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The purpose of this paper is to study the problem of optimal Ramsey taxation in a finite-planning-horizon, representative-agent endogenous growth model including government expenditures as a productive input in capital formation and also with hidden actions.

Technically, Malliavin calculus and forward integrals are naturally introduced into the macroeconomic theory when economic agents are faced with different information structures arising from a non-Markovian environment.

The major result shows that the well-known Judd-Chamley Theorem holds almost surely if the depreciation rate is strictly positive, otherwise Judd-Chamley Theorem only holds for a knife-edge case or on a Lebesgue measure-zero set when the physical capital is completely sustainable.

The author believes that the approach developed as well as the major result established is new and relevant.

Scheduling of production in a wire rope factory is complicated by several features: (a) the simultaneous requirement for two types of limited resource, machines and bobbins; (b) multi‐stage production with normally two or three stranding and one or two closing operations; (c) queuing at the closing machines; the typical job splits into sub‐batches when passing from the stranding to the closing operation; these sub‐batches usually queue at the closing operations which, being faster than stranding operations, generally receive work from several queues; (d) alternative choices in the selection of machines and bobbin sizes for any given stranding or closing operation; (e) the presence of random elements in the timing of machine breakdowns and repairs. In this case study factory in a developing country, the existing control of production flows was ad hoc rather than according to a specified method. The management needed to know whether a scientific scheduling approach could significantly improve the low utilisation of machines. As a first attempt a strategy was synthesised based on well‐known concepts from the theory of scheduling in static and dynamic environments, taking into consideration certain effects of the complicating factors mentioned above. Simulation revealed that a significant improvement was possible.

A newly developed model for performing reliability and availability analysis of mechanical devices subject to multiple failure modes is presented. Using this model, reliability analyses of mechanical devices such as brakes, bearings, engines, fans, gears, generators, heat exchangers and pumps are developed. Real life failure rate data for these devices are obtained from various sources and are used in their reliability analyses. Principal failure modes of these devices are identified and expressions for reliability, state probabilities, mean time to failure and variance of time to failure are developed. For known field failure data reliability and state probability plots are shown.

The purpose of this paper is to establish a version of a theorem that originated from population genetics and has been later adopted in evolutionary computation theory that will lead to novel Monte‐Carlo sampling algorithms that provably increase the AI potential.

In the current paper the authors set up a mathematical framework, state and prove a version of a Geiringer‐like theorem that is very well‐suited for the development of Mote‐Carlo sampling algorithms to cope with randomness and incomplete information to make decisions.

This work establishes an important theoretical link between classical population genetics, evolutionary computation theory and model free reinforcement learning methodology. Not only may the theory explain the success of the currently existing Monte‐Carlo tree sampling methodology, but it also leads to the development of novel Monte‐Carlo sampling techniques guided by rigorous mathematical foundation.

The theoretical foundations established in the current work provide guidance for the design of powerful Monte‐Carlo sampling algorithms in model free reinforcement learning, to tackle numerous problems in computational intelligence.

Establishing a Geiringer‐like theorem with non‐homologous recombination was a long‐standing open problem in evolutionary computation theory. Apart from overcoming this challenge, in a mathematically elegant fashion and establishing a rather general and powerful version of the theorem, this work leads directly to the development of novel provably powerful algorithms for decision making in the environment involving randomness, hidden or incomplete information.

This chapter has been seminal work of Dr K.S.S. Iyer, which has taken time to develop, for over the last 56 years to be presented here. The method in advance predictive analytics has developed, from his several other applications, in predictive modeling by using the stochastic point process technique. In the chapter on advance predictive analytics, Dr Iyer is collecting his approaches and generalizing it in this chapter. In this chapter, two of the techniques of stochastic point process known as Product Density and Random point process used in modelling problems in High energy particles and cancer, are redefined to suit problems currently in demand in IoT and customer equity in marketing (Iyer, Patil, & Chetlapalli, 2014b). This formulation arises from these techniques being used in different fields like energy requirement in Internet of Things (IoT) devices, growth of cancer cells, cosmic rays’ study, to customer equity and many more approaches.

The paper offers an intelligent approach to analyze and determine the design parameters minimizing the total cost and achieving the desired performance measures in the maintenance float systems. The expected total cost in a maintenance float system includes the cost of lost production, the cost of repair persons and the cost of standby machines. The developed design procedure integrates simulation, metamodel and genetic algorithms. Neural networks are able to approximate functions based on a set of sample data, i.e. construct metamodels from simulation results in this study. The objective of metamodels is to predict simulation responses in order to significantly reduce the amount of simulation runs. The predictive performance of neural metamodels comparably outperforms the traditional regression metamodels. The neural metamodels are further extended to formulate a decision model for optimizing the maintenance float systems by using genetic algorithms.

Credit ratings serve as an important input in several applications in risk management of the financial firms. The level of credit rating changes from time to time because of random credit risk and, thus, can be modeled by an appropriate stochastic process. Markov chain models have been widely used in the literature to generate credit migration matrices; however, emergent empirical evidences suggest that the Markov property is not appropriate for credit rating dynamics. The purpose of this article is to address the non-Markov behavior of the rating dynamics.

This paper proposes a model based on Markov regenerative process (MRGP) with subordinated semi-Markov process (SMP) to obtain the estimates of rating migration probability matrices and default probabilities. Numerical example is given to illustrate the applicability of the proposed model with the help of historical Standard & Poor’s (S&P) credit rating data.

The proposed model implies that rating of a firm in the future not only depends on its present rating, but also on its previous ratings. If a firm gets a rating lower than its previous ratings, there are higher chances of further downgrades, and the issue is called the rating momentum. The model also addresses the ageing problem of credit rating evolution.

The contribution of this paper is a more general approach to study the rating dynamics and overcome the issues of inappropriateness of Markov process applied in rating dynamics.

This paper models the deterioration process of a multi-component system. Each deterioration process is modelled by the Wiener process. The purposes of this paper are to address these issues and consider the cost process based on the multi-component system.

Condition-based Maintenance is a method for reducing the probability of system failures as well as the operating cost. Nowadays, a system is composed of multiple components. If the deteriorating process of each component can be monitored and then modelled by a stochastic process, the deteriorating process of the system is a stochastic process. The cost of repairing failures of the components in the system forms a stochastic process as well and is known as a cost process.

When a linear combination of the processes, which can be the deterioration processes and the cost processes, exceeds a pre-specified threshold, a replacement policy will be carried out to preventively maintain the system.

Under this setting, this paper investigates maintenance policies based on the deterioration process and the cost process. Numerical examples are given to illustrate the optimisation process.

The internet of things and just-in-time are the embryonic model of innovation for the state-of-the-art design of the service system. This paper aims to develop a fault-tolerant machining system with active and standby redundancy. The availability of the fault-tolerant redundant repairable system is a key concern in the successful deployment of the service system.

In this paper, the authors cogitate a fault-tolerant redundant repairable system of finite working units along with warm standby unit provisioning. Working unit and standby unit are susceptible to random failures, which interrupt the quality-of-service. The system is also prone to common cause failure, which tends its catastrophe. The instantaneous repair of failed unit guarantees the increase in the availability of the unit/system. The time-to-repair by the single service facility for the failed unit follows the arbitrary distribution. For increasing the practicability of the studied model, the authors have also incorporated real-time machining practices such as imperfect coverage of the failure of units, switching failure of standby unit, common cause failure, reboot delay, switch over delay, etc.

For deriving the explicit expression for steady-state probabilities of the system, the authors use a supplementary variable technique for which the only required input is the Laplace–Stieltjes transform (LST) of the repair time distribution.

For complex and multi-parameters distribution of repair time, derivation of performance measures is not possible. The authors prefer numerical simulation because of its importance in the application for real-time uses.

The stepwise recursive procedure, illustrative examples, and numerical results have been presented for the diverse category of repair time distribution: exponential (M), n-stage Erlang (Ern), deterministic (D), uniform (U(a,b)), n-stage generalized Erlang (GE_[n]) and hyperexponential (HE_[n]).

Concluding remarks and future scopes have also been included. The studied fault-tolerant redundant repairable system is suitable for reliability analysis of a computer system, communication system, manufacturing system, software reliability, service system, etc.

As per the survey in literature, no previous published paper is presented with so wide range of repair time distribution in the machine repair problem. This paper is valuable for system design for reliability analysis of the fault-tolerant redundant repairable.

The purpose of this paper is to provide simulation modelling for bulk arrival bulk service queueing system involved in a textile industry and analyze the performance metrics.

This paper describes the simulation modelling of a bulk queueing system with limited number of admissions and multiple vacations. The model is developed for the proposed queueing system using Flexsim 2017, and it is explained through an application observed in a textile industry involving the process of cone winding.

In this paper, the simulation model has been developed to study the behaviour of queues at different resources in a production system. Various performance measures such as average components, average waiting time, total number of inputs and outputs, processing time and idle time involved in a textile industry are evaluated using simulation and justified through numerical illustration.

The proposed simulation model may be used in various scenarios wherever a real time situation exists related to bulk queueing system. The results produced in this paper can be used by the manufacturing industries to enhance the need-based accuracy. It is worth pointing out that the findings are of direct practical relevance and can be successfully used for a number of industrial applications.

The approach suggested in this paper attempts to deal with the queueing system involved in a textile industry and provides numerical results in less time with less computer resources. It provides a reasonably good approximation for simple and complex queueing models where it is difficult to find closed form of theoretical results.