Murshid Kamal - Academia.edu (original) (raw)

Papers by Murshid Kamal

International Journal of Mathematics in Operational Research, 2020

This paper uses the fuzzy goal programming approach with different kinds of membership functions ... more This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.

DOAJ (DOAJ: Directory of Open Access Journals), Sep 1, 2022

Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from ... more Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority.

Algorithms, Jul 19, 2019

This paper deals with the modeling and optimization of a bi-level multi-objective production plan... more This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.

Research Square (Research Square), May 22, 2023

The attainment of a competitive advantage can be facilitated by the presence of a vendor who is b... more The attainment of a competitive advantage can be facilitated by the presence of a vendor who is both effective and efficient. The process of selecting a vendor is a complex decisionmaking task that entails consideration of multiple quantitative and qualitative factors. The objective of this study is to minimise the net ordering cost, transportation cost, and late deliveries. When examining the various circumstances of existence, it is impossible to make anticipatory prognostications. The utilisation of Interval type-2 trapezoidal fuzzy numbers has been employed to effectively demonstrate the presence of uncertainty in the input parameters. A precise equivalent form has been derived through the calculation of the expected value. Exponential smoothing forecasting analysis has been utilised to ascertain the precise demand for the product in order to mitigate the risk of shortages and consequent financial losses. Ultimately, an effective methodology utilising fuzzy goal programming has been employed to attain a mutually satisfactory solution. The proposed methodology has been elucidated through the addition of a numerical illustration of its underlying concepts.

Research Square (Research Square), Oct 31, 2022

The attainment of a competitive advantage can be facilitated by the presence of a vendor who is b... more The attainment of a competitive advantage can be facilitated by the presence of a vendor who is both effective and efficient. The process of selecting a vendor is a complex decisionmaking task that entails consideration of multiple quantitative and qualitative factors. The objective of this study is to minimise the net ordering cost, transportation cost, and late deliveries. When examining the various circumstances of existence, it is impossible to make anticipatory prognostications. The utilisation of Interval type-2 trapezoidal fuzzy numbers has been employed to effectively demonstrate the presence of uncertainty in the input parameters. A precise equivalent form has been derived through the calculation of the expected value. Exponential smoothing forecasting analysis has been utilised to ascertain the precise demand for the product in order to mitigate the risk of shortages and consequent financial losses. Ultimately, an effective methodology utilising fuzzy goal programming has been employed to attain a mutually satisfactory solution. The proposed methodology has been elucidated through the addition of a numerical illustration of its underlying concepts.

International Journal of Mathematics in Operational Research, 2019

This paper uses the fuzzy goal programming approach with different kinds of membership functions ... more This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.

Transport, Nov 24, 2021

The problem of transportation in real-life is an uncertain multi-objective decision-making proble... more The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the "rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to" (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

Annals of Data Science, Oct 20, 2022

International Journal of Operational Research, 2018

World Academy of Science, Engineering and Technology, International Journal of Economics and Management Engineering, Mar 15, 2018

Quality and Reliability Engineering International

Selective maintenance refers to the problem of decision‐making on how to maintain a multi‐compone... more Selective maintenance refers to the problem of decision‐making on how to maintain a multi‐component complex system that can be repaired or replaced. The goal is generally to plan ahead in order to improve the likelihood of success for future maintenance tasks. In this article, we proposed a multi‐objective decision‐making model for maximizing the system reliability of a multi‐component systems. The objective functions represent the reliability of the sub‐systems arranged in series comprising of components arranged in parallel forms. The cost and total time incurred in the repair/replacement activities are considered as two sets of constraints in the proposed model. Fuzzy logic is incorporated to deal with the inherent uncertainty that exists in the parameters involved in the proposed model. To solve the uncertain multi‐objective selective maintenance model, we have proposed four‐valued neutrosophic technique. The proposed solution methodology combines the concept of four‐valued neut...

The attainment of a competitive advantage can be facilitated by the presence of a vendor who is b... more The attainment of a competitive advantage can be facilitated by the presence of a vendor who is both effective and efficient. The process of selecting a vendor is a complex decision-making task that entails consideration of multiple quantitative and qualitative factors. The objective of this study is to minimise the net ordering cost, transportation cost, and late deliveries. When examining the various circumstances of existence, it is impossible to make anticipatory prognostications. The utilisation of Interval type-2 trapezoidal fuzzy numbers has been employed to effectively demonstrate the presence of uncertainty in the input parameters. A precise equivalent form has been derived through the calculation of the expected value. Exponential smoothing forecasting analysis has been utilised to ascertain the precise demand for the product in order to mitigate the risk of shortages and consequent financial losses. Ultimately, an effective methodology utilising fuzzy goal programming has...

In today’s competitive environment, markets have made the purchasing function an ever more necess... more In today’s competitive environment, markets have made the purchasing function an ever more necessary action in supply chain management while in the same manner the survival of a business, for the most part, depends largely on its supplier’s. An effective and efficient supplier can give a competitive edge to a business. In general, the supplier selection is a multi-objective decision-making problem that involves several quantitative and qualitative factors that helps in minimizing the net ordering cost, minimizing the transportation cost, and minimizing the late deliveries. If we look at the different circumstances of life, we cannot predict anything in advanced. Therefore, we have taken the case of ambiguity in input parameters. Interval type-2 trapezoidal fuzzy numbers have been used to present the ambiguity in the input parameters, and crisp equivalent form has been obtained by taking the expected value. We also have used exponential smoothing forecasting analysis for getting the ...

The decision making of supplier selection and their allocation is one of the main concerns in sup... more The decision making of supplier selection and their allocation is one of the main concerns in supply chain management. In this paper, an attempt has been made to obtain an optimal allocation for supplier based on minimizing the net cost, minimizing the net rejections, and minimizing the net late deliveries subject to realistic constraints regarding buyer’s demand, vendors’ capacity, vendors’ quota flexibility, purchase value of items, budget allocation to individual vendor, etc. We convert the problem into single objective fuzzy goal programming problem by using weighted root power mean the method of aggregation with linear, exponential and hyperbolic membership functions. The comparison has been made by assigning different weights to the objective functions. A numerical illustration is provided for the verification of applicability of the approach.

Complex & Intelligent Systems, 2021

Selective maintenance problem plays an essential role in reliability optimization decision-making... more Selective maintenance problem plays an essential role in reliability optimization decision-making problems. Systems are a configuration of several components, and there are situations the system needs small intervals or break for maintenance actions, during the intervals expert carried out the maintenance actions to replace or repair the deteriorated components of the systems. Because of the uncertainty associated with the component’s operational time, failure, and next mission duration create a new challenge in determining optimal components allocation and evaluating future missions successfully. In this paper, a multi-objective selective maintenance allocation problem is formulated with fuzzy parameters under neutrosophic environment. A new defuzzification technique is introduced based on beta distribution to convert fuzzy parameters into crisp values. The neutrosophic goal programming technique is used to determine the compromise allocation of replaceable and repairable component...

Journal of Modern Applied Statistical Methods, 2018

A new model for the weighted method of goal programming is proposed based on minimizing the dista... more A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective subproblems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. Numerical illustrations are given for the proposed model.

Algorithms, 2019

This paper deals with the modeling and optimization of a bi-level multi-objective production plan... more This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.

International Journal of Operational Research, 2018

International Journal of Mathematics in Operational Research, 2019

This paper uses the fuzzy goal programming approach with different kinds of membership functions ... more This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.

International Journal of Mathematics in Operational Research, 2020

This paper uses the fuzzy goal programming approach with different kinds of membership functions ... more This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.

DOAJ (DOAJ: Directory of Open Access Journals), Sep 1, 2022

Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from ... more Multi-objective assignment problems (MOAPs) emerge in a wide range of real-world scenarios, from everyday activities to large-scale industrial operations. In this study, a MOAP with fuzzy parameters is investigated, and the fuzziness is represented by a Type-2 fuzzy logic system. Because the T2FLS is more efficient in dealing with the uncertainty of a decision-making process, the current problem's many parameters are represented by Type-2 trapezoidal fuzzy numbers (T2TpFNs). T2TpFNs are first reduced to Type-1 fuzzy numbers, then to crisp numbers. Finally, the neutrosophic compromise programming technique (NCPT) is applied to produce a problem compromise solution. A numerical problem is used to demonstrate the validity and applicability of the NCPT for the current MOAP. Furthermore, a comparison of NCPT to other techniques such as FPT and IFPT shows its superiority.

Algorithms, Jul 19, 2019

This paper deals with the modeling and optimization of a bi-level multi-objective production plan... more This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.

Research Square (Research Square), May 22, 2023

The attainment of a competitive advantage can be facilitated by the presence of a vendor who is b... more The attainment of a competitive advantage can be facilitated by the presence of a vendor who is both effective and efficient. The process of selecting a vendor is a complex decisionmaking task that entails consideration of multiple quantitative and qualitative factors. The objective of this study is to minimise the net ordering cost, transportation cost, and late deliveries. When examining the various circumstances of existence, it is impossible to make anticipatory prognostications. The utilisation of Interval type-2 trapezoidal fuzzy numbers has been employed to effectively demonstrate the presence of uncertainty in the input parameters. A precise equivalent form has been derived through the calculation of the expected value. Exponential smoothing forecasting analysis has been utilised to ascertain the precise demand for the product in order to mitigate the risk of shortages and consequent financial losses. Ultimately, an effective methodology utilising fuzzy goal programming has been employed to attain a mutually satisfactory solution. The proposed methodology has been elucidated through the addition of a numerical illustration of its underlying concepts.

Research Square (Research Square), Oct 31, 2022

The attainment of a competitive advantage can be facilitated by the presence of a vendor who is b... more The attainment of a competitive advantage can be facilitated by the presence of a vendor who is both effective and efficient. The process of selecting a vendor is a complex decisionmaking task that entails consideration of multiple quantitative and qualitative factors. The objective of this study is to minimise the net ordering cost, transportation cost, and late deliveries. When examining the various circumstances of existence, it is impossible to make anticipatory prognostications. The utilisation of Interval type-2 trapezoidal fuzzy numbers has been employed to effectively demonstrate the presence of uncertainty in the input parameters. A precise equivalent form has been derived through the calculation of the expected value. Exponential smoothing forecasting analysis has been utilised to ascertain the precise demand for the product in order to mitigate the risk of shortages and consequent financial losses. Ultimately, an effective methodology utilising fuzzy goal programming has been employed to attain a mutually satisfactory solution. The proposed methodology has been elucidated through the addition of a numerical illustration of its underlying concepts.

International Journal of Mathematics in Operational Research, 2019

This paper uses the fuzzy goal programming approach with different kinds of membership functions ... more This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.

Transport, Nov 24, 2021

The problem of transportation in real-life is an uncertain multi-objective decision-making proble... more The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the "rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to" (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

Annals of Data Science, Oct 20, 2022

International Journal of Operational Research, 2018

World Academy of Science, Engineering and Technology, International Journal of Economics and Management Engineering, Mar 15, 2018

Quality and Reliability Engineering International

Selective maintenance refers to the problem of decision‐making on how to maintain a multi‐compone... more Selective maintenance refers to the problem of decision‐making on how to maintain a multi‐component complex system that can be repaired or replaced. The goal is generally to plan ahead in order to improve the likelihood of success for future maintenance tasks. In this article, we proposed a multi‐objective decision‐making model for maximizing the system reliability of a multi‐component systems. The objective functions represent the reliability of the sub‐systems arranged in series comprising of components arranged in parallel forms. The cost and total time incurred in the repair/replacement activities are considered as two sets of constraints in the proposed model. Fuzzy logic is incorporated to deal with the inherent uncertainty that exists in the parameters involved in the proposed model. To solve the uncertain multi‐objective selective maintenance model, we have proposed four‐valued neutrosophic technique. The proposed solution methodology combines the concept of four‐valued neut...

The attainment of a competitive advantage can be facilitated by the presence of a vendor who is b... more The attainment of a competitive advantage can be facilitated by the presence of a vendor who is both effective and efficient. The process of selecting a vendor is a complex decision-making task that entails consideration of multiple quantitative and qualitative factors. The objective of this study is to minimise the net ordering cost, transportation cost, and late deliveries. When examining the various circumstances of existence, it is impossible to make anticipatory prognostications. The utilisation of Interval type-2 trapezoidal fuzzy numbers has been employed to effectively demonstrate the presence of uncertainty in the input parameters. A precise equivalent form has been derived through the calculation of the expected value. Exponential smoothing forecasting analysis has been utilised to ascertain the precise demand for the product in order to mitigate the risk of shortages and consequent financial losses. Ultimately, an effective methodology utilising fuzzy goal programming has...

In today’s competitive environment, markets have made the purchasing function an ever more necess... more In today’s competitive environment, markets have made the purchasing function an ever more necessary action in supply chain management while in the same manner the survival of a business, for the most part, depends largely on its supplier’s. An effective and efficient supplier can give a competitive edge to a business. In general, the supplier selection is a multi-objective decision-making problem that involves several quantitative and qualitative factors that helps in minimizing the net ordering cost, minimizing the transportation cost, and minimizing the late deliveries. If we look at the different circumstances of life, we cannot predict anything in advanced. Therefore, we have taken the case of ambiguity in input parameters. Interval type-2 trapezoidal fuzzy numbers have been used to present the ambiguity in the input parameters, and crisp equivalent form has been obtained by taking the expected value. We also have used exponential smoothing forecasting analysis for getting the ...

The decision making of supplier selection and their allocation is one of the main concerns in sup... more The decision making of supplier selection and their allocation is one of the main concerns in supply chain management. In this paper, an attempt has been made to obtain an optimal allocation for supplier based on minimizing the net cost, minimizing the net rejections, and minimizing the net late deliveries subject to realistic constraints regarding buyer’s demand, vendors’ capacity, vendors’ quota flexibility, purchase value of items, budget allocation to individual vendor, etc. We convert the problem into single objective fuzzy goal programming problem by using weighted root power mean the method of aggregation with linear, exponential and hyperbolic membership functions. The comparison has been made by assigning different weights to the objective functions. A numerical illustration is provided for the verification of applicability of the approach.

Complex & Intelligent Systems, 2021

Selective maintenance problem plays an essential role in reliability optimization decision-making... more Selective maintenance problem plays an essential role in reliability optimization decision-making problems. Systems are a configuration of several components, and there are situations the system needs small intervals or break for maintenance actions, during the intervals expert carried out the maintenance actions to replace or repair the deteriorated components of the systems. Because of the uncertainty associated with the component’s operational time, failure, and next mission duration create a new challenge in determining optimal components allocation and evaluating future missions successfully. In this paper, a multi-objective selective maintenance allocation problem is formulated with fuzzy parameters under neutrosophic environment. A new defuzzification technique is introduced based on beta distribution to convert fuzzy parameters into crisp values. The neutrosophic goal programming technique is used to determine the compromise allocation of replaceable and repairable component...

Journal of Modern Applied Statistical Methods, 2018

A new model for the weighted method of goal programming is proposed based on minimizing the dista... more A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective subproblems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. Numerical illustrations are given for the proposed model.

Algorithms, 2019

This paper deals with the modeling and optimization of a bi-level multi-objective production plan... more This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.

International Journal of Operational Research, 2018

International Journal of Mathematics in Operational Research, 2019

This paper uses the fuzzy goal programming approach with different kinds of membership functions ... more This paper uses the fuzzy goal programming approach with different kinds of membership functions like linear, exponential, parabolic, hyperbolic and quadratic membership; for solving the multi-objective sustainable supply chain (MOSSC) problem under the intuitionistic fuzzy environment. The primary objective is to maximise the minimum value of the membership function so the preferred compromise solution can achieve to the MOSSC problem. By attaining this preferred compromise solution, the optimum order quantity allocation to each supplier can also be determined. Additionally, a situation even has been considered where the decision maker tries to control the optimum order quantity and search for another satisfactory solution, for this, he uses the membership function. A case study of the sustainable supply chain has been used to show the usefulness of the proposed work.