Showing papers in "Opsearch in 2016"

Multi-criteria analysis of supply chain risk management using interval valued fuzzy TOPSIS

Abstract: The global supply chain in the past decade is relying heavily on the outsourced supply chain partners for competitive edge. Increased supplier risk vulnerability has lead firms to give more weightage to purchasing function and its associated decision makers. Hence determining which supplier to include in supply chain has become the key strategic consideration. Supplier selection problem requires a trade-off between multiple criteria exhibiting ambiguity and vagueness with the involvement of a group of decision makers. This paper formulates a multiple criteria decision making problem with linguistic variables and their transformation to interval valued fuzzy numbers. By appropriate extension of technique for order of preference by similarity to ideal solution (TOPSIS) method with interval valued fuzzy numbers, this paper considers the proposed signed distance measure developing a model to manage decision making problem under uncertainty. The performance rating values and weights of linguistic risk criteria are expressed as triangular interval-valued fuzzy numbers in normalized mode. The best alternative is selected according to both ideal and non-ideal solutions without defuzzification. Finally, the feasibility and effectiveness of the developed method is illustrated by a case study in Electronics supply chain with six risk based criteria and four alternatives (Li-ion based battery suppliers). We compare the results with some existing methods to show the validity of the extended method. A sensitivity analysis is performed with six different sets of criteria weights for analyzing the robustness of the proposed method.

Performance evaluation of Indian states in tourism using an integrated PROMETHEE-GAIA approach

Abstract: Tourism development has a unique responsibility in regional policy of almost all countries. It is a well known fact that tourism has a remarkable contribution in sustainable development, economic growth and social benefits for a country, if planned methodically. This is due to its unquestionable advantages and benefits for the local community with respect to economic, social and environmental aspects. Since few decades, it has become a driving area in Indian economic planning strategy to deal with tourism issues for effective utilization of its wide range of destination resources and also optimize the intensity of financial involvement for developing tourist infrastructure in a restraint economic province. This paper applies a simple methodology to quantify the tourism potential of Indian states using an integrated visual decision aid model of preference ranking organization method for enrichment evaluation (PROMETHEE) and geometrical analysis for interactive aid (GAIA). Several social and physical attributes are considered to evaluate and rank the Indian states with respect to their performance in tourism. The adoption of this integrated visual decision aid model identifies Jammu and Kashmir, and Jharkhand as the best and the worst performing states respectively. In GAIA plane, the position of Jammu and Kashmir is the farthest from origin, followed by Madhya Pradesh. A close comparison between these two top performing states reveals that Jammu and Kashmir mainly outperforms Madhya Pradesh with respect to budget allocation, population density, pollution index and cost of living index criteria. The performance of Jharkhand is not at all the best with respect to even a single criterion. In GAIA plane, it is also observed that the considered beneficial and non-beneficial criteria form two different clusters, as expected. This performance evaluation problem is identified to be not at all a hard problem to solve.

An EOQ inventory system of ameliorating items for price dependent demand rate under retailer partial trade credit policy

Abstract: This paper studies the optimal ordering decision in the economic ordering quantity framework under two levels of trade credit policy where demand rate is a selling price dependent with ameliorating items whose value or utility or quantity increase over the time. In this paper, it is assumed that the retailer maintains a powerful decision-making right and can obtain the full trade credit offered by the supplier yet retailer just offers the partial trade credit to his/her customers. Furthermore, we consider that the items which were already sold but not yet paid for by customers would also incur interest charges or capital cost, which is not considered in the existing studies concerning retailer partial trade credit. For the objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally we obtain a lot of managerial insights from numerical examples. The results would provide valuable references for retailer in controlling the inventory of ameliorating items. The results also show that it is very necessary and realistic to consider the capital cost incurred by the items which were already sold but not yet paid for by customers under retailer partial trade credit policy.

An objective approach of balanced cricket team selection using binary integer programming method

Abstract: Selecting a balanced playing XI in the game of cricket with the right mix of players of different specialization is a difficult decision making problem for the team management. To make the process more objective, optimization techniques can be applied to the process of selection of players from a given squad. Such an exercise has two dimensions. First, a suitable tool for performance measurement of cricketers needs to be defined. Secondly, for selecting a balanced team of XI players, an appropriate objective function and some constraints need to be formulated. Since the captain gets an obvious inclusion in the cricket team, the area specialization of the captain influences the selection of other ten positions in the playing XI. This study attempts to select the optimum balanced playing XI from a squad of players given the specialization of the captain using binary integer programming. To validate the exercise, data from the fifth season of the Indian Premier League has been used.

Intuitionistic fuzzy T-sets based optimization technique for production-distribution planning in supply chain management

Abstract: Technique to find optimal solutions for production-distribution planning in supply chain management under imprecise environment is discussed in this paper. In 1997, Angelov first introduced an optimization technique under intuitionistic fuzzy environment. Several other researchers have worked on it in recent years. In 2015, Wu, Liu and Lur redefined membership functions of fuzzy set theory and proposed another two phase technique. In optimization problem under uncertainty, it is observed that prime intention to maximize up-gradation of most misfortunate is better served if some constraints present in existing, established techniques are removed. It is also observed that membership functions and non-membership functions are not utilized in the way they are defined in existing techniques. And in some cases, constraints in existing techniques may make model infeasible. Hence in this paper, new functions: T(+)-characteristic functions and T(-)-characteristic functions, are introduced to supersede membership functions and non-membership functions respectively; and subsequently new set: Intuitionistic fuzzy T-set is introduced to supersede intuitionistic fuzzy set to represent uncertainty. Moreover in this paper, one general algorithm has been developed to find optimal solutions to optimization problems under uncertainty. One standard production-distribution model is taken not only to allocate limited available resources and equipment to produce the products over time periods but also to determine economic distributors for dispatching product to the retailers. Real life numerical applications of this model further illustrate the limitations of existing techniques as well as advantages of using proposed technique. Finally conclusions are drawn.

Stochastic behaviour analysis of power generating unit in thermal power plant using fuzzy methodology

Abstract: The aim of this research is to study the stochastic behaviour of a PGU (power generating unit) of a medium size coal fired thermal power plant using fuzzy methodology (FM). The PN approach was used to depict series and parallel configurations of the subsystems constituting the PGU. To study the failure dynamics of the considered system, various reliability parameters such as failure rate, repair time, MTBF, ENOF, availability and reliability of the system were computed using fuzzy λ-τ approach. RCA was conducted to determine the failure causes of various subsystems of the PGU. FMEA was carried out to determine the RPN scores of the various failure causes of different components. On the basis of these RPN scores, critical components were identified and ranked on the basis of criticality. Further, the limitations of the traditional FMEA approach were overcome by introducing a Fuzzy decision support system (FDSS). Findings of this study would be communicated to field engineers/system analysts of the considered system to help them understand and anticipate system behavior, and implement appropriate and effective maintenance policies for improving system availability.

Analysis of an M [X] /G/1 unreliable retrial G -queue with orbital search and feedback under Bernoulli vacation schedule

Abstract: In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation

Abstract: In this article, we study a finite buffer single server variable batch service queue where customers arrive according to a batch Markovian arrival process. The server serves the customers with a variable batch size at the starting point of services. When all the customers are served in the system exhaustively, the server leaves for a vacation. Single as well as multiple vacation policies are analyzed. We derive the queue length distributions at different epochs. Some important performance measures such as blocking probabilities, mean queue lengths, mean waiting time have been obtained. A variety of computational results are presented for practitioners and others who would like to check their results with those of ours.

Design and evaluation of layout alternatives to enhance the performance of industry

Abstract: The present study provides an alternative way to handle the industrial layout problems. A procedural approach has been proposed by the authors to design the layout. The suggested approach consists of few easy and quite simpler steps. It only requires to apply predetermined steps consisting some simple mathematical calculation. An industrial layout problem has been resolved by adopting the suggested approach. The developed layout alternatives of the considered case study have been simulated with the ProModel tool for the evaluation purpose. The ranking of the alternatives has been carried out by the preference selection index (PSI) methodology. The output of the analysis demonstrated that the layout alternative designed by the suggested approach ranked higher as compared to the existing layout. A comparison of the proposed approach has also been carried out with the other approach from the literature.

Pricing and production decisions in multi-product single machine manufacturing system with discrete delivery and rework

Abstract: The classic economic production quantity (EPQ) inventory model assumes all items produced are of perfect quality. However, in most real-life manufacturing settings, generation of defective items is unavoidable. Reworking of imperfect items reduces the overall costs. The finished products can only be delivered to customers if the whole lot is quality assured at the end of rework. In addition, in many circumstances the delivery of the products is not continuous. This paper studies pricing and production decisions in multi-product single machine manufacturing system considering discrete delivery as well as rework. We solved this problem in two situations: first, when the condition is satisfied and second, when it is not satisfied. The obtained closed-form solution is optimal when the only constraint of the problem is satisfied; otherwise, the Lagrangian relaxation method is used to determine T* and Q*. At the end, numerical example is solved to illustrate the validity of the proposed solution procedure.

Queue-length distribution of a batch service queue with random capacity and batch size dependent service: M / G r Y / 1 $M/{G^{Y}_{r}}/1$

Abstract: This paper considers a single-server batch-service queue with random service capacity of the server and service time depends on the size of the batch. Customers arrive according to Poisson process and service times of the batches are generally distributed. We obtain explicit closed-form expression for the steady-state queue-length distribution at departure epoch of a batch based on roots of the associated characteristic equation of the probability generating function. Moreover, we also discuss the case when the characteristic equation has non-zero multiple roots. The queue-length distribution at random epoch is obtained using the classical principle based on ‘rate in = rate out’ approach. Finally, variety of numerical results are presented for a number of service time distributions including gamma distribution.

A retrial inventory system with priority customers and second optional service

Abstract: In this paper, we investigate a single server (s, Q) perishable inventory model consisting of two priority customers, say, type-1 and type-2. The customers arrival flows are independent Poisson processes, and the service times of the type 1 and type 2 customers are exponentially distributed. The server offers two different types of services - first with ordinary service (essential service) and the second with optional service. The idle server first gives ordinary service to the arriving customers (type 1/type 2). Upon first essential service completion, then the server gives additional service (second optional) only to the type 1 customers. We assume that the type 1 customers have both types of priorities (non-preemptive priority and preemptive priority) over the type 2 customers. We discussed retrial concepts only for type-2 customers. The stationary probability distribution of the inventory level, status of the server, number of customer in the orbit and number of customers in the waiting line are obtained by matrix methods and some numerical illustrations are provided.

Reverse logistics network design: a water flow-like algorithm approach

Abstract: This study investigates the reverse logistics network design problem, including collection/inspection, recovery and disposal centers that a mixed integer linear programming model is considered. In this network, returned products from customer zones are collected in collection/inspection centers and after quality inspection, and also after separation, recoverable products are shipped to recovery centers and scrapped ones are transported to disposal centers. NP-hardness of this problem is proved in many papers, so a novel meta-heuristic solution method aiming minimization of total costs comprised fixed opening cost of collection/inspection, recovery and disposal centers and transportation cost of products between opened centers using priority based encoding presentation is proposed. Comparison of outputs from this proposed algorithm and a modified genetic algorithm shows the excellence of this new solution method. Finally, some directions for future research are proposed.

A new Data Envelopment Analysis under uncertain environment with respect to fuzziness and an estimation of reliability

Abstract: Data envelopment analysis (DEA) is an effective technique for measuring the efficiency of decision-making units (DMUs) with several inputs and various outputs. Traditional DEA requires crisp data. However, the data in real applications are often imprecise. In order to dominate this restriction, the fuzzy sets may be utilized with the classical DEA to permit expert to integrate ambiguous data into the model. However, fuzzy sets encounter the limitation of not considering the estimation of reliability of information. In view of this, Z-number has been extended to model fuzzy numbers with a degree of confidence. In this paper, we introduce a new DEA (abbreviated as Z-DEA) for working out CCR in which the input and/or output are Z-number variables. We do this task by converting the Z-DEA to classical fuzzy model on the base of a fuzzy expectation of the fuzzy sets. In our study, the expert utilizes the linguistic terms for expressing judgment and an estimation of reliability. To the best of our knowledge, compared with the traditional DEA frameworks, The DEA with Z-data can more practically handle real-world problems.

Understanding the barriers of service supply chain management: an exploratory case study from Indian telecom industry

Abstract: The major theme of this research is to understand and model the interpretive features of barriers of Service Supply Chain Management in an Indian telecom service supply chain by considering a case organization. ISM is a well-proven system modelling approach for analyzing the synergic influences of various attributes to the overall system under study. The unique feature of ISM is that it analyzes the attributes based on their driving power and dependence. In the current study, the ISM has been developed for a leading Indian telecom service provider. The barriers in the service supply chain have been identified and subjected to study. Initial reachability metrics and final reachability metrics have been made. The hierarchy of various barriers has been established based on the outcomes of the final reachability metrics. The diagraphs have been constructed (i) considering transitivity and (ii) without considering transitivity. Finally MICMAC analysis has been carried out categorize the barriers in to four clusters. The paper is concluded with action plans and scopes for future work.

Relationship between randomized F -policy and randomized N -policy in discrete-time queues

Abstract: This paper investigates the interrelationship between the randomized F- policy and randomized N- policy in discrete-time queues with start-up time. The F-policy queuing system deals with the issue of controlling arrivals. The N-policy queueing system deals with the issue of controlling service, that is, when all the customers are served in the queue, the server is deactivated until N customers are accumulated in the queue. Using the recursive method, the steady-state probabilities are determined for both models. The relationships between the discrete-time G e o/G e o/1/K queues with (p, F)- and (q, N)-policies are established by a series of propositions. The benefit made by interrelationship is that the solution of one queue can be deduced from the other queue readily. Various performance measures and numerical results are carried out for illustration purposes. These queues are common in wireless communication systems, production systems, manufacturing systems.

Set-valued fractional programming problems under generalized cone convexity

Abstract: In this paper, we establish the sufficient Karush-Kuhn-Tucker (KKT) optimality conditions for the set-valued fractional programming problem (FP) via contingent epiderivative under ρ-cone convexity. We also study the duality results of parametric (PD), Mond-Weir (MWD), Wolfe (WD) and mixed (MD) types for the problem (FP).

A Newton method for capturing efficient solutions of interval optimization problems

Abstract: In this article, we propose a Newton method to obtain an efficient solution for interval optimization problems. In the concept of an efficient solution of the problem, a suitable partial ordering for a pair of intervals is used. The notion of generalized Hukuhara difference of intervals, and hence, the generalized Hukuhara differentiability of multi-variable interval-valued functions is analyzed to develop the proposed method. The objective function in the problem is assumed to be twice continuously generalized Hukuhara differentiable. Under this hypothesis, it is shown that the method has a local quadratic rate of convergence. In order to improve the local convergence of the method to a global convergence, an updated Newton method is also proposed. The sequential algorithms and the convergence results of the proposed methods are demonstrated. The methodologies are illustrated with suitable numerical examples.

Product form solution for some queueing-inventory supply chain problem

Abstract: In this paper we analyze a single server supply chain model in which stocks are kept in both the manufacturer warehouse (production centre) and the retail shop (distribution centre). Arrival of customers to the retail shop form a Poisson process and their service time are exponentially distributed. The maximum stock of the distribution centre is limited to s + Q(=S). When the inventory level depletes to s due to services, it demands Q units at a time from the production centre. The lead time follows an exponential distribution. If the production centre has the required stock on-hand, the items are supplied. Supply of items from the production centre to the distribution centre is done only as a packet of Q units at a time. So if a packet of size Q is not available the distribution centre has to wait till Q units accumulates in the production centre. The production inventory system adopts a (r Q, K Q) policy where the processing of inventory requires a positive random amount of time. Production time for unit item is exponentially distributed. Also we assume that no customer joins the queue when the inventory level in the distribution centre is zero. This assumption leads to an explicit product form solution for the steady state probability vector.

Simplex particle swarm optimization with arithmetical crossover for solving global optimization problems

Abstract: In this paper, we propose a new hybrid algorithm by combining the particle swarm optimization with a genetic arithmetical crossover operator after applying a modification on it in order to avoid the problem of stagnation and premature convergence of the population. In the final stage of the algorithm, we applied the Nelder-Mead method as a local search method in order to accelerate the convergence and avoid running the algorithm without any improvements in the results. We call the new proposed algorithm by simplex particle swarm optimization with a modified arithmetical crossover (SPSOAC). We test SPSOAC on 7 integer programming optimization benchmark functions, 10 minimax problems and 10 CEC05 functions. We present the general performance of the proposed algorithm by comparing SPSOAC against 13 benchmark algorithms. The Experiments results show the proposed algorithm is a promising algorithm and has a powerful performance.

A finite-source inventory system with postponed demands and modified M vacation policy

Abstract: We study a finite source (s, S) inventory system with postponed demands and server vacation. We adopt a modified M vacation policy which is defined as: Whenever the inventory level reaches zero, the server goes to inactive period which comprises the inactive-idle and vacation period. If replenishment occurs during the inactive-idle period, the server becomes active immediately, or otherwise he goes for a vacation period. The server can take at most M inactive periods repeatedly until replenishment takes place. This inactive-idle time, the vacation time and lead time follow independent PH distributions. After the M t h inactive period, the server remains dormant in the system irrespective of the replenishment of order. Demands that occur during stock out or inactive periods, enter the pool and these demands are selected if the inventory level is above s. The inter-selection time follows exponential distribution. The joint distribution of the mode of the server, server status, the inventory level and the number of demands in the pool is obtained in the steady state. We have derived several system performance measures and total expected cost function. The results are illustrated numerically.

Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables

Abstract: This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables with fuzzy means and fuzzy variances in proposed multi-objective fuzzy stochastic transportation problem. The first step in fuzzy simulation based genetic algorithm is to deal with aspiration level of the constraints with the help of alpha-cut technique to obtain multi-objective stochastic transportation problem. In next step, fuzzy probabilistic constraints (fuzzy chance constraints) are handled within fuzzy stochastic simulation based genetic algorithm to obtain a feasible region. The feasibilities of the chance constraints are checked by the stochastic programming with the genetic process without deriving the deterministic equivalents. The feasibility condition for the transportation problem is maintained through out the problem. Finally, multiple objective functions are considered in order to generate a Pareto optimal solutions for the fuzzy stochastic transportation problem using the proposed algorithm. The proposed procedure is illustrated by two numerical examples.

DEA-neural networks approach to assess the performance of public transport sector of India

Abstract: This paper proposes the integrated Data Envelopment Analysis-Neural Networks approach to measures the efficiency of public transport sector of India. Data have been collected for 30 State Road Transport Undertakings (STUs) for the year 2011–2012. Efficiency of the STUs is measured with the use of three inputs and single output. Fleet Size, Total Staff and Fuel Consumption are considered as inputs and Passenger Kilometers as output. On the basis of the status of efficiency, it is concluded that efficiency of the STUs are not good and very far from the optimal level. In order to check the robustness of the results, regression and correlation analysis are also conducted which reveal that the efficiency scores measured by all the models having the common trends. The most efficient and the lowest efficient STUs are found same by all the models. The results also demonstrate that the proposed models are highly flexible and don’t require any prior assumptions about the functional form between inputs and outputs. The models also handle the problem of the presence of the outliers and statistical noise in the data points.

Multiple customer order decoupling points within a hybrid MTS/MTO manufacturing supply chain with uncertain demands in two consecutive echelons

Abstract: For decades, manufacturers have dealt with uncertain demands, and many solutions—such as manufacturing semi-finished products–have been presented to help manage the uncertainties. This paper considers the demand uncertainties in two echelons of a supply chain, unlike most of the field research, which has focused on the final customers’ demand uncertainty. In order to decrease the operating costs of a manufacturer, a model is proposed to use hybrid manufacturing in two levels of a supply chain with two echelons of manufacturers. The output of the presented model is the quantity of semi-finished products ordered to the decoupling point upstream manufacturer. The number of processes that must be done based upon Make to Stock, the order quantity of the decoupling point downstream manufacturers, and the order quantity of the final customers are obtained by the presented model as well. A numerical example and a vast sensitivity analysis are presented to better show the applicability of the presented model.

Analysis of variant working vacations on batch arrival queues

Abstract: This paper analyzes a batch arrival infinite-buffer single server queueing system with variant working vacations in which customers arrive according to a Poisson process. As soon as the system becomes empty, the server takes working vacation. The service rate during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size when the server is in different states. In addition, we obtain some other performance measures and discuss their monotonicity and a cost model is formulated to determine the optimal service rate during working vacation.

A discrete-time Geom/G/1 retrial queue with balking customers and second optional service

Abstract: In this paper, we discuss a discrete-time Geom/G/1 retrial queue with balking customers and second optional service where the retrial time follows a geometrical distribution. If an arriving customer finds the server is busy, he will leave the service area and go to the orbit with probability θ or leave the system with probability 1−θ; otherwise, he will begin his service immediately. In this model, after a customer finishes his first essential service, he may leave the system with probability 1−α or asks for a second optional service with probability α. Through studying the Markov chain underlying the model, we establish the probability generating functions of the orbit size and system size. Finally, some performance measures and numerical examples are presented.

The grey linear programming approach and its application to multi-objective multi-stage solid transportation problem

Abstract: The multi-objective solid transportation problem (MOSTP) constitutes one of the foremost areas of application for linear programming problem. The aim of this problem is to obtain the optimum distribution of goods from different sources to different destinations with different mode of conveyances which minimizes the total transportation cost and time. But it may contain one or more stage to transport the commodities with different mode of transport. In this paper, two new multi-objective multi-stage solid transportation problems (MOMSSTP) are investigated under grey uncertainty. Since using interval grey number theory we can absorb stochastic and interval uncertainty at a time, for this reason we developed two multi-stage STP under interval grey environment. The goal programming approach and fuzzy goal programming approach are used to reduce the multi-objective programming problem into a single-objective programming problem. Finally, the equivalent crisp models are solved using generalized reduced gradient technique (LINGO.13.0 optimization software) and the nature of the results is discussed.

Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces

Abstract: In this paper we introduce a general iterative algorithm for finding the common element of the set of common fixed points of a finite family of Bregman nonexpansive mappings and the set of solutions of systems of generalized mixed equilibrium problems. As an application, we find a solution for system of mixed variational inequality.

Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and inflation over a finite time horizon

Abstract: This paper deals with an inventory model for single non – instantaneous deteriorating items with two separate warehouses (one is Owned Warehouse and other is Rented Warehouse) having different preserving facilities. After some fixed period of time, inventory deteriorates in the two warehouses at different constant rates. Demand is assumed to be known and constant. In view of that the effect of inflation and time value of money over a finite planning horizon are employed in this study for optimizing the replenishment lot-size and the time interval simultaneously with the objective of minimizing total cost of the inventory system. Shortages are allowed and partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. The necessary and sufficient conditions for an optimal solution are characterized. In addition, an efficient algorithm is developed to determine the optimal policy, and the computational effort and time are small for the proposed algorithm. It is simple to implement, and our approach is illustrated through some numerical examples to demonstrate the application and the performance of the proposed methodology. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented and the implications are discussed in detail.

Fuzzy analytic hierarchy process to a structure under 2-out-of-3:F modeling

Abstract: The lack of consistency in reliability modeling under human failure can lead to inconsistent conclusions. However, fuzzy logic allows an address to the ambiguity in reliability modeling. The Analytic Hierarchy Process (AHP) is one of the comprehensively used multi-criteria decision making methods. This paper reveals the application of fuzzy AHP in a structure consisting of a 2-out-of-3:F substructure under human failure. In reliability engineering, failure is a major concern for system design, planning and operations and it is imperative to focus more on system failures. The novelty of this paper is that the major failure rates of the system are selected and the weight of each failure rate is calculated after constructing a pair wise comparison matrix. The fuzzy reliability index is then evaluated with the help of the linguistic variables considered by experts in the form of performance ratings of different reliability indexes, and then the reliability is measured using multi-criteria decision making technique. The contribution of the paper is the ranking of failure rates which shows the relative importance of each failure rate and how it affects the overall system reliability to decide on a desirable action plan.