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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.16 No.4 pp.455-464
DOI : https://doi.org/10.7232/iems.2017.16.4.455

# Fuzzy Risk Analysis Using Fuzzy Sampling Method: Case Study of Design a Reconfigurable Multi-Agent Supply Chain Network under Risk

Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Faculty of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran
Industrial Engineering Department and Center of Excellence for the Optimization of Advanced Production and Service Systems, Iran University of Science and Technology, Tehran, Iran
Corresponding Author, mjtarokh@kntu.ac.ir
20170717 20170805 20170821

## ABSTRACT

First step of reconfigurable supply chain network developing is understanding of risk affects. Categorizing of risk module and results of risk events considered with gathering and analyzing of data from network design parameters. These obtained data have probability distribution that shows uncertainty in parameters. In the literatures supply chain risk categorized based on occurrences rate or frequency and period or duration time and also place of occurrence. Deal with uncertainty and complexity of risk, our proposed fuzzy method can solve these problems in two aspects. Also described a fuzzy based sampling method (FLHS) that developed and used in this paper can improve our results even more than previous works. This paper suggests a novel modelling and simulation method of fuzzy sampling and fuzzy analysis system to address the dynamic risks effects in the especially the consideration of uncertainty risk event system behavior in different operational conditions.

## 1.INTRODUCTION

Risk is defined as a future development or event that might adversely impact the achievement of corporate goals. Moeinzadeh and Hajfathaliha (2009) argues that risk management is an entrepreneurial need, which should be established by any company. Most developed countries also “support” this need by further regulation requiring risk management systems to contain the risk on a company level. But there seems to be no regulation demanding risk management which covers the supply chain and consequently, companies are free to extend the scope of risk management beyond the company level and develop inter- organizational approaches to managing risk.

Risk management has a long history among the academics and practitioners and it is a currently debated topic in the area of supply chain and in our case study especially HCSC management. The topic derives its importance due to several industry trends currently in place: market globalizations, increase use of outsourcing, short product lifecycle, unpredictable demand, uncertain supply and pressure for lean production.

In order to be more efficient, firms have adopted strategies such as outsourcing, global partnerships and lean practices. Although such strategies have tremendous abilities to improve the efficiencies but simultaneously they make the firms vulnerable to market uncertainties, dependencies and disruptions. Moreover, natural calamities and manmade crises have also put negative impact on strategic, operational and tactical performance of supply chains. These factors have triggered the interest of academia and industry to consider the risk issues as prime concerns. To capture the more fine-grained elements of diversified risk issues related to the supply chain (Udbye, 2014; Marzbanrad et al., 2015) employ a multi-layered top town taxonomy to classify and codify the literature and put forward the probable dimensions for future research.

In today’s global marketplace, individual firms do not compete as independent entities rather as an integral part of a supply chain. Peidro et al. (2009), proposes a fuzzy mathematical programming model for supply chain planning which considers supply, demand and process uncertainties. The model has been formulated as a fuzzy mixed-integer linear programming model where data are ill-known and modelled by triangular fuzzy numbers. The fuzzy model provides the decision maker with alternative decision plans for different degrees of satisfaction.

Fuzzy logic can be a powerful tool for managers to use instead of traditional mathematical models when measuring the of supply chains responsive. The flexibility of the model allows the decision maker to introduce vagueness, uncertainty, and subjectivity into the evaluation system. Responsiveness measurement represents a critically important decision that often involves subjective information. Fuzzy logic models provide a reasonable solution to these common decision situations. After extensive exploration of the literature, Omar et al. (2015) recommend an outcome of developing a Fuzzy logic framework in measuring qualitative aspects of supply chain responsiveness.

In recent years many methodologies have been developed in terms of quantitative measures but most of them merely focus on the control mechanism based on reported measures whereas the qualitative aspect of the work is still unexplored. Fuzzy logic can be a powerful tool for managers to use instead of traditional mathematical models when evaluating the performance of supply chains. The flexibility of the model allows the decision maker to introduce vagueness, uncertainty, and subjectivity into the evaluation system. Performance evaluations represent a critically important decision that often involves subjective information. Fuzzy logic models provide a reasonable solution to these common decision situations. After extensive exploration of the literature, we recommend an outcome of exploring Fuzzy logic approach in evaluating qualitative aspects of performance of supply chain management (Omar et al., 2015).

One of the essential tools for uncertainty bounding is the fuzzy logic and, therefore, the main objective of (Li et al., 2016b) is the analysis of the literature about the application of fuzzy logic in performance measurement systems operating within uncertainty environments with the aim of categorizing, conceptualizing and classifying the works written so far.

Explain a pricing model at farm level by consensus using stakeholder dialogue approach which is based on balancing the fuzzy risk utility preference that will be faced by all levels of the supply chain members. Fuzzy risk utility optimization was used to get consensus of supply chain stakeholder dialogue while basic risk utility function was derived by using fuzzy regression approach (Li et al., 2016a).

Managing risk has become a critical component of SC management. Different types of SC vulnerability management methodologies have been proposed for managing SC risk, most offer only point-based solutions that deal with a limited set of risks. Feyzioglu et al. (2007) research aims to reinforce SC risk management by proposing an integrated approach. SC risks are identified and a risk index classification structure is created. Then we develop a SC risk assessment approach based on the analytic network process (ANP) and the VIKOR methods under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers.

A combined fuzzy analytical hierarchy process (AHP) to calculate the weight of each risk criterion and sub-criterion and technique for order performance by similarity to ideal solution (TOPSIS) methodology to rank and assess the risks associated with implementation of (GSCM) practices under the fuzzy environment (Nazam et al., 2015; Wen and Xi, 2007; Malmir et al., 2013).

As the essential components in formulations, pharmaceutical excipients directly affect the safety, efficacy, and stability of drugs. Recently, safety incidents of pharmaceutical excipients posing seriously threats to the patients highlight the necessity of controlling the potential risks. Hence, it is indispensable for the industry to establish an effective risk assessment system of supply chain. An AHP-fuzzy comprehensive evaluation model was developed based on the analytic hierarchy process and fuzzy mathematical theory, which quantitatively assessed the risks of supply chain (Li et al., 2016b).

Using the method of fuzzy multi-criteria lattice-order decision-making to evaluate the potential risks through ranking and structuring the risks. Normalizing the fuzzy risk evaluation matrix, through triangular fuzzy number calculation and comparing each risk with the positive ideal risk (PIR) and negative ideal risk (NIR), making supply chain enterprise’ main risks’ ranking more reasonable so that the enterprise can take corresponding measure to the high rank risks, without doubt that such work can greatly help the supply chain risk management (Wen and Xi, 2007).

Aqlana and Lam (2015) research presents an integrated framework for supply chain risk assessment. The framework consists of three main components: survey, Bow-Tie analysis, and fuzzy inference system (FIS). Due to increase in customer environmental awareness, competitiveness and strict governmental policies, the approach of incorporating green supply chain management (GSCM), healthcare supply chain (HCSC) to conserve resources and sustainable production, is gradually becoming more imperative for organizations. However, the successful accomplishment of green supply chain (GSC) production HCSC services and business activities is relatively difficult due to involvement of different risks. These risks and their respective sources have a tendency to disturb the GSC functioning, and thereby, decline in the ecological-economic performance. Therefore, identification of risks and their subsequent analysis in the GSC are very important to know and understand. The present research analyzes the risks relevant to adoption and effective implementation of GSC practices at industrial viewpoint. A two-phase research approach has been proposed and used in (Ceryno et al., 2013). In the first phase, six categories of risks and twenty-five specific risks, associated with the GSC, were identified. The basis of identification of the risks was literature and inputs received from experts from industries. Experts’ opinion has been collected from the officials and managers of four Indian poly product-manufacturing companies. In the second phase, the fuzzy analytic hierarchy process (fuzzy AHP), a qualitative and quantitative analysis was used to analyze the identified risks for determining of their priority of concern.

## 2.DESIGN A RECONFIGURABLE MULTI-AGENT HEALTHCARE SUPPLY CHAIN NETWORK UNDER RISK

First step for developing of a reconfigurable healthcare supply chain network is understanding of risk affects. Categorizing of risk module and results of risk events considered with gathering and analyzing of data from network design parameters. These obtained data have probability distribution that shows uncertainty in parameters. In the literatures healthcare supply chain risk categorized based on occurrences rate or frequency and period or duration time and also place of occurrence as detailed as following:

• Risk frequency: 3 level of frequency high (6 times in year), medium (4 times in year) and low (2 times in year)

• Risk duration: 3 level of period happens: high (13- 15 days), medium (6-8 days) and low (0-2 days)

• Risk place: it happens in one of these layers of healthcare supply chain: source, production site, storage, or customer layer.

All possible states for risk occurrence is multiplication of 3, 3 and 4 that equals 36 states. However to consider of all possible states of risk events we need check all of these 36 states. Even though we consider for example 4 layer in risk place item maybe some who consider 2 or more layers than or method. Based on optional or scientific experimental every company can use different levels of risk module, but what happens in each category if a company want to use customized level of category? Or especially uses many further levels of category? Can we test any contribution of risk categories?

Organizations commonly develop and rely on rules as a primary tool for managing risk, equating compliance with overall effective risk management. While complying with rules may be adequate to manage certain types of risks, history has demonstrated that not all types of risk can be effectively dealt with through compliance-focused risk management. This article presents a new framework for defining and addressing an organization’s risks that expands beyond rules-based models.

Central to this framework is the idea that an organization’s risks can be broken down into the following three categories:

• Internal risks, relative to an organization, that can be controlled (e.g. the risk of employee misconduct)

• Strategic risks taken on by an organization in the pursuit of value (e.g. the risk associated with an investment in developing a new product line)

• External risks, relative to an organization, that are largely beyond control (e.g. the risk of impact from a natural disaster, like an earthquake)

For each risk category, the authors of this Harvard Business Review article discuss risk management mechanisms that have actually been put to effective use in the field by various organizations. Below is a summary of the risk management techniques discussed in the article for each category of risk.

Agents in our method contributed as five section, we want to use optimized risk values for gaining better results, and aim of our approach is reduction procedure that adapted to difference values of risk.

Firstly we should prove that variety in risk value is better than fixed one and in follow we mixed fuzzy approach to gaining better results and more precise than previous proved values. I.e. using fuzzy approach to different ranges of risk in every category.

### 2.1.Multi-Agent Simulation Model

A multi-agent system showed in Figure 1 has several properties that described in following sections.

Predefined assumptions in Multi-Agent Simulation (MAS):

• 1. Risk event occurs just once in every time

• 2. If risk event happens, production of that node stopped

• 3. The time for service one day after of the time for request

• 4. Time of reception between two nodes is one day

• 5. None of productions accepted in failure state

• 6. Initial price unit for ith day:

• 7. No request needed for not demand request

• 8. There is no direct path from company nodes to customer nodes

• 9. Cost of holding for every day equals 20% cost of movement

• 10. Prediction request for all nodes done with movement medium in 7 days period

• 11. Penalty cost for production equals with cost of 100 unit

• 12. Total action cost equals with summation of costs for move, hold and penalty

### 2.2.Multi-Agent Simulation Procedure

Study results on parameters of network including risks events simulated based on following steps:

• 1. Designing optimized configuration of healthcare supply chain based on cost values from mixed integer programming (MIP) model.

• 2. After computing optimize configuration of network MAS model obtained. Assume all of parameters are deterministic else consumer requests in each node

• 3. Simulation process done based on this model in order to observations of cost values, requests, facilities and node capacities.

• 4. In every loop just one risk event can occur.

Requests in each node as commonly distributed with 20% standard deviation of deterministic values for problem.

As a results of probability distribution, theoretical probability distributions are a good view to implementation but in our case it is not applicable because of following reasons.

• 1. Gathered data is not continues. So to fit data for theoretical methods, data relaxation is needed.

• 2. Some information related to costs of supply, production and warehouse are restricted. In MAS model lower bound for price of goods is 70% of mean price.

• 3. Problem of this research solved by numerical assumptions.

A sample developing of experimental distribution to optimization module

As shown in Figure 2, process of sample production to optimization module contains steps that first of it is risk analysis. With information about risk we can find that uncertain parameter in data base. Next step is using local uncertain parameter related to that kind of risk and configuration. Simulation of these processes done and obtained results sent to random sample generator step. In this step experimental probability distribution used to configuration of network.

Random optimization module of network is second main part of reconfigurable supply chain network as shown in Figure 3. Task of this part is designing new configuration in risk event time. Two entry is needed for implementation of this module. First one is a list of contain all possible nodes as like available producers, potential customers and present facilities in supply chain. Second important one in optimization under uncertainty is related data of probability distribution to parameters of network design.

Main idea for random optimization module of network is recognizing of potential risk in every loop of system. In this case deterministic model of healthcare supply chain based on MIP used for implementation of that model possibly is not sufficient for making decisions on nondeterministic environment, so our proposed method is using a two-step model based on risk events.

Mathematical model can be referred as a problem of reconfigurable supply chain under risk (SRR). Random optimization module composed three part that important part of this module is two-step random programming model for SRR problem. Also a Fuzzy Latin Hypercube Sampling (FLHS) method used to reducing of variance and execution time in this part of module. (FLHS is a sampling method that wrote by authors of this paper and under process)

Assumptions for formulation of random programming model for SRR problem:

• 1. HCSCN contains four layers (producer, company, warehouse and consumer) and production service form producers to consumers is continues.

• 2. Only one kind of production can be provided by HCSC.

One of important risk analysis approaches is fuzzy concept that encounter with uncertainty (Wen and Xi, 2007).

Optimized model of SRR and consecutively SRR with fuzzy modeling of SRR formulated as following:(1)

$M i n z = ∑ i ∈ F c 0 i ( y i , 1 − y i , 1 y i , 0 ) + ∑ i ∈ F c c i ( y i , 0 − y i , 1 y i , 0 ) ∑ i ∈ W l i c r i y i + ∑ i ∈ P c b i , y i , 1 + ∑ i ∈ W c b i ( y i , 1 + y i ) + E [ Q ( y 1 , Y , ξ ( ω k ) ) ] y i , 1 + y i ≤ 1 ∀ i ∈ W ∑ i ∈ F c 0 i ( y i , 1 − y i , 1 y i , 0 ) + ∑ i ∈ F c c i ( y i , 0 − y i , 1 y i , 0 ) + ∑ i ∈ W l i c r i y i ≤ b Y 1 ∈ { 0 , 1 } | F | Y ∈ { 0 , 1 } | W |$
(1)

where $Q ( ( Y 1 , Y , ξ ( ω k ) ) )$ is the optimal value of the following problem:(2)

$M i n ∑ ( i j ) ∈ A q ( ω k ) i j x i j + ∑ j ∈ c g j u j ∑ i ∈ N x i j − ∑ l ∈ N x j l = 0 ; ∀ j ∈ F ∑ i ∈ W x i j + u j ≥ d ( ω k ) j : ∀ j ∈ C ∑ J ∈ P x i j ≤ s ( ω k ) i ; ∀ i ∈ S r j ( ∑ i ∈ s x i j ) ≤ m ( ω k ) i ; ∀ j ∈ P r j ( ∑ i ∈ p x i j ) ≤ m ( ω k ) j ( y j , 1 + y j ) ; ∀ j ∈ W X ∈ R + | A | , U ∈ R + | C |$
(2)

Main problems:

• 1. Sampling model

• 2. Risk uncertainty

First problem discussed in another literature under processing (we use brief notation here):

## 3.PROPOSED FUZZY LHS SAMPLING

In argued method each element just belongs to one category, but in our approach each element include in all groups with one exception that membership values are different. For example consider age ranges.

When we categories such samples with LHS method, some errors raised for computing values like variance, mean, etc. in fuzzy approach precision level make up better. In fact each element is member of every category with a probability between 0 and 1. Our new approach is a combination of fuzzy and LHS. In this approach we assume that linguistic variables comprised as five parts and modeled in trapezoid.

Like stratified and LHS method we choose some random elements from each stratum for sampling, and then we identify the neighborhood of LHS to modeling fuzzy. Let $n 1 , n 2 , ⋯ , n m$ be the number of elements in each of the m sampled LHS. Let $X ¯ 1 , X ¯ 2 , ⋯ , X ¯ m$ be the means of the sampled LHS. The relative uncertainty itself can also be used without the subsequent statistical testing particularly if enough is known about the parameter being evaluated. Variance reduction techniques are methods that attempt to reduce the variance, i.e., the dispersion associated with the variations, of the parameter being evaluated. This can result in one of two outcomes. Either the variance is reduced for the same number of sampling or the number of sampling can be reduced for the same variance, the comparison of both being made when no variance reduction techniques are used. This therefore either increases the confidence in the results or reduces the computational burden. There are many forms of variance reduction techniques and a specialized text should be consulted if full details of all techniques are needed. This algorithm provides reduced variances and standard errors comparison with other traditional methods. Schematic of proposed method is shown in Figure 4.

Steps that are used for programming with use of fuzzy-LHS method are mentioned in following algorithm (Figure 4):

• Determine number of dimensions for problem

• Select m (No. of points) random elements from each set of LHS

• Determine neighborhood of selected point between sets of LHS

• Calculate membership values for each LHS

• Calculate mean value, variance, max confidence and min confidence from formulas

• Calculate values for each LHS with effect of LHS neighbors

• Calculate values with effect of element neighbors in each LHS

• Calculate values with effect of both element neighbors and LHS neighbors

## 4.PROPOSED METHOD FOR FUZZY RISK

As noted previously there are K-types of risks and must be implemented in simulations but in every risk types it’s unknown that exact values. For example consider risk duration parameter that vary from 0 to N days, if it is modeled in classic approach you should compute all of possible durations but it is not applicable or time consuming procedure. Another risk parameters have same conditions. This situations always occurred in real world problems, our approach to deal with this problem is choosing one of following solutions:

• 1. Discrete constrained approach

• 2. Fuzzy continues approach

From computational complexity view first approach is time consuming because there are many states that you should consider, and also it has low precision rate because lack of real information. So to encounter this problems our proposed method is using fuzzy logic.

Following steps transfers crisp values of risk parameters to fuzzy sets:

• 1. Determine lower and upper bound of risk types for each periods

• 2. Estimation or prediction of critical values for risk parameters in each period (like low, medium and high)

• 3. Create fuzzy demonstration for each boundary of critical values

Result fuzzy view for risk duration and risk frequency showed in Figure 5 and Figure 6 respectively. In this view by choosing every point of domain value it can be decidable that risk event happens, but in traditional discrete view it is not decidable. Choosing triangular or trapezoid view depends on risk values, i.e. if our risk parameter has range of values we should select trapezoid and if it has fixed numbers (countable) modeled as triangular view.

Properties of membership values for fuzzy demon- stration are very simple. Each point of domain belongs to 3 set with different membership values and sum of these membership values are 1.(4)

$μ ( x ) = μ low ( x ) + μ medium ( x ) + μ high ( x ) = 1$
(3)

$e.g. μ duration ( 5 ) = { μ low ( 5 ) = ˜ 0.3 μ medium ( 5 ) = ˜ 0.7 μ high ( 5 ) = ˜ 0.0$
(4)

That means if a risk duration event happens 5 days of a period time, simply by including risk event in system there can be configured for risk event. Efficiency of this approach arisen when you want to model discrete values in period cycle i.e. when your decisions made on points that have membership values equal to 1. In this case its computations done just for one point whereas all of them. And here if your model have 3 level of risk events in worst case with changing all of risk event parameters you should apply 3 parameters to system.

We have implemented our algorithm in MATLAB®, which has been resented in Appendix A1.

## 5.RESULTS AND EXPERIENCES

Formulation of this model for three types of companies and applying risk event summarized in Table 1.

Here efficiency of proposed method should be discussed in two aspects from view of comparison point. Firstly our sampling method must be challenged with following formula and secondly risk event and it`s efficiency.(5)

$Eff FLHS = Var min Var FLHS × Time min Time FLHS$
(5)

where Varmin is minimum value of variance for sampling methods and Timemin is the needed time for computation of sampling method. Comparative results of fuzzy risk event showed in Table 2.

Estimation of risk events and analysis in our method and traditional methods with and without fuzzy view showed that for this kind of uncertainty using fuzzy approach is a good solution. Also Figure 7 shows smooth improving in comparison with other algorithms.

Simulations based on fuzzy both in sampling and risk events have significant improvement and more precise than other methods and also it is very close to optimal values (these values obtained from estimation values and best conditions).

## 6.CONCLUSIONS AND FUTURE WORKS

Fuzzy concept have many features that suitable to real world problems, in fact uncertainty is a big deal problem that can be reduced using fuzzy approach. In this paper we modeled a healthcare supply chain network that have risk event, as a result of this event we must reconfigure our network to include risk parameters and hence described model have 3 types of risk it is so complicated to compute and redesign network. Then in study of uncertainty occurrence we used fuzzy model to reduce errors, even we used a sampling method that has contribution of fuzzy model. Finally we see that composition of fuzzy sampling and fuzzy risk modeling has a significance improvements in results and more accuracy than other mentioned works.

## Figure

An example configuration of healthcare supply chain network.

Procedure of control agent from risk analysis to optimization module.

MAS schema.

Flowchart of proposed sampling method.

Risk duration item modeling in fuzzy approach.

Risk frequency item modeling in fuzzy approach.

Fuzzy risk with fuzzy sampling in compare to others.

## Table

Parameters value range

Summary of fuzzy risk event comparative results

Sample MATLAB code.

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