Manifold learning based rescheduling decision

J Intell Manuf DOI 10.1007/s10845-016-1194-1

Manifold learning based rescheduling decision mechanism for recessive disturbances in RFID-driven job shops Chuang Wang1 · Pingyu Jiang1

Received: 12 July 2015 / Accepted: 5 January 2016 © Springer Science+Business Media New York 2016

Abstract In actual manufacturing processes, some unexpected disturbances, called as recessive disturbances (e.g., job set-up time variation and arrival time deviation), would gradually make the original production schedule obsolete. It is hard for production managers to perceive their presences. Thus, the impact of recessive disturbances can not be eliminated by rescheduling in time. On account of this, a rescheduling decision mechanism for recessive disturbances in RFID-driven job shops is proposed in this article, and a manifold learning method, which reduces the response time of manufacturing system, is applied in the mechanism to preprocess manufacturing data. The rescheduling decision mechanism is expected to answer the questions of whether to reschedule, when to reschedule, and which rescheduling method to be used. Firstly, RFID devices acquire the actual process completion time of all work in process (WIPs) at every WIP machining process completion time. Secondly, recessive disturbances are quantified to time accumulation error (TAE) which represents the difference between actual process completion time and planned process completion time. Lastly, according to the TAE and production managers’ experience, the rescheduling decision mechanism selects a proper rescheduling method to update or repair the original production schedule. The realization algorithms of rescheduling decision mechanism includes: (1) supervised locally linear embedding. (2) General regression neural network. (3) Least square-support vector Machine. Finally, a numerical experiment is used to demonstrate the implementation procedures of the rescheduling decision mechanism.

B 1

Pingyu Jiang [email protected] State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, China

Keywords Rescheduling decision mechanism · Recessive disturbances · Manifold learning · SLLE · RFID

Introduction In the future manufacturing, e.g., industry 4.0 which focuses on the establishment of intelligent products and manufacturing processes (Malte et al. 2014), dynamic business and engineering process require factories to respond flexibly to disruptions and failures in manufacturing processes (Katragjini et al. 2013). Thus, manufacturing system must acquire real-time progress information of production orders to balance the differences between original production schedule and actual manufacturing processes. The differences usually result from some unexpected disturbances e.g., inaccurate and inconstant set-up time, arrival time deviation, machine tools breakdown, adding new machine, new job arrival, job cancellation, changing processing time and due date, rush order, rework or quality problem, etc. (Sabuncuoglu and Bayız 2000; Katragjini et al. 2013; Wang et al. 2008; Dong and Jang 2011; Lv and Qiao 2014; Fattahi and Fallahi 2010). Different disturbances would cause different impacts on the original production schedule. The disturbances can be divided into two kinds (Liu et al. 2009, 2014): (1) Dominant disturbances which shut down the original production schedule immediately and lead to inevitable rescheduling (e.g., machine tools breakdown, arrival of urgent job), (2) Recessive disturbances which don’t shut down the original schedule immediately but cripple the schedule little by little and eventually lead to inevitable rescheduling (e.g., arrival time deviation, processing time deviation).

123

J Intell Manuf

Since the recessive disturbances always appear in the form of cumulative delay, it is difficult for production managers to evaluate their impact on the original production schedule and decide whether to reschedule or not. Time accumulation error (TAE) is defined as a real-time cumulative delay in this article, which is calculated by the actual process completion time and the planned process completion time, and it is used to quantify the real-time cumulative deviation of completion status of machining task caused by recessive disturbances. Although most of the rescheduling literatures present different disturbances as rescheduling factors, they only concentrate on the dominant disturbances. The recessive disturbances have not been studied well in those literatures. Therefore, it is urgent to study the rescheduling under recessive disturbances for dynamic business and engineering process. The manufacturing system cannot get the real-time process completion time in traditional job shops (Ovacik and Uzsoy 1997). However, with the advent of RFID, each manufacturing process completion time of WIPs can be captured by RFID devices that are deployed in job shops. Based on the completion time, the real-time TAE can be easily calculated to estimate the impact of recessive disturbances. RFID has been increasingly applied to production planning and scheduling (Mehrjerdi 2008; Brewer et al. 1999; Huang et al. 2007). It has positive impacts on production decision making (Zhong et al. 2013). However, RFID in rescheduling is facing challenges. First, the RFID-driven manufacturing system should find out the useful information from huge and redundant real-time manufacturing data. Second, the use of RFID would speed up the decision-making process, and demand more prompt actions from manufacturing system. Thus, the RFID data should be pre-processed before the rescheduling decision is made. Manifold learning is adept at pre-processing large data. Since manifold learning was proposed by Roweis and Saul (2000) and Tenenbaum et al. (2000), it has been successfully applied in image processing, fault diagnosis, wireless sensor networks, business, etc. (Martin and Anil 2006; Jiang et al. 2009; Ahmed and Lee 2004; Neal and Alfred 2004; Lin et al. 2011). From previous literatures about manifold learning, it can be seen that their application domains include visual surveillance systems and human identification. Although some researchers have introduced manifold learning into manufacturing, the application in RFID data analysis in RFID-driven manufacturing environment has not been studied well. In general, rescheduling problems include four research topics (Vieira et al. 2003): (1) The rescheduling environment which identifies the jobs to be rescheduled; (2) The rescheduling strategies which decide whether to reschedule or not; (3) The rescheduling policies which specify when to reschedule, e.g., periodic, event-driven, and hybrid policies (Suwa 2007); (4) The rescheduling methods which describe

123

how to reschedule, including right shift rescheduling (RSR), partial rescheduling (PR), and total rescheduling (TR) methods (Vieira et al. 2003). As for the rescheduling policies, periodic policy reschedules the original production schedule at a fixed time interval, which makes the manufacturing system lack the quick response ability to disturbances. Meantime, it would cause unnecessary rescheduling (Vieira et al. 2000). Event-driven policy triggers the rescheduling when the pre-specified disturbances occurred, but it only suits for dominant disturbances (Akturk and Gorgulu 1999; Liu et al. 2009). Hybrid policy combines the advantages of periodic and event-driven policies, but it increases the computation burden of manufacturing system. In a word, the existing rescheduling policies easily lead to system nervousness and unnecessary computational time (Sabuncuoglu and Bayız 2000). Therefore, they are not suitable for the recessive disturbances, especially in RFID-driven manufacturing environment where a large amount of manufacturing data exists. After the rescheduling policy is decided, a specific rescheduling method should be chosen. Different rescheduling methods are appropriate for different disturbance scenarios. In order to facilitate the understanding of rescheduling methods, their definitions are described respectively as follows (Qiao et al. 2011; Olumolade 1996; Abumaizar and Svestka 1997): Definition 1 RSR postpones each remaining operation by the amount of time needed to make the schedule feasible. Definition 2 PR reschedules only the operations affected directly or indirectly by the disturbances, and it preserves the original schedule as much as possible. Definition 3 TR reschedules the entire set of operations that are not processed before the rescheduling point. Different rescheduling methods have different advantages and disadvantages. RSR and PR can quickly respond to various disturbances, and tend to maintain original schedule stability with little nervousness. They, however, easily lead to a myopic rescheduling. Although TR can get a high performance rescheduling, it is rarely achievable in practice because of its excessive computational effort and unsatisfactory response time (Li 1995; Sabuncuoglu and Bayız 2000). Thus, for a specific disturbance scenario, the best rescheduling method should be chosen by production managers according to their long-term experience (Pratap et al. 2015; Qiao et al. 2011). This article attempts to address rescheduling problems against recessive disturbances. However, at present, there are few systematic studies on the rescheduling with recessive disturbances. The relevant existing studies minimize the impacts of recessive disturbances by: (1) using fuzzy processing time.

J Intell Manuf

The output of a fuzzy scheduling will normally be a fuzzy schedule, which indicates fuzzy starting and ending time for the activities (Herroelen and Roel 2005). This approach does not consider the real-time manufacturing data in production; (2) postponing backward all jobs. If the delivery time of all jobs is still satisfied after one or more operations are delayed, the rescheduling is not carried out. Otherwise, the rescheduling operation should be carried out (Zhou et al. 2011); (3) inspecting the existing schedule delays at planned times. If the cumulative delay is found to exceed a prescribed threshold, rescheduling is performed (Suwa 2007). This approach is, in effect, the periodic rescheduling. And the existing schedule would be modified periodically at planned times. As mentioned above, it is better to make a flexible choice at each rescheduling point depending on production managers’ experience. Machine learning is a good way to describe the experience. To study the rescheduling problem under recessive disturbances, this article chooses job shops as the rescheduling environment, and proposes a manifold learning based rescheduling decision mechanism which includes the rescheduling strategy, rescheduling policy and rescheduling method selection. Firstly, TAE is calculated to quantify the real-time recessive disturbances. Secondly, the rescheduling decision mechanism is designed to choose a proper rescheduling method depending on TAE and the production managers’ experience. Based on manifold learning, the realization algorithms of rescheduling decision mechanism in this article include: (1) supervised locally linear embedding (SLLE), which is one of manifold learning methods, is used to reduce the dimensionality of mass historical RFID data into lower dimensionality, (2) general regression neural network (GRNN) is used to establish the explicit mapping function from the data points in high-dimensional space to the data points in lowdimensional embedded space, (3) least square-support vector machine (LS-SVM) is used as a classifier to choose an appropriate rescheduling method, which is trained by the low-dimensional data points and label data (i.e., the digital representation of historical production managers’ experience). This article combines the efforts of the following three aspects: (1) focused on the rescheduling under recessive disturbances, TAE is firstly proposed to quantify the real-time impact of recessive disturbances on the original production schedule. Based on our previous work, different calculation formulas of TAE are given, which are correspondent with different phases of a machining process; (2) a rescheduling decision mechanism is proposed, which considers the rescheduling method according to the real-time TAE of all WIPs at each WIP machining process completion time and production managers’ experience; and (3) an explicit mapping function is used to shorten rescheduling decision time. By virtue of the explicit mapping function, the real-time

processing of RFID data is converted to the calculation of the function output. This actually simplifies the dimensionality reduction of real-time RFID data from high-dimensional space to low-dimensional embedded space. Manifold learning is used to provide training data for GRNN to establish the explicit mapping function. The remainder of this paper is organized as follows: Sect. 2 describes a framework of rescheduling decision mechanism. The RFID-based TAE calculation is depicted in Sect. 3. Manifold learning based rescheduling decision mechanism is discussed in Sect. 4. In Sect. 5, a numerical experiment is taken as an example to illustrate the utility of the proposed models and methods. Finally conclusions are presented in Sect. 6.

A framework of rescheduling decision mechanism Rescheduling decision mechanism is to address when to reschedule, whether to reschedule or not, and which rescheduling method to apply. As mentioned above, the traditional rescheduling policy for recessive disturbances is periodic. But it is not good for RFID-driven manufacturing environment, because frequent rescheduling and a huge amount of manufacturing data can degrade the performance of a manufacturing system. By virtue of the capability of RFID to track the state of WIPs, a new rescheduling policy based on manufacturing process completion time of WIPs is proposed. The existing rescheduling methods have different advantages and disadvantages. There is only one rescheduling method which is most suitable for the manufacturing environment under specific recessive disturbances. It means that the manufacturing system should use different rescheduling methods to update the original production schedule in manufacturing processes. Although there are many studies on choosing an appropriate rescheduling method by using certain performance indicators, the rescheduling method chosen in this way may not be the best one in practice because the processing time used in the indicators often deviates from the practice. Therefore, the rescheduling decision mechanism is to integrate three rescheduling methods into alternatives, and to dynamically select the rescheduling method according to the real-time TAE of all WIPs at each WIP machining process completion time. The rescheduling procedures for recessive disturbances are depicted in Fig. 1: (1) as the original production schedule is released to the job shop, manufacturing system can obtain the real-time manufacturing data of WIPs through RFID devices; (2) by comparing the real time manufacturing data with the original production schedule, TAE can be calculated; (3) at each WIP machining process completion time, the rescheduling decision mechanism assesses

123

J Intell Manuf

actual completion status

trigger at each manufacturing process completion of every WIP ideal completion status

the original production schedule

the cumulative deviation of completion status at time t

(1)

right shift rescheduling

recessive disturbances assessment

partial rescheduling total rescheduling

production experience

WIPs the real time production data captured by RFID

no rescheduling

rescheduling methods selection

the rescheduling decision mechanism

(2)

the alternative rescheduling methods

(3)

(4)

Fig. 1 The procedures of rescheduling decision mechanism for recessive disturbaces

M

I I I

O

M M

O O

I

I

M

I

M M t

(a) I: in-stock

(b) M: machining

O: out-stock

Fig. 2 RFID-driven tracking model of WIPs. a The original production schedule, b the tracking model of production progress

the impact of recessive disturbances according to production experience; and (4) the rescheduling decision mechanism chooses an appropriate rescheduling method for updating or repairing the original production schedule. The framework of rescheduling decision mechanism is shown in the third part of Fig. 1.

RFID-based TAE calculation The processing time of each planned manufacturing process includes set-up time, waiting time for machining, actual machining time, and other time (Katragjini et al. 2013; Wang et al. 2008). The different times represent different completion phases of WIP in a machining process. Those different completion phases are very important for assessing the manufacturing progress of WIPs. RFID-driven tracking model of WIPs In light of our previous work, a machining process can be divided into several phases, e.g., in-stock, machining, and out-stock. Through configuring RFID devices such as RFID antennas, RFID readers, and RFID tags into machine tools

123

and WIPs, the tracking system can detect the time-sensitive state and position changes of WIPs in job shops (Jiang and Cao 2013). The tracking model of RFID-driven manufacturing progress can be described as the part b in Fig. 2. The red line represents the current time. The left side of the red line represents the finished manufacturing processes. It can be clearly seen from the left side of red line that RFID devices can detect the actual time of each WIP entering in-stock, in-machining, and out-stock.

Real-time TAE based on RFID tracking model In ideal conditions, the real-time completion status of machining tasks is the same as the original production schedule, as Fig. 2b shows. But the actual completion status is either later or earlier than the original production schedule expectation. There are three kinds of cumulative deviation of completion status in practice, as Fig. 3 depicts. To quantify the real-time cumulative deviation of completion status, TAE between the actual process completion time and the planned process completion time is calculated as follows:

J Intell Manuf ideal completion status

M

I

O O

M

I

M

I

O

I

actual completion status

I

M

I

M

O

M

O t

Fig. 3 The cumulative deviation model of completion status

⎛ dci,t = ⎝

n−1  j=0

Ti, j

⎞

m−1      + t − tsi,n ⎠ − Ti,k + t − tsi,m

(2) RFID has captured the start time of the machining process. It means that the WIP is in machining. So t pi,m is the time captured by RFID. (3) RFID has monitored the WIP entering out-stock. It means that the WIP has finished the mth machining process, and it is waiting for transportation to the next process. So the Eq. (2) can be simplified as: ⎛ dai,t = ⎝

n−1  j=0

Ti, j

⎞

m−1    + t − tsi,n ⎠ − Ti,k + Ti,m k=0

(4)

k=0

Note that the WIP transportation time is already contained in (1) the processing time of corresponding process. This is in line with the design of the original production schedule. where dci,t is the TAE of WIP i at time t, Ti, j represents the When production managers make a rescheduling decision, processing time of jth process of WIP i, n − 1 is the number they should consider not only the real-time TAE, but also of planned finish processes at time t, m − 1 is the number whether the remaining manufacturing processes of the WIP of actual finish processes at time t, tsi,n is the planned start can be completed as planned or not. Here, the possibility time of the nth process, tsi,m is the actual start time of the coefficient of on-time delivery is quantified as follows.   mth process. ti,dd − t Equation (1) points out the theoretical TAE value of WIP

(5) pi,t =  N i at time t. According to the previous discussion, tsi,m repreT + T i,l i,m−r l=m+1 sents the time when the WIP arrives at the mth machine tools. where pi,t is the possibility coefficient of on-time delivery The actual machining start time of the mth process should of WIP i at time t, ti,dd represents the due date of WIP i, m be acquired by RFID devices. Thus, the accurate TAE can be is the current process number of WIP i, N is the total numgiven as: ber of WIP i machining processes, Ti,m−r is the remaining ⎞ ⎛ processing time of mth machining process of the WIP i. n−1    Based on the analysis mentioned above, the rescheduling Ti, j + t − tsi,n ⎠ dai,t = ⎝ decision mechanism could be interpreted as the following j=0 problems: at each WIP machining process completion time m−1

     t, the manufacturing system should take into account the real− Ti,k + t − tsi,m − t pi,m − tsi,m time manufacturing data of all WIPs (e.g., “dai,t ” and “ pi,t ”); k=0 refer to the production managers’ experience and histori(2) cal RFID data, and then select an appropriate rescheduling method. where dai,t is the accurate TAE of WIP i at time t, t pi,m The total number of WIPs in job shops is constantly denotes the actual machining start time of the mth process. changing. To avoid the impact of different total numbers on When the WIP is at different phases of the mth process, rescheduling decision mechanism, this article classifies the the simplified dai,t can be calculated as follows. parts of an order into different kinds, and uses the statistics of real-time manufacturing data of each kind of parts to rep(1) RFID has monitored the WIP entering in-stock, but it resent their production progress. does not capture the actual machining start time. It means Assuming that a job shop can produce u kinds of parts, an that the WIP is still in the in-stock, and waiting for order’s demand for the qth kind (q ≤ u) part is r . Thus, the machining. Actually, the mth machining process does real-time manufacturing data statistics of the qth kind part not start, and thus t pi,m should be equal to t. So the for the order can be calculated as: Eq. (2) can be simplified as: r 1 da = dai,t (6) q,t ⎛ ⎞

r n−1 m−1   i=1    Ti, j + t − tsi,n ⎠ − Ti,k (3) dai,t = ⎝ 1 r j=0 k=0 σdaq,t = (dai,t − daq,t )2 (7) i=1 r

123

J Intell Manuf

1 pi,t r i=1  1 r = ( pi,t − pq,t )2 i=1 r r

pq,t = σ pq,t

(8)

(9)

where daq,t is the mean value of dai,t of qth kind part for the order at time t, pq,t is the mean value of pi,t of qth kind part for the order at time t, σdaq,t represents standard deviation of dai,t of qth kind part for the order at time t, σ pq,t represents standard deviation of pi,t of qth kind part for the order at time t. Based on the statistics above, the input of the rescheduling decision mechanism can be described as: xi =

 da1,t , σda1,t , p1,t , σ p1,t ,   . . . , daq,t , σdaq,t , pq,t , σ pq,t ,   . . . , dau,t , σdau,t , pu,t , σ pu,t



(1) SLLE is used to calculate the corresponding 2-dimen sional coordinate values Y = y1 , y2 , . . . , y180 of X = {x1 , x2 , . . . , x180 }. Note that the dimensionality 2 is only used to explain this issue. (2) GRNN is trained by X and Y to establish the explicit mapping from 20-dimensional space to 2-dimensional space, because the SLLE can not provide this mapping function. (3) LS-SVM is trained by Y and Z to choose proper rescheduling method for new data.

(10)

where xi is the ith input data.

Manifold learning based rescheduling decision mechanism Usually, there are a lot of WIPs in job shops at the same time. As the number of WIPs increases, the real-time manufacturing data would increase dramatically. It is very difficult for the manufacturing system to make a rescheduling decision according to larger amounts of real-time manufacturing data. The manifold learning approach is often used to find the underlying relationships among large data. So it is well suited for pre-processing the real-time manufacturing data before the manufacturing system uses them to make a rescheduling decision. Since the manufacturing system depends on the pre-existing production experience for selecting a rescheduling method, a supervised manifold learning algorithm, called SLLE, is adopted to deal with the huge manufacturing data. Here, a smaller example is used to explain the procedures of rescheduling decision. Assuming there are 20 WIPs, which belong to five kinds of parts, in an RFID-driven job shop, and each WIP has three machining processes. At each WIP machining process completion time, the RFID devices can acquire the real-time manufacturing information of five kinds of parts, as Eq. 10 describes. So the rescheduling decision mechanism can obtain 60 data in one production cycle. According to Eq. 10, the dimensionality of the data is 20. At the beginning of production, the rescheduling decision is made by the production managers, and the rescheduling decision mechanism records the RFID data xi and the

123

corresponding production managers’ choice z i . When the data becomes very large, the rescheduling decision mechanism would acquire the relationship between xi and z i by analyzing historical data. Assuming that the historical data is X = {x1 , x2 , . . . , x180 } and Z = {z 1 , z 2 , . . . , z 180 } after three production cycles, the learning procedure of the rescheduling decision mechanism is shown as follows.

After the learning procedures mentioned above, the manufacturing system can make a rescheduling decision according to the real-time manufacturing information. For example, in the fourth production cycle, the rescheduling decision mechanism would receive a data x . The rescheduling decision mechanism uses GRNN to calculate its 2-dimensional coordinate values y , and then uses LS-SVM to choose a proper rescheduling method z  based on y . The realization of SLLE SLLE is a supervised manifold learning approach based on locally linear embedding algorithm (LLE) (Kouropteva et al. 2003). LLE does not make use of the label information (the digital representation of historical experience and knowledge), while the label information is very useful to improve the accuracy of the algorithm. Based on this idea, Kouropteva et al. (2003) used it to increase the inter-point distance in high-dimensional space if the data points belong to different classes. It implies that the different class data points would remain spatially separated in low-dimensional space after they are mapped. As an input, X = {x1 , x2 , . . . , xl } represents a set of l data points in a high-dimensional space R D , and supposing X lies on or near a smooth nonlinear manifold of lower dimensionality d(d  D), the goal of LLE is to find Y = y1 , y2 , . . . , yl , which is the d-dimensional embedding of X, by mapping the D-dimensional data into a single global coordinate system in Rd . The LLE consists of three steps (Saul and Roweis 2003). The difference between SLLE and LLE is in step 1, namely, calculating the Euclidean distance between data points. The implementation procedures of SLLE can be described as follows (Kouropteva et al. 2003).

J Intell Manuf

Step 1: finding k nearest neighbors of each data point xi , i = 1, . . . , l. The Euclidean distance is used as a similarity measure. The proximity information is collected in a matrix A (of size k × l). The Euclidean distance can be calculated as follows. ⎧ D, ⎪ ⎪ ⎨

if the points be long to a same class D = D + α max if the points belong (D), ⎪ ⎪ ⎩ to different classes

(11)

where D = xi − x j  is the initial Euclidean distance between xi and x j ; max (D) is the maximum Euclidean distance between data points. α represents the magnitude of a distance expansion, α ∈ [0, 1]. The smaller (larger) α, the less (more) class labels affect a choice of the nearest neighbors for each point. Step 2: reconstructing each data point from its nearest neighbors. The optimal reconstruction weights wi, j can be computed as:  2  l  k      wi, j∈Ai x j∈Ai  ε (W) = xi −   i=1  j=1

(12)

which is subjected to the constraints kj=1 wi, j∈Ai = 1 and wi, j = 0, if xi and x j are not neighbors. Step 3: computing a low-dimensional embedding based on the reconstruction weights wi, j of the high dimensional inputs xi . This is done by choosing the d-dimensional coordinates of each output yi to minimize the embedding cost function:  2  l  k      δ (Y) = wi, j∈Ai y j∈Ai  yi −   i=1  j=1

(13)

l which is subjected to the constraints i=1 yi = 0 and l 1 T = I. To find the matrix Y, a new matrix y y i=1 i i l M = (I − W)T (I − W) is constructed. Then SLLE computes the bottom d + 1 eigenvectors of M, associated with the d + 1 smallest eigenvalues. The first eigenvector whose eigenvalue is close to zero is excluded. The remaining d eigenvectors yield the final embedding Y. The key parameters d, k, and α, need to be determined before using SLLE. In order to find the appropriate values of the parameters, the sum of the Euclidean distance between sample data of jth rescheduling method and their mean value, and the Euclidean distance between different mean values, is used to evaluate the dimensionality reduction results. The sum can be calculated in the following equation:

⎞ ⎛ d    k1 m l − m j ⎠ ev = d q   + k2 ⎝ Yi − m j  j=1 i=1 l, j=1 (14) where ev is the evaluation index of the dimensionality reduction results, the larger the ev, the better the result of dimensionality reduction. m j represents the mean value of sample data of jth rescheduling method, q is the sample size of jth rescheduling method, k1 , k2 stand for the weight coefficient, k1 = 10,000, k2 = 4. The explicit mapping function between X and Y SLLE does not provide any explicit mapping function from high-dimensional space to low-dimensional embedded space. But this function is very necessary to obtain the embedded coordinate of the new unlabeled data points (Li and Zhang 2011). This paper uses GRNN to construct explicit mapping function. By introducing Gauss function as the transfer function, the output of GRNN can be given as:   l −Di2 y ex p i=1 i 2σ 2   (15)  y (x) = l −Di2 ex p 2 i=1 2σ where y is the predicted value of y, Di2 = (xi − x)T (xi − x) and σ represents the spread of network. Training the GRNN involves finding the optimal values for the parameters σ in the above equation (Mohsen et al. 2010). The realization of rescheduling decision mechanism When SLLE maps X in high-dimensional space R D to Y in low-dimensional space Rd , the classifier can be trained by Y and label data. Here LS-SVM is chosen as a classifier. Its formulation is shown as: 1 1 2 ei minω,b,e J (ω, b) = H T H + γ 2 2 i=1       s.t. z i H T ϕ yi + c ≥ 1 − ei l

(16)

where yi ∈ Rd is the mapping value of xi ∈ R D , z i ∈ Z is the label of xi . H and c are the slope and intercept of the regression line respectively, γ is a constant denoting the penalty parameter, ei is a measure of error in the LS-SVM, and the function ϕ is a transformation mapping the input vector into a high-dimensional feature space. Based on Lagrange multipliers method and Mercer’s theorem (Cristianini and John 2000), the LS-SVM classifier can be built as follows:

123

J Intell Manuf Fig. 4 The implementation procedures of rescheduling decision mechanism

1. The procedure of the model establishment of rescheduling decision mechanism

3

1 1

3 manifold learning (SLLE)

2

training LS-SVM

2 training GRNN

4

explicit mapping function

5 classifier

2. The procedure of rescheduling decision-making

f (y) = sign

l 

  z i αi K y, yi + b

(17)

sionality of real time manufacturing data x is the same as the sample data X.

i=1

  where αi is Lagrange multipliers, b is the bias value, K y, yi is the kernel function. The radial basis function (RBF) is often used as the kernel function, and so does in this paper. Based on the above discussion, it is easy to draw the implementation procedure of rescheduling decision mechanism, as Fig. 4 shows. The implementation procedure includes two steps: (1) make use of the training data to establish the model 1 of rescheduling decision mechanism, which includes  2 estabreducing the dimensionality of sample data X,  3 training the lishing the explicit mapping function, and  classifier by Y and Z; (2) use the established model to make rescheduling decision according to the real-time manufacturing data, 4 calculating the corresponding lowwhich includes  dimensional coordinate values y of real-time manufacturing data x by using the explicit mapping function, 5 classifying the low-dimensional coordinate values by  using the classifier, finally making a choice according to the classification results. It can be clearly seen from Fig. 4 that the manifold learning based rescheduling decision mechanism demands the dimen-

123

Numerical experiment The introduction of experiment environment and sample data In order to verify the effectiveness of our rescheduling decision mechanism, an RFID-driven job shop of a famous equipment manufacturing enterprise in Shanghai is chosen as an example. The machine type and the corresponding quantity in the job shop are listed in Table 1. This job shop mainly produces 10 different kinds of parts. The information of the parts can be found in Table 2, where part number is the index of part type and the number under machine model represents the planned processing time of the part. The demands for different kinds of parts of different orders are variable. The information about some orders is given in Table 3, for example, in the first line the number 80 under Part 1 means that Order 1 requires 80 pieces of Part 1. Based on the historical manufacturing data of the job shop captured by RFID devices, 400 data points of rescheduling decision are chosen as sample data, as listed in Table 4. Three hundreds data points are used as training samples and one hundred data points as test samples, i.e., the training samples:

J Intell Manuf Table 1 The information about machines in the job shop Machine type

CNC Lathe

Boring

CNC milling

Processing center

Machining center

NC boring and milling

CNC milling

Machine model

CKA6163L

TPX6113

XD-40A

DGMA1320

VDWA50

TK6516

XW2416

Quantity

3

2

2

2

1

1

1

Table 2 The planned processing time of each kind of parts Part number

Part type

Planned processing time (h) CKA 6163L

TPX 6113

XD-40A

DGMA 1320

VDWA 50

TK 6516

XW 2416

1

Cylinder block

5.5

6.5

0

4

5.2

2.5

3

2

Cylinder head

3

0

2

1.5

0

4

5.1

3

Shell

6.1

3.5

5.2

4.1

0

2.5

1.5

4

Crankcase

4

5.5

2

0

3.5

0

1.5

5

Crankshaft

2

0

1

3

3.1

0

0

6

Piston

3

0

1.5

0

4

1

2

7

Flange disk

4

1

3

7

1

0

0

8

Shaft

7.5

3

0

0

6.1

2

5

9

Cylinder liner

5

0

0

4.2

1

0

1

10

Bearing ring

4.5

0

0

0

1.5

2

0

Table 3 The quantity of parts in different orders

Order no.

Quantity demanded (pieces) Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7

Part 8

Part 9

Part 10

1

80

0

60

40

0

50

70

40

70

0

2

0

60

45

55

55

40

0

50

60

50

3

30

50

85

40

0

23

55

0

60

40

4

50

45

53

135

55

89

45

95

65

120

5

85

0

26

53

0

54

68

32

75

0

Table 4 The training and testing samples Sample no.

Part no.

Rescheduling method 2 ··· 9

10

σ p1

···

da10

2.72

1.27

···

0

0

···

1.56

0.36

14.53

3.92

10.53

2.72

.. .

.. .

1 da1

σda1

1

−28.9

21.53

2

0

0

3

15.6

12.54

4

−7.9

5

27

.. .

.. .

p1

No

RSR

PR

TR

0

1

0

0

0

4.23

1

0

0

0

1.13

1

0

0

0

σda10

p10

σ p10

0

0

0

35

15.46

5.4

···

31.77

9.45

2.13

1.23

···

30

14.64

5.05

1.4

1

0

0

0

1.27

···

0

0

0

0

1

0

0

0

.. .

···

.. .

.. .

.. .

.. .

.. .

.. .

.. .

.. .

396

0

0

0

0

···

0

0

0

0

0

0

0

1

397

63

18.11

3.53

1.23

···

38

24.16

6.31

6.23

0

0

0

1

398

74

21.76

2.62

1.15

···

27

25.96

6.56

3.21

0

0

0

1

399

98.43

15.41

1.77

0.61

···

17.22

43.46

6.33

2.24

0

0

0

1

400

101

24.18

1.6

1.22

···

12

37.41

10.3

7.23

0

0

0

1

123

J Intell Manuf

k = 10 d = 3 α = 0.5

k = 60 d = 3 α = 0.5

(a)

k = 20 d = 3 α = 0.5

k = 20 d = 4 α = 0.5

(b)

k = 20 d = 3 α = 0.5

k = 20 d = 3 α = 0.7

(c) Fig. 5 The SLLE dimensionality reduction results under different parameter values. a The dimensionality reduction results under different k. b The dimensionality reduction results under different d. c The dimensionality reduction results under different α

X = {x1 , x2 , . . . , x300 }, Z = {z 1 , z 2 , . . . , z 300 } and test  }. samples: X = {x1 , x2 , . . . , x1100 }, Z  = {z 1 , z 2 , . . . , z 100  Note that the label data of test samples Z is only used to verify the rescheduling method chosen by rescheduling decision mechanism.

123

The experiment of SLLE based rescheduling decision mechanism From Table 4, the dimension of samples is 40. Firstly, 300 training samples should be mapped into low-dimensional

J Intell Manuf

Fig. 6 The optimization process of SLLE parameters

Fig. 7 The dimensionality reduction results of SLLE under k = 46, d = 3 and α = 0.4

space by using SLLE. The dimensionality reduction results are deeply affected by the values of key parameters, as Fig. 5 shows. It should note that, for clarity, the first three dimensional data of the dimensionality reduction results (i.e., d1, d2, d3 in Fig. 5) is used to illustrate the results. Considering Genetic Algorithm (GA) has been widely studied in manufacturing fields, it is used to find the appropriate values of key parameters of SLLE. The evaluation index of the dimensionality reduction results is used as the GA fitness criteria. The value ranges of k ∈ [5, 60], d ∈ [3, 7], and α ∈ [0.1, 1] are determined according to the experiments and experience. A simulation implementation is constructed based on GAOT toolbox in MATLAB, and the simulation parameters are normal geometric selection, arithmetic crossover, non-uniform mutation, 100 generations and

Fig. 8 The relationship between σ and difference (error)

a population size of 20. The optimization process is shown in Fig. 6. From the optimization process, it can be found that the evaluation index of the dimensionality reduction results reaches the best after 35 iterations. The corresponding best solution is k = 46, d = 3 and α =   0.4, and the lowdimensional coordinate values Y = y1 , y2 , . . . , y300 of training data points X = {x1 , x2 , . . . , x300 } can be obtained in Fig. 7. Next step is to obtain the coordinates of 100 test data points in low-dimensional space by GRNN. GRNN establishes the explicit mapping from 40-dimensional space to 3-dimensional embedded space by making use of training data X and Y. The spread value of GRNN—σ , is determined according to the difference between the predicted output  y and training data y. Figure 8 is obtained in the experiment which reflects the relationship between σ and difference (error). It can be seen from the Fig. 8 that the optimal value for σ parameter is 0.5. Then the corresponding low-dimensional coordinate val  = y , y , . . . , y of 100 test data points X  = ues Y 1 2 100     x1 , x2 , . . . , x100 are calculated by GRNN as listed in Table 5. In the last step, the LS-SVM classifier decides which rescheduling methods shouldbe used. Firstly, the LS-SVM classifier is trained by Y = y1 , y2 , . . . , y300 and the corresponding label data Z = {z 1 , z 2 , . . . , z 300 }. It should be noted that the label data actually represents the numeral order of rescheduling method, for example, 1 represents no rescheduling, 2 is RSR, 3 is PR, and 4 means TR. Secondly, the LS-SVM classifier chooses an appropriate rescheduling method z  , z  ∈ {1, 2, 3, 4}, for the test data point xi , i = 1, . . . , 100 depending on its low-dimensional coordinate values yi , i = 1, . . . , 100. This means that the z  th rescheduling

123

J Intell Manuf Table 5 The corresponding low-dimensional coordinate values of test data points y1

y2

y3

y4

···

 y22

 y23

 y24

−0.02184

−0.02175

−0.02162

−0.02187

···

−0.02187

−0.02187

−0.02187

−0.02187

0.000141

0.00077

0.000306

4.39E–07

···

−3.2E–10

5.06E–11

6.55E–09

9.3E–11

−1.9998

−1.99885

−1.99959

−2

···

−2

−2

−2

−2

 y26

 y27

 y28

 y29

···

 y47

 y48

 y49

 y50

1.184657

1.192047

1.236502

1.005253

···

0.605884

0.608391

0.351773

0.460528

1.482662

1.484968

1.488829

1.454099

···

1.432208

1.432471

1.406391

1.418883

−2.7E–07

−2.7E–06

−4.9E–06

−1.3E–11

···

−5.2E–06

−2.6E–06

−4E–15

−5E–11

 y51

 y52

 y53

 y54

···

 y72

 y73

 y74

 y75

0.693471

0.682176

0.271433

0.656068

···

1.082466

1.075545

0.939798

0.914301

−1.26612

−1.27741

−1.12575

−1.26854

···

−1.49557

−1.43149

−1.44288

−1.42262

−3.2E–06

−1E–11

−5.6E–14

−1.4E–13

···

−1E–14

2.66E–15

3.11E–15

2.66E–15

 y76

 y77

 y78

 y79

···

 y97

 y98

 y99

 y100

−1.77301

−1.95998

−1.94808

−1.92059

···

−1.43084

−1.45549

−1.34025

0.131656

0.116418

−0.08506

−0.09254

−0.09072

···

0.39584

0.290339

0.292092

−0.26449

−7.5E–10

−2.5E–11

−2.6E–12

−8.7E–11

···

−2.1E–07

−8.4E–15

−0.00033

−6.9E–06

method should be applied to update the original production schedule. The results of rescheduling method selection for test data point xi , i = 1, . . . , 100 are listed in Table 6. From the results, it can be seen that the rescheduling method chosen by SLLE based rescheduling decision mechanism z  is nearly the same as production managers’ experience z  . Comparison with LLE + LS-SVM and LS-SVM To illustrate the advantages of the proposed method, an experiment compared with other methods is conducted. Since SLLE is a supervised LLE as discussed previously, a rescheduling decision mechanism based on LLE can be used as the comparison algorithm. LLE is simpler than SLLE, because it doesn’t need the label information. So the test data points can be reduced the dimensionality with training data points together. Thus the LLE based rescheduling decision mechanism consists of LLE and LS-SVM, namely LLE + LS-SVM. As with SLLE, LLE needs to determine the key parameters, lower dimensionality d, nearest neighbors k, before calculation. The optimization process of k and d is shown in Fig. 9. The best solution is k = 278, d = 4 and the dimensionality reduction result of samples is described in Fig. 10. The LS-SVM classifier of rescheduling decision mechanism based on LLE is the same as the one based on SLLE. Additionally, the LS-SVM classifier can be directly trained by X = {x1 , x2 , . . . , x300 } and the corresponding

123

 y25

label data Z = {z 1 , z 2 , . . . , z 300 }, and then predict the label  data z  , z  ∈ {1, 2, 3, 4}, of test data point xi , i − 1, . . . , 100. All the methods proposed above have been implemented in MATLAB R2013a and run on Intel(R) Xeon(R) CPU E52630 v2 @2.60GHz, 192GB RAM, on Windows Server 2008 R2 datacenter. Comparisons of the experiment results are given in Table 7. It uses the average training time, average decision time and average accuracy to represent the average performance of each method after 10 runs. Some useful information can be found in Table 7. (1) The SLLE based rescheduling decision mechanism is the best one. It can effectively improve the accuracy of rescheduling decision-making by making use of GRNN and SLLE although they lead to a slight increase of training time and decision time. (2) The LLE + LS-SVM based rescheduling decision mechanism would take a long time to make decisions, because LLE needs to calculate low-dimensional coordinate values of new test data points and re-train the LSSVM classifier. (3) LLE would lose more spatial information between data points than SLLE. And it eventually deteriorates the accuracy of the decision. In general, a job shop can only produce little kind of parts, even though it can produce a large number of parts. Different job shops produce different kinds of parts in a manufacturing enterprise. And the number of kinds of parts is slightly different among different job shops. To demonstrate the efficacy of decision mechanisms under different numbers of kinds of parts, two other RFID-driven job shops in same manufacturing enterprise are taken as examples, which mainly produce

J Intell Manuf Table 6 The result of rescheduling method selection for test data point

Test data

z 

z

Test data

z 

z

Test data

z 

z

Test data

z 

z

x1

1

1

 x26

2

2

 x51

3

3

 x76

4

4

3

3

4

4

3

3

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

3

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

x2 x3 x4 x5 x6 x7 x8 x9  x10  x11  x12  x13  x14  x15  x16  x17  x18  x19  x20  x21  x22  x23  x24  x25

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

1

1

1

1

1

1

1

1

1

1

1

1

 x27  x28  x29  x30  x31  x32  x33  x34  x35  x36  x37  x38  x39  x40  x41  x42  x43  x44  x45  x46  x47  x48  x49  x50

Fig. 9 The optimization process of LLE parameters

17 and 21 different kinds of parts respectively. As Fig. 11a shows, the average training time of SLLE + GRNN + LSSVM under different kinds of parts (10, 17, and 21) is much

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

 x52  x53  x54  x55  x56  x57  x58  x59  x60  x61  x62  x63  x64  x65  x66  x67  x68  x69  x70  x71  x72  x73  x74  x75

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

 x77  x78

 x79  x80  x81  x82  x83  x84  x85  x86  x87  x88  x89  x90  x91  x92  x93  x94  x95  x96  x97  x98  x99  x100

Fig. 10 The dimensionality reduction results of LLE under k = 278, d = 4

less than the time of LLE + LS-SVM. Its average decision time with different kinds of parts is close to the time of LSSVM (as Fig. 11b shows). And its average accuracy is still

123

J Intell Manuf Table 7 Experiment results under different decision mechanism Decision mechanism

SLLE + GRNN + LS-SVM

LLE + LS-SVM

LS-SVM

Average training time CPU time (s)

12.2569

19.1971

10.6794

Average decision time CPU time (s)

0.0920

19.1971

0.0372

Average accuracy (%)

98.6

90.1

95.4

the highest in all decision mechanisms under different kinds of parts, as Fig. 11c shows. It can be seen from the numerical experiment that SLLE based rescheduling decision mechanism has three advantages as follows. (1) SLLE based rescheduling decision mechanism can effectively make use of historical rescheduling decision experience. The label data in samples actually represents the production managers’ choice for a specific manufacturing environment. This choice depends on the production managers’ experience and knowledge. SLLE can use it to improve the dimensionality reduction results. (2) By introducing GRNN, the rescheduling decision mechanism can directly obtain the low-dimensional coordinate values of new test data points, while LLE should re-calculate low-dimensional coordinate values of all data points which include new and original data points. So the rescheduling decision mechanism can effectively shorten the response time of manufacturing system. (3) Although LS-SVM can achieve high decision-making accuracy, SLLE based rescheduling decision mechanism can further improve the accuracy by reducing the dimensionality of large manufacturing data before making decisions. However, there are some disadvantages in SLLE based rescheduling decision mechanism. For example, the key parameters of SLLE have a great influence on the result of dimensionality reduction, and they are different for different sample data.

Conclusions This article focuses on the rescheduling decision mechanism under recessive disturbances, and uses TAE to assess the impact of recessive disturbances on the original production schedule. A manifold learning based rescheduling decision mechanism for recessive disturbances in RFID-

123

Fig. 11 The efficacy of decision mechanisms under different kinds of parts. a The average training time of decision mechanisms under different kinds of parts. b The average decision time of decision mechanisms under different kinds of parts. c The average accuracy of decision mechanisms under different kinds of parts

J Intell Manuf

driven job shops is proposed. Firstly, RFID devices capture all WIPs actual process completion time at each WIP machining process completion time. Next, TAE is calculated according to the difference between the actual process completion time and the planned process completion time. Finally, the rescheduling decision mechanism chooses a proper rescheduling method based on TAE and historical rescheduling decision experience. The implementation procedures of rescheduling decision mechanism include four steps: (1) SLLE converts the high-dimensional historical RFID data which includes the production managers’ experience as label data into lowdimensional data. (2) GRNN is trained to establish the explicit mapping function from high-dimensional space to low-dimensional embedded space. (3) LS-SVM is used as a classifier and trained by the low-dimensional data points and label data. (4) The rescheduling decision mechanism obtains the coordinate value of new manufacturing data in low-dimensional embedded space by GRNN, and puts it to LS-SVM classifier to choose a proper rescheduling method. Lastly, a numerical experiment based on real manufacturing data of an RFID-driven job shop is used to verify the validity of the rescheduling decision mechanism. Additionally, the advantages of the proposed method are fully demonstrated by comparing with LLE + LS-SVM and LSSVM. Future work in this area includes two aspects: (1) the importance of different orders should be taken into account when the rescheduling decision mechanism decides whether to reschedule or not; (2) the rescheduling decision mechanism should update its knowledge according to newly added manufacturing data. Acknowledgments The research work presented in this paper is under the support of National Natural Science Foundation of China with Grant No. 51275396 and National Basic Research Program of China with Grant No. 2011CB706805.

References Abumaizar, R. J., & Svestka, J. A. (1997). Rescheduling job shops under random disruptions. International Journal of Production Research, 35(7), 2065–2082. Ahmed, E., & Lee, C. S. (2004). Inferring 3D body pose from silhouettes using activity manifold learning. In Paper Presented at the 2013 IEEE Conference on Computer Vision and Pattern Recognition. Akturk, M. S., & Gorgulu, E. (1999). Match-up scheduling under a machine breakdown. European Journal of Operational Research, 112(1), 81–97. Brewer, A., Sloan, N., & Landers, T. L. (1999). Intelligent tracking in manufacturing. Journal of Intelligent Manufacturing, 10(3), 245– 250. Cristianini, N., & John, S. (2000). An introduction to support vector machines and other kernel-based learning methods. Cambridge: Cambridge University Press.

Dong, Y., & Jang, J. (2011). Production rescheduling for machine breakdown at a job shop. International Journal of Production Research, 50(5), 2681–2691. Editor (Ed.). (2013). Recommendations for implementing the strategic initiative INDUSTRIE 4.0: Securing the future of German manufacturing industry. In Final Report of the Industrie 4.0 Working Group, Forschungsunion. Fattahi, P., & Fallahi, A. (2010). Dynamic scheduling in flexible job shop systems by considering simultaneously efficiency and stability. CIRP Journal of Manufacturing Science and Technology, 2(2), 114–123. Herroelen, W., & Roel, L. (2005). Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research, 165(2), 289–306. Huang, G. Q., Zhang, Y. F., & Jiang, P. Y. (2007). RFID-based wireless manufacturing for walking-worker assembly islands with fixed-position layouts. Robotics and Computer-Integrated Manufacturing, 23(4), 469–477. doi:10.1016/j.rcim.2006.05.006. Jiang, P., & Cao, W. (2013). An RFID-driven graphical formalized deduction for describing the time-sensitive state and position changes of work-in-progress material flows in a job-shop floor. Journal of Manufacturing Science and Engineering, 135(3), 189– 197. Jiang, Q., Jia, M., Hu, J., & Feiyun, X. (2009). Machinery fault diagnosis using supervised manifold learning. Mechanical Systems and Signal Processing, 23(1), 2301–2311. Katragjini, K., Vallada, E., & Ruiz, R. (2013). Flow shop rescheduling under different types of disruption. International Journal of Production Research, 51(3), 780–797. Kouropteva, O., Okun, O., Ainen, M. P. (2003). Supervised Locally Linear Embedding Algorithm for Pattern Recognition. Paper presented at the IbPRIA,. (2003). Puerto de Andratx. Spain: Mallorca. Li, B., & Zhang, Y. (2011). Supervised locally linear embedding projection (SLLEP) for machinery fault diagnosis. Mechanical Systemsand Signal Processing, 25(8), 3125–3134. Li, R. K. (1995). A new rescheduling method for computer based scheduling systems. International Journal of Production Research, 33(8), 2097–2110. Lin, F., Yeh, C., & Lee, M. (2011). The use of hybrid manifold learning and support vector machines in the prediction of business failure. Knowledge-Based Systems, 24(1), 95–101. Liu, M., Shan, H., Jiang, Z., Ge, M., Hu, J., & Zhang, M. (2009). Dynamic rescheduling optimization of job-shop under uncertain conditions. Journal of Mechanical Engineering, 45(10), 137–142. Liu, M., Zhang, X., Zhang, M., Ge, M., & Hu, J. (2014). Rescheduling decision method of manufacturing shop based on profit-loss cloud model. Control and Decision, 29(8), 1458–1464. Lv, S., & Qiao, L. (2014). Process planning and scheduling integration with optimal rescheduling strategies. International Journal of Computer Integrated Manufacturing, 27(7), 638–655. Malte, B., Niklas, F., Michael, K., & Marius, R. (2014). How virtualization, decentralization and network building change the manufacturing landscape: An Industry 4.0 Perspective. International Journal of Science. Engineering and Technology, 8(1), 37–44. Martin, H. C. L., & Anil, K. J. (2006). Incremental nonlinear dimensionality reduction by manifold learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(3), 377–391. Mehrjerdi, Y. Z. (2008). RFID-enabled systems: A brief review. Assembly Automation, 28(3), 235–245. Mohsen, S., Razieh, S., & Ziari, M. B. (2010). QSAR study of anthranilic acid sulfonamides as inhibitors of methionine aminopeptidase-2 using LS-SVM and GRNN based on principal components. European Journal of Medicinal Chemistry, 45(10), 4499–4508.

123

J Intell Manuf Neal, P., & Alfred, O. H. I. (2004). Manifold learning algorithms for localization in wireless sensor networks. In Paper presented at the 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing. Olumolade, M. O. (1996). Reactive scheduling system for cellular manufacturing with failure-prone machines. International Journal of Computer Integrated Manufacturing, 9(2), 131–144. doi:10.1080/ 095119296131742. Ovacik, I. M., & Uzsoy, R. (1997). Decomposition methods for complex factory scheduling problems. Berlin: Springer. Pratap, S., Daultani, Y., Tiwari, M. K., & Mahanty, B. (2015). Rule based optimization for a bulk material handling port operation. Journal of Intelligent Manufacturing. doi:10.1007/s10845-015-1108-7. Qiao, F., Wu, Q., Li, L., Wang, Z., & Shi, B. (2011). A fuzzy Petri net-based reasoning method for rescheduling. Transactions of the Institute of Measurement and Control, 33(3), 435–455. doi:10. 1177/0142331208100100. Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(22), 2323–2326. Sabuncuoglu, & Bayız, M. (2000). Analysis of reactive scheduling problems in a job shop environment. European Journal of Operational Research, 126(3), 567–586. Saul, L. K., & Roweis, S. (2003). Think globally, fit locally: Unsupervised learning of low dimensional manifolds. The Journal of Machine Learning Research, 4(12), 119–155.

123

Suwa, H. (2007). A new when-to-schedule policy in online scheduling based on cumulative task delays. International Journal of Production Economics, 110(1), 175–186. doi:10.1016/j.ijpe.2007.02. 015. Tenenbaum, J. B., de Silva, V., & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(22), 2319–2323. Vieira, G. E., Herrmann, J. W., & Lin, E. (2003). Rescheduling manufacturing systems: A framework of strategies, policies, and methods. Journal of Scheduling, 6(1), 39–62. Vieira, G. E., Herrmann, W. J., & Lin, E. (2000). Predicting the performance of rescheduling strategies for parallel machine systems. Journal of Manufacturing Systems, 19(4), 256–266. Wang, S., Xi, L., & Zhou, B. (2008). FBS-enhanced agent-based dynamic scheduling in FMS. Engineering Applications of Artificial Intelligence, 21(4), 644–657. Zhong, R. Y., Li, Z., Pang, L. Y., Pan, Y., Qu, T., & Huang, G. Q. (2013). RFID-enabled real-time advanced planning and scheduling shell for production decision making. International Journal of Computer Integrated Manufacturing, 26(7), 649–662. doi:10. 1080/0951192X.2012.749532. Zhou, G., Zheng, M., & Xiao, Z. (2011). Dynamic job rescheduling using RFID technology. Internet Manufacturing and Services, 3(1), 42–58.