Supply chain performance monitoring using Bayesian network ...

Int. J. Business Performance and Supply Chain Modelling, Vol. 5, No. 2, 2013

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Supply chain performance monitoring using Bayesian network Meysam Maleki* and V. Cruz-Machado UNIDEMI, Department of Mechanical and Industrial Engineering, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Campus Universitário, 2829-516 Caparica, Portugal Fax: +351212948546 E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: Performance measures of supply chain have been investigated through recent scholar works and different tools have been proposed to follow, monitor, and analyse them. This research addresses the embedded uncertainty as well as mutual dependency among supply chain performance measures and proposes employing Bayesian network (BN) to monitor them. BN has been successfully used in related areas, however, in this particular context it is lacking in published literature. In addition, a framework is proposed to provide researchers and practitioners with step by step procedure of developing BN to monitor the performance measures of their supply chain. Finally, a case study is presented, which takes advantage of proposed methodology and follows the framework. Keywords: supply chain; performance measure; Bayesian network; data modelling. Reference to this paper should be made as follows: Maleki, M. and Cruz-Machado, V. (2013) ‘Supply chain performance monitoring using Bayesian network’, Int. J. Business Performance and Supply Chain Modelling, Vol. 5, No. 2, pp.177–197. Biographical notes: Meysam Maleki is a Researcher in R&D Unit in Mechanical and Industrial Engineering (UNIDEMI) at Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal. He holds an MSc in Production Engineering from Chalmers University of Technology, Sweden. In parallel with his research in UNIDEMI, he is a PhD candidate at Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal. His main scientific field of interest is supply chain management. V. Cruz-Machado holds a PhD in CIM from Cranfield University, UK. He is a Full Professor at Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal. He coordinates post-graduate programmes in industrial engineering, project and lean management. He teaches operations and production management and has published more than 150 papers in scientific journals and conferences, in addition to having supervised 50 MSc and PhD students. His main scientific activities are directed to the design of lean supply chains. He is the President of UNIDEMI (R&D Unit in Mechanical and Industrial Engineering) and the President of the IIE Portugal Chapter.

Copyright © 2013 Inderscience Enterprises Ltd.

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1

M. Maleki and V. Cruz-Machado

Introduction

Many companies have been concerned with development of supply chain measures through which they can measure and eventfully increase the profitability of participants of their supply chain. A key issue in supply chain management is to develop a measurement system to enable coordination mechanism for joint decision making (Kim and Oh, 2005) that can align objectives of independent members and coordinate their activities so as to optimise performance of the whole chain (Wang, 2010). In addition, a smooth and well controlled material flow lies at the heart of best supply chain design and practice (Towill et al., 2002). According to a research conducted by Hoole (2005) companies that are measuring the performance of their supply chain and employing more mature supply chain practices are faster in reducing costs comparing to their less mature peer companies. More precisely, supply chain costs may vary as much as 5% to 6% of annual revenue among companies of the same industry sector. Therefore, modelling of the performance in order to improve its mechanism is crucial for supply chain growth (Panchal and Jain, 2011; Panicker and Sridharan, 2011). Randomness and uncertainty is inherent in most real-world system performances including supply chain. One approach used to understand uncertainty is data mining also referred as knowledge discovery. Data mining extracts information of non-trivial, previously unknown, and implicit and potential information from available data (Witten and Frank, 2005). Different tools can be used in data mining. For instance, Algarni et al. (2006) developed an artificial neural network model to predict the failure rate of De Havilland Dash-8 airplane tyres. Chen et al. (2005) defined the root-cause machine set identification problem to analyse correlations between combinations of machines and the defective products. Kumar et al. (2011) used analytic hierarchy process based on fuzzy simulation to deal with supply chain issues. Meena et al. (2012) took suppliers’ perspective to identify satisfaction factors in buyer-supplier relationships. Balanced score is another approach which articulates the links between leading inputs, processes, and lagging outcomes and focuses on the importance of managing these components to achieve the organisation’s strategic priorities (Bullinger et al., 2002). For example, Hult et al. (2008) took resource-based view and examined the links between a higher-order latent construct to label supply chain orientation and four balanced scorecard outcomes: customer performance, financial performance, internal process performance, and innovation and learning performance. Balanced scorecard can be employed as a strategic performance management tool but it does not encompass the inherent uncertainty of complex environments (Bhagwat and Sharma, 2007). In case the nature of effective factors is probabilistic and there is conditional dependencies among factors, Bayesian network (BN) is recommended as a comprehensive method of indicating relationships and influences of factors in system (Cai et al., 2011). Performance measures in this context have such uncertain characteristics as well as mutual influence. There are some examples of employing this tool in supply chain related area (presented in Section 3 of this paper), however there is a gap of taking advantage of this tool in monitoring performance measures in this context. In the complex and inclement business environment it is necessary for managers to use data mining tools to monitor behaviour and back up decision making process in their company. In this regard BN is widely accepted as a tool in artificial intelligence to solve problems which deal with uncertainties (Nadkarni and Shenoy, 2001). It can be used in different contexts in supply chain like disturbance management, sensitivity analysis, risk

Supply chain performance monitoring using Bayesian network

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analysis, scenario planning, customer lifecycle, decision making, and behaviour monitoring (Chen et al., 2009). Table 1 represents what is expected from the tool to monitor the performance measures of supply chain and what are BN characteristics. Table 1

Research question demands and BN

Research question demands from tool

BN characteristics

1

Dealing with uncertainty

1

Consistent, theoretically solid mechanism for processing uncertain information

2

Different units

2

Different variable types can be modelled in BN

3

Incomplete information

3

Allows one to learn about causal relationships

4

Measurements

4

Facilitates use of prior knowledge

5

Not very sensitive to small changes or minor incorrect inputs

5

Small alterations in the model do not affect the performance of the system dramatically

6

External factors

6

Missing data is marginalized out by integrating over all the possibilities of the missing values

7

Decision support system

7

Efficient model learning algorithm

8

Scenario planning

9

Complex network analysis

Table 2

Focus of researches in application of BN in supply chain related areas (selected publications)

Selected research works

Field of focus

Cai et al. (2011)

Identifying product failure rate

Chin et al. (2009)

Risk assessment of new product development

Cinar and Kayakutlu (2010)

Scenario analysis

Dada et al. (2003)

finding the order quantity

Kiekintveld et al. (2009)

Forecasting customer demand

Li and Gao (2010)

Enterprises collaborative sensitivity analysis

Li and Wang (2011)

Analysis of new product development

Shevtshenko and Wang (2009)

Decision support under uncertainty in collaborative networks

Wang (2010)

Application of imprecise probability for system reliability assessment

Wong (2009)

Measure the supply chain performance with combining data envelopment analysis and Monte Carlo simulation

Xing et al. (2010)

Reverse supply chain and product failure rate

Yuan et al. (2009)

Suppliers evaluation

The focus of applying BN in supply chain is presented in Table 2. It worth to point out: finding the order quantity (Dada et al., 2003), risk assessment of new product development (Chin et al., 2009), track the mean customer demand and trend (Wang, 2010), and identifying product failure rate (Xing et al., 2010). Wong (2009) employs data envelopment analysis in combination with Monte Carlo simulation to measure the supply chain performance. However, fewer researches have been conducted on effectively

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perceiving uncertainty of performance measures. Among those few, Tomlin (2008) presents a relevant research on impact of supply learning when suppliers are unreliable using BN model. The current paper can also be considered as an extension of the approach used by Li and Gao (2010) which focuses on collaborative sensitivity analysis but here a more macro view perspective has been taken to monitor performance measures. In addition the framework and case study presented in this paper fills the lack of practical procedure and example in the work done by Li and Gao (2010). BN have been recently employed by researchers in different contexts as well as supply chain. During last 10 year application of this tool has increased from 26 in the year 2001 till 747 in the year 2011 that is more than 28 times more (Figure 1). Besides, a large number of software packages have been developed by companies and academic institutes which show the trend of using this tool by practitioners as well as researchers. This research uses GeNIe 2.0 modelling environment developed by the Decision Systems Laboratory of the University of Pittsburgh. Figure 1

Accumulative bar chart of presence of BN in supply chain area

After this section, performance measures of supply chain have been investigated and a recent classification of measures is selected as the one that will be used in the case study. Thereafter, BN is presented including BN inference and application of BN in supply chain related areas. It is followed by proposing a framework that will provide structure for researchers and practitioners to develop BN of their supply chain to monitor its performance measures. Finally, a case study is presented in the last section.

2

Performance measures of supply chain

The term ‘supply chain’ firstly was used in early 1980s when writers coined this phrase in order to describe the emerging management discipline (Christopher and Peck, 2004). Supply chain can be considered as a set of procedures which are coordinated to combine suppliers, manufacturers, warehouses, and stores to ensure proper production and distribution of right quantities to the right location in right time and thereby reducing the total supply chain costs together with providing appropriate service level (Leung, 2012;


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Radhakrishnan et al., 2009). Table 3 provides a number of supply chain definitions which are welcomed and frequently referred in the literature. Table 3

Known definitions of supply chain

Reference

Definition

Oliver and Webber (1982)

Coined expression supply chain generally encompasses the set of organizations and processes involved in supplying a firm’s products, from its suppliers’ suppliers to its customers’ customers...

Cooper et al. (1997)

Supply chain management is “... an integrative philosophy to manage the total flow of a distribution channel from supplier to the ultimate user.”

Handfield and Nichols (1999)

The supply chain encompasses all activities associated with the flow and transformation of goods from raw materials stage (extraction), through to the end user, as well as the associated information flows. Material and information flow both up and down the supply chain. Supply chain management (SCM) is the integration of these activities through improved supply chain relationships to achieve a sustainable competitive advantage.

Sengupta et al. (2006)

The supply network structure includes the upstream supply chain for a company, including a variety of decisions related to outsourcing, supplier certification and rationalization of the supply base.

Lambert (2008)

Supply chain management is the integration of key business processes across the supply chain for the purpose of creating value for customers and stakeholders.

Radhakrishnan et al. (2009)

Supply chain can be described as a beneficial coordination and incorporation of organizations with distinct objectives to achieve a common goal.

Council of Supply Chain Management Professionals (CSCMP, Retrieved 2012)

Supply chain management encompasses the planning and management of all activities involved in sourcing and procurement, conversion, and all logistics management activities. Importantly, it also includes coordination and collaboration with channel partners, which can be suppliers, intermediaries, third party service providers, and customers. In essence, supply chain management integrates supply and demand management within and across companies.

Literature reveals the fact that improving supply chain performance has become one of the critical issues for gaining competitive advantages for enterprises. Abd El-Aal et al. (2011) conducted a case study on simulated supply chain and concluded that performance evaluation plays an important role in setting objectives, evaluating performance and determining future courses of actions. They note that most valuations studies in supply chains are focused on financial aspects and there is a lack of performance evaluating methods which involves non-financial aspects. Performance measures and metrics are needed to test and reveal the viability of strategies without which a clear direction for improvement and realisation of goals would be highly difficult (Gunasekaran et al., 2001; Muogboh, 2010). Furthermore, performance measures facilitate the understanding of mutual interactions in the diverse and complex context of supply chain (Goncharuk, 2009). They are crucial for understanding the behaviour of supply chain and integrate the behaviour of its members (Azevedo et al., 2011; Carvalho et al., 2010). Supply chain complexity in different levels such as industry, geographical region or business (Bozarth et al., 2009) makes it challenging to set boundaries and identify specific measures for it.

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Askariazad and Wanous (2009) proposed prioritisation of performance measures according to their importance in value-added activities in the entire supply chain. Sengupta et al. (2006) examined the effects of eight supply chain management strategic initiatives on the organisational performance measures as well as two performance measures (operational and financial). Supply chain performance measures are usually categorised into four groups: quality (Shepherd and Gunter, 2006), time (Whicker et al., 2009), cost (Gunasekaran et al., 2004), flexibility (Angerhofer and Angelides, 2006). They have also been grouped by quality and quantity, cost and non-cost, strategic/operational/tactical focus, and supply chain processes (Cai et al., 2009). In the recent research by Azevedo et al. (2011) supply chain performance measures are extracted from literature in terms of environmental, economic, and operational performances. The current research is based on the performance measures which are identified by Azevedo et al. (2011) presented in Table 4. Table 4

Supply chain performance measures Measures

Economic performance

Operational performance

Quality

Indicators

Customer reject rate In plant defect rate Increment products quality Customer satisfaction After-sales service efficiency Rates of customer complaints Out-of-stock ratio Delivery On time delivery Delivery reliability Responsiveness to urgent deliveries Time Lead time Cycle time Delivery time Inventory levels Finished goods equivalent units Level of safety stocks Order-to-ship Cost New product flexibility Manufacturing cost Cost per operating hour Efficiency Overhead expenses Operating expenses Environmental Revenues from ‘Green’ products revenues Recycling revenue Cost avoidance from environmental actions Environmental costs Cost of scrap/rework Fines and penalties Costs of purchasing environmentally friendly materials Disposal costs Recycling costs R&D expenses ratio Source: Azevedo et al. (2011)


Environmental performance

Table 4

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Supply chain performance measures (continued) Measures

Indicators

Green image Business wastage

Number of fairs/symposiums related to environmentally Total flow quantity of scrap Percentage of materials remanufactured Percentage of materials recycled /re-used Hazardous and toxic material output Solid and liquid wastes Energy consumption Green house gas emissions Air emission

Emissions

Source: Azevedo et al. (2011)

3

Bayesian network

BN, also known as belief network or Bayes nets in short form, belong to the family of probabilistic graphical models which are employed to represent knowledge about uncertain domain. BN combine principles from graph theory, probability theory, computer science, and statistics (Gopnik and Tenenbaum, 2007; Li and Gao, 2010). It has been appeared as a powerful practical tool to represent knowledge, primarily through the seminal research by Professor Judea Pearl at UCLA. Since then, BN have presented strong computational power for deep understanding of complex and high dimensional problems. Efficiency in computation and inherently visual structure of this tool has made it even more attractive for researchers and practitioners to explore and explain complex problems (Pearl and Russell, 1998). It worth noticing that BN can be considered as a disruptive technology due to the fact that it challenges a number of common practices in business and science (Bayes theorem has had the same challenge since the time it was introduced in the 18th century). BN consists of two parts B = (G, θ). The first part is a directed acyclic graph (DAG) which includes nodes and arcs. DAG is commonly used in statistics, machine learning, and artificial intelligence It is the visual representation of the network in which variables of data set X1, …, Xn are nodes and arcs indicates dependencies among nodes (Baesens et al., 2004). The second part of BN is the conditional dependency distribution of θ where θxi|πxi = PB (xi | πxi) is the set of direct parent variables of xi in G (Abad-Grau and Arias-Aranda, 2006). Finally, the network B can be formulated by the following joint probability distribution:

PB ( X 1 ,… , X n ) =

n

∏ i =1

PB ( X i π X i ) =

n

∏X

i

π Xi

i =1

In a BN, nods are representative of random variables and edges between the nodes represent probabilistic dependencies among the corresponding random variables. Statistical and computational methods are being used to find out the conditional dependencies in the graph (Gopnik and Tenenbaum, 2007). A BN eventually is a statistical model which is capable of computing the posterior probability distribution of

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any unobserved stochastic variables, given the observation of complementary subset variables (Gambelli and Bruschi, 2010). BN have following advantages: a

it is a powerful method to treat missing value problem

b

it is good in prediction due to the knowledge of casual relationship between variables

c

it allows the easy use of prior knowledge

d

the probability propagation can be used ‘backwards’ also, when the aim is to find the most probable scenario explaining the evidence set (Neapolitan, 2003).

3.1 Inference in BN Inference is “the act of passing from one proposition, statement, or judgment considered as true to another whose truth is believed to follow from that of the former” (Merriam-Webster Collegiate Dictionary). There are two types of inference support: predictive and diagnostic support for nod Xi predictive support for nod Xi is a top-down approach which is based on evidence nodes connected to Xi through its parent nodes. In contrast, diagnostic support for node Xi is a bottom-up approach which is based on evidence nodes connected to Xi through its child nodes (Gopnik and Tenenbaum, 2007). Another approach is to group structure learning algorithms into unsupervised and supervised learning algorithms. Unsupervised structure learning algorithms are used to find the links between the variables. There are two major families of unsupervised learning algorithms: constraint-based methods (use the semantic of BN and are based on statistical tests) and score-based methods (use a metric to qualify the BN of the dataset). As the search spaces are impossible to exhaustively explore, learning algorithms are based on heuristics, and, depending on dataset, the relative performances of those algorithms can vary. On the other hand, if your goal is to predict one specific target variable, you will then have to use supervised learning algorithms such as Naive-Bayes, Tree augmented Naive-Bayes (TAN), BN augmented Naive-Bayes (BAN), Bayesian multi-nets and general Bayesian networks (GBN). In that case, the learning algorithms do not try to find the best representation of the joint probability distribution but try to find the best probabilistic characterisation of the target variable (Figure 2). Inference algorithms are available and they are also implemented in some software to draw inference from BN. Due to the plethora of nodes and arcs in this network, without such algorithms and software it is close to impossible to get this done. Algorithms which are used by available software are: clustering, polytree, stochastic sampling (such as relevance-based decomposition, backward sampling, self-importance sampling, adaptive importance sampling), Metropols Hastings, variable elimination (varelim), and Monte Carlo method are used to draw inference from a BN. However in situation where the network is so large and complex approximate and stochastic algorithms such as stochastic sampling algorithms can be used to save time and memory. The clustering algorithm is used in the case study of this paper which works in two phases: 1

compilation of a directed graph into a junction tree

2

probability updating in the junction tree.

Supply chain performance monitoring using Bayesian network Figure 2

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BN supervised learning algorithms, (a) Naive-Bayes (b) tree augmented Naive-Bayes (c) BN augmented Naive-Bayes (d) general Bayesian network (e) Bayesian multi-nets

(a)

(b)

(c)

(d)

(e)

3.2 Application of BN in supply chain related areas BN is a statistical model which is capable of computing the posterior probability distribution of any unobserved stochastic variables, given the observation of complementary subset variables (Gambelli and Bruschi, 2010; Maleki et al., 2011). Several authors (Boudali and Dugan, 2005; Langseth, 2007; Mahadevan et al., 2001; Muller et al., 2008; Weber and Jouffe, 2006) have recommended this approach as a comprehensive method to derive relationships and influences among variables. This approach has also been successfully used in a variety of topics related to supply chain (Table 4). In most cases supervised learning algorithms are used in order to build the structure of the network.

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4


Framework

BN makes managers capable of monitoring the performance of their supply chain (or a particular section of supply chain) or/and try different scenarios to ensure the sufficiency of their outcomes before actually implementing them. Development of statistical aspect of BN has been done by researchers in different fields such as analysing microwave expression data (Baldi and Long, 2001), natural statistics (Zhang et al., 2008), word segmentation (Goldwater et al., 2009), combining simulation and physical observation (Biegler et al., 2011), and image reconstruction (Wu et al., 2011). However, step by step framework to be followed by industrial practitioners is missing in the literature. Development of the framework in this section is inspired by design research methodology (DRM) by Blessing and Chakrabarti which was initially proposed in 1992. They continued improving DRM and published its last version with new terminology in 2009 in the book ‘DRM, a Design Research Methodology’. DRM aims to put together different research perspectives to encourage a reflection on the research approach applied. This methodology is mainly used in design projects where researchers need to follow almost the same procedure as this research. The prerequisite of making BN of a supply chain is to define what type of entities should be considered. Since BN is based on probability theory, its entities (represented by nodes) have probabilistic nature. For instance, the frequency of production planning that might be once or twice a week will not be considered as an entity. However, the efficiency of production planning which has a probabilistic presentation can be included in the network. Connections among nodes are defined based on the influence among them which is dependent on the context. As an example, efficiency of production planning might be influenced by availability of raw materials. As it has been implied by this example, accuracy of BN is tightly dependent to the understanding of the supply chain so it should be done by someone who knows about the behaviour and interactions among entities of the system. To back up the procedure of building BN model of supply chain performance measures, a step by step framework is provided for practitioners (Figure 3). This framework is divided into two major parts: part A is giving instruction to develop the BN model and part B is dedicated to scenario planning based on the model which is developed in part A. Part A starts with identifying performance measures of current supply chain. Large number of performance measures is introduced by scholars among which the research by Azevedo et al. (2011) is recommended. Practitioners should notice that performance measures are mostly general and it is required to customise and interpret them for their specific supply chain. Data collection is the second step. The best source to collect data is the ERP system. However, not all data is prepared in ERP system in this case paractitioners may conduct interview with experts to use their tacit knowledge. Then, dependency and independency of measures should be introduced to the BN model (Pochampally et al., 2009). It is folowed by using a unsupervised learning algorithms to learn the BN network from given data. Thereafter, quality of the network should be assessed to make sure that it represents the real world. At this level the BN model of perfromance measures is ready to be used to monitor performance measures.


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Framework of developing BN of supply chain

Part B is managed to provide scenario planning framework. Apparently, the BN model developed in part A is required to initiate this part. After clarifying what is supposed to be monitored in the scenario, its coverage boundary should be set. The next step is to find out what performance measures are directly corresponding to the proposed scenario. Then, evidences of the scenario is assigned to the corresponding performance measures. In other words, we assume that we know the exact value of those measures so they are not probabilistic or dependent to other nodes anymore. Thereafter, a supervised learning algorithm is used to follow the influence of set evidences on other nodes. One can continure trying different evidences to understand how the studied supply chain is behaving in different scenarios.

5

Case study

In the most of available case studies on supply chain the common way is to divide it into supply chain role players (suppliers, manufacturers, distributors, market) then individually conduct case study on each of them. Thereafter, they put together the outcome of each individual case study to reach overall result for the whole supply chain. In contrast, this case study considers the supply chain as a whole integrated body. The model is being applied to the whole chain rather than individual role players (particularly operational performance of the whole supply chain). Taking such view assists to reach measures for the whole supply chain which might be different from summing up

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individual measures. In addition, this view takes mutual interactions into consideration which gives a more realistic perspective. Finally, the outcome of such case study can be used by decision makers to set strategies based on the information of that they can receive from the model as well as observing the influence of different scenarios on the overall behaviour of their supply chain. The current case study follows the framework presented in Section 4. Accordingly it is divided into part A and part B. Figure 4

Histogram of measure indicators of operational performance (see online version for colours)

Quality

Customer reject rate

In plant defect rate

Increment products quality

Customer satisfaction

After-sales service efficiency

Rates of customer complaints

Out-of-stock ratio

Delivery

On time delivery

Delivery reliability

Responsiveness to urgent deliveries

Time

Lead time

Cycle time

Delivery time

Inventory levels

Finished goods equivalent units

Level of safety stocks

Order-to-ship


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5.1 Part A: Performance measures monitoring Performance measures monitoring starts with identifying performance measures of the supply chain. Azevedo et al. (2011) have categorised all performance measures into three categories as operational, economic and environmental performances. This cases study focuses on the operational performances which were provided in Table 4. In order to make the data more, visual histogram of each measure indicator is presented in Figure 4. These histograms illustrate the data distribution of each performance measure. In Figure 4 vertical axes are percentage and the horizontal axes are the quantitative data of each measure. Due to the fact that BN is a statistical method and looks into data based on proportion of data, there is no confusion of measurement units. Therefore, it is possible to put together different measures such as time and inventory level in the same network. In addition, statistics of performance measures is given in Table 5. Table 5 contains mean, min, max, and variance values of each indicator as well as a dedicated code to them (these codes are later on used in Table 6, Figures 5, 6, 7). Since this data will be used in BN model, the most important factor to be observed is variance of the data which indicates how far the set is spread out. High variance influences more when trying different scenarios on the model. In case of this data set, levels of safety stocks and order-to-ship indicators have highest variance in the dataset. Table 5

Performance measures’ statistics

Masure

Indicator

Mean

Min

Max

Variance

Code in the model

Quality

Customer reject rate

0.025

0.01

0.05

0.00

OQ 1

In plant defect rate

0.060

0.03

0.1

0.00

OQ 2

Customer satisfaction Delivery

Time

Inventory levels

Increment products quality

0.060

0.02

0.1

0.00

OQ 3

After-sales service efficiency

0.781

0.7

0.9

0.00

OC 1

Rates of customer complaints

0.585

0.51

0.7

0.00

OC 2

Out-of-stock ratio

0.205

0.1

0.3

0.00

OC 3

On time delivery

0.398

0.3

0.5

0.01

OD 1

Delivery reliability

0.215

0.1

0.3

0.00

OD 2

Responsiveness to urgent deliveries

0.547

0.5

0.6

0.00

OD 3

Lead time

0.199

0.1

0.29

0.00

OT 1

Cycle time

0.281

0.2

0.4

0.00

OT 2

Delivery time

0.446

0.4

0.5

0.00

OT 3

Finished goods equivalent units

0.162

0.03

0.29

0.01

OI 1

Level of safety stocks

0.304

0.1

0.5

0.02

OI 2

Order-to-ship

0.499

0.26

0.7

0.02

OI 3

190 Figure 5

M. Maleki and V. Cruz-Machado Relations diagram of operational performances

Figure 5 illustrates three indicators assigned to each operational performance measures which are: quality, customer satisfaction, delivery, time, and inventory levels. Therefore, for instance in order to measure quality (as an operational performance measure) three indicators are used namely customer reject rate, in plant defect rate, and increment products quality. This data is introduced to the BN model as the prior probability of child nodes. Using prior probability of child nodes, prior probability of parent nodes (in this case operational performance measures) is calculated (Figure 6). The resulted BN works both in forward and backward ways. In another words, once the data is introduced to the model, we can set evidence on any of child (or parent) nodes and get the posterior probability of other nodes. Due to the dataset the level of dependency among network nodes may differ. In the case of this case study, there is strong dependency to the first level child nodes. For instance time as a performance measure is strongly dependent to delivery time which is one of its indicators (this is shown in part B: scenario planning). On the other hand, practitioners should notice that once evidence is introduced to a node, theoretically that specific node will be independent from its child nodes. A practical notice is that adding extra measure or measure indicator results in an extra node, consequently increases the complexity of network. Relations among performance measures are given in Figure 5 (measure indicators are illustrated with their corresponding code). Up until this step enough information has been collected so a BN can be built using unsupervised learning algorithm. In order to get a better output visualisation, indicator’s records are discretised using normal width into two states (Figure 6). Using this model, managers and decision makers can get an overall picture of their supply chain which will assists them to develop it.


191

Operational performance BN of supply chain

5.2 Part B: Scenario planning In this section, the BN model developed in part A will be used to monitor the influence of three scenarios and the way they are influencing the operational performance of supply chain. Scenarios presented according to their influence on performance measures and indicators in Table 6. The BN model of each scenario is provided in Figure 7. These three scenarios are exploring sensitivity of the operational performance to three indicators of the system. Such sensitivity analysis is a way to predict the future state of the network if a situation turns out to be different compared to other indicators. The three scenarios look into in plant defect rate, delivery time, and order-to-ship time. In plant defect rate is a quality indicator which measures the rate of defects caused by facilities inside factory walls. Delivery time is a time indicator which measures the transportation period to customer. Order-to-ship is an inventory level indicator which measures the period of receiving an order to ship it out of factory walls. Table 6

Influence of three scenarios on operational performance of supply chain Evidence node (indicator measure)

Influence on corresponding measure

Influence on overall operational performance

Scenario 1

OQ 2

Quality: +6%

+1%

Scenario 2

OT 3

Time: –19%

+3%

Scenario 3

OI 3

Inventory level: –14%

+2%

Scenario 1 considers the situation in which the ‘in plant defect rate’ (OQ 2) is observed to be in the first state. According to the BN model it increases the quality measure by +4% as well as operational performance by +1%. The second scenario assumes the situation in which there is evidence that ‘delivery time’ (OT 3) is on the second state. Consequently, the BN model illustrates the influence of such evidence on time by –19% and the whole operational performance by +3%. The last scenario is planned for the time when the ‘order-to-ship’ (OI 3) is observed on the second state which influences inventory level by –14% and overall performance by +2%. Accordingly, the second scenario which is about

192


delivery time (OT 3) will be selected due to the fact that it increases the overall performance of supply chain more than other two scenarios (Figure 7). Figure 7

BN model of scenarios

Scenario 1: In plant defect rate (OQ 2) OD 1 OC 1 S1 56% S2 44% OC 2 S1 69% S2 31%

OD 2

S1 56% S2 44%

S1 34% S2 66%

Customer Satisfaction S1 67% S2 33%

Delivery S1 46% S2 54%

OD 3 S1 56% S2 44%

OT 1 S1 47% S2 53% Time

S1 64% S2 36%

OT 2 S1 78% S2 22%

OC 1

OT 3

S1 62% S2 38%

S1 59% S2 41% Operational Performance S1 57% S2 43%

OQ 3 S1 34% S2 66% OQ 2 S1100% S2 0%

Quality

OI 1 S1 47% S2 53% Inventory Levels S1 47% S2 53%

S1 42% S2 58%

OI 2 S1 50% S2 50%

OQ 1

OI 3

S1 69% S2 31%

S1 31% S2 69%

Scenario 2: Delivery time (OT 3) OD 1 OC 1 S1 56% S2 44% OC 2 S1 69% S2 31%

OD 2

S1 56% S2 44%

S1 34% S2 66%



OD 3 S1 56% S2 44%

OT 1 S1 47% S2 53% Time

S1 45% S2 55%

OT 2 S1 78% S2 22%

OC 1

OT 3

S1 62% S2 38%

S1 0% S2100% Operational Performance S1 59% S2 41%

OQ 3 S1 34% S2 66% OQ 2 S1 63% S2 37%

Quality


S1 36% S2 64%

OI 2 S1 50% S2 50%

OQ 1

OI 3

S1 69% S2 31%

S1 31% S2 69%

Scenario 3: Order-to-ship (OI 3) OD 1 OC 1 S1 56% S2 44% OC 2 S1 69% S2 31%

OD 2

S1 56% S2 44%

S1 34% S2 66%



OD 3 S1 56% S2 44%

OT 1 S1 47% S2 53% Time

S1 64% S2 36%

OT 2 S1 78% S2 22%

OC 1

OT 3

S1 62% S2 38%

S1 59% S2 41% Operational Performance S1 58% S2 42%

OQ 3 S1 34% S2 66% OQ 2 S1 63% S2 37%

Quality S1 36% S2 64%


OI 2 S1 50% S2 50%

OQ 1 S1 69% S2 31%

OI 3 S1 0% S2100%


193

Such analyses are planned to improve decision making by allowing outcome monitoring of some predefined assumptions. In this section, three evidences were introduced to the model to monitor the behaviour of the system in their presence.

6

Conclusions

Supply chain includes diverse variables with different work characteristics. Besides, it is a complex network which is difficult to clearly monitor its performance. Performance measures are used in order to evaluate and monitor the performance of supply chain as a unified body. Considering the conditional dependencies among such measures, this paper proposes employing BN to monitor them. According to the findings of this paper, BN can be used in supply chain context to learn structure and parameters of network from given data and draw inference. In addition, this paper proposes a framework which provides the procedure of developing BN in supply chain. Finally, the case study illustrates that having BN model makes the platform to try different scenarios and observe influence of one measure on the network. Both managers and practitioners may benefit from employing BN in their supply chains. Wide variety of inference can be drawn using this tool from strategic to economical and technical perspectives. Although it is theoretically possible but our practical recommendation is not to combine technical and strategic entities in one network. It is due to the fact that it increases the complexity of the network resulting in an unrealistic inference. In both cases the proposed framework and the presented case study provide foundation to develop strategic and technical networks. Application of BN is recommended when entities of system are well defined and there is probabilistic relationship among them. For instance in our case inventory level is a definable term and it can be one of entities of the network. In case the system includes fuzzy entities, fuzzy logic can be used instead of BN. In a nut shell, the system characteristics define the appropriate tool to be used. In case of probabilistic relationship between definable entities, BN is a competitive tool.

Acknowledgements This research is funded by Fundação para a Ciência e Tecnologia (Project MIT-Pt/EDAM-IASC/0033/2008). Meysam Maleki is supported by a PhD fellowship from this foundation.

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