selection and operation sequence in flexible machining job shops, Journal of Cleaner Production (2014), http://dx.doi.org/10.1016/j.jclepro.2014.10.006