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An application of principal component analysis and logistic regression to facilitate production scheduling decision support system: an automotive industry case

  • Saeed Mehrjoo
  • Mahdi Bashiri
Open Access
Original research

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 system 

Introduction

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 NP-hard (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 Simchi-Levi 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

The production planning control models can be characterized in a variety of approaches, but most common categorizations are specific to the application areas (Brucker 2007). In this article, we have classified the production planning problem solving approaches in two groups in terms of their environment and condition: unconditional/deterministic analytic production planning and production planning under uncertainties (see Table 1).
Table 1

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 small-scale 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

DSS, decision support system; MRP, material requirement planning; ERP, enterprise resource planning.

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 small-scale 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 MRP-based 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 decision-making 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 MRP-based. A hierarchical two-level 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 MRP-PBC approach.

Master production schedule (MPS) outcomes are used to calculate components and material requirements. The final plan is made by revision on a weekly basis using the feedback from the detailed scheduling module. The weekly plan is released by PAC, and detailed production planning is issued as the daily schedule. The daily schedule is derived from a complicated decision-making process which uses shop floor data, inventory status data, BOM, and sequence of PB in stock. Figure 1 demonstrates this process.
Figure 1

The current MRP-based PPC process.

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 line-side 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 touch-up 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 custom-built DSS using statistical multivariate techniques.

The integrated approach that will be presented introduces facilities to analyze data which are directly unavailable from the current planning system. This approach is introduced through the use of PCA to decrease the dimension of input-independent variables (Aguilera et al. 2006) and the use of logistic regression (LR) to predict the first priority of available and suitable type of product which can be selected to make a practical and effective detailed production schedule. These are used at different steps as shown in Figure 2.
Figure 2

Process of establishing a multivariate statistical tool for DSS development.

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 decision-making 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.

The core idea of PCA is to reduce the dimensionality of a data set comprising a large number of interrelated variables while retaining as much as possible the data set variance (Jolliffe 2002). This is obtained by transforming original variables to a new set of variables or principal components (ξ i ) which are a linear combination of original (p) variables. Due to their properties, they are uncorrelated and are ordered such that the first (mp) that are retained contain most of the variation presented in the original data:
PC = ξ 1 ξ m ; ξ i = w i 1 x 1 + w i 2 x 2 + + w ip x p , Open image in new window

where principal component (PC) = {ξ1ξ 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 decision-making 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

To simplify the discussion and interpretation of estimation model, the notation is introduced and variables are defined which can be recognized from collected data. Table 2 shows a code sheet for definition of preliminary selected variables from collected data.
Table 2

Description of variables

Variable

Description

Code/values

TYP

Compressed natural gas equipped

CNG

CNG and hydraulic steering wheel

CNG-H

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

0-400

SEQ

Compatibility of PB sequence

1 = Low compatibility

2 = Fair compatibility

3 = Good compatibility

4 = High compatibility

INV1

Warehouse and line-side inventory PC 1

0 to 2,000

INV2

Warehouse and line-side 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 = Non-emergency

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

There are two models of logistic regression to contain binomial/binary logistic regression and multinomial logistic regression. Binary logistic regression is typically utilized when the dependent variable is dichotomous and the independent variables are either categorical or continuous variables (Sharma 1996). Logistic regression is the best to use in this condition. The result of this type of regression can be expressed by a logit function as follows:
logit p = Ln p 1 - p = β 0 + β 1 x 1 + β 2 x 2 + + β k x k = β 0 + X β , Open image in new window
(1)

where p 1 - p Open image in new window is the odds.

The model can either be interpreted using the logit scale, or the log of odds (the relative probability) can be converted back to the probability such that
p = exp β 0 + XB 1 + exp β 0 + XB Open image in new window
(2)
In order to calculate the parameters β0, β1, β2,…, β k , the logistic regression transforms the dependent into a logit variable and then uses maximum likelihood estimation. In this paper, logistic regression is used to estimate the daily production planning capability (DPC) from the shop floor data. According to the variables summarized in Table 2, the logit can be defined for this case as follows:
logit = β 0 + β 1 TYP 1 + β 2 TYP 2 + β 3 TYP 3 + β 4 TYP 4 + β 5 TYP 5 + β 6 TYP 6 + β 7 INV 1 + β 8 INV 2 + β 9 CLR 1 + β 10 CLR 2 + β 11 CLR 2 + β 12 CLR 3 + β 13 CLR 4 + β 14 DPP + β 15 PBS + β 16 SEQ 1 + β 17 SEQ 2 + β 18 SEQ ( 3 ) β 19 SRT + β 20 ACP β 21 RWP β 22 ESD ( 1 ) + β 23 ESD ( 2 ) β 24 * ESD ( 3 ) . Open image in new window
(3)

To find out how effective the model expressed in Equation 3 is, the statistical significance of individual regression coefficients is tested using the Wald chi-square statistic. Goodness-of-fit test assesses the fitness of a logistic model against actual outcomes. Hosmer-Lemeshow test is an inferential goodness-of-fit 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 non-events. 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

The fitted model, which has successfully passed the goodness-of-fit tests, can be used to calculate the predicted Logit (probability) of DPC for a given value of shop floor data. For example, assume that at the end of the working day, the production planner wants to make a decision about tomorrow's production plan and would like to predict the capability of a given production schedule. At first, using the PCA method (‘Reduction of inventory data by PCA’ section), the inventory level of line-side and related warehouses can be estimated by two principal components (INV1 and INV2), and then, according to the shop floor data, the amount of other independent variables (TYP, PBS, RWP, ESD, and DPP) are defined. Therefore, the probably of response variable (DPC) can be calculated by Equation 4:
p = e β 0 + β 1 TYP 1 + β 2 TYP ( 2 ) + β 3 TYP ( 3 ) + β 4 TYP ( 4 ) + β 5 TYP ( 5 ) + β 6 TYP ( 6 ) + β 7 INV 1 + β 8 INV 2 + β 9 CLR ( 1 ) + β 10 CLR ( 2 ) + β 11 CLR ( 3 ) + β 12 CLR 4 + β 13 DPP + β 14 PBS + β 15 SEQ ( 1 ) + β 16 SEQ ( 2 ) + β 17 SEQ ( 3 ) + β 18 SRT + β 19 ACP + β 20 RWP + β 21 ESD ( 1 ) + β 22 ESD ( 2 ) + β 23 ESD ( 3 ) 1 + e β 0 + β 1 TYP 1 + β 2 TYP ( 2 ) + β 3 TYP ( 3 ) + β 4 TYP ( 4 ) + β 5 TYP ( 5 ) + β 6 TYP ( 6 ) + β 7 INV 1 + β 8 INV 2 + β 9 CLR ( 1 ) + β 10 CLR ( 2 ) + β 11 CLR ( 3 ) + β 12 CLR 4 + β 13 DPP + β 14 PBS + β 15 SEQ ( 1 ) + β 16 SEQ ( 2 ) + β 17 SEQ ( 3 ) + β 18 SRT + β 19 ACP + β 20 RWP + β 21 ESD ( 1 ) + β 22 ESD ( 2 ) + β 23 ESD ( 3 ) , Open image in new window
(4)
or
p = exp l ogit 1 + exp l ogit . Open image in new window

Customized DSS to facilitate detailed production scheduling

Predicting the capability of daily production planning facilitates the decision making of the PPC system, and as a result, the customized DSS can be defined and applied. The new hierarchical planning framework is depicted in Figure 3. The main procedural sequence does not exhibit any remarkable change in comparison with the current PPC process (Figure 1). The MPS calculates long-term end item needs and feeds the PPC system which creates the production order backlog according to MRP procedures. The weekly production plans are issued by the MRP module and feeds detailed scheduling.
Figure 3

Role of the proposed method in the production planning control framework.

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 decision-making 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

According to the defined variables, the 42-week shop floor and inventory data have been collected. Every day, the line-side inventory level of special and important parts as well as warehouse inventory level have been recorded. Table 3 illustrates the sample data which were recorded on the first and second days in the warehouse. Data were collected over a period of 8 months and included PB stock, sale online requests, inventory data, MRP weekly plan, inventory status data schedule, and actual production.
Table 3

Sample data format of warehouse and line-side 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

CNG-H

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

ENGN engine; AXLE, rear axle; PIPE, fuel pipe set; CONT, compressed net gas container; BODY, special parts of body; DASH, dashboard or instrument panel; ECUT, electronic central unit; STWL, steering wheel; EXST, exhaust; TRIM, trim parts; WIRE, wiring set; SNSR, sensors set; DMPR, dampers set; SNGK, compressed net gas kit; HYDK, hydraulic kit; SUB, sub assembly required parts.

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.

By the results of data reduction, we can make a new shop floor control (SFC) data which can be used for calculating logit more easily and practically. Table 4 shows the sample format of SFC data table which must be created for logistic regression analysis. Using Equation 4, the probable response variable (DPC) can be calculated by the coefficients derived from logistic regression analysis.
logit = 0.93153 - 0.39432 TYP 1 - 0.56284 TYP ( 2 ) - 0.7653 TYP ( 3 ) - 0.56226 TYP ( 4 ) - 2.28933 TYP ( 5 ) - 1.43129 TYP 6 - 0.00502 INV 1 - 0.00157 INV 2 + 0.21325 CLR ( 1 ) + 0.29959 CLR ( 2 ) - 1.13775 CLR ( 3 ) - 0.44392 CLR 4 + 0.01631 DPP - 0.00162 PBS + 0.2752 SEQ ( 1 ) + 0.23753 SEQ ( 2 ) + 0.20142 * SEQ ( 3 ) - 0.00016 SRT + 0.00042 ACP - 0.00047 RWP - 0.01292 ESD 1 + 0.48281 ESD ( 2 ) - 0.02589 ESD ( 3 ) Open image in new window
p = exp l ogit 1 + exp l ogit . Open image in new window
(5)
Table 4

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

CNG-H

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

Table 5 summarizes the test results of null hypothesis in which all the coefficients associated with predictors equal 0. The test statistic G = 230.037 with a p-value of 0.000 implies that there is at least one estimated coefficient that is different from 0. The results of Pearson, deviance, and Hosmer-Lemeshow goodness-of-fit tests have been also summarized in Table 5.
Table 5

Goodness-of-fit tests

Test

 

df

P value

All slopes are zero (G)

230.037

23

0.000

Pearson (χ2)

514.679

584

0.982

Deviance (χ2)

631.625

584

0.947

Hosmer-Lemeshow (χ2)

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.

The association between the response variable and predicted probabilities has been evaluated by some measures such as Somers' D, Goodman-Kruskal's gamma, and Kendall's tau-a in our case; the summary of results is listed in Table 6. The measures indicate that there is a close correspondence between DPC and its predicted probabilities.
Table 6

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

Goodman-Kruskal's gamma

0.70

151

0.2

Kendall’s tau-a

0.30

Total

80,095

100

  

The accuracy of the proposed method

Utilizing the discussed PCA and LR model, 42 working weeks of shop floor data (including 1,256 records) were used to evaluate its prediction quality. In addition to real data, Monte Carlo-based simulated data were generated to extend our samples to 100 weeks. The simulation was run under a variety of conditions such as production line, seasonal demand, and probable disruption in production line. Every 4 weeks (1 month), the outcomes of classical detailed planning were compared with the corresponding outcomes of the proposed method. These results have been reported in Table 7, including 10 instances which have been selected from the worst to the best states.
Table 7

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 pre-check 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

40092_2012_44_MOESM1_ESM.pdf (117 kb)
Authors’ original file for figure 1
40092_2012_44_MOESM2_ESM.pdf (82 kb)
Authors’ original file for figure 2
40092_2012_44_MOESM3_ESM.pdf (168 kb)
Authors’ original file for figure 3

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Copyright information

© Mehrjoo and Bashiri; licensee Springer. 2013

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.

Authors and Affiliations

  1. 1.Industrial Engineering DepartmentPayme Noor University (PNU)TehranIran
  2. 2.Industrial Engineering DepartmentShahed UniversityTehranIran

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