Dr. Ather A Raina | Baba Ghulam Shah Badshah University (original) (raw)

Papers by Dr. Ather A Raina

The present survey is based on the principle of retrials in queueing theory i.e. the customers wh... more The present survey is based on the principle of retrials in queueing theory i.e. the customers who repeatedly try to avail the services from the server, on finding dejection, because of the inactivity of the server to provide service at an instant of selection from the queue. A bunch of work has previously been done on this front from past since it is realistic phenomena of many service system. The current investigation aims to present a brief review of the major works done on retrial queueing systems in recent years. The bibliography consists of research articles which were published in journals of repute during the period 2010-2015. In addition to the above references, an exhaustive list of books and survey papers on retrial queueing systems is also prepared so as to provide a detailed enough catalog for further understanding and research in retrial queueing domain. We have classified the journal papers according to the year of publishing. The aim of the present study is to turn up at a broad enough for a collection of important results in the theory of retrial queueing systems and their applications in solving several realistic problems. The main contribution is the bibliography of recent papers and books collected from different databases and private sources. At last, we have arranged some of the references according to the classification based on analysis and solution technique. The author(s) hope that this survey paper could be of help to learners contemplating research on retrial queues.

In mathematical programming different types of cuts have been developed in the past to get an int... more In mathematical programming different types of cuts have been developed in the past to get an integer value of the decision variables. In this paper, we have developed a new integer cut for getting an integer solution of the fractional linear programming problem (FLPP). This technique allows the decision-maker to solve the formulated FLPP to be conveniently using the Branch and Bound approach in order to achieve the optimum final solution. The process of development of the integer cut is shown with sufficient detail and a numerical illustration is used for clarification purpose.

Applications of Advanced Optimization Techniques in Industrial Engineering, 2022

Journal of the National Science Foundation of Sri Lanka

This license permits use, distribution and reproduction, commercial and non-commercial, provided ... more This license permits use, distribution and reproduction, commercial and non-commercial, provided that the original work is properly cited and is not changed in anyway.

Sri Lankan Journal of Applied Statistics

In this investigation, we use SAI method (Gupta et al. 2016), for solving sequencing problem when... more In this investigation, we use SAI method (Gupta et al. 2016), for solving sequencing problem when processing time of the machine is certain or uncertain in nature. The procedure adopted for solving the sequencing problems is easiest and involves the minimum numbers of iterations to obtain the sequence of jobs. The uncertainty in data is represented by triangular or trapezoidal fuzzy numbers. Yager's ranking function approach is used to convert these fuzzy numbers into a crisp at a prescribed value of . Stepwise SAI method is then used to obtain optimal job sequence for the problem. Further, the result obtained by SAI method is compared with Johnson's Method. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

Sri Lankan Journal of Applied Statistics

The generalization of linear programming is a fractional programming where the objective function... more The generalization of linear programming is a fractional programming where the objective function is a proportion of two linear functions. Likewise, in fractional transportation problem the aim is to optimize or improve the ratio of two cost functions or damage functions or demand functions. Since the ratio of two functions is considered, the fractional programming models become more appropriate for dealing with real life problems. The fractional transportation problem (FTP) plays a very important role in supply management for reducing cost and amending service. In real life, the parameters in the models are rarely known exactly and have to be evaluated. This paper investigates the fractional transportation problem (FTP) with some discount cost that avails during the shipment time. The transportation problem, which is one of integer programming problems, deals with distributing any commodity from any group of 'sources' to any group of destinations or 'sinks' in the most effective way with a given 'supply' and 'demand' constraints. The volume of goods to be transported from one place to another incurs some discount cost that could effectively reduce the shipment cost which is directly related to the profit associated with the shipment. This paper is aimed at studying the optimal solution for the problem has been achieved by using Karush-Kuhn-Tucker (KKT) optimality algorithm. Finally, a numerical example is illustrated to support the algorithm.

Arabian Journal for Science and Engineering

This paper is concerned with the maintainability issues and standby workstations provisioning whi... more This paper is concerned with the maintainability issues and standby workstations provisioning which are the key concerns of the system designers in manufacturing system to overcome the unpredictable interruptions due to workstation failures. An optimal F policy is proposed to control the admission of jobs in the case when the capacity of the system is full. By using queue theoretic approach, the performance of manufacturing system consisting of finite identical workstations in parallel is explored. Various realistic features including minor and major breakdowns of the service facility, degraded failure rate of workstations and controlled admission of failed workstations are also taken into account for modeling the repairable manufacturing system. The spectral method is employed to compute the transient state probabilities for the governing model. Greedy selection and Newton-quasi methods are used to determine the optimal parameter/threshold by minimizing the total cost associated with different activities.

International Journal of Quality & Reliability Management

Purpose The purpose of this paper is to study the performance metrics of redundant repairable mac... more Purpose The purpose of this paper is to study the performance metrics of redundant repairable machining system which is applicable in various systems like computer and communication system, manufacturing and production system, etc. Design/methodology/approach In the present investigation, the authors develop Markov model for the system consisting of identical active operating machines which are prone to breakdown. The operating machines are under the care of one permanent repair facility that provides time-sharing basis repair services. The maintenance is facilitated with the provision of standby machines of mixed type and permanent as well as additional repair facility. From the economic point of view, F-policy and N-policy to control the service and arrival of failed machines effectively are included. Findings For the performance analysis of the system in long run, the authors compute steady-state probabilities using product-type solution method recursively. Sensitivity analysis i...

International Journal of System Assurance Engineering and Management

The present paper deals with the reliability analysis of fault tolerant multi-component machining... more The present paper deals with the reliability analysis of fault tolerant multi-component machining system having multi-warm spares and reboot provisioning. The time-to-breakdown and repair of active/spare units and server are assumed to be exponentially distributed. The reboot process and recovery delay are also counterfeited exponentially distributed. The spectral method is adapted to compute the transient state probabilities of the system states. In order to predict the transient behavior of the system, various performance measures such as reliability function, mean-time-to-failure \left( {MTTF} \right)$$MTTF, etc. have been established. To show the practicability of the developed model, we present numerical results by taking an illustration. The sensitivity of various system parameters on the reliability function and MTTF$$MTTF has also been examined.

In this investigation, a nonlinear compartment model has been developed for the awareness of medi... more In this investigation, a nonlinear compartment model has been developed for the awareness of media coverage on controlling and prevention of infectious diseases, namely HIV/AIDS and TB within a population of varying size. The population has been divided into four sub-classes of susceptible, TB infected, HIV infected and AIDS patients. Using the stability analysis, the model has been studied quantitatively by taking small perturbation about equilibrium points. The developed mathematical model shows four equilibrium points, namely disease free, population free from HIV/AIDS, population free from TB and co-infection equilibrium point. It has been shown that the co-infection equilibrium point is always locally stable. The concept of the basic reproduction number has also been introduced in the model. It is predicted that the disease dies out if a reproduction number is less than unity and it becomes endemic if it is greater than unity.

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.

Yugoslav Journal of Operations Research

The aim of the present article is to give a historical survey of some important research works re... more The aim of the present article is to give a historical survey of some important research works related to queues in machining system since 2010. Queues of failed machines in machine repairing problem occur due to the failure of machines at random in the manufacturing industries, where different jobs are performed on machining stations. Machines are subject to failure what may result in significant loss of production, revenue, or goodwill. In addition to the references on queues in machining system, which is also called `Machine Repair Problem' (MRP) or `Machine Interference Problem' (MIP), a meticulous list of books and survey papers is also prepared so as to provide a detailed catalog for understanding the research in queueing domain. We have classified the relevant literature according to a year of publishing, methodological, and modeling aspects. The author(s) hope that this survey paper could be of help to learners contemplating research on queueing domain.

In this investigation, an epidemic Markov queueing model with alert, infection, vaccination and d... more In this investigation, an epidemic Markov queueing model with alert, infection, vaccination and death has been considered. The main focus of this work is on the vaccination to provide the infection in a population. Healthy person may be affected from some disease that may cause death. The vaccination is the power tool for the prevention of the diseases spreading over the population size. Healthy person become alert when symptoms of the disease can be seen on them and the alert may be injected due to more infection. The provision of vaccination is provided in both alert and infected stages. The transition rates as followed by exponential distribution. A Markov model is developed by using inflow and outflow transition rates of the model. The transient state probabilities are evaluated by solving the transient state equations by using runge kutta method which are further used for calculating the model performances. A numerical illustration is also provided to validate the model.

Decision Science Letters, 2017

This study deals with the performance modeling and reliability analysis of a redundant machining ... more This study deals with the performance modeling and reliability analysis of a redundant machining system composed of several functional machines. To analyze the more realistic scenarios, the concepts of switching failure and geometric reneging are included. The time-tobreakdown and repair time of operating and standby machines are assumed to follow the exponential distribution. For the quantitative assessment of the machine interference problem, various performance measures such as meantime to failure , reliability, reneging rate, etc. have been formulated. To show the practicability of the developed model, a numerical illustration has been presented. For the practical justification and validity of the results established, the sensitivity analysis of reliability indices has been presented by varying different system descriptors.

International Journal of Mechanisms and Robotic Systems

International Journal of Mathematics in Operational Research, 2017

International Journal of Mechanisms and Robotic Systems

The present survey is based on the principle of retrials in queueing theory i.e. the customers wh... more The present survey is based on the principle of retrials in queueing theory i.e. the customers who repeatedly try to avail the services from the server, on finding dejection, because of the inactivity of the server to provide service at an instant of selection from the queue. A bunch of work has previously been done on this front from past since it is realistic phenomena of many service system. The current investigation aims to present a brief review of the major works done on retrial queueing systems in recent years. The bibliography consists of research articles which were published in journals of repute during the period 2010-2015. In addition to the above references, an exhaustive list of books and survey papers on retrial queueing systems is also prepared so as to provide a detailed enough catalog for further understanding and research in retrial queueing domain. We have classified the journal papers according to the year of publishing. The aim of the present study is to turn up at a broad enough for a collection of important results in the theory of retrial queueing systems and their applications in solving several realistic problems. The main contribution is the bibliography of recent papers and books collected from different databases and private sources. At last, we have arranged some of the references according to the classification based on analysis and solution technique. The author(s) hope that this survey paper could be of help to learners contemplating research on retrial queues.

In mathematical programming different types of cuts have been developed in the past to get an int... more In mathematical programming different types of cuts have been developed in the past to get an integer value of the decision variables. In this paper, we have developed a new integer cut for getting an integer solution of the fractional linear programming problem (FLPP). This technique allows the decision-maker to solve the formulated FLPP to be conveniently using the Branch and Bound approach in order to achieve the optimum final solution. The process of development of the integer cut is shown with sufficient detail and a numerical illustration is used for clarification purpose.

Applications of Advanced Optimization Techniques in Industrial Engineering, 2022

Journal of the National Science Foundation of Sri Lanka

This license permits use, distribution and reproduction, commercial and non-commercial, provided ... more This license permits use, distribution and reproduction, commercial and non-commercial, provided that the original work is properly cited and is not changed in anyway.

Sri Lankan Journal of Applied Statistics

In this investigation, we use SAI method (Gupta et al. 2016), for solving sequencing problem when... more In this investigation, we use SAI method (Gupta et al. 2016), for solving sequencing problem when processing time of the machine is certain or uncertain in nature. The procedure adopted for solving the sequencing problems is easiest and involves the minimum numbers of iterations to obtain the sequence of jobs. The uncertainty in data is represented by triangular or trapezoidal fuzzy numbers. Yager's ranking function approach is used to convert these fuzzy numbers into a crisp at a prescribed value of . Stepwise SAI method is then used to obtain optimal job sequence for the problem. Further, the result obtained by SAI method is compared with Johnson's Method. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

Sri Lankan Journal of Applied Statistics

The generalization of linear programming is a fractional programming where the objective function... more The generalization of linear programming is a fractional programming where the objective function is a proportion of two linear functions. Likewise, in fractional transportation problem the aim is to optimize or improve the ratio of two cost functions or damage functions or demand functions. Since the ratio of two functions is considered, the fractional programming models become more appropriate for dealing with real life problems. The fractional transportation problem (FTP) plays a very important role in supply management for reducing cost and amending service. In real life, the parameters in the models are rarely known exactly and have to be evaluated. This paper investigates the fractional transportation problem (FTP) with some discount cost that avails during the shipment time. The transportation problem, which is one of integer programming problems, deals with distributing any commodity from any group of 'sources' to any group of destinations or 'sinks' in the most effective way with a given 'supply' and 'demand' constraints. The volume of goods to be transported from one place to another incurs some discount cost that could effectively reduce the shipment cost which is directly related to the profit associated with the shipment. This paper is aimed at studying the optimal solution for the problem has been achieved by using Karush-Kuhn-Tucker (KKT) optimality algorithm. Finally, a numerical example is illustrated to support the algorithm.

Arabian Journal for Science and Engineering

This paper is concerned with the maintainability issues and standby workstations provisioning whi... more This paper is concerned with the maintainability issues and standby workstations provisioning which are the key concerns of the system designers in manufacturing system to overcome the unpredictable interruptions due to workstation failures. An optimal F policy is proposed to control the admission of jobs in the case when the capacity of the system is full. By using queue theoretic approach, the performance of manufacturing system consisting of finite identical workstations in parallel is explored. Various realistic features including minor and major breakdowns of the service facility, degraded failure rate of workstations and controlled admission of failed workstations are also taken into account for modeling the repairable manufacturing system. The spectral method is employed to compute the transient state probabilities for the governing model. Greedy selection and Newton-quasi methods are used to determine the optimal parameter/threshold by minimizing the total cost associated with different activities.

International Journal of Quality & Reliability Management

Purpose The purpose of this paper is to study the performance metrics of redundant repairable mac... more Purpose The purpose of this paper is to study the performance metrics of redundant repairable machining system which is applicable in various systems like computer and communication system, manufacturing and production system, etc. Design/methodology/approach In the present investigation, the authors develop Markov model for the system consisting of identical active operating machines which are prone to breakdown. The operating machines are under the care of one permanent repair facility that provides time-sharing basis repair services. The maintenance is facilitated with the provision of standby machines of mixed type and permanent as well as additional repair facility. From the economic point of view, F-policy and N-policy to control the service and arrival of failed machines effectively are included. Findings For the performance analysis of the system in long run, the authors compute steady-state probabilities using product-type solution method recursively. Sensitivity analysis i...

International Journal of System Assurance Engineering and Management

The present paper deals with the reliability analysis of fault tolerant multi-component machining... more The present paper deals with the reliability analysis of fault tolerant multi-component machining system having multi-warm spares and reboot provisioning. The time-to-breakdown and repair of active/spare units and server are assumed to be exponentially distributed. The reboot process and recovery delay are also counterfeited exponentially distributed. The spectral method is adapted to compute the transient state probabilities of the system states. In order to predict the transient behavior of the system, various performance measures such as reliability function, mean-time-to-failure \left( {MTTF} \right)$$MTTF, etc. have been established. To show the practicability of the developed model, we present numerical results by taking an illustration. The sensitivity of various system parameters on the reliability function and MTTF$$MTTF has also been examined.

In this investigation, a nonlinear compartment model has been developed for the awareness of medi... more In this investigation, a nonlinear compartment model has been developed for the awareness of media coverage on controlling and prevention of infectious diseases, namely HIV/AIDS and TB within a population of varying size. The population has been divided into four sub-classes of susceptible, TB infected, HIV infected and AIDS patients. Using the stability analysis, the model has been studied quantitatively by taking small perturbation about equilibrium points. The developed mathematical model shows four equilibrium points, namely disease free, population free from HIV/AIDS, population free from TB and co-infection equilibrium point. It has been shown that the co-infection equilibrium point is always locally stable. The concept of the basic reproduction number has also been introduced in the model. It is predicted that the disease dies out if a reproduction number is less than unity and it becomes endemic if it is greater than unity.

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.

Yugoslav Journal of Operations Research

The aim of the present article is to give a historical survey of some important research works re... more The aim of the present article is to give a historical survey of some important research works related to queues in machining system since 2010. Queues of failed machines in machine repairing problem occur due to the failure of machines at random in the manufacturing industries, where different jobs are performed on machining stations. Machines are subject to failure what may result in significant loss of production, revenue, or goodwill. In addition to the references on queues in machining system, which is also called `Machine Repair Problem' (MRP) or `Machine Interference Problem' (MIP), a meticulous list of books and survey papers is also prepared so as to provide a detailed catalog for understanding the research in queueing domain. We have classified the relevant literature according to a year of publishing, methodological, and modeling aspects. The author(s) hope that this survey paper could be of help to learners contemplating research on queueing domain.

In this investigation, an epidemic Markov queueing model with alert, infection, vaccination and d... more In this investigation, an epidemic Markov queueing model with alert, infection, vaccination and death has been considered. The main focus of this work is on the vaccination to provide the infection in a population. Healthy person may be affected from some disease that may cause death. The vaccination is the power tool for the prevention of the diseases spreading over the population size. Healthy person become alert when symptoms of the disease can be seen on them and the alert may be injected due to more infection. The provision of vaccination is provided in both alert and infected stages. The transition rates as followed by exponential distribution. A Markov model is developed by using inflow and outflow transition rates of the model. The transient state probabilities are evaluated by solving the transient state equations by using runge kutta method which are further used for calculating the model performances. A numerical illustration is also provided to validate the model.

Decision Science Letters, 2017

This study deals with the performance modeling and reliability analysis of a redundant machining ... more This study deals with the performance modeling and reliability analysis of a redundant machining system composed of several functional machines. To analyze the more realistic scenarios, the concepts of switching failure and geometric reneging are included. The time-tobreakdown and repair time of operating and standby machines are assumed to follow the exponential distribution. For the quantitative assessment of the machine interference problem, various performance measures such as meantime to failure , reliability, reneging rate, etc. have been formulated. To show the practicability of the developed model, a numerical illustration has been presented. For the practical justification and validity of the results established, the sensitivity analysis of reliability indices has been presented by varying different system descriptors.

International Journal of Mechanisms and Robotic Systems

International Journal of Mathematics in Operational Research, 2017

International Journal of Mechanisms and Robotic Systems