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Dr. Irfan Ali
ALIGARH MUSLIM UNIVERSITY, ALIGARH, INDIA

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0 applied statistics
0 Sampling survey
0 Reliability Optimization
0 fuzzy optimization techniques
0 Optimization theory and its applications

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Optimization theory and its applications
Sampling survey
Reliability Optimization

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Journal article
Published: 23 July 2021 in Sustainability
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The demand for cost-efficient and clean power energy cannot be overemphasised, especially in a developing nation like India. COVID-19 has adversely affected many nations, power sector inclusive, and resiliency is imperative via flexible and sustainable power generation sources. Renewable energy sources are the primary focus of electricity production in the world. This study examined and assessed the optimal cost system of electricity generation for the socio-economic sustainability of India. A sustainable and flexible electricity generation model is developed using the concept of flexible fuzzy goal programming. This study is carried out with the aim of achieving the government’s intended nationally determined contribution goals of reducing emission levels, increasing the capacity of renewable sources and the must-run status of hydro and nuclear, and technical and financial parameters. The result shows an optimal cost solution and flexibility in how increased electricity demand would be achieved and sustained via shifting to renewable sources such as solar, wind and hydro.

ACS Style

Mohammad Khan; Asif Pervez; Umar Modibbo; Jahangir Chauhan; Irfan Ali. Flexible Fuzzy Goal Programming Approach in Optimal Mix of Power Generation for Socio-Economic Sustainability: A Case Study. Sustainability 2021, 13, 8256 .

AMA Style

Mohammad Khan, Asif Pervez, Umar Modibbo, Jahangir Chauhan, Irfan Ali. Flexible Fuzzy Goal Programming Approach in Optimal Mix of Power Generation for Socio-Economic Sustainability: A Case Study. Sustainability. 2021; 13 (15):8256.

Chicago/Turabian Style

Mohammad Khan; Asif Pervez; Umar Modibbo; Jahangir Chauhan; Irfan Ali. 2021. "Flexible Fuzzy Goal Programming Approach in Optimal Mix of Power Generation for Socio-Economic Sustainability: A Case Study." Sustainability 13, no. 15: 8256.

Journal article
Published: 05 June 2021 in Alexandria Engineering Journal
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The ever increasing pressure to conserve the environment from global warming cannot be overemphasized. Emission from the inventory and production process contributes immensely to global warming and hence, the need to device a sustainable green inventory by the operational managers. In this paper, a multi-item multi-objective inventory model with back-ordered quantity incorporating green investment in order to save the environment is proposed. The model is formulated as a multi-objective fractional programming problem with four objectives: maximizing profit ratio to total back-ordered quantity, minimizing the holding cost in the system, minimizing total waste produced by the inventory system per cycle and minimizing the total penalty cost due to green investment. The constraints are included with budget limitation, space restrictions, a constraint on cost of ordering each item, environmental waste disposal restriction, cost of pollution control, electricity consumption cost during production and cost of greenhouse gas emission in the production process. The model effectiveness is illustrated numerically, and the solution obtained to give a useful suggestion to the decision-markers in the manufacturing sectors.

ACS Style

Abdullah Ali H. Ahmadini; Umar Muhammad Modibbo; Ali Akbar Shaikh; Irfan Ali. Multi-objective optimization modelling of sustainable green supply chain in inventory and production management. Alexandria Engineering Journal 2021, 60, 5129 -5146.

AMA Style

Abdullah Ali H. Ahmadini, Umar Muhammad Modibbo, Ali Akbar Shaikh, Irfan Ali. Multi-objective optimization modelling of sustainable green supply chain in inventory and production management. Alexandria Engineering Journal. 2021; 60 (6):5129-5146.

Chicago/Turabian Style

Abdullah Ali H. Ahmadini; Umar Muhammad Modibbo; Ali Akbar Shaikh; Irfan Ali. 2021. "Multi-objective optimization modelling of sustainable green supply chain in inventory and production management." Alexandria Engineering Journal 60, no. 6: 5129-5146.

Journal article
Published: 20 May 2021 in Journal of King Saud University - Science
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Achieving sustainable development goals agenda 2030 is the aspiration of all the United Nation’s member countries. Countries have an uneven distribution of natural resources, economic strength, and capacity building. Many studies analyze these goals using various models and considering different aspects of the kingdom of Saudi Arabia's (KSA) economy. However, none of the studies modelled the key indicators mathematically to quantify the achievement level towards vision 2030; hence aims to bridge the existing literature gap In this paper, the sustainable development goals (SDGs) of KSA are considered, a mathematical model is formulated in light of fuzzy and weighted goal programming using membership function. The model comprises three goals related to the gross domestic product, sustainable energy consumption and employment capacity of the economy's contributing sectors. The analytic hierarchy process integrated to compute the goals’ weights using row geometric mean method. The study established the goals's satisfaction level with 57% overall achievement of the vision 2030. Individually, economic growth goal is 45% achievable. The clean energy consumption-related goal is 67% realizable. The employment-related goal is 78% attainable within the time frame of the vision 2030. The study suggests that KSA diversify its energy sector by concentrating and investing more resources in alternative energy sources, including renewable energy such as solar, wind, biomass, and nuclear energy. Also, there is a need to involve more vibrant and talented youths in the critical decision-making process. The model is simple and can be replicable in a similar country with slight modifications.

ACS Style

Ali AlArjani; Umar Muhammad Modibbo; Irfan Ali; Biswajit Sarkar. A new framework for the sustainable development goals of Saudi Arabia. Journal of King Saud University - Science 2021, 33, 101477 .

AMA Style

Ali AlArjani, Umar Muhammad Modibbo, Irfan Ali, Biswajit Sarkar. A new framework for the sustainable development goals of Saudi Arabia. Journal of King Saud University - Science. 2021; 33 (6):101477.

Chicago/Turabian Style

Ali AlArjani; Umar Muhammad Modibbo; Irfan Ali; Biswajit Sarkar. 2021. "A new framework for the sustainable development goals of Saudi Arabia." Journal of King Saud University - Science 33, no. 6: 101477.

Original article
Published: 15 May 2021 in Complex & Intelligent Systems
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Determining the methods for fulfilling the continuously increasing customer expectations and maintaining competitiveness in the market while limiting controllable expenses is challenging. Our study thus identifies inefficiencies in the supply chain network (SCN). The initial goal is to obtain the best allocation order for products from various sources with different destinations in an optimal manner. This study considers two types of decision-makers (DMs) operating at two separate groups of SCN, that is, a bi-level decision-making process. The first-level DM moves first and determines the amounts of the quantity transported to distributors, and the second-level DM then rationally chooses their amounts. First-level decision-makers (FLDMs) aimed at minimizing the total costs of transportation, while second-level decision-makers (SLDM) attempt to simultaneously minimize the total delivery time of the SCN and balance the allocation order between various sources and destinations. This investigation implements fuzzy goal programming (FGP) to solve the multi-objective of SCN in an intuitionistic fuzzy environment. The FGP concept was used to define the fuzzy goals, build linear and nonlinear membership functions, and achieve the compromise solution. A real-life case study was used to illustrate the proposed work. The obtained result shows the optimal quantities transported from the various sources to the various destinations that could enable managers to detect the optimum quantity of the product when hierarchical decision-making involving two levels. A case study then illustrates the application of the proposed work.

ACS Style

Srikant Gupta; Ahteshamul Haq; Irfan Ali; Biswajit Sarkar. Significance of multi-objective optimization in logistics problem for multi-product supply chain network under the intuitionistic fuzzy environment. Complex & Intelligent Systems 2021, 1 -21.

AMA Style

Srikant Gupta, Ahteshamul Haq, Irfan Ali, Biswajit Sarkar. Significance of multi-objective optimization in logistics problem for multi-product supply chain network under the intuitionistic fuzzy environment. Complex & Intelligent Systems. 2021; ():1-21.

Chicago/Turabian Style

Srikant Gupta; Ahteshamul Haq; Irfan Ali; Biswajit Sarkar. 2021. "Significance of multi-objective optimization in logistics problem for multi-product supply chain network under the intuitionistic fuzzy environment." Complex & Intelligent Systems , no. : 1-21.

Journal article
Published: 22 April 2021 in Journal of King Saud University - Science
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In a multivariate stratified sampling design, the individual optimum allocation of one character may not remain optimum to other characteristics. For the solution of such problems, a usable allocation must be required to get precise estimates of the unknown population parameters, which may be near optimum to all characteristics in some sense. The compromise criterion is required to obtain such usable allocation in sampling literature. In this paper, the sample allocation problem is considered as a stochastic nonlinear programming problem and thereafter formulated into a multiobjective programming problem to provide the usable allocation. The formulated problem is solved by using different models of stochastic optimization. Afterwards, the proposed allocation is worked out and compared with some other allocations, which are well defined in sampling, to give a comparative study. Also, the numerical study defines the practical utility of the proposed technique.

ACS Style

Abdullah Ali H. Ahmadini; Rahul Varshney; Mradula; Irfan Ali. On multivariate-multiobjective stratified sampling design under probabilistic environment: A fuzzy programming technique. Journal of King Saud University - Science 2021, 33, 101448 .

AMA Style

Abdullah Ali H. Ahmadini, Rahul Varshney, Mradula, Irfan Ali. On multivariate-multiobjective stratified sampling design under probabilistic environment: A fuzzy programming technique. Journal of King Saud University - Science. 2021; 33 (5):101448.

Chicago/Turabian Style

Abdullah Ali H. Ahmadini; Rahul Varshney; Mradula; Irfan Ali. 2021. "On multivariate-multiobjective stratified sampling design under probabilistic environment: A fuzzy programming technique." Journal of King Saud University - Science 33, no. 5: 101448.

Journal article
Published: 19 April 2021 in Mathematics
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In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples.

ACS Style

Sadikur Rahman; Ali Shaikh; Irfan Ali; Asoke Bhunia; Armin Fügenschuh. A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations. Mathematics 2021, 9, 908 .

AMA Style

Sadikur Rahman, Ali Shaikh, Irfan Ali, Asoke Bhunia, Armin Fügenschuh. A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations. Mathematics. 2021; 9 (8):908.

Chicago/Turabian Style

Sadikur Rahman; Ali Shaikh; Irfan Ali; Asoke Bhunia; Armin Fügenschuh. 2021. "A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations." Mathematics 9, no. 8: 908.

Journal article
Published: 18 March 2021 in Reliability Engineering & System Safety
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Designing an optimal reliability system with a minimum cost is one of the challenging problems in engineering field over the years. Estimating the subsystem reliability and determining the optimal number of component allocation will give an insight into the adequate performance of the entire system under study. In some scenarios, if a subsystem fails, then the whole system will fail, thus posing a severe threat to the safety of engineers and personnel involved. Hence, the need to optimally determine and allocate the required number of components as well as estimating their reliability so that the system’s safety would be guaranteed. In this paper, two procedures for estimating system reliability function are proposed using the maximum likelihood estimators and uniformly minimum variance unbiased estimators. The reliability functions of some selected lifetime distributions are estimated using the proposed procedures via a simulation study. The study presents a hybrid concept of estimation and optimization theory in reliability allocation problem. The work illustrated through a case study, and an optimization technique used to determine the optimal number of components at a minimum cost. The study would be useful for decision-makers in heavy industries/complex systems to help estimate the reliability of system components, optimize the allocation and manufacturer selection problems.

ACS Style

Umar Muhammad Modibbo; Mohd. Arshad; Omer Abdalghani; Irfan Ali. Optimization and estimation in system reliability allocation problem. Reliability Engineering & System Safety 2021, 212, 107620 .

AMA Style

Umar Muhammad Modibbo, Mohd. Arshad, Omer Abdalghani, Irfan Ali. Optimization and estimation in system reliability allocation problem. Reliability Engineering & System Safety. 2021; 212 ():107620.

Chicago/Turabian Style

Umar Muhammad Modibbo; Mohd. Arshad; Omer Abdalghani; Irfan Ali. 2021. "Optimization and estimation in system reliability allocation problem." Reliability Engineering & System Safety 212, no. : 107620.

Journal article
Published: 04 March 2021 in IEEE Access
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In this article, a multiobjective multiproduct production planning (MOMPP) problem discussed for a hardware firm. The hardware firm produces various types of hardware locks and other items in a production run. The firm manager’s objectives are minimizing the production cost and inventory holding cost while maximizing the net profit subject to some system constraints. The multiproduct production planning is solved with the last production run information precisely known to the decision-maker, and finally, the model is solved using the intuitionistic and neutrosophic programming approaches, respectively. Also, the multiproduct production planning problem is discussed for situations when the product information is vague. The interval-valued trapezoidal neutrosophic numbers used to define this Vagueness. The multiobjective multiproduct production planning problem under fuzziness is solved using the neutrosophic compromise programming. The stepwise solution procedures are discussed using the case study.

ACS Style

Mohammad Faisal Khan; Ahteshamul Haq; Aquil Ahmed; Irfan Ali. Multiobjective Multi-Product Production Planning Problem Using Intuitionistic and Neutrosophic Fuzzy Programming. IEEE Access 2021, 9, 37466 -37486.

AMA Style

Mohammad Faisal Khan, Ahteshamul Haq, Aquil Ahmed, Irfan Ali. Multiobjective Multi-Product Production Planning Problem Using Intuitionistic and Neutrosophic Fuzzy Programming. IEEE Access. 2021; 9 ():37466-37486.

Chicago/Turabian Style

Mohammad Faisal Khan; Ahteshamul Haq; Aquil Ahmed; Irfan Ali. 2021. "Multiobjective Multi-Product Production Planning Problem Using Intuitionistic and Neutrosophic Fuzzy Programming." IEEE Access 9, no. : 37466-37486.

Journal article
Published: 01 March 2021 in RAIRO - Operations Research
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In this paper, a supply chain model between a manufacturing firm and a group of retailers has been developed. Manufacturing firm produces simultaneously both perfect and imperfect items which are separated by screening process. Then the perfect items are transferred to the retailers’ showroom/warehouse located in different places and a part of imperfect items are repaired by rework process. Retailers receive the products from the manufacturer with paying partial pre-payment to ensure the replenishment of order. On the other hand, the manufacturer provides partial free transportation facility to the retailers due to pre-payment. The corresponding problem has been formulated mathematically as a profit maximization problem and then solved it analytically. As an illustration of this supply chain model, three numerical examples have been considered and solved. Finally, post optimality analyses have been carried out to investigate the effects of changes of different parameters on the optimal policy.

ACS Style

Amalesh Kumar Manna; Rajan Mondal; Ali Akbar Shaikh; Irfan Ali; Asoke Kumar Bhunia. Single-manufacturer and multi-retailer supply chain model with pre-payment based partial free transportation. RAIRO - Operations Research 2021, 55, 1063 -1076.

AMA Style

Amalesh Kumar Manna, Rajan Mondal, Ali Akbar Shaikh, Irfan Ali, Asoke Kumar Bhunia. Single-manufacturer and multi-retailer supply chain model with pre-payment based partial free transportation. RAIRO - Operations Research. 2021; 55 (2):1063-1076.

Chicago/Turabian Style

Amalesh Kumar Manna; Rajan Mondal; Ali Akbar Shaikh; Irfan Ali; Asoke Kumar Bhunia. 2021. "Single-manufacturer and multi-retailer supply chain model with pre-payment based partial free transportation." RAIRO - Operations Research 55, no. 2: 1063-1076.

Original article
Published: 20 January 2021 in Complex & Intelligent Systems
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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 components based on the system reliability optimization. A numerical illustration is used to validate the model and ascertain its effectiveness. The result is compared with two other approaches and found to be better. The method is flexible and straightforward and can be solved using any available commercial packages. The extension of the concept can be useful to other complex system reliability optimization.

ACS Style

Murshid Kamal; Umar Muhammad Modibbo; Ali AlArjani; Irfan Ali. Neutrosophic fuzzy goal programming approach in selective maintenance allocation of system reliability. Complex & Intelligent Systems 2021, 7, 1045 -1059.

AMA Style

Murshid Kamal, Umar Muhammad Modibbo, Ali AlArjani, Irfan Ali. Neutrosophic fuzzy goal programming approach in selective maintenance allocation of system reliability. Complex & Intelligent Systems. 2021; 7 (2):1045-1059.

Chicago/Turabian Style

Murshid Kamal; Umar Muhammad Modibbo; Ali AlArjani; Irfan Ali. 2021. "Neutrosophic fuzzy goal programming approach in selective maintenance allocation of system reliability." Complex & Intelligent Systems 7, no. 2: 1045-1059.

Case study
Published: 06 October 2020 in Environment, Development and Sustainability
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Sustainability of developmental goals remains the significant challenges for every nation in the world. In an environment of flexibility coupled with multiple and conflicting objectives on social economic, energy and environmental issues, a fuzzy goal programming approach proves to be suitable in helping policymakers for attaining their aspirational goals as it takes imprecise information into account. In this study, we proposed a multi-objective goal programming model to analyse the socio-economic, environmental and energy sector of Nigeria. The sectors relating to the gross domestic product, electricity consumption, employment and greenhouse gases emissions are regarded as the key sustainable development goals (SDGs) for the year 2030, upon which all other goals depend on directly or indirectly. We considered four scenarios based on decision-makers' value judgments using the analytic hierarchy process (AHP). Moreover, we have developed a weighted fuzzy goal programming model for the SDGs incorporating the AHP. The model reveals that individual goals are achievable at 81, 83, and 89 per cents, respectively, while the overall achievement function indicated only 73 per cent achievement is possible. The optimal employment for the various economic sectors is also computed at various tolerance values and presented alongside Pareto objective values. The results yielded an economic justification mathematically and provided insight for critical and future strategic planning towards achieving sustainable economic policies. The models can be replicated in the context of other nations in addressing long-term socio-economic planning and indispensable requirements for renewable sources inclusion to satisfy future energy demand economically without environmental damages.

ACS Style

Umar Muhammad Modibbo; Irfan Ali; Aquil Ahmed. Multi-objective optimization modelling for analysing sustainable development goals of Nigeria: Agenda 2030. Environment, Development and Sustainability 2020, 23, 9529 -9563.

AMA Style

Umar Muhammad Modibbo, Irfan Ali, Aquil Ahmed. Multi-objective optimization modelling for analysing sustainable development goals of Nigeria: Agenda 2030. Environment, Development and Sustainability. 2020; 23 (6):9529-9563.

Chicago/Turabian Style

Umar Muhammad Modibbo; Irfan Ali; Aquil Ahmed. 2020. "Multi-objective optimization modelling for analysing sustainable development goals of Nigeria: Agenda 2030." Environment, Development and Sustainability 23, no. 6: 9529-9563.

Journal article
Published: 19 September 2020 in Mathematics
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Vendor selection is an established problem in supply chain management. It is regarded as a strategic resource by manufacturers, which must be managed efficiently. Any inappropriate selection of the vendors may lead to severe issues in the supply chain network. Hence, the desire to develop a model that minimizes the combination of transportation, deliveries, and ordering costs under uncertainty situation. In this paper, a multi-objective vendor selection problem under fuzzy environment is solved using a fuzzy goal programming approach. The vendor selection problem was modeled as a multi-objective problem, including three primary objectives of minimizing the transportation cost; the late deliveries; and the net ordering cost subject to constraints related to aggregate demand; vendor capacity; budget allocation; purchasing value; vendors’ quota; and quantity rejected. The proposed model input parameters are considered to be LR fuzzy numbers. The effectiveness of the model is illustrated with simulated data using R statistical package based on a real-life case study which was analyzed using LINGO 16.0 optimization software. The decision on the vendor’s quota allocation and selection under different degree of vagueness in the information was provided. The proposed model can address realistic vendor selection problem in the fuzzy environment and can serve as a useful tool for multi-criteria decision-making in supply chain management.

ACS Style

Irfan Ali; Armin Fügenschuh; Srikant Gupta; Umar Muhammad Modibbo. The LR-Type Fuzzy Multi-Objective Vendor Selection Problem in Supply Chain Management. Mathematics 2020, 8, 1621 .

AMA Style

Irfan Ali, Armin Fügenschuh, Srikant Gupta, Umar Muhammad Modibbo. The LR-Type Fuzzy Multi-Objective Vendor Selection Problem in Supply Chain Management. Mathematics. 2020; 8 (9):1621.

Chicago/Turabian Style

Irfan Ali; Armin Fügenschuh; Srikant Gupta; Umar Muhammad Modibbo. 2020. "The LR-Type Fuzzy Multi-Objective Vendor Selection Problem in Supply Chain Management." Mathematics 8, no. 9: 1621.

Article
Published: 30 April 2020 in Environment, Development and Sustainability
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Modelling for long-term goals involving multiple factors and criteria often require incorporating decision-makers preferences to realize optimum satisfaction. Goal programming (GP) is an operational research technique that is relevant to analysing decision-making problems with multiple competing and conflicting objectives. Multi-objective goal programming approach takes advantage of striking the trade-off between the overachievement and underachievement of the decision-makers future aspirations. The concept of GP with a satisfaction function integrates the preference of the decision-makers explicitly. In this paper, we proposed a multi-objective optimization model integrating economic growth, electricity consumption, greenhouse gas emission and the number of employees across the primary, secondary and tertiary sectors of Indian economy using the concept of GP with a satisfaction function. The model validated with data from the three economic sectors, and the results provided a quantitative justification for achieving economic growth, electricity consumption, with optimal employment strength across the sectors, for the sustainable development goals of India vision 2030. Also, a strong suggestion for improvement and encouragement in the use of renewable energies such as wind and solar and reduction in fossil fuels utilization to arrest the high emission tendencies shortly was evidence by the solution.

ACS Style

Irfan Ali; Umar Muhammad Modibbo; Jahangir Chauhan; Maryam Meraj. An integrated multi-objective optimization modelling for sustainable development goals of India. Environment, Development and Sustainability 2020, 23, 3811 -3831.

AMA Style

Irfan Ali, Umar Muhammad Modibbo, Jahangir Chauhan, Maryam Meraj. An integrated multi-objective optimization modelling for sustainable development goals of India. Environment, Development and Sustainability. 2020; 23 (3):3811-3831.

Chicago/Turabian Style

Irfan Ali; Umar Muhammad Modibbo; Jahangir Chauhan; Maryam Meraj. 2020. "An integrated multi-objective optimization modelling for sustainable development goals of India." Environment, Development and Sustainability 23, no. 3: 3811-3831.

Article
Published: 12 November 2018 in Journal of the Operations Research Society of China
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Survival of a company in today’s competitive business environment depends mainly on its supply chain. An adequate supply chain gives a competitive edge to a company. Sourcing, which is the initial stage of a supply chain, can be made efficient by making an appropriate selection of vendors. Appropriate vendor selection results not only in reduced purchasing costs, decreased production lead time, increased customer satisfaction but also in improved corporate competitiveness. In general, the vendor selection problem is a multi-objective decision-making problem that involves some quantitative and qualitative factors. So, we have considered a multi-objective vendor selection problem (MOVSP) with three multiple objective goals: minimization of net ordering price, minimization of rejected units and minimization of late delivered units. In most of the cases, information about the price of a unit, percentage of rejected units, percentage of late delivered units, vendor rating value and vendor quota flexibility may not be known precisely due to some reasons. In this paper, imprecision in input information is handled by the concept of a simulation technique, where the parameter follows the uniform distribution. Deterministic, stochastic, \( \alpha \)-cut and ranking function approaches are used to get the crisp value of the simulated data sets. The four different algorithms, namely—fuzzy programming, goal programming, lexicographic goal programming and D1-distance algorithm, have been used for solving the MOVSP. In last, three different types of simulated data sets have been used to illustrate the work.

ACS Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. Multi-Objective Vendor Selection Problem of Supply Chain Management Under Fuzzy Environment. Journal of the Operations Research Society of China 2018, 9, 33 -62.

AMA Style

Srikant Gupta, Irfan Ali, Aquil Ahmed. Multi-Objective Vendor Selection Problem of Supply Chain Management Under Fuzzy Environment. Journal of the Operations Research Society of China. 2018; 9 (1):33-62.

Chicago/Turabian Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. 2018. "Multi-Objective Vendor Selection Problem of Supply Chain Management Under Fuzzy Environment." Journal of the Operations Research Society of China 9, no. 1: 33-62.

Application article
Published: 01 October 2018 in OPSEARCH
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In this paper we addressed supply chain network (SCN) as bi-level programming problem in which the primary objective is to determine optimal order allocation of products where the customer’s demands and supply for the products are fuzzy. In the proposed SCN model, we suppose that the first level (leader) and second level (follower) operate two separate groups of SCN. The leader, who moves first, determines quantities shipped to retailers, and then, the follower decides his quantities rationally. The leader’s objective is to minimize the total transportation costs, and similarly, the follower’s objective is to minimize the total delivery time of the SCN and at the same time balancing the optimal order allocation from each source, plant, retailer and warehouse respectively. The fuzzy goal programming approach has been used to achieve the highest degree of the membership goals by minimizing the deviational variables so that most satisfactory or the preferred solution for both the levels to be obtained. A numerical example is given to demonstrate the proposed methodology.

ACS Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. Multi-objective bi-level supply chain network order allocation problem under fuzziness. OPSEARCH 2018, 55, 721 -748.

AMA Style

Srikant Gupta, Irfan Ali, Aquil Ahmed. Multi-objective bi-level supply chain network order allocation problem under fuzziness. OPSEARCH. 2018; 55 (3-4):721-748.

Chicago/Turabian Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. 2018. "Multi-objective bi-level supply chain network order allocation problem under fuzziness." OPSEARCH 55, no. 3-4: 721-748.

Original paper
Published: 27 August 2018 in Granular Computing
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This paper discusses a solution procedure of a multi-objective capacitated transportation problem (MOCTP) in an uncertain environment. In MOCTP, the primary objective is to find the optimum quantity of the shipment subject to some capacitated restriction on each route. Due to uncertainty in MOCTP, the formulated problem cannot be solved directly for the optimum allocation. The uncertainty in MOCTP has been presented by the multi-choices and probabilistic distributions, respectively. The multi-choice and probabilistic distributions have been transformed into an equivalent deterministic form using the binary variable and stochastic programming approach, respectively. It has been assumed that the demand and supply parameter of the formulated problem follows different kinds of probabilistic distributions, namely, Pareto, Weibull, Normal, Extreme value, Cauchy and Logistic distribution, respectively. The maximum likelihood estimation approach has been used to estimate the unknown parameters of the probabilistic distributions with specified probability level. Finally, Akaike’s information criterion and Bayesian information criterion have been used to identify the goodness-of-fit of probability distributions for the given scenarios. The fuzzy goal-programming technique has been used to obtain the best optimum compromise solution for an equivalent crisp MOCTP model. A case study has been given to illustrate the computational procedure.

ACS Style

Srikant Gupta; Irfan Ali; Sachin Chaudhary. Multi-objective capacitated transportation: a problem of parameters estimation, goodness of fit and optimization. Granular Computing 2018, 5, 119 -134.

AMA Style

Srikant Gupta, Irfan Ali, Sachin Chaudhary. Multi-objective capacitated transportation: a problem of parameters estimation, goodness of fit and optimization. Granular Computing. 2018; 5 (1):119-134.

Chicago/Turabian Style

Srikant Gupta; Irfan Ali; Sachin Chaudhary. 2018. "Multi-objective capacitated transportation: a problem of parameters estimation, goodness of fit and optimization." Granular Computing 5, no. 1: 119-134.

Original article
Published: 21 July 2018 in International Journal of System Assurance Engineering and Management
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In this paper, we have assumed an inventory multi-objective optimization model under intuitionistic fuzziness. In modelling, we have considered the situations where triangular intuitionistic fuzzy numbers used to express some of the input information which associated with decision variables. Further, a ranking function approach by considering linear and the nonlinear degree of membership functions have been used to obtain the crisp form of the fuzzy parameters. Finally, the fuzzy goal programming approach has been used to solve the resultant model to obtain the optimal ordering quantity. Also, a comparative study of the formulated problem under intuitionistic fuzziness has been done with a deterministic model of inventory. The concept of the paper is explained through a numerical example.

ACS Style

Irfan Ali; Srikant Gupta; Aquil Ahmed. Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment. International Journal of System Assurance Engineering and Management 2018, 10, 173 -189.

AMA Style

Irfan Ali, Srikant Gupta, Aquil Ahmed. Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment. International Journal of System Assurance Engineering and Management. 2018; 10 (2):173-189.

Chicago/Turabian Style

Irfan Ali; Srikant Gupta; Aquil Ahmed. 2018. "Multi-objective linear fractional inventory problem under intuitionistic fuzzy environment." International Journal of System Assurance Engineering and Management 10, no. 2: 173-189.

Journal article
Published: 18 April 2018 in Journal of Statistics and Management Systems
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In this paper, we study a special class of transportation problem with capacitated restrictions. The formulated multi-objective capacitated transportation problem (MOCTP) has some of the objective functions are linear and fractional; these objectives are conflicting in nature. This problem defined in an uncertain environment where the uncertainty in input information presented by the multi-choices and trapezoidal fuzzy numbers. The multi-choice in input information dealt with the binary numbers and transformed it into the equivalent deterministic form by the suitable method. While the other pattern of uncertainty in input information defined by the trapezoidal fuzzy numbers and handled by ranking function approach to get the crisp value. Due to the presence of the uncertainties, and the conflicting objective functions, we cannot directly solve the formulated multi-choice MOCTP. So, therefore, we solve the formulated MOCTP in two phases. In the first stage, we transform the uncertain MOCTP into the deterministic form by using the suitable solution procedure of multi-choice and fuzzy numbers respectively. In the second stage, we have suggested a goal programming solution procedure to linearise the fractional objective function and then solve the resultant MOCTP for the compromise solution. A case study has also done to illustrate the stepwise solution procedure.

ACS Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. Multi-choice multi-objective capacitated transportation problem — A case study of uncertain demand and supply. Journal of Statistics and Management Systems 2018, 21, 467 -491.

AMA Style

Srikant Gupta, Irfan Ali, Aquil Ahmed. Multi-choice multi-objective capacitated transportation problem — A case study of uncertain demand and supply. Journal of Statistics and Management Systems. 2018; 21 (3):467-491.

Chicago/Turabian Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. 2018. "Multi-choice multi-objective capacitated transportation problem — A case study of uncertain demand and supply." Journal of Statistics and Management Systems 21, no. 3: 467-491.

Original paper
Published: 27 March 2018 in International Journal of Applied and Computational Mathematics
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This paper comprises of modelling and optimization of a production–distribution problem with the multi-product. The proposed model combined three well-known approaches, fuzzy programming, goal programming and interactive programming to develop an efficient fuzzy goal programming (EFGP) model for multi-objective production distribution problem (MOPDP). In this approach decision maker (DM) decide the goals and constructed membership functions for each objective, and they changed according to the iterative decision taken by the DM. The proposed EFGP model for MOPDP attempts to simultaneously minimize total transportation costs and total delivery time concerning inventory levels, available initial stock at each source, as well as market demand and available warehouse space at each destination, and the constraint on the total budget. The main aid of the proposed model is that its offerings an organized outline that enables fuzzy goal decision-making for solving the MOPDP under an uncertain environment.

ACS Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. Efficient Fuzzy Goal Programming Model for Multi-objective Production Distribution Problem. International Journal of Applied and Computational Mathematics 2018, 4, 1 -19.

AMA Style

Srikant Gupta, Irfan Ali, Aquil Ahmed. Efficient Fuzzy Goal Programming Model for Multi-objective Production Distribution Problem. International Journal of Applied and Computational Mathematics. 2018; 4 (2):1-19.

Chicago/Turabian Style

Srikant Gupta; Irfan Ali; Aquil Ahmed. 2018. "Efficient Fuzzy Goal Programming Model for Multi-objective Production Distribution Problem." International Journal of Applied and Computational Mathematics 4, no. 2: 1-19.

Journal article
Published: 12 March 2018 in Sustainability
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There is an ever-growing demand for sustainable development (SD) plans, in order to foster a country’s economic growth by implementing suitable policies and initiative programs for the development of the primary, the secondary and the tertiary sectors. We present a multi-criteria modeling approach using the linear programming problem (LPP) framework for a simultaneous optimization of these three sectors. Furthermore, we develop a fuzzy goal programming (FGP) model that provides an optimal allocation of resources by achieving future goals on the gross domestic product (GDP), the electricity consumption (EC) and the greenhouse gas (GHG) emissions. Furthermore, a weighted model of FGP is presented to obtain varying solutions according to the priorities set by the decision-maker for achieving future goals of GDP growth, EC and GHG emissions. The presented models provide useful insight for decision-makers when implementing strategies across different sectors. As a model country, we chose India by the year 2030. A study of economic policies and sustainable development goals (SDGs) for India is finally carried out.

ACS Style

Srikant Gupta; Armin Fügenschuh; Irfan Ali. A Multi-Criteria Goal Programming Model to Analyze the Sustainable Goals of India. Sustainability 2018, 10, 778 .

AMA Style

Srikant Gupta, Armin Fügenschuh, Irfan Ali. A Multi-Criteria Goal Programming Model to Analyze the Sustainable Goals of India. Sustainability. 2018; 10 (3):778.

Chicago/Turabian Style

Srikant Gupta; Armin Fügenschuh; Irfan Ali. 2018. "A Multi-Criteria Goal Programming Model to Analyze the Sustainable Goals of India." Sustainability 10, no. 3: 778.