Simulation optimization of lean production strategy by considering resilience engineering in a production system with maintenance policies

Abstract

Lean production aims are to reduce work-in-process and maintain close to zero inventories and resilience is about reacting quickly to disruptions impacting manufacturing systems. In this study, a manufacturing organization with maintenance strategy is simulated to evaluate the impacts of resilience engineering (RE) principles on lean practices. The process of simulation is conducted for different scenarios. Each scenario includes a set of resilience principles. Using computer simulation, many outputs are calculated namely, utility and availability of machines and maintenance operators, time in system, total cost, and number of failures. The optimal values of scenarios’ efficiencies are achieved using data envelopment analysis (DEA) model, which is a mathematical programming approach. The results of the DEA are validated by using principal component analysis. In addition, an analysis is performed to determine which factor of RE has the maximum effect on the system’s performance. The results show that the redundancy among the RE principles, has the maximum impact on the system’s performance. To the best of my knowledge, this is the first study that evaluates the performance of lean production considering RE in a production line with maintenance policies.

Keywords

Computer simulation data envelopment analysis (DEA)lean production maintenance policies principal component analysis (PCA)resilience engineering (RE)

1. Introduction

The concept of leanness is based on increasing the flexibility and reducing cost. It focuses on the elimination or at least reduction of all types of wastes. In lean production, all activities that consume resources without creating value for the customers are eliminated.¹ The main objective of lean practices is the removal of seven types of wastes (i.e., overproduction, waiting, transportation, excessive processing, inventory, motion, defects) that leads to decrease the costs.² Recently, utilizing workforce creativity below its potential has been considered as the eighth waste.³ On the other hand, for different fields of system management such as safety, flexibility and cost, the principles of resilience are important factors,⁴ because with the help of resilience the system can recover its statuses after incidents have occurred, instead of preventing misfortunes from happening.⁵

A resilient manufacturing system must have enough inventories to react to the impacts of disruptions and interruptions which may happen in a system; a lean manufacturing system means nearly zero inventories. These concepts seem to be contradictory. However, it would be ideal to have both systems working together in an organization. These facts suggest further research in supply chain management and production system; resilient and lean concepts need to be modeled on a compatibility basis.

Actually, we can characterize the disruptions in terms of our ability to predict the disruption or plan for it. Things such as earthquakes are unpredictable. You can choose not to build the factory in an earthquake zone (but some choose not to worry about that if you can build the structure “resiliently”). We cannot always predict or anticipate other system stressors such as labor disruptions, mineral or material shortages, equipment malfunction, etc. But we can try to take steps to reduce the impact (or inoculate our system from their effects). Planning, redundancy, alternate sources, careful choice of components/suppliers/sources, etc. all can help. According to the literature, resilience is defined as “the capability of the systems to respond to an unexpected disruption and to return rapidly to their original state or move to a new state that is more advantageous, after the disturbance”.⁶

For assessment and evaluation of leanness,⁷ Vinodh identified five enablers. Each of these enablers is identified based on a number of leanness criteria to evaluate and assess a series of attributes related to leanness.⁷ The enablers are:

the responsibility of management system;

the leanness related to manufacturing management;

the leanness related to workforce;

the leanness related to technology;

the leanness related to strategy of manufacturing.

In RE, failures do not lead to a malfunctioning or breakdown of normal system functions, but rather represent the converse of the adaptations necessary to deal with the real world complexity.⁸ Organizations and individuals must always modify their performance to the current situations; and because time and resources are finite it is unavoidable that such modifications are predicated. Success has been ascribed to the capability of organizations, individuals, and groups to forecast the changing shape of risk before damage happens; failure is simply the permanent or temporary absence of that. After extensive research in the areas of lean manufacturing and RE and according to experts’ experiences, this study employs some RE principles which are related to the enablers of leanness. The RE principles (or factors) are top management commitment, reporting culture, visibility, awareness, velocity, redundancy, and flexibility. These factors are briefly described below.

Top management commitment (R1): based on this principle, the lean production is the major challenge with which organizations are faced. This principle should be permanently taken into account in all levels of organization. This principle recognizes the problems and concerns of the human performance. The main object of this principle is to try to solve these concerns.⁹

Reporting culture (R2): this principle implies that issues of lean production should be reported up through the organization or system, considering this fact that innocent behaviors are unacceptable. The willingness of operators to report the problems and issues is increased if there is an appropriate reporting culture.⁹

Visibility (R3): this principle implies that in a company a clear and perfect view of upstream and downstream products, demand, conditions of system, schedules of purchasing and production and the lines of communications and agreement should exist.⁶

Awareness (R4): this principle implies that personnel should be aware of the present situation and the defenses situation in the system. By collecting data, managers have the opportunity to be aware of all that happens in the company. For executing this principle two comprehensive methods by Rasmussen et al.¹⁰ are proposed: (1) measuring the performance of system based on proactive criteria, and (2) the design of observable boundaries of the system performance.

Velocity (R5): this principle refers to the rate at which the system can return to normal after the disturbance.¹¹

Redundancy (R6): this principle has different definitions depending on different perspectives. Redundancy is a form of resilience that ensures system availability in the event of component failure. In engineering perspective, it implies that in a manufacturing system for essentials part and basic equipment a copy should be existed to improve the reliability of the system.¹² Redundancy also can be defined as the availability of different paths of resources to answer to the demands and the capacity of supporting under ordinary circumstances.¹³

Flexibility (R7): this principle refers to the ability of a system to self-organization when the possible fluctuations and pressures from outside occur. Flexibility is an important criterion to confront unanticipated happenings.

For modeling the manufacturing system based on leanness factors, providing an exact mathematical model is not easy because of the complex nature of these factors and different and conflicting objectives. Therefore, using the simulation approach is appropriate to alleviate this complexity.¹⁴ In different areas of engineering the simulation models are developed to solve various problems, for example production planning and control,¹⁵ understanding the concepts of lean manufacturing,¹⁶ providing a tool for evaluating the impact of applying lean principles to the design process¹⁷ and production life cycle analysis.¹⁸ Managers can use the information obtained from the simulation process to compare the performance between the lean system and the existing system. Also they can determine the superior system, and provide a convincing basis for the implementation of lean.

According to the proposed methodology, the impacts of leanness factors in the manufacturing system are assessed by simulating the actual process and the accidental behavior of a real system. In this study, to achieve the required data related to the system, different scenarios which are the combinations of several RE factors are generated. The preferred scenario is determined based on different goals such as time in system (TIS) and total cost. This study shows that applying resilience factors on a manufacturing system leads to improve the performance of lean production strategy. The value added of the RE is that it provides a way to address the issues of emergent accidents and the often disproportionate consequences that are an outcome of ever more complex technologies and ever more integrated organizations.

1.1. Motivation and significance

The organizational environment is always changing; these changes originate from several sources such as suppliers, customers, government, and competitors. With the presence of new entrants to global market, the level of competition has been significantly enhanced. In most organizations, managers are looking for ways to reduce the cost and increase the performance, simultaneously. Therefore, considering efficient management concepts such as lean production can be very significant and applicable to these objectives. Resilience is seen as a key organizational capability for sustainability in the current turbulent environment. Also, the leanness can be considered as a challenge for most manufacturing systems because staying competitive requires looking for new ways of reducing costs and increase the quality of the company’s products. Lean thinking was and is considered to be one potential approach for improving organizational performance. By applying the principles of resilience, systems can respond to challenges and interruptions efficiently. Therefore, if the leanness enablers are taken into account as a challenge for the production system, the concept of resilience engineering (RE) can be very useful for coping with this challenge. This study, for the first time, assesses the impact of resilience factors on lean production by simulation optimization and DEA approach. The results of DEA are validated using PCA method. Also, the results are analyzed in order to determine the degree of effect of each RE factor on our lean production system.

The systematic application of the concepts proposed in this paper allows businesses the opportunity to improve their performance, adding concepts and tools that will contribute to improvement in organizational culture and organizational processes. Table 1 highlights the RE factors considered in this paper in competition with the previous works.

Table 1.

Resilience engineering (RE) factors considered in this paper vs. previous works.

Study	Resilience principle
Study	Top management commitment	Flexibility	Visibility	Reporting culture	Awareness	Velocity	Redundancy
This study	✓	✓	✓	✓	✓	✓	✓
Yang et al.¹⁹	✓		✓			✓
Shah and Ward²⁰	✓	✓
Metternich et al.²¹		✓
Wahab et al.²²	✓	✓	✓			✓
Staats et al.²³	✓	✓			✓

The rest of this study is presented as follows. In Section 2, the literature on leanness and resilience is reviewed. The methodology of this study is represented in Section 3. The case study of a manufacturing organization is presented in detail in Section 4, and the numerical results are presented in Section 5. Finally, Section 6 presents the conclusions of this study.

2. Literature review

In this section, some recent studies in the fields of leanness and resilience engineering are briefly reviewed.

2.1. Leanness

After World War II in Japan, because of the existing conditions such as shortage of raw materials, lack of funding and financial support, and a sharp decrease in human resources, a new concept called “lean” production emerged.²⁴ For the sector of make-to-order, Muda and Hendry²⁵ represented a concept of world-class manufacturing combined with the lean principles. Within the framework of lean manufacturing, Sullivan et al.²⁶ assessed the performance of equipment replacement based on the decision problems in lean manufacturing execution. For providing the required data, they applied value stream mapping (VSM) as a road map. Holden²⁷ reviewed the changes occurred in several emergency departments (EDs), after applying the principles of lean.

Ringen and Holtskog²⁸ discussed how intrinsic motivation is affected by lean enablers such as Customer Requirements (CRs), clear project objectives, cross-functional teams and continuous improvement. Susilawati et al.²⁹ proposed a fuzzy logic based method for the measurement of degree of leanness. Their model can deal with the multi-dimensional concept, unavailability benchmark, and uncertainty, which arises from the subjective and vague human judgments. Azadeh et al.³⁰ presented a new method to assess and optimize organizational leanness. They used fuzzy cognitive map and multivariate analysis for the evaluation. A number of packing and printing organizations was assessed in their study.

Lean, agile, resilient, and green (LARG or LARGe) paradigms develop a deep understanding of interrelationships, conflicts and trade-offs across lean, agile, resilient and green paradigms. This understanding is believed to be vital to render these concepts really compatible. Several studies are carried out in LARG management. Cabral et al.,³¹ proposed an integrated LARG analytic network process (ANP) model to support decision-making in selecting the most appropriate practices and key performance indicators to be implemented by companies in a supply chain. The model is applied in a case study in an automaker supply chain to validate it. Carvalho and Azevedo³² used an exploratory case study approach to identify the LARG paradigms trade-offs in the automotive supply chain context. Their results showed that for the automaker, quality should be developed first, then flexibility, environmental protection, cost, and finally delivery. Espadinha-Cruz et al.³³ presented a model for evaluating the overall business interoperability and establish what measures can reduce interoperability problems in the supply chain management.

Dües et al.³⁴ explored several explanatory frameworks to evaluate previous work focusing on the relationship between LARG supply chain management practices. They suggested that implementation of Lean has positive impact on Green practices and the Green practices are beneficial for existing Lean business practices. Govindan et al.³⁵ identified the critical green, resilient and lean practices on which top management should focus for improving the automotive supply chain’s performance. The results showed that the practices with the main driving power are environmentally friendly packaging (green practice), flexible transportation (resilient practice), and just-in-time (lean practice).

2.2. Resilience engineering

The aim of Resilience Engineering is not only to prevent things from going wrong, but also to ensure that things go right, i.e., to facilitate normal outcomes. Woods³⁶ presented some basic concepts regarding resilience and current debates regarding understanding how a system adapts and to what kinds of conflicts in the environment it adapts as well. Dijkstra³⁷ defined the functional structure of a safety management system (SMS). Johansson and Lindgren³⁸ represented a framework based on a quick and dirty evaluation method to assess the resilience properties of the safety-critical system.

Ouedraogo et al.³⁹ proposed a functional construction to study resilience. Shirali et al.⁴⁰ identified and classified challenges in the process of constructing RE and its adaptive ability in a petrochemical plant. They classified challenges into nine classes including the intangibility of RE level, lack of explicit experience about RE, choosing production over safety, religious beliefs, lack of reporting systems, out-of-date manuals, economic problems, and poor feedback loop. Shirali et al.⁴¹ represented a new model, for the first time, to quantitative evaluating of RE by using questionnaire and principal component analysis (PCA). Finally, the characteristics of this study and previous studies are summarized in Table 2.

Table 2.

The characteristics of this study and previous studies.

Study	Methodology	Solution approach	Case study	Remark
Al-Aomar⁴²	Simulation-based	Simulated annealing algorithm	Production line	Developing a lean production systemThree lean measures: productivity, cycle time, and work-in-process inventory
Vimal and Vinodh⁴³	Fuzzy logic approach	Artificial neural network	Electronic manufacturing organization	Performing fuzzy logic for leanness assessment
Wahab²²	Conceptual model	Empirical approach	Manufacturing systems	Providing a general guideline for all companies and industries in the manufacturing sector
Staats²³	A new lean production framework	Empirical analysis	An Indian software services firm	Examining the applicability of lean production to knowledge work by investigating the implementation of a lean production system
Diaz-Elsayed et al.⁴⁴	Simulation-based model	Simulation	Automotivecompany	Identifying an approach for incorporating both lean and green strategies into a manufacturing system in discrete production environments
This study	Simulation-based	DEA and PCA	Production line	Improving and evaluating lean production strategy by principles of resilience engineering in an assembly line with maintenance policies

DEA: data envelopment analysis; PCA: principal component analysis.

In the recent years, simulation–optimization approaches have been developed and used in various areas. For instance, Attar et al.⁴⁵ proposed a hybrid simulation–optimization method to handle real conditions in base-stock policy including continuous-review, general random lead times, lost sales and compound demands. Their method could find the optimal stock level for the traditional base-stock policy in a real-world case study. Owing to the complex and stochastic nature of hybrid flow shop problems in a real semiconductor back-end assembly facility, Lin and Chen⁴⁶ presented a simulation-optimization method to attain the feasible minimal flow time by finding the optimal assignment of the machine type and production line. Peng et al.⁴⁷ developed a bi-level optimization programming model based on simulation (VisSim) and optimization (shuffled complex evolution algorithm) approach in order to reduce the total travel time of travelers and to improve traffic efficiency. They applied their proposed model for one-way traffic reconfiguration in Dalian Harbour Plaza. For sizing hybrid renewable energy systems, Chang⁴⁸ presented a quantile-based simulation optimization model based on an efficient stochastic optimizer, quantile estimation techniques and Monte Carlo simulation method in order to enable the control of the upside risk and, consequently, to improve the decision quality about the sizing of energy systems.

3. Methodology

In leanness view point and according to the mentioned definitions of RE, the performance of the manufacturing system can be increased by implementation of RE principles. In this study, RE factors are employed to improve the performance of a lean production system. First, the most important criteria of leanness are determined, and based on them, the suitable factors of RE are selected. These principles with respect to the nature of lean production strategy are shown in Figure 1. Different scenarios are defined according to the different effects that each factor of RE has on the level of leanness. The efficiency of each scenario is determined using DEA and the DEA’s results are verified by PCA.

3.1. Simulation framework

Visual Simulation Language for Analogue Modelling (Visual SLAM) is used to design the simulation network. Visual SLAM is a simulation language that is completely object-oriented.⁴⁹ The system is simulated by Visual SLAM. The outputs obtained from the performing simulation are the average TIS, the number of failures, the average resource availability and total cost of the manufacturing system. The outputs of the simulation have been considered as the inputs and outputs of DEA model. The structure of this study is shown in Figure 2.

According to the most researches regarding preventive maintenance (PM), PM policies are more expensive than programs that only repair broken equipment.⁵⁰ The flaw in this line of thought arises from the random nature of equipment failure. This reactive mode of maintenance usually means that the maintenance personnel must temporarily patch the equipment and defer the substantive repair until time allows. Unfortunately, since the equipment already has suffered lost time owing to the initial breakdown, the likelihood of finding repair time decreases.

A proposed necessity for lean is that machinery be in top running condition at all times. When using small lot sizes, management can ill afford unanticipated downtime in production flow. Equipment must be in condition to produce whenever it is needed, whatever is needed. Therefore, a little time should be scheduled each day to ensure that machinery is capable of producing top quality outcomes. PM is required for long-term, continuous improvement in the quality of the production process. Lean manufacturing is a way of production that emphasizes minimizing the amount of all resources (including operator utilization and process time) used in various activities in manufacturing system.

The use of lean can improve the lean system’s internal quality, as well as the quality of suppliers. Defect detection is naturally enhanced if lot sizes are drastically reduced. Also, the quality of feedback will be immediate if a worker produces a lot size of one and passes it to the next station. In this way, defects are discovered quickly and their causes can be adjusted immediately. Production of large lots with high defect rates is avoided. Therefore, the use of lean decreases the number of failures and waste percentage in manufacturing systems.

3.2. Data envelopment analysis

In DEA method, the term of decision-making unit (DMU) denotes the entities in the group of assessment. A surface known as the frontier has been generated by DEA method. This frontier follows the peak performers and envelops the remainder.⁵¹ The theoretical frontier denotes the upper limit of absolute potential production that a DMU is able to attain in any input level. However, definition and showing the mathematical relationship between input and output factors of a system is problematic normally. Therefore, the theoretical frontier is typically unidentified. Therefore, the empirical or relative frontier, according to real DMU is utilized. In the observed population the empirical frontier links all the relatively best DMUs. It should be mentioned that, the empirical frontier gives only the best of a bad lot, if we are faced with condition that the performance of all observed DMUs is generally poor. The poor DMUs, if really poor, have been indicated clearly, by empirical or relative frontier.^52,53

When the performances of observed of individual DMUs have been provided, the DEA might help to discover potential measures towards which performance can be viewed as a target. Ability of detecting possible role or peer models along with simple efficiency scores is an advantage over the other benchmarks for DEA. Finding the weights to maximize the performance of DMU which is under consideration is the aim of DEA. Take note that the performance values obtained from the DEA are credible only within that specific group of peers. In view of the different groups, a DMU can be effective in a specific group while it could be quite inefficient in some other groups. Likewise, if the number of DMUs is low, then discrimination between them is less.

By providing the observed efficiencies of DMUs, DEA can be used to identify benchmarks towards which performance is targeted. The weighted combinations of peers and the peers themselves may provide benchmarks for relatively less efficient DMUs. The ability of DEA to detect possible role models or peers as well as simple technical efficiency scores gives it an edge over the other measures.⁵⁴ The four basic DEA models are the Banker, Charnes and Cooper (BCC) model, the Charnes, Cooper and Rhodes (CCR) model, additive model, and multiplicative model.

The objective of DEA is to calculate the weights which maximize the performance of the specific DMU under assessment. Note that, the values of efficiency obtained by DEA are valid only within the specific role models. In other words, if a group of very poor DMUs are assessed using DEA, there will still be effective DMUs. Also, if the set of DMUs is small, then there is little discrimination between them.^52,53

The basic fractional CCR model evaluates the relative efficiencies of n DMUs ( $j = 1, 2, \dots, j_{k}, \dots, n$ ) while each DMU includes m inputs ( $i = 1, 2, \dots, m$ ) and s outputs ( $o = 1, 2, \dots, s$ ) as show in Model (1).

\begin{array}{l} Max E_{k} = \frac{\sum_{o = 1}^{s} u_{o} y_{o k}}{\sum_{i = 1}^{m} v_{i} x_{i k}} \\ Subject to \\ \frac{\sum_{o = 1}^{s} u_{o} y_{o j}}{\sum_{i = 1}^{m} v_{i} x_{i j}} ⩽ 1; j = 1, 2, \dots, j_{k}, \dots, n \\ u_{o} ⩾ ρ; o = 1, 2, \dots, s \\ v_{i} ⩾ ρ; i = 1, 2, \dots, m \end{array}

Model (1)

where $E_{k}$ is the relative efficiency of $DM U_{k}$ , $u_{o}$ and $v_{i}$ are the weights to be calculated by the model for output o and input i, respectively. $ρ$ is equal to a small positive value. This model is non-convex, nonlinear, with fractional (nonlinear) objective function and fractional and linear constraints. Charnes et al.⁵¹ developed a simple transformation to reduce Model (1) to the linear programing (LP) form (i.e., Model (2)) so that the LP methods can be easily used. In this new model, the weighted sums of the inputs has been set equal to 1 and the weighted sums of the outputs is being maximized.

\begin{matrix} Max E_{k} = \sum_{o = 1}^{s} u_{o} y_{ok} \\ Subject to \\ \sum_{o = 1}^{s} u_{o} y_{oj} - \sum_{i = 1}^{m} v_{i} x_{ik} ⩽ 1; j = 1, 2, \dots, j_{k}, \dots, n \\ \sum_{i = 1}^{m} v_{i} x_{ik} = 1 \\ u_{o} ⩾ ρ; o = 1, 2, \dots, s \\ v_{i} ⩾ ρ; i = 1, 2, \dots, m \end{matrix}

Model (2)

The primal and dual forms of CCR models are one of the most widely known and used DEA models. Using the standard forms (equations) by creating and adding slack ( $S^{+}$ ) and surplus ( $S^{-}$ ) variables to Model (2), the dual model for the standard form of Model (2) is as follows:⁵⁵

\begin{matrix} Min Z_{k} - ρ (\sum_{o = 1}^{s} S_{o}^{+} + \sum_{i = 1}^{m} S_{i}^{-}) \\ Subject to \\ \sum_{j = 1}^{n} λ_{j} y_{oj} - S_{o}^{+} = y_{ok}; o = 1, 2, \dots, s \\ Z_{k} x_{ik} - \sum_{j = 1}^{n} λ_{j} x_{ik} - S_{o}^{-} = 0; i = 1, 2, \dots, m \\ λ_{j} ⩾ 0; j = 1, 2, \dots, j_{k}, \dots, n \\ S_{o}^{+} ⩾ 0; o = 1, 2, \dots, s \\ S_{o}^{-} ⩾ 0; o = 1, 2, \dots, s \end{matrix}

Model (3)

Banker et al.⁵⁶ introduced one of the most significant extensions of the basic CCR model in where an additional constraint (i.e., $\sum_{j = 1}^{n} λ_{j} = 1$ ) was added to Model (2). This added constraint allows variable returns to scale (VRS) as well as allows the reference set is molded as a convex arrangement of DMUs.

\begin{matrix} Min Z_{k} - ρ (\sum_{o = 1}^{s} S_{o}^{+} + \sum_{i = 1}^{m} S_{i}^{-}) \\ Subject to \\ \sum_{j = 1}^{n} λ_{j} y_{oj} - S_{o}^{+} = y_{ok}; o = 1, 2, \dots, s \\ Z_{k} x_{ik} - \sum_{j = 1}^{n} λ_{j} x_{ik} - S_{o}^{-} = 0; i = 1, 2, \dots, m \\ \sum_{j = 1}^{n} λ_{j} = 1 \\ λ_{j} ⩾ 0; j = 1, 2, \dots, j_{k}, \dots, n \\ S_{o}^{+} ⩾ 0; o = 1, 2, \dots, s \\ S_{o}^{-} ⩾ 0; o = 1, 2, \dots, s \end{matrix}

Model (4)

Since the linear CCR programming model assigns an equal index of one to all efficient DMUs, it does not rank the efficient units. Therefore, Andersen and Petersen⁵⁷ modified this model for full ranking purposes. In the Anderson–Peterson (AP) model, the efficient unit scores can be more than 1 by dropping the constraint that bounds the efficiency score of the evaluated DMU, thus the efficient units are ranked just as inefficient units.

3.3. Principal component analysis

PCA is one of the data reduction methods and a common tool practicable in multivariate statistics such as correlation analysis. This method is employed when one desires to lessen the number of the variables under consideration, and therefore to rank, evaluate, and analyze decision-making units (DMUs) such as universities, airports, cities, industries, and hospitals.

Following the terminology proposed by Zhu,⁵⁸ we have 23 DMUs, where each unit $U_{j}$ ( $j = 1, 2, \dots, 23$ ) produces two outputs $y_{oj}$ ( $o = 1, 2$ ) by utilizing four inputs $x_{ij}$ ( $i = 1, 2, 3, 4$ ) in this study. It is possible to look at the ratios of individual output to individual input, $d_{io}^{j} = y_{oj} / x_{ij}$ ( $i = 1, 2, 3, 4$ and $o = 1, 2$ ) for each unit $U_{j}$ (j = 1, 2,…, 23). $d_{io}^{j}$ gives the ratio of every output to every input. Now, suppose $d_{k}^{j} = d_{io}^{j}$ , where k = 1 corresponds to i = 1, o = 1 and k = 2 corresponds to i = 1, o = 2, and so on. Obviously, $k = 1, \dots, p$ and $p = m \times s = 2 \times 4 = 8$ . We have to find some weights that combine those p = 8 individual ratios of $d_{k}^{j}$ for each DMU_n. Take into account the following $n \times p = 23 \times 8$ data matrix composed of $d_{k}^{j}$ : $D = {(d_{1}, d_{2} \dots, d_{8})}_{23 \times 8}$ . Each row represents $p = 8$ individual ratios of $d_{k}^{j}$ for each DMU and each column shows a specific output/input ratio. That is, $d_{k} = {(d_{k}^{1}, d_{k}^{2}, \dots, d_{k}^{23})}^{T}$ .

PCA is employed to search for a component structure by factoring the sample correlation matrix D and to find out new independent measures, which are respectively different linear combinations of $d_{1}, d_{2} \dots, d_{8}$ . Principal components can be combined with their eigenvalues to achieve a weighted measure of $d_{k}^{j}$ . The PCA procedure of D is conducted as follows.

Step 1. Calculate the average matrix $\bar{D}$ and the corresponding correlation matrix R.

\bar{d} = {({\bar{d}}_{1}, {\bar{d}}_{2}, \dots, {\bar{d}}_{8})}_{1 \times 8}

(2)

Step 2. Solve Equation (3).

| R - λ I_{8} | = 0

(3)

$I_{8}$ is a $p \times p = 8 \times 8$ identity matrix. The ordered $p \times p = 64$ characteristic roots (eigenvalues) are obtained, $λ_{1} ⩾ λ_{2} ⩾ \dots ⩾ λ_{8}$ with $\sum_{k = 1}^{p} λ_{k} = 8$ ( $k = 1, \dots, 8$ ) and the related eight characteristic vectors (eigenvectors) ( $l_{1}^{k}, l_{2}^{k}, \dots, l_{8}^{k}$ ). Those characteristic vectors form the principal components $Y_{k}$ (Equation (4)):

Y_{k} = \sum_{t - 1}^{p = 8} l_{t}^{k} {\bar{d}}_{t}^{j} j = 1, 2, \dots, 23; k = 1, 2, \dots, 8

(4)

where ${\bar{d}}_{t}^{j}$ denotes the standardized $d_{t}^{j}$ .

Step 3. Calculate the weights ( $w_{k}; k = 1, \dots, 8$ ) associated with the principal components and PCA scores ( $z_{n}$ ) of each DMU ( $n = 1, 2, \dots, 23$ ). Moreover, the z vector ( $z_{1}, z_{2}, \dots, z_{23}$ ) that illustrates the score of nth DMU is given by Equation (5).

z_{n} = \sum_{k = 1}^{8} w_{k} Y_{k}, n = 1, 2, \dots, 23

(5)

4. Experiment: The case study

The main production line of an Iranian vehicle manufacturer, with headquarters in Tehran, has been considered as the case study. The factory has four main production lines and 16 managers as well as 170 employees. Press shop is where the production process starts, with most of the metal parts getting pressed out of steel sheets. The boot lid, bonnet, roof, door panels etc. are typically pressed in to form the basic structure of the automobile. The pressing process is a multi-step process where the sheets are pressed into shape in stages. The press shop line of our case study consists of six machines and one maintenance operator. The data for 70 periods are used to fit the distribution functions of input parameters using IBM SPSS 22.0 software (see http://www-01.ibm.com/software/analytics/spss/). These distribution functions are shown in Table 3. The fixed and variable costs of machines are presented in Table 4. Maintenance interval and setup time waste percentage for each machine are equal to the mean of historical data of them. To evaluate and quantify the RE principles’ impacts on the production line, ten experts who are completely familiar with RE principles are asked to fill in the questionnaires. The experts evaluate the impacts on the simulation’s inputs and assign a number between 0 (without effect) and 100 (very effective) to each question of the questionnaire. For example, the experts answer to this question, “to what extent top management commitment factor can affect the repair time in your system?” Then, the mean values of the experts’ judgments are used to apply the appropriate changes on the inputs of simulation network.

Table 3.

The best fitted distribution function using IBM SPSS 22.0 software.

Machine	Repair time (Minute)	Maintenance time (Minute)	Process time (Minute)	Time between failures (Minute)	Percentage of wastes
Machine 1	Normal (10, 1.94)	Normal (9, 0.54)	Normal (10, 0.99)	Normal (914, 12.21)	1
Machine 2	Normal (10, 1.93)	Normal (9, 0.32)	Normal (8, 1.41)	Normal (2475.7, 17.01)	1
Machine 3	Normal (8, 1.70)	Normal (9,0.31)	Normal (8, 1.40)	Normal (1663.1, 14.50)	1
Machine 4	Normal (9, 1.71)	Normal (10, 0.57)	Normal (8, 1.36)	Normal (1326.5, 11.52)	4
Machine 5	Normal (10, 1.96)	Normal (10, 0.44)	Normal (8, 1.31)	Normal (1842, 12.02)	2
Machine 6	Normal (8, 1.72)	Normal (9, 0.43)	Normal (8, 0.54)	Normal (994.6, 15.90)	2

Note. $Normal ~ mean (μ), standard deviation (σ)$ .

Table 4.

Fixed and variable costs.

Machine	Fixed cost ($)	Variable cost (Per piece) ($)
Machine 1	10 000	10
Machine 2	12 000	8
Machine 3	10 000	10
Machine 4	11 000	10
Machine 5	14 000	12
Machine 6	10 000	8

The process of this line production is shown in Figure 3. The main network of the line production designed by Visual SLAM is shown in Figure 4. Some basic nodes are briefly explained below.

CREATE node: entities are created by this node and routed into the system over activities that emanate from this node.

TERMINATE node: entities are terminated (destroyed) by this node. This node reclaims disk space used to store information about the entity which is terminated. The node is used to delete or destroy entities from the network.

QUEUE node: queue in which entities are queued. A QUEUE is a location in the network where entities are queued for service. When an entity arrives at a QUEUE node, its disposition depends on the status of the server that follows the QUEUE node. The entity passes through the QUEUE node and goes immediately into the service activity if the server is idle (free). The entity waits in the QUEUE node until a server can process it if no server is available. When a server becomes free (available), the entity will automatically be taken out of the queue and service will be initiated.

ACCUMULATE node: entities accumulate at this node; once the specified number of entities have accumulated, a new entity is released which denotes the group of entities which accumulated.

GOON node: This node is used in the modeling of sequential activities since 2 consecutive activity statements are used to model parallel activities. GOON node is used to provide linkage for activities in series and connect activity branches. Also, branching of probabilities and/or deterministic can happen following GOON nodes.

ASSIGN node: this node assigns values to network variables or entities. Generally, this node is used to set values to the attributes of an entity passing through it or to the prescribed values to the system variables that pertain to the network.

For simulating preventive maintenance sub-network shown in Figure 3, one entity is created and the determined conditions are defined by a GOON node. If the planned time is passed since the last time of repair and maintenance, the periodic maintenance is performed. If there is a condition that required a preventive maintenance, entity waits until the machine finishes its job and waits for maintenance operator. Therefore, an ALTER node altered the value of machine resource to zero and enters the machine into maintenance sub network. When the preventive maintenance is finished, the value of machine resource is changed to one. The preventive maintenance sub-network related to the machine 1 is shown in Figure 5.

For simulating the sub-network of unpredicted failure repair shown in Figure 3; if the prearranged time is passed since the last times of repair and maintenance, the repair is performed. One entity is created and if the condition of repair is satisfied, the entity preempts the machine from service and waits for repairing by maintenance/repair operator. For this purpose, a PREEMPT node is used. After the repairing process, the machine and maintenance operator will be free using FREE node. The repair sub-network related to machine 1 is shown in Figure 6. In this case study, the maintenance operator can perform both repair and maintenance tasks. Interested readers can refer to Pritsker and O’Reilly⁴⁹ for more information regarding the nodes and their applications and specifications in Visual SLAM.

4.1. Verification and validation of simulation model

As mentioned before, to fit the best distribution functions of input parameters of simulation model, the data for 70 periods are used. It should be noted that the structure of simulated model (shown in Figure 3) has been approved by experts of the company. Based on the empirical data collected from the manufacturing system, the simulation model has been developed using AweSim. The behavior of the simulation model has been examined against the actual system in the system by t-Test. For verification and validation of the simulated model, the data related to 70 based on TIS periods is used. After testing the normality of data (see Figures 7 and 8) and equality of variances, a two-sample t-Test has been conducted to test the equality of means. The hypothesis to be tested is H₀: the mean of real values = the mean of simulated values, versus H₁: the mean of real values ≠ the mean of simulated values. The results of paired t-Test between the real values of TIS and the simulated values are presented in Table 5. It is concluded that there is no difference between the simulation model and the actual system with respect to sum of the differences between TIS at α=0.05.

Table 5.

Paired t-Test for real values and simulated values of TIS.

Paired t-Test and CI: Real value, Simulated value
	N	Mean	StDev	SE Mean
Real value	70	53.021	1.390	0.166
Simulated value	70	53.412	1.340	0.160
Difference	70	−0.392	1.788	0.214

95% CI for mean difference: (-0.818, 0.035).

t-test of mean difference = 0 (vs not = 0); t-value = -1.83; p-value = 0.071. TIS: time in system.

4.2. Steady-state and warm-up time

In this study, the simulation model is treated as steady-state. The problem of determining when a model reaches steady-state exists in modeling steady-state behavior. This start-up period is usually known as the warm-up period. It is necessary to wait until after the warm-up period before gathering any statistics. Using this method, any bias owing to observations taken during the transient state of the model is eliminated. The most straightforward and easiest method for determining warm-up time is to run a preliminary simulation of the system, preferably with several replications, and observe at what time one or more key response variables over the time achieve statistical stability.⁵⁹

Because the cumulative plot tends to average out instability in data, after each period, it is better to reset the response variable(s) rather than use the cumulative value of the variable(s). When the variable(s) begin to exhibit steady-state, we can add a 30% safety factor and be reasonably safe in using that period as the warm-up period.⁵⁹ In this study, TIS and the number of breakdowns are used as two key response variables to determine the steady-state. Figures 9 and 10 illustrate the values of TIS and number of breakdowns, respectively.

Since statistical stability is reached at about 700 hours for TIS and 750 hours for number of breakdowns, $750 \times 1.30 ≅ 1000$ hours is probably a safe warm-up period to use for the simulation.

4.3. Scenarios

The main objective of this study is assessing the impact of RE on a lean production system in order to improve the system’s performance. As mentioned previously, to assess the resilience strategies in the production line, 23 different scenarios are defined as follows.

Basic scenario (Scenario 0): In this scenario, the main production line without resilience policies and failures’ sub-networks is considered. This scenario is needed for comparing the states in which there is a possibility of failures or interruptions.

Interruption scenario (Scenario 1): In this scenario, the failures happen, but the resilience policy has not been implemented. The breakdown happens with a certain time interval. To assess the effectiveness of resilience policies in different disturbance situations, this scenario is required.

Resilient policy 1 (Scenario 2): In this scenario the first resilience factor is taken into account. The factor is top management commitment that causes an increase in rate of system management responsibility. Top management commitment is one of the lean factors, and creates an agile scenario.

Resilient policy 2 (Scenario 3): In this scenario, the impact of reporting culture on improving the leanness is taken into account. Considering this factor causes the ability of a system to detect its weaknesses to be improved because with the spread of this culture in the organization, all personnel will be taught to report all problems and issues quickly.

Resilient policy 3 (Scenario 4): The visibility factor which means the rapid answer of the manufacturing system to any interruption is considered in this scenario. In our case, instantly after a failure in line production, the system can rapidly respond. In other words, there is no postponement between breakdown of a resource (machine or operator) and replacing it. Then, the visibility can be one of the lean factors.

Resilient policy 4 (Scenario 5): In this scenario, the awareness factor is taken into account. This factor directly relates to the system’s performance calculated based on proactive criteria. It means that the system is fully prepared to deal with any unexpected events. The system rapidly reacts to any interruption and the rate of repair is increased.

Resilient policy 5 (Scenario 6): In this scenario, the rate of recovery in the manufacturing system is taken into account. For improving this rate, the velocity factor can be very pertinent. This factor is generally focused on the system restore speed to normal situation after a failure.

This factor and the visibility are the important factors related to responding quickly to unpredictable changes such as the variations in the amount of demand.

Resilient policy 6 (Scenario 7): For this scenario, redundancy factor is taken into account. Redundancy means the ability of manufacturing system to consider the alternative resource.

Resilient policy 7 (Scenario 8): This scenario considers the flexibility factors. This factor increases the ability of system to self-organization. Considering this factor, the ability of manufacturing system to deal with failure that is imposed from outside the organization is increased. Also, the flexibility can help the system to confront unexpected events.

After defining the scenarios, different combinations of RE factors are considered to define other scenarios. Note that these combinations are defined based on the opinions of experts. These scenarios are presented in Table 6.

Table 6.

Different policies of RE which are considered in different scenarios.

Scenario No.	Resilience Factors
Scenario No.	R1 (Top management commitment)	R2 (Reporting culture)	R3 (Visibility)	R4 (Awareness)	R5 (Velocity)	R6 (Redundancy)	R7 (Flexibility)
0
1
2
3
4
5
6
7
8
9	✓	✓
10			✓		✓
11		✓	✓		✓	✓
12	✓			✓
13		✓			✓
14			✓	✓
15	✓					✓
16		✓	✓				✓
17	✓			✓
18		✓		✓
19	✓	✓		✓
20		✓				✓
21			✓	✓	✓
22	✓	✓	✓	✓	✓	✓	✓

As mentioned before, the judgments of 10 experts have been used for applying the impacts of each RE principle on the simulation network. The average values of the judgments are shown in Table 7. In this table, when the experts assign 17.5 to the impact of top management commitment (R1) on process time, this time for all machines is decreased as much as 17.5 percentage in the simulation network and for other inputs except “Time between failures”, the same procedure is done. Note that, “Time between failures” is increased as much as 25% after applying the impacts of the RE principles. Consider Scenario 9 in which R1 and R2 are taken into account, for changing the simulation network to apply the impacts of the R1 and R2, the process time, repair time, maintenance time, wastage percentage, and number of failures are decreased as much as 12.5% ( $= mean {17.5, 7.5}$ ), 25.8% ( $= mean {25, 26.25}$ ), 22.5% ( $= mean {26.25, 18.75}$ ), 21.875% ( $= mean {21.25, 22.5}$ ), 25.75% ( $= mean {25, 26.25}$ ), 25% ( $= mean {27.5, 22.5}$ ), respectively. The value of “Time between failures” is increased as much as 20% ( $= mean {25, 15}$ ). In other hand, implementation and applying RE principles in the system have some additional costs which should be considered in performance evaluation. Therefore, the additional costs are considered as the input variable in DEA model to take into account the trade-off between RE principles and cost.

Table 7.

The result of experts’ judgments.

Inputs of simulation network	RE principles
Inputs of simulation network	R1	R2	R3	R4	R5	R6	R7
Process time (In 1)	17.5	7.5	11.25	7.5	27.5	40	17.5
Repair time (In 2)	25	26.25	11.25	33.75	36.25	43.75	25
Maintenance time (In 3)	26.25	18.75	22.5	30	35	33.75	26.25
Wastage percentage (In 4)	21.25	22.5	33.75	22.5	38.75	23.75	21.25
Time between failures (In 5)	25	15	25	28.75	47.5	46.25	25
Number of failures (In 6)	27.5	22.5	21.25	25	40	20	27.5

When each of the RE factors are taken into account, the traditional structure of the line production is changed. As might be expected, these changes impose additional costs on the system and have different consequences on the system such as the need to train personnel, changing the management structure of the system and updating/upgrading the equipment in line production. But it should be noted that these costs are temporary and applying the resilience factors in system will be very helpful in the long term. These types of costs are estimated based on experts’ opinions. Therefore, to assess the efficiency of scenarios, some measures are identified containing the total cost of line production, average utilization of machines and maintenance operator, TIS, total number of failures and average wait time of machines.

5. Results and discussion

In this section, the results obtained from running simulation for each scenario are reported. Each scenario has been simulated at the same way by combining the appropriate networks together and making the suitable changes based on the impacts which various policies have on the line production. Based on experts’ opinions these changes have been applied to the simulation network. According to the experts’ experiments additional costs has been added to the total cost for the scenarios in which the resilience factor(s) has/have been considered. The results obtained from the simulation (simulation’s outputs) as well as the additional costs related to each scenario are shown in Table 8. The total cost related to each scenario is equal to summation of repair and maintenance operations costs, fixed and variable costs, installation and additional costs.

Table 8.

Simulation’s outputs and total cost related to each scenario.

Scenario	Simulation’s outputs					Total cost
Scenario	TIS	Number of breakdowns	Average wait time of machines	Average utilization of machines	Average utilization of operator	Total cost
SC00	51.226	8798	0.2090	0.6698	0	4 637 770
SC01	55.471	8760	0.9118	0.6708	0.449	4 651 496
SC02	46.227	8622	0.6200	0.5700	0.450	4 653 796
SC03	55.552	5699	0.9250	0.6760	0.450	4 721 056
SC04	55.386	8771	0.8900	0.6700	0.450	4 650 088
SC05	54.012	8777	0.6670	0.6700	0.386	4 651 012
SC06	53.920	8707	0.6530	0.6710	0.386	4 654 686
SC07	32.109	8780	0.4180	0.3990	0.449	4 718 326
SC08	55.473	8710	0.9120	0.6710	0.449	4 654 792
SC09	55.467	6042	0.9115	0.6760	0.449	4 719 012
SC10	50.440	8792	0.9010	0.6700	0.450	4 649 844
SC11	26.367	8828	0.0940	0.3490	0.234	4 721 728
SC12	49.571	8858	0.5640	0.6070	0.450	4 653 446
SC13	41.993	7867	0.5779	0.5820	0.395	3 907 611
SC14	52.639	6249	0.5942	0.5767	0.359	4 775 100
SC15	30.797	8331	0.3395	0.3980	0.401	4 376 265
SC16	43.935	7666	0.9501	0.5605	0.422	4 766 310
SC17	43.777	5494	0.9258	0.6798	0.350	3 825 031
SC18	45.780	7469	0.8978	0.5834	0.416	3 898 711
SC19	55.521	5844	0.9300	0.6780	0.449	4 745 364
SC20	29.563	8794	0.0950	0.3900	0.234	4 720 068
SC21	51.509	6403	0.9200	0.6740	0.449	4 703 814
SC22	38.417	6441	0.2600	0.5000	0.322	4 778 808

For ranking the scenarios which contain different RE factors, DEA approach is used because it can handle multiple inputs and outputs. In this regard, the inputs and outputs variables of the DEA should be determined. The inputs and outputs are factors whose values should be decreased and increased, respectively. Therefore, the inputs of the DEA model are TIS, total cost, number of failures and average wait times of machines, and the outputs are utilizations of machines and maintenance operator. The results obtained by DEA are shown in Table 9. As is clear in this table, Scenario 0 (SC00) reaches the first place. This is the basic scenario in which the repair operations are not performed because there is no failure. As expected, Scenario 22 (SC22) in which all RE factors are taken into account reaches the third place. This shows that the RE factors can significantly affect the lean production strategy.

Table 9.

DEA’s results.

Scenario	Efficiency	Rank	Scenario	Efficiency	Rank
SC00	1.175622	1	SC12	1.039361	6
SC01	0.999908	19	SC13	1.02391	8
SC02	1.00144	17	SC14	0.977856	23
SC03	1.001729	15	SC15	1.015571	10
SC04	1.001446	16	SC16	0.980118	22
SC05	0.998024	21	SC17	1.088221	2
SC06	1.005267	14	SC18	1.027568	7
SC07	1.069976	4	SC19	1.059416	5
SC08	0.999854	20	SC20	1.0177	9
SC09	1.001202	18	SC21	1.011745	12
SC10	1.006407	13	SC22	1.073744	3
SC11	1.013799	11

Average value of efficiencies = 1.026.

However, scenario 17 (ranked 2nd) reaches a better efficiency by only applying three RE factors (top management commitment, awareness and flexibility). On the one hand, referring to the total cost, number of breakdowns and average utilization of machines related to this scenario, it can be realized that the minimum values of the total costs and number of breakdowns as well as maximum value of average utilization of machines belong to this scenario. On the other hand, three of the most significant factors in RE concept are taken into account in this scenario. Therefore, these lead this scenario to reach an acceptable efficiency.

As mentioned before, the results of DEA are compared with those of PCA. To this end, the scenarios are ranked by PCA as well. The ranking results of PCA as well as DEA are shown in Figure 11. The correlation coefficients between ranking scores of DEA and PCA is also calculated which is equal to 0.997. The comparison and the value of correlation verify DEA’s results.

5.1. Analysis of results

In this section, the simulation’s outputs are analyzed to determine how each factor affects the results of DEA. After running DEA model, the individual effects of each input on the efficiency of the scenarios are analyzed. For this purpose, the inputs are eliminated from the DEA model one by one to realize how the results would change. For example, the data related to “Time in System (TIS)” are eliminated from the data set, the DEA model is performed again and the mean value of scenarios’ efficiencies is calculated. Then, the mean values of efficiency of the models in which one factor (inputs or outputs) is omitted is compared with those of the main model (i.e., the model in which all inputs and outputs are taken into account). According to this analysis, it can be determined which factor has the maximum/minimum impact on the mean value of efficiencies. Table 10 presents the results of this analysis.

Table 10.

Mean values of efficiencies and correlation coefficient between the models.

Omitted simulation’s outputs	Mean value	Correlation coefficient
Time in system	1.020	0.944
Number of breakdowns	1.018	0.940
Total cost	1.021	0.947
Average wait time of machines	1.000	0.467
Average utilizations of machines	0.980	0.462
Average utilization of operator	0.992	0.402

According to the results provided in Table 10, when the data related to “Average utilizations of machines” are omitted from the model, the mean value decreases to 0.980. This indicates that this factor has the maximum impact in the obtained result since elimination of it from the assessment of mean value of efficiency will have an adverse effect on system’s efficiency. On the other hand, eliminating data related to “Total cost” the mean value is equal to 1.021. This shows that this factor has the minimum impact on the evaluation because omitting this factor did not significantly change the results of the main model.

For validation of the results provided in Table 10, the correlation coefficient between the ranking scores of the main model and other models have been also calculated and shown in last column of Table 10. According to these results, when the data related to “Average utilizations of machines” is omitted from the model, the correlation coefficient is equal to 0.462. This shows that this factor has the maximum impact because omitting its data will have an adverse effect on the evaluation. Also, omitting “Total cost” from the model, the correlation coefficient is equal to 0.947. Compared with other factors, this indicates and validates that this factor has the minimum impact on the evaluation. The situations of other simulation’ inputs are shown in Figure 12.

5.1.1. Analysis of RE factors

In this section, the RE factors are analyzed to determine which factors of RE has the maximum and minimum effects on increasing of system’s efficiency. For this purpose, we compare the efficiencies of scenarios in which just one factor of RE has been considered. These scenarios are scenarios 2 to 8. The result of this comparison is presented in Figure 13.

As shown in Figure 13, when “Redundancy” is applied to the system, the maximum value of efficiency is obtained in comparison with other factors. Redundancy at first seems counterproductive to a company’s Lean efforts, where the focus is driving out all waste and an efficient JIT flow of goods. But, in fact, redundancy is one of the best ways to ensure Lean operations because redundancy is designed to help facilities avoid the significant waste of time, effort and money involved in a system breakdown. Organizations build resiliency into their operations by creating redundancies throughout the manufacturing system. The organization could hold extra inventory, maintain low capacity utilization, use of multiple equipment for each section of system, etc. These measures, of course, come at a cost. Although keeping inventories and use of multiple equipment drive down material costs and maximizes efficiency, if that organization were to encounter a natural disaster or significant plant accident, not having redundancies in those and other areas could cripple production – and the company.

As mentioned before, one of the leanness’ goals is to reduce work-in-process WIP. In this study one of the measures used for evaluating efficiency of the system is the average TIS of products. This time needs to produce one unit or to complete the production cycle. One of the best and possible options to improve WIP in production systems, is reducing TIS. With the resulting decline in TIS, WIP drops and the processes get done faster and better. In other words, by reducing TIS of products, WIP reduces and as a result, one of the main leanness’ goals (i.e., WIP) is reached.

Within standardized work, it requires recovery time to be built into a worker’s cycle for repetitive operations to avoid fatigue. We could call this necessary redundancy. Using a skill matrix and cross-training program to develop multiple people to perform the same task, even when most days these skills may be idle is yet another example of built-in redundancy, which adds no value but avoids the waste of system breakdown should there be an absence of a skilled person to perform the work. The number and types of threats that can undermine a manufacturing system are greater than ever, and the reason redundancy has taken on even more importance in the manufacturing system. Of course, there is no way to prevent disruptive or catastrophic events from occurring, but a company can take smart steps to prepare for and deal with them and, in the process, ensure business continuity. When it comes to the manufacturing system, the best way to ensure your company’s ability to quickly get back up and running is to institute redundancies in the system.

In this study, the subjective opinion of 10 experts of the specific system under study is used to evaluate the influence of each resilience policy in some input variables (e.g., processing time, time between failures, or number of failures; see Table 6). Consequently, the results are biased by experts’ opinion and are limited to the specific system under study. In other words, the arguments and conclusions of this study are restricted to the studied system, and the results cannot be generalized to other systems. But, the proposed structure (Figure 2) can be developed for other systems and the influence of each resilience policy in some input variables of the systems are evaluated.

6. Conclusions

Production systems are facing many unanticipated conditions which increase their vulnerability to failures. Therefore, production systems should be resilient to survive in today’s competitive market. In this regard, the strategy of lean production may be very significant. In this study, this study applied RE factors on a line production system and assessed their impacts on system’s efficiency. In this study, the leanness enablers were extracted from the literature and then seven RE factors were defined based on them. A production line with six machines was considered as case study and simulated by Visual SLAM. Twenty-three different scenarios are generated based on the experts’ opinions; each scenario contains some RE factors. The RE factors used in this study, were top management commitment, reporting culture, visibility, awareness, velocity, redundancy and flexibility. These factors help lean production strategy to improve its enablers. DEA method was developed for ranking and calculating the efficiency of each scenario. The simulation’s outputs were analyzed to determine which one of them has the maximum and minimum effect on the calculation of efficiency of each scenario. According to the obtained results of this analysis, it was determined that “Average utilizations of machines” and “Total cost” had respectively the maximum and minimum effect on the efficiencies. Also, a similar analysis was performed on the RE factors. In this analysis, it can be concluded that applying redundancy policy leads to better efficiency in comparison with other RE factors (i.e., velocity, reporting culture, top management commitment, flexibility, awareness, and visibility). It was recommended that the production system should be redesigned considering the redundancy features.

In the future research, the impacts of external factors such as fluctuations of demand can be considered as a disturbance. Also, assessment of the other resilience factors in such line production under uncertain situations can be the subject of future studies.

Footnotes

Acknowledgements

The author is grateful for the valuable comments and suggestions from the respected reviewers. Their valuable comments and suggestions have enhanced the strength and signiﬁcance of our paper.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Author biography

Mansour Zarrin obtained his MSc in Industrial Engineering at the University of Tehran. He received the 2015 Distinguished Researcher Student Award for excellence in research and innovation of published papers at University of Tehran. Mansour has published more than 15 papers in reputable academic journals and conference proceedings. His fields of interest include performance assessment, human resource management, safety and health science, ergonomics, data analysis, optimization, artificial neural networks, expert systems, and fuzzy sets theory.

Professor Ali Azadeh is an eminent university professor and founder of Department of Industrial Engineering and co-founder of Research Institute of Energy Management and Planning at University of Tehran. Dr. Azadeh is the director of Simulation and CAD Laboratory at University of Tehran. He is also member of Center of Excellence for Intelligent Based Experimental Mechanic. He obtained his Ph.D. in Industrial and Systems Engineering from the University of Southern California. He received the 1992 Phi Beta Kappa Alumni Award for excellence in research and innovation of doctoral dissertation in USA. Professor Azadeh is the recipient of seven all university awards at the University of Tehran. He is also the recipient of National Eminent Researcher Award in Iran. He has been selected as top 1 percent scientist in the world by Thomson Reuters in 2015. He has also been selected as the most cited scientist by ISC in 2014. Professor Azadeh has published more than 750 papers in reputable academic journals and conference proceedings. He is the recipient of best paper awards in international conferences in Japan and Azerbaijan.

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