# An Entropy-Based Formulation for Assessing the Complexity Level of a Mass Customization Industry 4.0 Environment

Authors: César Martínez-Olvera
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

It has been stated that Industry 4.0’s goal is, among others, the sustainable success in a market characterized by exigent and informed consumers demanding personalized products and services, where the level of manufacturing complexity increases with level of product customization. Even though different manufacturing complexity measures have been developed, there seems to be a lack of a comprehensive metric that address both the mass customization variety-induced complexity, and the complexity derived from the adoption of the Industry 4.0 paradigm. The main original contribution of this paper is the development of an entropy-based (entropic) formulation to address this last issue. Its validity and usefulness is put to the test via a discrete-event simulation study of a mass customization production system operating within an Industry 4.0 context. Our findings show that the entropic formulation acts as a fairly good trend indicator of the system’s performance parameter increase/decrease, but not as an estimator of the final values. A discussion of the managerial implications of the obtained results is offered at the end of the paper.


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## Body

## 1. Introduction

The global dynamic competition impose manufacturing companies a series of business challenges such as operating with high levels of flexibility, efficiency, and adaptability in the face of product and process complexity [1], and to fast develop, design, and manufacture high quality, low cost, smart, mass customized products [2, 3], at a reasonable cost and with reduced energy and resources consumption [4]. In this scenario, the business survival demands the ability to react to rapid product changes through reconfigurability [5], via the intensive use of automation, computer systems, and software [6]. These are the main features related to Industry 4.0, a concept that is becoming much popular among organizations [7]. Industry 4.0 deals with the real time availability of all relevant information involved in the value creation process and the interconnection between human beings and machines [8–10]. This is carried out by combining manufacturing, automation, information, computing, communication, and control technologies, via the use of Internet of Things (IoT), Big Data, and cyber-physical system (CPS) associated technologies, in order to establish an interconnected industrial value creation process [11, 12]. This implies giving the customer the constant opportunity to become part of the value creation process through the development of tailored services [13]. It has been stated that Industry 4.0’s goal is—among others—the sustainable success in a market characterized by exigent and informed consumers demanding personalized products and services [14], that is, a mass customization market, where customers increase variant diversity [15], designed to their individual specifications [16, 17], and without paying a high price premium [18]. In simple terms, mass customization is a value chain-based manufacturing strategy [19] that aims to offer customized goods at low cost [20]. Within this context, there is a high level of uncertainty result of the variety of customer needs/preferences [21], which when viewed in terms of an increased number of components/parts, setups, and production processes is translated into a high level of manufacturing complexity [22], referred by [23, 24] as product variety-induced complexity. Moreover, the use of the Industry 4.0 potentialities is seen as an enabler of mass customization [25], when considering that Industry 4.0 is a business-wide transformation—rather than a collection of technological projects—that allows a great potential for business value creation if information is properly exploited [26]. However, a collateral effect of the adoption of the Industry 4.0 initiative, for mass customization purposes, is the increase of the manufacturing system complexity [27], which in turn translates into a system efficiency decrease, mostly because of the involved big information and material flows [20]. Now, it has been mentioned that both production flexibility and information technology can provide the means to carry out mass customization [28, 29]:(i)
A common way to deal with mass customization issues (i.e., product variety-induced complexity) is production flexibility [30], as the use of a flexible manufacturing system can improve manufacturing performance, by reducing setup and manufacturing lead times [24, 31](ii)
The smart components of Industry 4.0 can help reduce the complexity inherent to managing the mass-customization production system [32], via the use of information technologies [21], as long as there is no lack of information quality and availability for the use of these associated technologies [33]Tjahjono et al. [9] mention that, in order for Industry 4.0 to truly achieve a sustainable success in a mass customization market, it is required to rapidly identify the customer needs, to simplify the customization process, and to assure—at no extra cost—the production system reconfigurability. This last fact has implications at the operational level as this requires the integration of the plug-and-produce, fully automated, digitized, and highly cost efficient CPS units [6]. For this reason, Section 1.1 reviews the topics of complexity and flexibility and their relationship with a Mass Customization Industry 4.0 environment (defined in this paper, as a mass customization production system operating within a reconfigurable CPS context). Derived from this literature review, the research features of this paper are defined, the research gaps and opportunities are identified, and the research goals—as well as the proposed research methodology to achieve them—highlighting the research originality, usefulness, and contributions are stated.


### 1.1. Literature Review

Complexity is considered to be a factor that influences productivity reduction [34]. According to [35, 36], there is a tradeoff between customization and complexity, where this last can be both good (required to customize products) and bad (failure by companies to address the tradeoff between the costs associated with customization). Sonsino et al. [37] talk about negative complexity, when referring to the probability decrease of choosing a “feasible” alternative (a product without incompatible components) as the complexity of that alternative increases. More specifically, References [24, 31, 38] claim that mass customization can both increase and decrease complexity. It is increased in the form of production program (i.e., planning and control), manufacturing (i.e., products’ diversity/variants), and configuration (i.e., information overload) complexity. It is decreased in the form of order taking process (i.e., product’s configurators), product (i.e., modular architectures), and inventory’s (i.e., customer, “pull” strategy) complexity. Now, according to [30, 39], major contributors to the complexity of a product and a system are the increasing number of components, variants, and changes. ElMaraghy and Urbancic [40, 41] state that manufacturing process complexity is associated with the content (effort needed, i.e., number of stages or tools, to perform the task), quantity (quantity of information needed using entropy measurement), and diversity (ratio between the specific information needed for the task, to the total information) of information for a process. Regarding the role of information, Gullander et al. [30] claim that information flow creates both complexity and at the same time introduces possibilities of handling it, so an information support system is vital for the production system and needs to be considered as a parameter in relation to complexity. Now, several approaches have been developed for the quantification of complexity, mainly based on statistics, probabilities, and heuristics [42].In this context, Shannon’s entropy-based information theory [43] has found a wide area of application as a measure of uncertainty. In example, Breithaupt [44] developed an analytical model for quantitatively measuring the system complexity—due to different part routings, processing times, and mix ratios—of a manufacturing system, using information entropy. ElMaraghy et al. [45] defined a code-based structural complexity index. Suh [46] successfully adopted complexity in the context of a system design, in achieving functional or design requirements. Zhu at al. [47] applied the information entropy to complexity model generation on the level of station and system at mixed-model assembly systems. Smart et al. [48] extended the information-based measures to the dynamic measurements of the systems. Sönmez and Koç [49] offer an entropy-based evaluation for the quantification of the overall manufacturing complexity, which takes into account the type of machinery, number and type of operations, and routing for each product. Soltysova and Bednar and Modrak et al. [31, 50] offer an extensive review of the complexity concept in the manufacturing arena.Regarding the manufacturing complexity measure issue, Arteta and Giachetti [51] state that different measures have been developed over the years, i.e., manufacturing complexity measure [51–54]; operational complexity [55]; structural complexity index [56]; internal static manufacturing complexity measure [57]; and static/dynamic complexity [58–60]. Specific examples about the approaches used for measuring structural complexity of manufacturing systems can be found in [23, 42, 61, 62]. For a complete review of entropy-based measures for manufacturing complexity quantification, the readers should consult [63–66]. Now, even though the previous work suggests the product, process, and resources elements (or information categories) as necessary to describe a manufacturing system’s complexity, there seems to be a lack of a comprehensive metric that combines both the amount and type of information needed to describe a system’s complexity [56].Regarding the issue of mass customization variety-induced complexity, the current manufacturing complexity metrics do not reflect the true aspect of this last [24], and quantification approaches that investigate how the adoption of the Industry 4.0 paradigm increases its complexity are limited [27]. Some of the work in this venue includes Nielsen and Brunoe [67], who proposed two indexes to measure the level of mass customization, namely, the differentiation point index and the setup index, which take into account elements like number of different manufacturing processes, number of different manufactured varieties, average throughput time, number of setup, and related costs. Mourtzis et al. [68, 69] proposed an entropic measure to quantify the complexity before and after shifting from a traditional manufacturing system into a Manufacturing 4.0 manufacturing system. Mourtzis et al. [27] propose a metric for the quantification of customization complexity, from an Industry 4.0 point of view, taking into account the quantity of the information managed, the diversity/variants of the exchanged information, and the content of the messages that transfers the information (the premise is that the increase in any of these elements increases the system’s complexity significantly). Martínez-Olvera and Mora-Vargas [70] develops the system dynamics model of the mass customization paradigm and use it to study the effect the level of flexibility has on the level of fulfilled demand.Regarding the role of flexibility: a key mass customization capability—understood this last as a bundle of routines and resources that contribute to performance [71]—is process flexibility [72]. In this case, two fundamental flexibility requirements for mass customization production systems are product mix, ability adapt, and produce to diverse customer requirements; and changeover flexibility, ability to switch between different products and/or components in a fast-paced and cost-efficient manner [22]. Bellemare [73] refers to these as flexibility and changeability—critical enablers for efficient mass customization [74]—as they allow the runtime capabilities such as fast and easy reconfiguration of production facilities, that without them, product variability and customization would result in tremendous increase of production costs [75]. However, the higher flexibility a system has, the more difficult it is to achieve high efficiency, an issue that can be properly addressed by the use of automation that can improve manufacturing productivity and efficiency, but contributing the system complexity, as they are highly integrated with the products, processes, information, resources, human, tasks, and organization [30]. For this reason, it is that an enterprise competing within a mass customization Industry 4.0 environment depends on the manufacturing efficiency of the transforming processes [16, 17, 27].


### 1.2. Research Features

The previous sections can be summarized as follows: mass customization production systems exhibit product variety-induced complexity, which it is increased when operating within an Industry 4.0 context. Flexibility can help reducing the level of complexity, but at the same time, it makes difficult achieving high levels of efficiency. This presents a potential problem for an Industry 4.0 mass customization environment, as it depends—for its successful operation—on the manufacturing efficiency of the transforming processes. Now, from the presented literature review (see Table1) the following research gaps and opportunities are defined:(1)
Current manufacturing complexity metrics do not reflect the variety-induced complexity of mass customization [24](2)
The quantification of the complexity increases due to the adoption of the Industry 4.0 paradigm—more specifically, due to resources reconfigurability—is limited [27]Table 1
Literature review summarizing table.
Topic addressed
References
Good/bad/negative complexity
[35–37]
Complexity increase/decrease
[24, 31, 38]
Complexity and information flow
[30]
Product complexity
[30, 39]
Complexity quantification
[42–48]
Manufacturing process complexity
[23, 31, 40–42, 49–54, 61, 62]
Operational/structural/internal
[55–57]
Complexity entropy-based measures
[58–60, 63–66]
Mass customization measurement
[24, 27, 67]
Mass customization and complexity
[27, 68, 69]
Mass customization and flexibility
[22, 72–75]
Flexibility and complexity
[30]As a first step into the development of a comprehensive metric that covers both sources of complexity, this research effort proposes an exploratory approach, with its main goal being addressing the possibility of using an entropic formulation for assessing the complexity level of a Mass Customization Industry 4.0 environment (known henceforth as theβɛMC4.0 expression). The originality of the βɛMC4.0 expression comes from its predictive and constructive validity. The predictive validity refers to the ability to “predict” a theorized outcome, which is provided by following an entropy-based approach, as suggested by Reference [56]. The construct validity refers to the formality of the development process, which is based on previous published work by the author [76, 77], where an entropy-based metric of a product’s BOM blocking effect is derived. The usefulness of the βɛMC4.0 expression is demonstrated via the use of a discrete-event simulation model of a mass customization production system operating within an Industry 4.0 environment. The rest of the paper is organized as follows: Section 2 presents the case of a mass customization production system, upon which, a discrete-event simulation model is built, with the idea of generating statistical output that reflects the behavior of the system. Based on these results, Sections 3 presents the theory foundation of the βsɛMC4.0 expression, where Section 4 adds the Industry 4.0 complexity component—in the form of flexibility through the system reconfigurability—and put to the test the validity of the βɛMC4.0 expression. Derived from the obtained results, Section 5 presents the final conclusions and the identified future research venues.


## 1.1. Literature Review

Complexity is considered to be a factor that influences productivity reduction [34]. According to [35, 36], there is a tradeoff between customization and complexity, where this last can be both good (required to customize products) and bad (failure by companies to address the tradeoff between the costs associated with customization). Sonsino et al. [37] talk about negative complexity, when referring to the probability decrease of choosing a “feasible” alternative (a product without incompatible components) as the complexity of that alternative increases. More specifically, References [24, 31, 38] claim that mass customization can both increase and decrease complexity. It is increased in the form of production program (i.e., planning and control), manufacturing (i.e., products’ diversity/variants), and configuration (i.e., information overload) complexity. It is decreased in the form of order taking process (i.e., product’s configurators), product (i.e., modular architectures), and inventory’s (i.e., customer, “pull” strategy) complexity. Now, according to [30, 39], major contributors to the complexity of a product and a system are the increasing number of components, variants, and changes. ElMaraghy and Urbancic [40, 41] state that manufacturing process complexity is associated with the content (effort needed, i.e., number of stages or tools, to perform the task), quantity (quantity of information needed using entropy measurement), and diversity (ratio between the specific information needed for the task, to the total information) of information for a process. Regarding the role of information, Gullander et al. [30] claim that information flow creates both complexity and at the same time introduces possibilities of handling it, so an information support system is vital for the production system and needs to be considered as a parameter in relation to complexity. Now, several approaches have been developed for the quantification of complexity, mainly based on statistics, probabilities, and heuristics [42].In this context, Shannon’s entropy-based information theory [43] has found a wide area of application as a measure of uncertainty. In example, Breithaupt [44] developed an analytical model for quantitatively measuring the system complexity—due to different part routings, processing times, and mix ratios—of a manufacturing system, using information entropy. ElMaraghy et al. [45] defined a code-based structural complexity index. Suh [46] successfully adopted complexity in the context of a system design, in achieving functional or design requirements. Zhu at al. [47] applied the information entropy to complexity model generation on the level of station and system at mixed-model assembly systems. Smart et al. [48] extended the information-based measures to the dynamic measurements of the systems. Sönmez and Koç [49] offer an entropy-based evaluation for the quantification of the overall manufacturing complexity, which takes into account the type of machinery, number and type of operations, and routing for each product. Soltysova and Bednar and Modrak et al. [31, 50] offer an extensive review of the complexity concept in the manufacturing arena.Regarding the manufacturing complexity measure issue, Arteta and Giachetti [51] state that different measures have been developed over the years, i.e., manufacturing complexity measure [51–54]; operational complexity [55]; structural complexity index [56]; internal static manufacturing complexity measure [57]; and static/dynamic complexity [58–60]. Specific examples about the approaches used for measuring structural complexity of manufacturing systems can be found in [23, 42, 61, 62]. For a complete review of entropy-based measures for manufacturing complexity quantification, the readers should consult [63–66]. Now, even though the previous work suggests the product, process, and resources elements (or information categories) as necessary to describe a manufacturing system’s complexity, there seems to be a lack of a comprehensive metric that combines both the amount and type of information needed to describe a system’s complexity [56].Regarding the issue of mass customization variety-induced complexity, the current manufacturing complexity metrics do not reflect the true aspect of this last [24], and quantification approaches that investigate how the adoption of the Industry 4.0 paradigm increases its complexity are limited [27]. Some of the work in this venue includes Nielsen and Brunoe [67], who proposed two indexes to measure the level of mass customization, namely, the differentiation point index and the setup index, which take into account elements like number of different manufacturing processes, number of different manufactured varieties, average throughput time, number of setup, and related costs. Mourtzis et al. [68, 69] proposed an entropic measure to quantify the complexity before and after shifting from a traditional manufacturing system into a Manufacturing 4.0 manufacturing system. Mourtzis et al. [27] propose a metric for the quantification of customization complexity, from an Industry 4.0 point of view, taking into account the quantity of the information managed, the diversity/variants of the exchanged information, and the content of the messages that transfers the information (the premise is that the increase in any of these elements increases the system’s complexity significantly). Martínez-Olvera and Mora-Vargas [70] develops the system dynamics model of the mass customization paradigm and use it to study the effect the level of flexibility has on the level of fulfilled demand.Regarding the role of flexibility: a key mass customization capability—understood this last as a bundle of routines and resources that contribute to performance [71]—is process flexibility [72]. In this case, two fundamental flexibility requirements for mass customization production systems are product mix, ability adapt, and produce to diverse customer requirements; and changeover flexibility, ability to switch between different products and/or components in a fast-paced and cost-efficient manner [22]. Bellemare [73] refers to these as flexibility and changeability—critical enablers for efficient mass customization [74]—as they allow the runtime capabilities such as fast and easy reconfiguration of production facilities, that without them, product variability and customization would result in tremendous increase of production costs [75]. However, the higher flexibility a system has, the more difficult it is to achieve high efficiency, an issue that can be properly addressed by the use of automation that can improve manufacturing productivity and efficiency, but contributing the system complexity, as they are highly integrated with the products, processes, information, resources, human, tasks, and organization [30]. For this reason, it is that an enterprise competing within a mass customization Industry 4.0 environment depends on the manufacturing efficiency of the transforming processes [16, 17, 27].


## 1.2. Research Features

The previous sections can be summarized as follows: mass customization production systems exhibit product variety-induced complexity, which it is increased when operating within an Industry 4.0 context. Flexibility can help reducing the level of complexity, but at the same time, it makes difficult achieving high levels of efficiency. This presents a potential problem for an Industry 4.0 mass customization environment, as it depends—for its successful operation—on the manufacturing efficiency of the transforming processes. Now, from the presented literature review (see Table1) the following research gaps and opportunities are defined:(1)
Current manufacturing complexity metrics do not reflect the variety-induced complexity of mass customization [24](2)
The quantification of the complexity increases due to the adoption of the Industry 4.0 paradigm—more specifically, due to resources reconfigurability—is limited [27]Table 1
Literature review summarizing table.
Topic addressed
References
Good/bad/negative complexity
[35–37]
Complexity increase/decrease
[24, 31, 38]
Complexity and information flow
[30]
Product complexity
[30, 39]
Complexity quantification
[42–48]
Manufacturing process complexity
[23, 31, 40–42, 49–54, 61, 62]
Operational/structural/internal
[55–57]
Complexity entropy-based measures
[58–60, 63–66]
Mass customization measurement
[24, 27, 67]
Mass customization and complexity
[27, 68, 69]
Mass customization and flexibility
[22, 72–75]
Flexibility and complexity
[30]As a first step into the development of a comprehensive metric that covers both sources of complexity, this research effort proposes an exploratory approach, with its main goal being addressing the possibility of using an entropic formulation for assessing the complexity level of a Mass Customization Industry 4.0 environment (known henceforth as theβɛMC4.0 expression). The originality of the βɛMC4.0 expression comes from its predictive and constructive validity. The predictive validity refers to the ability to “predict” a theorized outcome, which is provided by following an entropy-based approach, as suggested by Reference [56]. The construct validity refers to the formality of the development process, which is based on previous published work by the author [76, 77], where an entropy-based metric of a product’s BOM blocking effect is derived. The usefulness of the βɛMC4.0 expression is demonstrated via the use of a discrete-event simulation model of a mass customization production system operating within an Industry 4.0 environment. The rest of the paper is organized as follows: Section 2 presents the case of a mass customization production system, upon which, a discrete-event simulation model is built, with the idea of generating statistical output that reflects the behavior of the system. Based on these results, Sections 3 presents the theory foundation of the βsɛMC4.0 expression, where Section 4 adds the Industry 4.0 complexity component—in the form of flexibility through the system reconfigurability—and put to the test the validity of the βɛMC4.0 expression. Derived from the obtained results, Section 5 presents the final conclusions and the identified future research venues.


## 2. The Mass Customization Production System

According to [31], the mass customization paradigm involves a design-sell-make-assemble cycle. Dean et al. and Daaboul et al. [78–80] put this cycle into six fundamental processes, while Latorre-Biel et al. [14] establishes a five step sequence for the execution of the mass customization approach, within an Industry 4.0 environment:(1)
Customers personalize their purchase through a website or mobile application software(2)
The purchasing information is sent directly to the production line not requiring a fabrication order from a management level of decision(3)
The purchased product is associated to a sequence of services required during its manufacturing process (fabrication list)(4)
Each product requests services (via IoT) to one or several machines with the purpose of manufacturing the final product(5)
Once all services are completed, the product is packed and deliveredThe mass customization production system proposed in this research effort focuses only on steps 3 and 4 of the previous list. It is theoretical in nature—similar to the one presented in Bednar et al.[81], where a mass customized assembly uses three stable and two optional components resulting in four complete product configurations—and complies with the set of mass customization configuration attributes presented in Martínez-Olvera and Mora-Vargas [70]. The set of products to be processed by this production system is presented in Figure 1, and Table 2 shows the manufacturing process routes for each of these products, in terms of type of manufacturing resource Mi used (Figure 2) and processing time (i.e., product 1B uses manufacturing resource M2 for three time units, followed by the use of manufacturing resource M4 for three time units).Figure 1
Set of products processed by the mass customization production system.Table 2
Manufacturing process routes.
Product number
Product type
Manufacturing process routes
1
1B
3M2 + 3M4
2
1C
4M3 + 4M4
3
2AB
2M1 + 2M2 + 2M4
4
2AC
2M1 + 4M3 + 6M4
5
2A1B1C
2M1 + 1M2 + 2M3 + 5M4
6
1A2B1C
1M1 + 2M2 + 2M3 + 7M4
7
3AB
3M1 + 3M2 + 6M4
8
3AC
3M1 + 6M3 + 9M4
9
3A1B2C
3M1 + 1M2 + 4M3 + 8M4
10
2A3B1C
2M1 + 3M2 + 2M3 + 9M4Figure 2
Types of manufacturing resources used by the mass customization production system.


### 2.1. Simulation Model

The discrete-event simulation (DES) model of the mass customization production system was build following an approach similar to the one presented in Raza et al. [20], where the impact of introducing the Industry 4.0 paradigm within a Mass Customization environment is studied. This DES model was developed in ARENA [82] and used to generate statistical output regarding its performance (measured in terms of the manufacturing resources’ queue length, and the products’ waiting time). The logic behind the DES model was implemented based on the structure of the model “A Small Manufacturing System,” presented in [82], specifically with the use of the STATION and ROUTE modules. Figure 3 presents an excerpt of the DES model, for the case of manufacturing resource M1. The simulation run output was verified and validated according to the recommendations proposed by Hwarng et al. [83]. The trace and debugging functions were used to check the logic of the activities an entity encounters in the system, and the DES model output was examined for reasonableness by setting the processing times to some known deterministic value and compared with manual calculations (finding no discrepancies between the simulation and manual results). In this case, the DES model can be considered as a research instrument for theory testing [84] rather than for theory development [85]. A simulation run time, long enough to allow the total processing of twelve units of each product type, was used. The mass customization production system is assumed to be operating continuously, i.e., breakdowns, changeover, setup, and load/unload times are assumed to be negligible, and each manufacturing resource is capable of processing only one unit at a time. All the manufacturing resources were subject to certain degree of variation (reflected as an exponential normal distribution for the processing times). Thirty replications were used in order to avoid significant variation in the observed results. Confidence intervals of 90% were used in order to provide the proper statistical basis for making inferences and conclusions. Ten different scenarios were tested under these operative conditions (Table 3).Figure 3
Excerpt of the DES model, manufacturing resourceM1 case.Table 3
Tested scenarios.
Scenario number
Product type processed
Simulation run time (min)
Number of units produced
1
1B
60
12
2
1B, 1C
110
24
3
1B, 1C, 2AB
140
36
4
1B, 1C, 2AB, 2AC
210
48
5
1B, 1C, 2AB, 2AC, 2A1B1C
230
60
6
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C
370
72
7
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB,
380
84
8
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB, 3AC
530
96
9
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB, 3AC, 3A1B2C
630
108
10
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB, 3AC, 3A1B2C, 2A3B1C
650
120


### 2.2. Simulation Results

Table4 shows the simulation results of the ten tested scenarios (Table 3), for each of the four manufacturing resources (i.e., Machines M1, M2, M3, and M4, Figure 2), in terms of waiting time (Wt, minutes) and queue length (Lq, number of units). Figures 4(a) through 4(d) shows the normalized values of Table 4, where in each case Series 1 (solid line) refers to Wt and Series 2 (short dotted-double line) refers to Lq. It can be observed that the behavior of both Wt and Lq follows a similar trend, where for the case of M1 and M4, both trend lines are almost superposed. Section 3 focuses on deriving the βɛMC4.0 expression, capable of resembling the observed behavior of the system.Table 4
Simulation results for all the manufacturing resourcesMi.
Manufacturing resourceMi
Performance measure
Scenario number
1
2
3
4
5
6
7
8
9
10
M
1
W
t
0
0
5.0831
1.6936
0.8237
0.6505
4.4763
5.746
17.7376
28.2154
L
q
0
0
0.6172
0.2177
0.1325
0.0826
0.7068
0.7264
2.2805
4.4277
M
2
W
t
1.2277
1.2665
2.7831
2.9662
3.3501
4.4514
5.782
5.3816
5.8239
9.0689
L
q
0.2947
0.1327
0.3854
0.2996
0.6222
0.7742
0.672
0.6295
0.9502
1.0796
M
3
W
t
0
2.083
4.5715
6.8466
14.324
17.3799
17.7636
22.3587
39.8257
59.6567
L
q
0
0.1488
0.5403
0.739
1.5832
2.1518
2.2409
3.8885
5.628
5.92
M
4
W
t
0.1429
24.3277
20.0246
55.0574
29.1356
50.6609
68.965
144.81
148.04
200.79
L
q
0.00342
5.3079
5.1492
12.5846
7.6006
9.8553
15.2449
26.2297
27.33
34.219Figure 4
(a)M1 behavior; (b) M2 behavior; (c) M3 behavior; (d) M4 behavior.
(a)
(b)
(c)
(d)


## 2.1. Simulation Model

The discrete-event simulation (DES) model of the mass customization production system was build following an approach similar to the one presented in Raza et al. [20], where the impact of introducing the Industry 4.0 paradigm within a Mass Customization environment is studied. This DES model was developed in ARENA [82] and used to generate statistical output regarding its performance (measured in terms of the manufacturing resources’ queue length, and the products’ waiting time). The logic behind the DES model was implemented based on the structure of the model “A Small Manufacturing System,” presented in [82], specifically with the use of the STATION and ROUTE modules. Figure 3 presents an excerpt of the DES model, for the case of manufacturing resource M1. The simulation run output was verified and validated according to the recommendations proposed by Hwarng et al. [83]. The trace and debugging functions were used to check the logic of the activities an entity encounters in the system, and the DES model output was examined for reasonableness by setting the processing times to some known deterministic value and compared with manual calculations (finding no discrepancies between the simulation and manual results). In this case, the DES model can be considered as a research instrument for theory testing [84] rather than for theory development [85]. A simulation run time, long enough to allow the total processing of twelve units of each product type, was used. The mass customization production system is assumed to be operating continuously, i.e., breakdowns, changeover, setup, and load/unload times are assumed to be negligible, and each manufacturing resource is capable of processing only one unit at a time. All the manufacturing resources were subject to certain degree of variation (reflected as an exponential normal distribution for the processing times). Thirty replications were used in order to avoid significant variation in the observed results. Confidence intervals of 90% were used in order to provide the proper statistical basis for making inferences and conclusions. Ten different scenarios were tested under these operative conditions (Table 3).Figure 3
Excerpt of the DES model, manufacturing resourceM1 case.Table 3
Tested scenarios.
Scenario number
Product type processed
Simulation run time (min)
Number of units produced
1
1B
60
12
2
1B, 1C
110
24
3
1B, 1C, 2AB
140
36
4
1B, 1C, 2AB, 2AC
210
48
5
1B, 1C, 2AB, 2AC, 2A1B1C
230
60
6
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C
370
72
7
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB,
380
84
8
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB, 3AC
530
96
9
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB, 3AC, 3A1B2C
630
108
10
1B, 1C, 2AB, 2AC, 2A1B1C, 1A2B1C, 3AB, 3AC, 3A1B2C, 2A3B1C
650
120


## 2.2. Simulation Results

Table4 shows the simulation results of the ten tested scenarios (Table 3), for each of the four manufacturing resources (i.e., Machines M1, M2, M3, and M4, Figure 2), in terms of waiting time (Wt, minutes) and queue length (Lq, number of units). Figures 4(a) through 4(d) shows the normalized values of Table 4, where in each case Series 1 (solid line) refers to Wt and Series 2 (short dotted-double line) refers to Lq. It can be observed that the behavior of both Wt and Lq follows a similar trend, where for the case of M1 and M4, both trend lines are almost superposed. Section 3 focuses on deriving the βɛMC4.0 expression, capable of resembling the observed behavior of the system.Table 4
Simulation results for all the manufacturing resourcesMi.
Manufacturing resourceMi
Performance measure
Scenario number
1
2
3
4
5
6
7
8
9
10
M
1
W
t
0
0
5.0831
1.6936
0.8237
0.6505
4.4763
5.746
17.7376
28.2154
L
q
0
0
0.6172
0.2177
0.1325
0.0826
0.7068
0.7264
2.2805
4.4277
M
2
W
t
1.2277
1.2665
2.7831
2.9662
3.3501
4.4514
5.782
5.3816
5.8239
9.0689
L
q
0.2947
0.1327
0.3854
0.2996
0.6222
0.7742
0.672
0.6295
0.9502
1.0796
M
3
W
t
0
2.083
4.5715
6.8466
14.324
17.3799
17.7636
22.3587
39.8257
59.6567
L
q
0
0.1488
0.5403
0.739
1.5832
2.1518
2.2409
3.8885
5.628
5.92
M
4
W
t
0.1429
24.3277
20.0246
55.0574
29.1356
50.6609
68.965
144.81
148.04
200.79
L
q
0.00342
5.3079
5.1492
12.5846
7.6006
9.8553
15.2449
26.2297
27.33
34.219Figure 4
(a)M1 behavior; (b) M2 behavior; (c) M3 behavior; (d) M4 behavior.
(a)
(b)
(c)
(d)


## 3. Theory Foundation of theβɛMC4.0 Expression

At this point, it must be noted that, in order for theβɛMC4.0 expression to truly represent the manufacturing complexity of a mass customization production system operating within an Industry 4.0 environment, the complexity contribution of the product, process, and resources elements must be taken into account. These elements refer to(i)
Product: the different number of manufactured products, the number of number of corresponding components and functions, and the overall products’ mix ratio(ii)
Process: the different routings for each product and the corresponding processing times(iii)
Resources: the different types of machinery, number and type of operations capable of performing, and number of required setupsNow, Martínez-Olvera explained in his work of [76] (equation (1)) and [77] (equation (2)) why formulations such as the ones presented by [58, 86] need to be modified in order to reflect the impact the BOM structure has on the process flow. In a similar way, equations (1) and (2) must be adapted in order to reflect the manufacturing complexity contribution to the mass customization production system operating within an Industry 4.0 environment:(1)βεΝΒ=11/PNB∗log21/PNB,(2)βεNB=1PX∗log211−PNBY∗PNBY.For this matter, both equations (1) and (2) were manipulated for different combinations of the P log2 P expression, i.e., P log2 P, P log2 (1/P), (1/P) log2 P, (1/P) log2 (1/P), and 1/[(1/P) log  2 (1/P)], until one combination resembled the observed behavior of the system (Figures 4(a) through 4(d)). In this case, the βɛMC4.0 expression took the form of (3)βεMC4.0=1P∗log21P,where Pi is calculated as shown in Table 5 (for the case of manufacturing resource M1, Table 5). It must be noted that whenever a product processing time on M1 appears as NA, its contribution to βεMC4.0 expression value is considered to be negligible. Now, the term Σ processing time is the accumulated time for each tested scenario (Table 3). In this way, Σ processing time for scenario 7 = 10 and is the result of adding up the processing time of product 1 up to product 7 (i.e., 0 + 0 + 2 + 2 + 2 + 1 + 3 = 10). Plugging these probabilities Pi into the βεMC4.0 expression, the values shown in Table 6 are obtained. Appendix at the end of this document shows more details of the mechanics of these calculations.Table 5
ProbabilitiesPi for all the ten tested scenarios.
Product number
1
2
3
4
5
6
7
8
9
10
Processing time onM1 (from Table 2)
NA
NA
2
2
2
1
3
3
3
2
Σ processing time
0
0
2
4
6
7
10
13
16
18
P
1
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
P
2
NA
NA
NA
NA
NA
NA
NA
NA
NA
P
3
1
0.5
0.333
0.285
0.2
0.153
0.125
0.111
P
4
0.5
0.333
0.285
0.2
0.153
0.125
0.111
P
5
0.333
0.285
0.2
0.153
0.125
0.111
P
6
0.142
0.1
0.0769
0.0625
0.0555
P
7
0.3
0.230
0.187
0.166
P
8
0.230
0.187
0.166
P
9
0.1875
0.166
P
10
0.111
Scenario number
1
2
3
4
5
6
7
8
9
10Table 6
βɛ
MC4.0 values for manufacturing resource M1.
Scenario number
1
2
3
4
5
6
7
8
9
10
P
1
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
P
2
NA
NA
NA
NA
NA
NA
NA
NA
NA
P
3
0
2
4.754
6.325
11.609
17.552
24
28.529
P
4
2
4.754
6.325
11.609
17.552
24
28.529
P
5
4.754
6.325
11.609
17.552
24
28.529
P
6
19.651
33.219
48.105
64
75.058
P
7
5.789
9.167
12.880
15.509
P
8
9.167
12.880
15.509
P
9
12.880
15.509
P
10
28.529
βɛ
MC4.0
NA
NA
0
4
14.264
38.628
73.838
119.098
174.6406
235.705Table7 shows the βɛMC4.0 expression values for all the rest of the manufacturing resources Mi. Figures 5(a) through 5(d) show the normalized values of Table 7 (Series 3, long dotted-double line), where again, in each case Series 1 (solid line) refers to Wt and Series 2 (short dotted-double line) refers to Lq. It can be observed that the normalized values of the βɛMC4.0 expression follow the trend of the normalized values of Wt and Lq, where in some cases (i.e., M3 and M4) this following is really close. A look to the accumulated workload per manufacturing resource Mi (shown in Table 8) reveals that it is precisely these two manufacturing resources that are the ones exhibiting the highest values (20.68% and 50.86%, respectively), leading us to think that there is a relationship between the accuracy of the βɛMC4.0 expression and the level of workload of a manufacturing resource Mi. So up to this point, the βɛMC4.0 expression acts as a fairly good trend indicator of the system’s performance parameters increase/decrease, but not as an estimator of the final values. This conclusion is consistent with the previous reported findings, i.e., [76, 77].Table 7
βɛ
MC4.0 values for all the manufacturing resources Mi.
Manufacturing resource type
βɛ
MC4.0 value
Scenario number
1
2
3
4
5
6
7
8
9
10
M
1
Actual
NA
NA
NA
4
14.264
38.628
73.838
119.098
174.6406
235.705
Normalized
NA
NA
NA
0.016
0.0605
0.163
0.313
0.505
0.7409
1
M
2
Actual
0
0
4.533
4.533
22.264
43.773
78.853
78.853
133.0586
195.638
Normalized
0
0
0.0231
0.0231
0.113
0.223
0.403
0.403
0.6801
1
M
3
Actual
0
0
0
4
18.219
40.529
40.529
81.342
123.561
183.587
Normalized
0
0
0
0.0217
0.0992
0.2207
0.2207
0.443
0.673
1
M
4
Actual
0
4.265
17.151
43.866
76.865
128.2303
185.4705
272.136
364.0225
475.45
Normalized
0
0.0089
0.036
0.0922
0.161
0.269
0.39009
0.572
0.765
1Figure 5
(a)M1βɛMC4.0 value behavior; (b) M2βɛMC4.0 value behavior; (c) M3βɛMC4.0 value behavior; (d) M4βɛMC4.0 value behavior.
(a)
(b)
(c)
(d)Table 8
Accumulated workload per manufacturing resourceMi.
Scenario
∑ti per Mi
∑ti per Mi (%)
M
1
M
2
M
3
M
4
Total ∑t
M
1
M
2
M
3
M
4
1
0
36
0
36
72
50
50
2
0
36
48
84
168
21.42
28.57
50
3
24
60
48
108
240
10
25
20
45
4
48
60
96
180
384
12.5
15.62
25
46.87
5
72
72
120
240
504
14.28
14.28
23.80
47.61
6
84
96
144
324
648
12.96
14.81
22.22
50
7
120
132
144
396
792
15.15
16.66
18.18
50
8
156
132
216
504
1008
15.47
13.09
21.42
50
9
192
144
264
600
1200
16
12
22
50
10
216
180
288
708
1392
15.51
12.93
20.68
50.86Now, before proceeding to Section4, a couple of things must be mentioned. According to [87], the “what,” “where,” and “how” of a production process is known as the execution function, which depends on the relatively static physical configuration of the production system. On the other hand, the “what,” “where,” and “when” is known as the decision-making function, which depends on the relatively dynamic physical configuration of the production system (due to the presence of alternative manufacturing resources). In this case, the βɛMC4.0 expression (as developed so far) only reflects the “execution” part of the mass customization production system, as the manufacturing process for all the ten products is always the same. Section 4 tests the validity of the βɛMC4.0 expression for the “decision-making” part, as the Industry 4.0 complexity component (in the form of manufacturing resources flexibility) is added to the operation of the mass customization production system.Figure 6
(a) Product-to-product operation mode. (b) Machine-to-machine operation mode.
(a)
(b)


## 4. Adding the Industry 4.0 Complexity Component

Among the main pillars of Industry 4.0 mentioned by [88](1)
Smart products: the product itself requests the required resources and orchestrates the production processes for its completion.(2)
Smart machines; machines can self-organize within the production network to orchestrate the production processes for its completion; therefore, it becomes a matter of interest to test the validity of theβɛMC4.0 expression when these operation modes are added to the mass customization production system. More specifically, now there are two new types of manufacturing resources (i.e., M14 and M23, as shown in Figure 2) within the mass customization production system. Because of this last, now each product has a “variable” manufacturing process, which changes dynamically, depending on the operation mode of the production system. In this way,(a)
Pillar #1, product-to-product operation mode (Figure6(a)): products “talk” to each other and decide which one is processed next by a certain manufacturing resource(b)
Pillar #2, machine-to-machine operation mode (Figure6(b)): manufacturing resources “talk” to each other and decide which product is processed next by each one of themFigure6(a) refers to the product-to-product operation mode, where products trade place depending on which type of manufacturing resource is free. For example, M23 is free and can fulfill 50% of the manufacturing process of Product 2A1B1C (and because of this Product 1B trades its first place on the waiting queue). In the case of Figure 6(b), the machine-to-machine operation mode, each manufacturing resource drags to its waiting queue the type of product that is more convenient to be processed next. For example, M23 drags Product 2A1B1C from M2 waiting queue (for the same reason expressed above) and M2 proceeds in a similar way (dragging Product 1B from M23 waiting queue). In this way—as a first step in this research line—it becomes necessary to adapt the discrete-event simulation model (described in Section 2.1) in order to reflect the product-to-product operation mode (leaving the machine-to-machine operation mode for future research, mainly to not overextend the length of this research document), use the same operative conditions of the ten tested scenarios (presented in Section 2.1), and arbitrarily assigning products 5 and 6 priority of use of manufacturing resources M14 and M23, respectively. The logic behind the product-to-product operation mode was implemented based on the structure of the model “Service Model with Balking and Reneging,” presented in Reference [82], specifically with the use of the SEARCH and REMOVE modules. Figure 7 presents an excerpt of the DES model, for the case of manufacturing resource M1 and M14.Figure 7
Excerpt of the DES model, manufacturing resourceM1 and M14 case.Now, regarding the calculation of the probabilitiesPi (used in equation (3)), as these depend upon the processing time of each product’s manufacturing process route—which now varies due to the fact that there are multiple alternative manufacturing process routes (result of including machines M14 and M23)—there is a need of making an adjustment to the calculation of Pi. Table 9 presents all the alternative manufacturing process routes each product can follow, the frequency on which these routes are followed (for this matter, the number of simulations replications was varied until no significant variation in the frequency was observed), and the impact of these frequencies have on the corresponding processing times of each product (Appendix at the end of this document shows the calculations that verify the validity of these values. In this way, the processing times on M1—presented on Table 5 (second row)—become the processing times, as shown in Table 10 (second row), and the calculation of Pi is performed as established previously.Table 9
Alternative manufacturing process routes, frequency, and processing time impact.Table 10
Processing times onM1, product-to-product operation mode.
Product number
1
2
3
4
5
6
7
8
9
10
Processing time onM1 (from Table 8)
NA
NA
1.456
1.403
1.884
0.567
2.1
2.526
2.069
1.647
Scenario number
1
2
3
4
5
6
7
8
9
10Appendix at the end of this document shows more into details the mechanics of the calculations that verify the validity of the values, as shown in Table9. Table 11 shows the simulation results of the new ten tested scenarios and each of the six manufacturing resources (original machines M1, M2, M3, and M4 plus the new M14 and M23), while Table 12 shows the respective βɛMC4.0 values, and Figures 8(a) through 8(f) show the normalized values presented on Tables 11 and 12. In this case, Wt is Series 1 (solid line), Lq is Series 2 (short dotted-double line), and βɛMC4.0 is Series 3 (long dotted-double line). Once again, the normalized values of the βɛMC4.0 expression follow the trend of the normalized values of Wt and Lq. However, an analysis similar to the one presented on Table 13 reveals that, in this case, the really close trend following occurs for the alternative, and more flexible, manufacturing resources M14 and M23 (which by the way are not necessarily the manufacturing resources Mi with the highest accumulated workload. See values in Table 13, cursive letters).Table 11
Simulation results for all the manufacturing resourcesMi, product-to-product operation mode.
Manufacturing resource type
Performance measure
Scenario number
1
2
3
4
5
6
7
8
9
10
M
1
W
t
0
0
2.92238
9.28534
10.3184
9.91678
10.35529
22.97604
36.93882
37.81155
L
q
0
0
0.58448
1.80882
1.60989
1.79299
2.12701
4.68359
7.07289
7.78699
M
2
W
t
0.068015
0.04397
0.03248
0.15121
0.31276
0.86571
0.94587
1.36474
1.63628
1.72897
L
q
0.026831
0.00736
0.00401
0.02487
0.04988
0.11504
0.08575
0.24988
0.28741
0.63056
M
3
W
t
0
1.0568
7.4287
9.65
10.1475
23.034
23.404
28.4089
25.7417
34.3669
L
q
0
0.06216
0.7718
0.9608
1.6419
3.0547
2.5648
2.803
3.6526
4.3138
M
4
W
t
6.5205
8.2246
19.5139
55.7554
74.9685
89.057
95.1337
99.86
113.39
146.11
L
q
1.6827
1.8534
7.3464
14.1199
15.1477
17.7343
18.0254
18.6403
23.011
27.7217
M
14
W
t
0
0
0.62612
2.91039
3.37538
4.74147
5.17198
8.1691
8.95613
12.5698
L
q
0
0
0.12522
0.532
0.65754
0.8005
1.08044
1.69192
1.83971
2.41296
M
23
W
t
0.01098
0.02437
0.06484
0.12747
0.15551
0.22679
0.44441
0.68015
1.72897
2.18371
L
q
0.00184
0.00301
0.0233
0.02863
0.03568
0.09589
0.1067
0.2683
0.39983
0.63056Table 12
βɛ
MC4.0 values for all the manufacturing resources Mi, product-to-product operation mode.
Manufacturing resource type
βɛ
MC4.0 value
Scenario number
1
2
3
4
5
6
7
8
9
10
M
1
Actual
0
0
0
4.0043
14.8442
48.5124
87.2767
142.3354
201.6518
267.3943
Normalized
0
0
0
0.01497
0.05551
0.1814
0.3263
0.5323
0.7541
1
M
2
Actual
0
0
4.7742
4.7742
21.8159
44.3254
80.0908
80.0908
139.6183
229.7801
Normalized
0
0
0.0207
0.0207
0.0949
0.1929
0.3485
0.3485
0.6076
1
M
3
Actual
0
0
0
4.0267
28.7594
57.2397
57.2397
112.08805
159.6902
221.2003
Normalized
0
0
0
0.0182
0.13001
0.2587
0.2587
0.5067
0.7219
1
M
4
Actual
0
4.2354
20.5223
44.5156
79.5022
120.9563
174.9743
261.0525
340.8966
436.4710
Normalized
0
0.0097
0.04701
0.1019
0.1821
0.2771
0.4008
0.59809
0.78102
1
M
14
Actual
0
4.9030
43.4703
180.3520
243.1385
518.7584
737.7693
967.6952
1353.8182
1748.8002
Normalized
0
0.0028
0.0248
0.1031
0.1390
0.2966
0.4218
0.5533
0.7741
1
M
23
Actual
0
6.3650
18.4740
38.1322
71.1841
114.1881
164.1948
226.5268
325.0292
417.8465
Normalized
0
0.0152
0.0442
0.0912
0.1703
0.2732
0.3929
0.5421
0.7778
1Figure 8
(a)M1βɛMC4.0 values behavior; (b) M2βɛMC4.0 values behavior; (c) M3βɛMC4.0 values behavior; (d) M4βɛMC4.0 values behavior; (e) M14βɛMC4.0 values behavior; (f) M23βɛMC4.0 values behavior.
(a)
(b)
(c)
(d)
(e)
(f)Table 13
Accumulated workload per manufacturing resourceMi.
Scenario
∑ti per Mi
∑ti per Mi (%)
M
1
M
2
M
3
M
4
M
14
M
23
Total ∑ti
M
1
M
2
M
3
M
4
M
14
M
23
1
0
20.076
0
33.924
2.076
15.924
72
27.883
47.116
2.883
22.116
50
50
22.116
2.883
(2.883)
(22.116)
2
0
20.076
41.004
78.42
5.58
22.92
168
11.95
24.407
46.678
3.321
13.642
21.42
28.57
50
9.47
4.162
3.322
(3.322)
(9.47 + 4.162)
3
17.472
32.424
41.004
95.424
19.092
34.572
239.988
7.280
13.510
17.085
39.761
7.955
14.405
10
25
20
45
2.719
11.489
2.914
5.238
(4.162 + 5.238)
(11.489 + 2.914)
4
34.308
32.424
78.408
142.176
51.504
45.168
383.988
8.934
8.444
20.419
37.026
13.412
11.762
12.5
15.62
25
46.87
3.565
7.175
4.580
9.843
(3.565 + 9.843)
(7.175 + 4.580)
5
56.916
39.204
89.892
194.352
60.72
62.904
503.988
11.293
7.778
17.836
38.562
12.047
12.481
14.28
14.28
23.8
47.61
2.986
6.501
5.963
9.047
(2.986 + 9.047)
(6.501 + 5.963)
6
63.72
54.96
104.22
236.976
107.292
80.82
647.988
9.833
8.481
16.083
36.571
16.557
12.472
12.96
14.81
22.22
50
3.126
6.328
6.136
13.428
(3.126 + 3.126)
(6.328 + 6.328)
7
88.92
75.96
104.22
287.376
139.692
95.82
791.988
11.227
9.591
13.159
36.285
17.638
12.098
15.15
16.66
18.18
50
3.922
7.068
5.020
13.714
(3.922 + 13.714)
(7.068 + 5.020)
8
119.232
75.96
159.168
369.792
170.952
112.872
1007.976
11.828
7.535
15.790
36.686
16.959
11.197
15.47
13.09
21.42
50
3.641
5.554
5.629
13.313
(3.641 + 13.313)
(5.554 + 5.629)
9
144.06
82.164
183.996
426.072
221.844
141.84
1199.976
12.005
6.847
15.333
35.506
18.487
11.820
16
12
22
50
3.994
5.152
6.666
14.493
(3.994 + 14.493)
(5.152 + 6.666)
10
163.824
113.928
202.344
489.6
270.552
151.728
1391.976
11.769
8.184
14.536
35.173
19.436
10.900
15.51
12.93
20.68
50.86
3.740
4.745
6.143
15.686
(3.740 + 15.686)
(4.745 + 6.143)If the accuracy of theβɛMC4.0 expression is related to the level of workload of a manufacturing resource Mi, an explanation for these results lies in (1) the fact that these two manufacturing resources (that is, M14 and M23) split the workload of manufacturing resources M4 and M3, respectively, and (2) the fact that these two manufacturing resources (that is, M14 and M23) have priority of use for some of the products. Table 13 shows how the workload is split, by comparing the values of Table 13, cursive letters, and Table 10 (bold letters). These results lead us to conclude that up to this point, the βɛMC4.0 expression acts as a fairly good trend indicator of the system’s performance parameters increase/decrease, even for the case of a “variable” manufacturing process, which changes dynamically.


### 4.1. Managerial Implications

The results obtained suggest that theβɛMC4.0 expression can be used as a trend indicator tool, but not as a predictor tool. It is our belief that the managerial implications of the βɛMC4.0 expression are promising, specifically in the area of production scheduling and programing of a manufacturing system operating within and Industry 4.0 context. As mentioned by [86], developing a production program/schedule is about to squeeze products through available resources, a very difficult task specially when dealing with a complex system—where this last fact is expressed in terms of options and constraints—and that often result on unfeasible or difficult-to-follow schedules [59]. Due to the flexibility exhibited by a manufacturing system operating within and Industry 4.0 context, the machine assignment and operation sequencing is known as flexible job shop scheduling, a very complex problem where traditional mathematic optimization methods are difficult to tackle within a reasonable amount of time [89]. By using the βɛMC4.0 as a basis, a methodology to assess the degree of complexity of a production program/schedule could be developed and use it to find (or choose) more attractive and beneficial options.


## 4.1. Managerial Implications

The results obtained suggest that theβɛMC4.0 expression can be used as a trend indicator tool, but not as a predictor tool. It is our belief that the managerial implications of the βɛMC4.0 expression are promising, specifically in the area of production scheduling and programing of a manufacturing system operating within and Industry 4.0 context. As mentioned by [86], developing a production program/schedule is about to squeeze products through available resources, a very difficult task specially when dealing with a complex system—where this last fact is expressed in terms of options and constraints—and that often result on unfeasible or difficult-to-follow schedules [59]. Due to the flexibility exhibited by a manufacturing system operating within and Industry 4.0 context, the machine assignment and operation sequencing is known as flexible job shop scheduling, a very complex problem where traditional mathematic optimization methods are difficult to tackle within a reasonable amount of time [89]. By using the βɛMC4.0 as a basis, a methodology to assess the degree of complexity of a production program/schedule could be developed and use it to find (or choose) more attractive and beneficial options.


## 5. Conclusions and Future Research

The international global dynamic competition impose a series of pressures due to the fact that customers tend to increase variant diversity, ask for smaller lot sizes, and demand shorter cycle times, while at the same time, to have the opportunity to design their own products/services without a high price premium. This concept of mass customization falls within the possibilities of an Industry 4.0 environment, where the level of manufacturing complexity increases with level of product customization. As currently there is no comprehensive metric that addresses the complexity derived from both the mass customization variety-induced complexity and from the adoption of the Industry 4.0 paradigm, in this research, it was proposed the first step—in the form of an entropy-based (entropic) formulation—into the development of a comprehensive metric that covers both sources of complexity. The original contribution of this paper (theβɛMC4.0 expression) was put to the test via a DES model of a mass customization production system operating within an Industry 4.0 context. From our findings, we can derive several conclusions:(1)
TheβɛMC4.0 expression acts as a fairly good trend indicator of the system’s performance parameter increase/decrease(2)
TheβɛMC4.0 expression fails to act as an estimator of the system’s performance parameter final values(3)
The accuracy of theβɛMC4.0 expression—regarding how close it follows the system’s performance behavior—is related to the level of workload of a manufacturing resource Mi(4)
The system’s performance behavior (i.e., queue length and the products’ waiting time) is dependent on the number (and frequency of use) of all the alternative manufacturing process routes followed (when flexible manufacturing resourcesMi are present)(5)
The number (and frequency of use) of all the alternative manufacturing process routes followed—when flexible manufacturing resourcesMi are present—is dependent on the priority assignation of the products using the flexible manufacturing resources MiThe recommendations for future research include(1)
To explore the use of conditional probabilitiesPi on equation (1), in order to reflect the priority assignation of the products using the flexible manufacturing resources Mi(2)
To assess the validity of theβɛMC4.0 expression under failure conditions of the manufacturing resources Mi(3)
To introduce a complexity element derived from the information flow present in the product-to-product and machine-to-machine operation modes, as in this study it is assumed to be accurate, timely, consistent, and in the proper format, and that its handling is flawless(4)
To derive a correcting factor, so the proposedβɛMC4.0 expression can be used a highly accurate predictor tool of the system’s performance parameters’ final values and not only as a trend indicator.



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*Source: 6376010-2020-02-08.xml*