An application of principal component analysis and logistic regression to facilitate production scheduling decision support system: an automotive industry case
 7.4k Downloads
 4 Citations
Abstract
Production planning and control (PPC) systems have to deal with rising complexity and dynamics. The complexity of planning tasks is due to some existing multiple variables and dynamic factors derived from uncertainties surrounding the PPC. Although literatures on exact scheduling algorithms, simulation approaches, and heuristic methods are extensive in production planning, they seem to be inefficient because of daily fluctuations in real factories. Decision support systems can provide productive tools for production planners to offer a feasible and prompt decision in effective and robust production planning. In this paper, we propose a robust decision support tool for detailed production planning based on statistical multivariate method including principal component analysis and logistic regression. The proposed approach has been used in a real case in Iranian automotive industry. In the presence of existing multisource uncertainties, the results of applying the proposed method in the selected case show that the accuracy of daily production planning increases in comparison with the existing method.
Keywords
Principal component analysis Logistic regression Production planning control Decision support systemIntroduction
Effective planning and control of production processes are usually seen as key to the success of a manufacturing company. During the last 50 years, both academic institutes/universities and industries have put great effort into developing and designing successful approaches and methods for manufacturing planning and control. Indeed, the methods and approaches of how to plan and control production have been changed over time. This occurs in line with changes in customer requirements and technology improvements (Vollmann et al. 2005).
Detailed production scheduling is an extremely complex problem (Brucker 2007) wherein most cases are considered NPhard (Günther and van Beek 2003). In order to deal with complexities and uncertainties, a detailed production scheduling system should be equipped with all the necessary decision support tools for rendering production problems visible within a planning period and shift dispatching control from the foremen to the planner (Sotiris et al. 2008). According to SimchiLevi et al. (2008), the decision support system (DSS) is an analytical tool to aid operations and production planning. The DSS can range from simple tools to expert systems. The DSS helps to solve the problems such as network planning to tactical planning all the way to daily operational problems. Thus, the effective DSS can help managers or production planners to manage uncertainties and achieve better results in daily fluctuations.
The stimulus for this work has been to understand whether or not the historical daily shop floor data can be used for creating more robust daily production plan. Moreover, the paper studies the feasibility of using the multivariate statistical analysis of daily shop floor data as an appropriate solver tool for detailed production scheduling decision support system. In order to answer these, we represent an Iranian automotive case of detailed production planning in applied material requirement planning (MRP) system. The results may not be generalized to JIT and lean manufacturing principles which have a pull approach of planning and control of production. The rest of the paper has been organized as follows: in next section, the related literature has been reviewed, whilst the problem has been defined and the selected case has been presented in the ‘Case problem statement’ section. The ‘Methodology of problem analysis’ section has outlined the proposed multivariate DSS as subsequent specifications arising from the ‘Case problem statement’ section. The ‘Proposed multivariate DSS method’ section has demonstrated the implementation results, and finally, in the ‘Conclusions’ section, the conclusions have been drawn and further research efforts have been mapped out.
Literature review
Classification of related literatures
Approach  

Deterministic production planning  Production planning under uncertainties  
Exact methods  Heuristic methods  Simulation  DSS developing  Statistical analysis  Hybrid/combinational methods  
Literatures  Brucker (2007)  Sotiris et al. (2008)  Aytug et al. (2005)  McKay and Wiers (2003)  Mele et al. (2005)  Cunha and Wiendahl (2005) 
Maravelias and Sung (2009)  Jourdan et al. (2009)  Jahangirian et al. (2010)  Sotiris et al. (2008)  Hatzikonstantinou et al. (2012)  Aytug et al. (2005)  
Farrella and Maness (2005)  
Framinan and Ruiz (2010)  Ribas et al. (2010)  Volling and Spengler (2011)  Mok (2009)  Peidroa et al. (2009)  Volling and Spengler (2011)  
Ribas et al. (2010)  Jahangirian et al. (2010)  Rolo and Martinez (2012)  Caricato and Grieco (2009)  Verderame and Floudas (2009)  
Yao et al. (2012)  Ross and Bernardo (2011)  Ko and Wang (2010)  
<This paper>  
Comments  Seldom applicable in actual shop floors since they may only solve smallscale problems with distinct parameters and scale of time  Simulation needs a great deal of efforts to make a practical schedule by some expert and expensive production planners  DSS tools are concerned with complementary applications to ERP/MRP software. They are practical with lack of ERP system  Statistical and hybrid methods are useful to control uncertainties in real condition and improve the effectiveness of both evaluation and decision making; however, they are not independent and complete tools. They have to be designed for each case problem 
In the case of unconditional analytic models, we are referring to models which are simplifications of a real system in terms of mathematical expressions and can be solved by exact or heuristic methods. The literature on the exact algorithms in scheduling and production planning problems is extensive. A thorough review of scheduling problems, modeling approaches, and solution methods can be found in Brucker (2007), Framinan and Ruiz (2010), and Ribas et al. (2010). Whereas fluctuations and uncertainties have key roles in real world, deterministic, or exact approaches, such that branch and bound (Yao et al. 2012) and mixed integer linear programming (Maravelias and Sung 2009) are seldom applicable in actual shop floors since they may only solve smallscale problems with distinct parameters and scale of time.
Several heuristics and hybrid methods are recommended in the literature (Jourdan et al. 2009). Ribas et al. (2010) have classified the approximate methods into constructive and improvement heuristics. However, the application of heuristic algorithms is believed to be more applicable for real shop floors due to their lower computations, but they are still limited by the dimension of problems and uncertainties. Therefore, their implementation should be coupled with some decision support tools to aid the production planners (Ross and Bernardo 2011; Sotiris et al. 2008).
To cope with uncertainties in production control, it is worth to investigate a new customized framework for planning and scheduling under uncertainty. Another challenging issue is to investigate the ways of controlling a large number of uncertain parameters. Hence, scheduling under uncertainty has received a lot of attention in recent years (e.g., Hatzikonstantinou et al. 2012; Vargas and Metters 2011; Torabi et al. 2010; Verderame and Floudas 2009). Uncertainty can be derived from many aspects, such as demand or product orders, alternation or priority of orders, equipment failures, resource changes, and processing time variability. To adapt uncertainties during the manufacturing process, the proposed methods are divided into two main groups: reactive scheduling and preventive scheduling (Aytug et al. 2005). Simulation approach is able to analyze the behavior of the environment when it is characterized by several constraints and uncertainties (Rolo and Martinez 2012; Volling and Spengler 2011; Jahangirian et al. 2010). In these approaches, the outcomes of the simulation software can be used in preventive scheduling and decision support systems, but they need a great deal of efforts to make a practical schedule by some expert production planners.
By the emersion of enterprise resource planning (ERP) systems, the utilization of data becomes more important in production planning and control (PPC). The incredible wealth of available data in SCM and PPC software raises the question of how to help decision makers in harnessing the organization. The answer to this question has defined the production activity control (PAC) subsystem at the lowest level of MRPII (Vollmann et al. 2005). By means of the PAC system, the sequence of the orders is defined with their release and due times. In fact, PAC cannot take into account the real state of the production environment, and it may produce unrealistic or impractical production plan.
Whereas the MRPbased system cannot follow the large number of shop floor fluctuations, production managers bow to the inevitable complex task of scheduling/rescheduling at the shop floor control. Poor production control may cause serious problems to a firm's ability to meet production requirements and constraints. Many researches have focused on developing DSS tools to face this problem (e.g., Ko and Wang 2010; Caricato and Grieco 2009; Mok 2009; Farrella and Maness 2005; McKay and Wiers 2003). These tools are concerned as complementary applications to the ERP/MRP software.
Unfortunately, few success stories have been reported on creating production planning and logistics in a real factory, and there are still many challenges that remain (McKay and Black 2007). In the absence of one sole issue for PPS success or failure (McKay and Wiers 20032004), one potential issue related to the failure of a planning system is the lack of information system and DSS tools for detailed production planning. This was the first insight obtained from this case study (see Table 1).
Meanwhile, combination use of statistical analysis with other methods to control the uncertainties in real condition decision making has been proposed by some literatures (Mele et al. 2005). Cunha and Wiendahl (2005) have proposed an evaluation method based on the use of multivariate techniques: principal component analysis (PCA) and cluster analysis (CA) to improve the effectiveness of evaluation and decision making, monitoring and manufacturing control. The idea of using multivariate statistical analysis to develop existing DSS is the second and major contribution of this study. The proposed method in this paper is based on the use of multivariate techniques on shop floor data. We intend to improve the effectiveness of the decisionmaking tasks undertaken when dealing with detailed production plans in an uncertain condition.
Case problem statement
The case study of detailed production planning has been done in an Iranian automotive manufacturing company. SAIPA Corporation (Tehran, Iran) is a holding company that assembles several types of passenger cars, vans, minibuses, buses, and trucks. As with any other car manufacturing company, the production process followed has a high degree of complexity, coupling the complex bill of materials (BOMs) with equally complex routings that transgress the shop floor boundaries.
The main problem of the selected case has been inferred from logistics staff answers to a set of questions and interviews. It is reported that the accuracy of daily production plans is directly affected by some alternate constraints and probable parameters. Hence, either the rescheduling or planning diversity and related extra material handling or extra/shortage parts and production line stop are enviable tasks every day. By their complaint about the alternate decisions to manage stochastic or abnormal events, we have made inferences about the lack of DSS tools to provide a practical detailed production planning.
Methodology of problem analysis
The following three aspects of the problem have been specified in the analysis of the current situation:

Layout and physical constraint. It focuses on the production flow and is concerned with constraints of layout and any physical limitation in the production lines.

Production planning and control system. It is concerned with the daily activities of the production planners during their detailed production planning in the shop floor control process. Shop floor data in a multi period range was gathered from this aspect of analysis.

Uncertainties and stochastic factors. It is concerned with the source of uncertainties and stochastic factors.
To investigate the mentioned aspects, a mixture of interviews and observation has been applied. The major part of observation and a small part of the meetings were concerned with information about the production process and the production planning control.
In the following two subsections, the basic results concerning the first two aspects of the case problem analysis have been presented. These results are normally used to design the system architecture and functionality as well as the shop floor model of the plant. The results of the third aspect, namely uncertainties, are used to construct a multivariate analysis tool of simplified real production.
Layout and physical constraints
A trim shop is located at the end of the production process. Therefore, it has the highest level of complexity in comparison with subsequent production activity control processes. The main assembly production line is equipped with a conveyor. According to production rate and types of products (seven types), the length of production line is not quite enough for assigning individual locations to keep the minimum stock level of all parts according to the type of product BOM. The logistic area is not available near the line far distance from the main warehouses; thus, the order of completion lead time is long and is influenced by probable accidents.
There is a painted body (PB) stock at the end of the paint shop process. The stock of PB is the same as a single line queue before the entrance of the trim shop, and each PB can be transferred to the trim shop by the sequence of its location. Incapability of selecting the desired PB from the PB stock constrains the production planner to make a daily plan according to the PB color and type sequence. Although the elimination of the layout and physical constraints have been investigated in recent years, due to outstanding required cost and time, the progress of development is not noticeable.
Production planning and control system
Although KANBAN cards and pull production control system have been tried to be applied by production planning and the logistic department, the production control system is still MRPbased. A hierarchical twolevel planning framework is used prior to the detailed production scheduling. At the top level, aggregate production planning which controls demand management with a yearly time horizon, has been located. The second planning level which is called midterm planning incorporates a hybrid MRPPBC approach.
PPC suffers from several sources of inconsistencies as a consequence of incomplete ERP implementation. As a result of its complex production process and lack of information technology (IT) infrastructure, the presented case study during the last few years faced numerous problems concerning violated due dates, accumulated late orders, supernumerary production orders, excessive component inventory, poor releasing policies, and low shop floor visibility. The lack of online and integrated information may cause a misunderstanding of the real condition; thus, the production planner faces some unknown parameters in daily scheduling. In this situation, it is not weird if the daily schedule encounters some mistakes. Although the design and implementation of the ERP software is in progress, production planners cannot wait and do not get along with increasing complexity. They really need some practical tools to help them in perfect decision making.
Uncertainties and stochastic factors
Since there are some lineside space constraints, mixed production suffers from lots of problems and obstacles and forces managers to act on the basis of batch production. Meanwhile, there are many sources of stochastic events and uncertainties that batch production such as demand, process, and supply uncertainties (Peidroa et al. 2009). One of the main sources of stochastic factors that have been identified in this study is derived from the paint shop process and PB stock constraint. Due to some small defects on bodies, some of the PBs are selected to go into a touchup area, and after doing all necessary reworks, they are transferred to the PB stock line. Almost all of the procedures in the defect inspection process are performed manually through human vision and influenced by stochastic factors. On the other hand, the required rework process times depend on the type and the level of defects which are not really exact and deterministic. Hence, the sequence of painted bodies in the queue of stock line cannot be absolutely defined. Meanwhile, supply uncertainties have a key role in unreliability of the production schedule. Each type of products has special parts which are from different suppliers. The availability of all special parts related to the desired type of products is the other vital information for the production planner to make the daily production schedule. According to our observation, the stock levels of these items are not expected to follow exact patterns.
Proposed multivariate DSS method
The complexity of production planning and control process, stochastic factors, physical constraint, uncertainties, and the shortcomings of the underlying IT infrastructure would pose significant drawbacks to the current detailed production scheduling. In this light, to the aforementioned production planning process and fully interoperable, both with the PPC system and existing software package, the proposed approach has been developed on the basis of a custombuilt DSS using statistical multivariate techniques.
Shop floor and production plan historical data acquisition
The manner and logical behavior of the production planner to create a weekly plan or change daily detailed scheduling is an important factor through the practical decisionmaking process which can be used for finding an effective DSS tool. As answer to the main question of this research, the objective has been to find the statistical analysis appropriate for reducing this logical behavior. Hence, it has been required to collect daily shop floor data and historical data of the daily schedule issued by the production planner. The historical data of PB stock, existing PB quantity, and PB types in paint shop, sale online requests, inventory data, MRP weekly plan, released daily production schedule, and related orders with actual production were the main fields of data that have been collected for this analysis.
Reduction of inventory data by PCA
In this study, the collected inventory data sets (warehouse and line side separately) have at least 40 fields related to each types of products. This high volume and dimension of data matrix increase the complexity of analysis. If a substantial amount of the total variance in these data is accounted for by a few (preferably far fewer) principal components or new variables, then these few principal components can be used for interpretational purposes or in further analysis of the data instead of the original variables. PCA can be viewed as a dimensional reduction technique (Sharma 1996), and it is the appropriate technique for achieving the mentioned objective.
where principal component (PC) = {ξ_{1}… ξ_{ m }} are the m principal components and w_{ ij } is the weight of the j th variable for the i th principal component.
The reduction in complexity is achieved by performing PCA on collected inventory data. Thus, the original data of inventory can be substituted by PCs, and the new matching table of the shop floor data and corresponding production schedule is established as a contingency table.
Logistic regression model fitting, validation, and review to improvement
The fundamental question in this research motivated us to understand the logical behavior of the production planner in the decisionmaking process through daily production scheduling. As illustrated in Figure 2, the historical input/output of the decision process is analyzed and the relationship among them is discovered by logistic regression. In the remainder of this section, we briefly discuss about the basic concept and details of developing the logistic regression model and, finally, the validation procedure and review method for the improvement of this model.
Definition of variables
Description of variables
Variable  Description  Code/values 

TYP  Compressed natural gas equipped  CNG 
CNG and hydraulic steering wheel  CNGH  
Hydraulic steering wheel  HYD  
SABA simple injection system  GLXi  
Reinforced new body  X132  
Morvarid hatchback  DM  
Other new models  NEW  
CLR  Color production plan  W = white 
G = gray  
B = black  
R = red  
S = silver  
PBS  Painted body stock  0400 
SEQ  Compatibility of PB sequence  1 = Low compatibility 
2 = Fair compatibility  
3 = Good compatibility  
4 = High compatibility  
INV1  Warehouse and lineside inventory PC 1  0 to 2,000 
INV2  Warehouse and lineside inventory PC 2  0 to 1,000 
SRT  Scheduled receipt  0 to 1,000 
ACP  Available colored parts  0 to 1,000 
RWP  Remainder quantity of weekly plan  0 to 5,000 
ESD  Emergency sales/demand  1 = Critical 
2 = Urgent  
3 = Normal  
4 = Nonemergency  
ADP  Actual daily product  0 to 1,100 
DPP  Daily production plan  0 to 1,100 
DPC  Daily production plan capability  0 = No 
1 = Yes 
Basic theory on logistic regression
where $\phantom{\rule{0.25em}{0ex}}\left(\frac{p}{1p}\right)\phantom{\rule{0.25em}{0ex}}$ is the odds.
To find out how effective the model expressed in Equation 3 is, the statistical significance of individual regression coefficients is tested using the Wald chisquare statistic. Goodnessoffit test assesses the fitness of a logistic model against actual outcomes. HosmerLemeshow test is an inferential goodnessoffit test which is utilized in this paper. Meanwhile, the consequent predicted probabilities can be revalidated with the actual outcome to determine if high probabilities are indeed associated with events and low probabilities with nonevents. The readers are referred to Bewick et al. (2005) and Hosmer and Lemeshow (2000) for more information about the assessment of fitted model.
Predicting capability of daily production planning
Customized DSS to facilitate detailed production scheduling
The proposed multivariate method contributes in the DSS module which is denoted in Figure 3 in the dashed box. As we have described in the previous sections, the online shop floor data is used by this customized DSS tool and the predicted amount of DPC index is calculated. This production planning capability index can facilitate the decisionmaking process of detailed scheduling. The production planner can typically run this customized DSS at the beginning of each planning period (commonly one working day), and after making the decision about final changes on the detailed schedule, data of production order is extracted. When detailed scheduling is finalized, the production orders are handed down to the foremen for beginning of production. If dynamic events take place (e.g., a machine breaks down, a rush order arrives, or a subcontractor violates due dates), the planner reschedules to accommodate them.
Numerical experiment and results
Sample data format of warehouse and lineside inventory levels
Date  TYP  ENGN  AXLE  PIPE  CONT  BODY  DASH  ECUT  STWL  EXST  TRIM  WIRE  SNSR  DMPR  CNGK  HYDK  SUB 

09/01  CNG  138  154  129  102  158  96  404  251  157  259  250  451  253  320    306 
09/01  DM  63  66  67    94  41  80  83  46  91  42  88  93    49  73 
09/01  GLXi  189  159  156    150  103  153    123  229  266  157  126      100 
09/01  HYD  46  60  72    104  48  117  98  69  108  185  205  170    27  139 
09/01  NEW  27  112  122    180  43  174    119  164  185  285  219      142 
09/01  X132  127  310  128    137  246  256  220  181  250  255  263  268    267  302 
09/02  CNG  106  153  129  95  152  96  403  250  154  259  259  457  255  300    314 
09/02  CNGH  65  62  65  57  75  50  124  126  156  81  167  182  130  236  219  110 
09/02  DM  63  64  64    139  39  73  81  52  176  49  87  85    91  77 
09/02  GLXi  171  151  159    155  102  158    129  266  253  155  126      104 
09/02  NEW  23  117  124    184  53  168    124  163  182  285  222      142 
09/02  X132  120  243  121    139  246  255  223  181  258  259  266  268    271  300 
According to the data reduction method described in the ‘Reduction of inventory data by PCA’ section, the following PC scores can be derived by applying PCA. In this study, the result of PCA shows that the first two principal component variables account for about 90% of the total variance of data, and the screen plot shows that the appropriate number of PCs is two. Using these PCA scores, the PC formulas are defined, and then the amount of PCs by the exact amount of each variable every morning can be calculated.
SFC table data format: input of LR analysis
Week  Working day  TYP  PCs  Daily plan  PBS  SEQ  SRT  ACP  RWP  ESD  ADP  DPC  

INV1  INV2  CLR  DPP  
1  1  CNG  316  166  W  450  180  3  400  385  968  3  446  1 
1  DM  157  44  R  50  50  4  100  86  300  1  51  1  
1  GLXi  127  255  S  100  80  4  100  85  500  3  98  1  
1  HYD  171  36  G  100  80  3  100  65  200  3  105  1  
1  NEW  79  195  S  150  100  1  100  0  430  4  131  0  
1  X132  417  192  W  250  200  2  300  85  1,400  4  212  0  
1  2  CNG  293  136  B  200  50  1  100  20  522  2  154  0 
2  CNGH  208  67  S  150  100  2  150  150  350  3  132  0  
2  DM  253  56  B  250  131  3  130  100  252  3  248  1  
2  GLXi  185  262  W  150  100  4  100  100  395  4  153  1  
2  NEW  66  195  W  100  55  3  100  83  330  4  82  0  
2  X132  409  199  G  250  250  4  400  186  1,105  2  253  1  
↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓ 
↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓  ↓ 
Goodnessoffit tests
Test  df  P value  

All slopes are zero (G)  230.037  23  0.000 
Pearson (χ^{2})  514.679  584  0.982 
Deviance (χ^{2})  631.625  584  0.947 
HosmerLemeshow (χ^{2})  3. 474  8  0.901 
In this study, there is insufficient evidence to claim that the LR model does not fit the data adequately because the P values for all tests are larger than the significance level of 0.05. Therefore, the LR model shown in Equation 5 is appropriate in explaining the DPC prediction.
Measures of association
Pairs  Number  Percent  Summary measures  P value 

Concordant  67,781  84.6  Somers' D  0.69 
Discordant ties  12,163  15.2  GoodmanKruskal's gamma  0.70 
151  0.2  Kendall’s taua  0.30  
Total  80,095  100 
The accuracy of the proposed method
The comparison of DSS method accuracy
Applied methods  Total observations  Actual daily production capability  Predicted daily production capability  Daily planning accuracy (%)  

DPC = 1  DPC = 0  DPC = 1  DPC = 0  Error  
Instance 1  Classic DSS method  124  81  43  124  0  43  65 
Revised proposed method  124  117  7  7  94  
Instance 2  Classic DSS method  136  88  48  136  0  48  65 
Revised proposed method  136  127  9  9  93  
Instance 3  Classic DSS method  110  81  32  110  0  32  74 
Revised proposed method  110  105  5  5  95  
Instance 4  Classic DSS method  116  93  23  116  0  23  80 
Revised proposed method  116  109  7  7  94  
Instance 5  Classic DSS method  84  62  22  64  0  25  74 
Revised proposed method  84  76  8  8  90  
Instance 6  Classic DSS method  64  39  25  64  0  25  61 
Revised proposed method  64  55  9  9  86  
Instance 7  Classic DSS method  88  75  13  88  0  13  74 
Revised proposed method  88  86  2  2  98  
Instance 8  Classic DSS method  101  66  35  101  0  66  74 
Revised proposed method  101  95  6  6  94  
Instance 9  Classic DSS method  76  33  43  76  0  43  43 
Revised proposed method  76  69  7  7  91  
Instance 10  Classic DSS method  121  80  41  121  0  41  66 
Revised proposed method  121  120  1  1  99 
From the perspective of daily planning accuracy, the logistic regression model correctly identified 109 of 124 observations (refer to instance 1). The accuracy of each method can be simply calculated by dividing the number of observed actual productions, which are respondents of production plans (DPC = 1), to the total number of production plans. As shown in Table 7, by the proposed DSS method, more reliable detailed production plans can be submitted than by the classic method.
Conclusions
This study presents an application of statistical multivariate method together with the solver module in production activity control of an Iranian automotive manufacturer and introduces a revised decision support system which can provide a productive tool for knowledge workers to offer more reliable detailed production plans.
The proposed method is based on the use of principal component analysis to reduce the extensive dimension of shop floor data and logistic regression analysis to make a predictive tool and precheck of daily production plan capability to improve the effectiveness of decision making. In this case study, it is shown that the revised DSS works more reliably and more accurately.
For future studies, either prediction accuracy or data reduction techniques may be improved by applying other specialized models of logistic regression. Manufacturers can also further adjust the proposed prediction models to accord with their production environments and data availability.
Authors’ information
SM is a PhD student at Payme Noor University. MB is an associate professor at Shahed University.
Notes
Acknowledgments
The authors would like to thank the Logistic and Industrial Engineering department and Production Logistics department of SAIPA Company for supporting this case study in data acquisition and serious cooperation.
Supplementary material
References
 1.Aguilera AM, Escabias M, Valderrama MJ: Using principal components for estimating logistic regression with highdimensional multi collinear data. Computational Statistics & Data Analysis 2006, 50: 1905–1924. 10.1016/j.csda.2005.03.011MathSciNetCrossRefGoogle Scholar
 2.Aytug H, Lawley MA, McKay K, Mohan S, Uzsoy R: Executing production schedules in the face of uncertainties: a review and some future directions. European Journal of Operational Research 2005,161(1):86–110. 10.1016/j.ejor.2003.08.027MathSciNetCrossRefGoogle Scholar
 3.Bewick V, Cheek L, Ball J: Statistics review 14: logistic regression. Critical Care 2005,9(1):112–118. 10.1186/cc3045CrossRefGoogle Scholar
 4.Brucker P: Production control: a universal conceptual framework. Production Planning and Control 2007,1(1):3–16.Google Scholar
 5.Caricato P, Grieco A: A DSS for production planning focused on customer service and technological aspects. Robotics and ComputerIntegrated Manufacturing 2009, 25: 871–878. 10.1016/j.rcim.2009.06.003CrossRefGoogle Scholar
 6.Maravelias CT, Sung C: Integration of production planning and scheduling: overview challenges and opportunities. Computers Chemical Engineering 2009, 33: 1919–1930. 10.1016/j.compchemeng.2009.06.007CrossRefGoogle Scholar
 7.Cunha PF, Wiendahl HP: Knowledge acquisition from assembly operational data using principal components analysis and cluster analysis. CIRP Annals  Manufacturing Technology 2005,54(1):27–30. 10.1016/S00078506(07)600420CrossRefGoogle Scholar
 8.Farrella RR, Maness TC: A relational database approach to a linear programmingbased decision support system for production planning in secondary wood product manufacturing. Decision Support Systems 2005, 40: 183–196. 10.1016/j.dss.2004.02.001CrossRefGoogle Scholar
 9.Framinan JM, Ruiz R: Architecture of manufacturing scheduling systems: literature review and an integrated proposal. European Journal of Operational Research 2010, 205: 237–246. 10.1016/j.ejor.2009.09.026MathSciNetCrossRefGoogle Scholar
 10.Günther HO, Beek P van (Eds): Advanced planning and scheduling solutions in process industry. Springer, Berlin; 2003.Google Scholar
 11.Hatzikonstantinou O, Athanasiou E, Pandelis DG: Realtime production scheduling in a multigrade PET resin plant under demand uncertainty. Computers and Chemical Engineering 2012, 40: 191–201.CrossRefGoogle Scholar
 12.Hosmer DW, Lemeshow S: Applied Logistic Regression. 2nd edition. John Wiley & Sons, New York; 2000.CrossRefGoogle Scholar
 13.Jahangirian M, Eldabi T, Naseer A, Stergioulas LK, Young T: Simulation in manufacturing and business: a review. European Journal of Operational Research 2010, 203: 1–13. 10.1016/j.ejor.2009.06.004CrossRefGoogle Scholar
 14.Jolliffe IT: Principal component analysis. 2nd edition. Springer Series in Statistics, Springer Verlag, New York; 2002.Google Scholar
 15.Jourdan L, Basseur M, Talbi E: Hybridizing exact methods and metaheuristics: a taxonomy. European Journal of Operational Research 2009,199(3):620–629. 10.1016/j.ejor.2007.07.035MathSciNetCrossRefGoogle Scholar
 16.Ko CH, Wang SF: GAbased decision support systems for precast production planning. Automation in Construction 2010,19(7):907–916. 10.1016/j.autcon.2010.06.004CrossRefGoogle Scholar
 17.McKay KN, Black GW: The evolution of a production planning system: a 10year case study. Computers in Industry 2007, 58: 756–771. 10.1016/j.compind.2007.02.002CrossRefGoogle Scholar
 18.McKay KN, Wiers VCS: Integrated decision support for planning scheduling and dispatching tasks in a focused factory. Computers in Industry 2003,50(1):5–14. 10.1016/S01663615(02)00146XCrossRefGoogle Scholar
 19.McKay KN, Wiers VCS: Practical production control: a survival guide for planners and schedulers. J Ross Publishers, Boca Raton; 2004.Google Scholar
 20.Mele FD, Musulin E, Puigjaner L: Supply chain monitoring: a statistical approach. Computer Aided Chemical Engineering 2005, 20: 1375–1380.CrossRefGoogle Scholar
 21.Mok PY: A decision support system for the production control of a semiconductor packaging assembly line. Expert Systems with Applications 2009, 36: 4423–4424. 10.1016/j.eswa.2008.05.021CrossRefGoogle Scholar
 22.Peidroa D, Mulaa J, Polera R, Verdegay JL: Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets and Systems 2009, 160: 2640–2657. 10.1016/j.fss.2009.02.021MathSciNetCrossRefGoogle Scholar
 23.Ribas I, Leisten R, Framin JM: Review and classification of hybrid flowshop scheduling problems from a production system and a solutions procedure perspective. Computers & Operations Research 2010, 37: 1439–1454. 10.1016/j.cor.2009.11.001MathSciNetCrossRefGoogle Scholar
 24.Rolo M, Martinez E: Agentbased modeling and simulation of an autonomic manufacturing execution system. Computers in Industry 2012, 63: 53–78. 10.1016/j.compind.2011.10.005CrossRefGoogle Scholar
 25.Ross JW, Bernardo AL: Single and parallel machine capacitated lotsizing and scheduling: new iterative MIPbased neighborhood search heuristics. Computers & Operations Research 2011,38(12):1816–1825. 10.1016/j.cor.2011.02.005CrossRefGoogle Scholar
 26.Sharma S: Applied Multivariate Techniques. John Wiley & Sons, New York; 1996.Google Scholar
 27.SimchiLevi D, Kaminsky P, SimchiLevi E: Designing and managing the supply chain: concepts, strategies and case studies. 3rd edition. McGrawHill/Irwin, Boston; 2008.Google Scholar
 28.Sotiris G, Athanasios S, Ilias T: A decision support system for detailed production scheduling in a Greek metal forming industry. MIBES Transactions 2008,2(1):41–59.Google Scholar
 29.Torabi SA, Ebadian M, Tanha R: Fuzzy hierarchical production planning (with a case study). Fuzzy Sets and Systems 2010,161(11):1511–1529. 10.1016/j.fss.2009.11.006MathSciNetCrossRefGoogle Scholar
 30.Vargas V, Metters R: A master production scheduling procedure for stochastic demand and rolling planning horizons. Int J Production, Economics 2011, 132: 296–302. 10.1016/j.ijpe.2011.04.025CrossRefGoogle Scholar
 31.Verderame PM, Floudas CA: Integrated operational planning and scheduling under uncertainty. Computer Aided Chemical Engineering 2009, 26: 381–386.CrossRefGoogle Scholar
 32.Volling T, Spengler TS: Modeling and simulation of orderdriven planning policies in buildtoorder automobile production. International Journal of Production Economics 2011,131(1):183–193. 10.1016/j.ijpe.2011.01.008CrossRefGoogle Scholar
 33.Vollmann ET, Berry WL, Whybark CP, Jacobs CP: Manufacturing planning and control for supply chain management. 5th edition. McGrawHill Education, Singapore; 2005.Google Scholar
 34.Yao S, Jiang Z, Li N: A branch and bound algorithm for minimizing total completion time on a single batch machine with incompatible job families and dynamic arrivals. Computers & Operations 2012,39(5):939–951. 10.1016/j.cor.2011.06.003MathSciNetCrossRefGoogle Scholar
Copyright information
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.