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Lalwani et al. devised a controllable state-space model for a general APVIOBPCS production and inventory system. However, their procedure did not cater for production delays of other than one time unit. The authors have sought to devise a model that allows for any value of production delay.

A discrete z transform model of APVIOBPCS inventory is obtained using conventional algebra and converted to a state-space model using a reachable control formulation. This is then analysed to produce an analytic expression for the eigenvalues and then the general stability solution is derived from the unit circle condition.

This model allows a state-space model conversion from a discrete time input-output model using an exponential production delay with no loss of generality and is fully controllable and observable. Stability of these models can be obtained from the system eigenvalues and agrees with the authors' previously published stability boundaries using transform models.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations. It does not include any past history of sales demand and responses.

This work allows a model to be implemented in a spreadsheet of APVIOBPCS PIC that can be used for any production delay and can be modified to include different sales smoothing procedures.

This present model is an extension and improvement of the model devised by Lalwani, in that it allows more accurate modelling of inventory production systems by permitting a more flexible selection of delay parameter values, closer to those of real systems.

The purpose of this paper is to investigate a control engineering-based system model that allows for any value of production delay for a three-tier supply chain with information delays between tiers or systems with epos.

A discrete z transform model of automatic pipeline, variable inventory and order based production control system three-tier supply chain is obtained using a state-space model using a reachable control formulation. This model provides a discrete time state-space model conversion using an exponential production delay with no loss of generality.

This work allows a three-tier supply chain model to be computed via a spreadsheet using any production delay and can be modified to include different sales smoothing procedures. The model is fully controllable and observable. Stability of these models is obtained from the system eigenvalues and agrees with our previously published stability boundaries.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations, including history of sales demand and response.

This present model is an extension of the model devised by White and Censlive, in that it allows accurate modelling of multi-tier inventory production systems by permitting flexible selection of delay parameter values for real systems.

The objective of this work is to develop a model that can be used for simulation of different parameters including price, subjected to different control strategies.

The entire supply chain can be modelled by combining the transfer function into a closed loop system. The transfer function of each entity in the supply chain can be obtained by using the control theory tools. The model can be approximated as a linear discrete system with various operating constants, like lead time, price, order policy and supply.

The continuous replenishment ordering policy for a distribution node in a supply chain was analyzed using the z-transform. Characteristic equations of the closed loop transfer function are obtained. The bullwhip (BW) effect is analyzed. Study proves that the BW effect is in evitable if the standard heuristic ordering policy is employed with demand forecasting; also the paper analysed price supply trade-off for dynamic demand and supply. Simulation results show that BW is less in PI and simple p-only with cascade control. Robust control and PD, PID control results are not shown in this literature, and it is subject to further research.

Research is original, it can be applicable in today's dynamic world, due to globalization, it is necessary to have a automated machine that can handle most of supply chain decision.

The purpose of this study is to propose a new dynamic model of a production-inventory control system. The objective of the new model is to maximise the flexibility of the system so that it can be used by decision makers to design inventory systems that adopt various strategies that provide a balance between reducing the bullwhip effect and improving the responsiveness of inventory performance.

The proposed production-inventory control system is modelled and analysed via control theory and simulations. The production-inventory feedback control system is modelled through continuous time differential equations. The simulation experiments design is conducted by using the state-space model of the system. The Automatic Pipeline Inventory and Order-Based Production Control System (APIOBPCS) model is used as a benchmark production-inventory control system.

The results showed that the Two Automatic Pipelines, Inventory and Order-Based Production Control System (2APIOBPCS) model outperforms APIOBPCS in terms of reducing the bullwhip effect. However, the 2APIOBPCS model has a negative impact on Customer Service Level. Therefore, with careful parameter setting, it is possible to design control decisions to be suitably responsive while generating smooth order patterns and obtain the best trade-off of the two objectives.

This research is limited to the dynamics of single-echelon production-inventory control systems with zero desired inventory level.

This present model is an extension and improvement to Towill’s (1982) and John et al.’s (1994) work, since it presents a new dynamic model of a production-inventory control system which utilises an additional flow of information to improve the efficiency of order rate decisions.

This paper aims to optimise the dynamic performance of production–inventory control systems in terms of minimisation variance ratio between the order rate and the consumption, and minimisation the integral of absolute error between the actual and the target level of inventory by incorporating the Pareto optimality into particle swarm optimisation (PSO).

The production–inventory control system is modelled and optimised via control theory and simulations. The dynamics of a production–inventory control system are modelled through continuous time differential equations and Laplace transformations. The simulation design is conducted by using the state–space model of the system. The results of multi-objective particle swarm optimisation (MOPSO) are compared with published results obtained from weighted genetic algorithm (WGA) optimisation.

The results obtained from the MOPSO optimisation process ensure that the performance is systematically better than the WGA in terms of reducing the order variability (bullwhip effect) and improving the inventory responsiveness (customer service level) under the same operational conditions.

This research is limited to optimising the dynamics of a single product, single-retailer single-manufacturer process with zero desired inventory level.

PSO is widely used and popular in many industrial applications. This research shows a unique application of PSO in optimising the dynamic performance of production–inventory control systems.

The purpose of this paper is to examine the impact of applying two classical controller strategies, including two proportional (P) controllers with two feedback loops and one proportional–integral–derivative (PID) controller with one feedback loop, on the order and inventory performance within a production-inventory control system.

The simulation experiments of the dynamics behaviour of the production-inventory control system are conducted using a model based on control theory techniques. The Laplace transformation of an Order–Up–To (OUT) model is obtained using a state-space approach, and then the state-space representation is used to design and simulate a controlled model. The simulations of each model with two control configurations are tested by subjecting the system to a random retail sales pattern. The performance of inventory level is quantified by using the Integral of Absolute Error (IAE), whereas the bullwhip effect is measured by using the Variance ratio (Var).

The simulation results show that one PID controller with one feedback loop outperforms two P controllers with two feedback loops at reducing the bullwhip effect and regulating the inventory level.

The production-inventory control system is broken down into three components, namely: the forecasting mechanism, controller strategy and production-inventory process. A state-space approach is adopted to design and simulate the different controller strategy.

Shukla et al. (2012) proposed a signature and index to detect and measure rogue seasonality in supply chains, but which, however, were not effectively validated. The authors have sought to investigate rogue seasonality using control theory and realistic multi echelon systems and rigorously validate these measures, so as to enable their application in practice. The paper aims to discuss these issues.

Frequency domain analysis of single echelon and simulated four echelon Beer game system outputs are used in the investigation, with the simulation incorporating realistic features such as non-linearities from backlogs and batching, hybrid make to order-make to stock ordering system and the shipment variable. Lead time, demand process parameters, ordering parameters and batch size are varied in the simulation to rigorously assess the validity of the index.

The signature based on the cluster profiles of variables, specifically whether the variables cluster together with or away from exogenous demand, was validated. However, a threshold for the proportion of variables that could be clustered with exogenous demand and the system still being classified as exhibiting rogue seasonality, would require to be specified. The index, which is derived by quantifying the cluster profile relationships, was found to be a valid and robust indicator of the intensity of rogue seasonality, and which did not need any adjustments of the kind discussed for the signature. The greater effectiveness of the frequency domain in comparison to time for deriving the signature and index was demonstrated.

This work enables speedy assessment of rogue seasonality in supply chains which in turn ensures appropriate and timely action to minimize its adverse consequences.

Detailed and specific investigation on rogue seasonality using control theory and Beer game simulation and rigorous validation of the signature and index using these methods.

To assess the state of supply chain management (SCM) research in India and to understand the research trends and methodologies used. The present study also aims to create a taxonomy of the subject areas researched in India.

The present study employed the systematic literature review methodology. Literature from 395 peer journal papers in 67 leading journals over a 20-year period (2000–2020 Quarter-1) was comprehensively reviewed and assessed.

SCM research in India started around the year 2000. The quantum of research was low (single digit) until 2010. There has been steady growth over the last decade, and over 50% of the total papers up until now has been published in the last four years. The present study created a three-tiered taxonomy of the subject areas and classified the papers as per it. The first tier (level-1) has seven categories (SCM strategy, network design, SCM processes and integration, IT systems, skills, performance measurement and others). A perusal of the newly created taxonomy revealed that, except for a few areas under level-1 categories (such as SCM processes and SCM strategy), the other level-1 categories have not seen much research. Similarly, there is little or no research in a large number of level-2 categories (such as outsourcing strategy, channel strategy, demand management, demand fulfillment, customer relationship management, integrated supply chain planning, new product development, returns, supply chain orientation, performance monitoring, performance improvement, SCM adoption process, SCM implementation issues and quantified benefits of SCM). Methodologically, the rigor of SCM research in India needs improvement.

A comprehensive taxonomy of SCM subject areas researched in India at three cascading levels was created for the first time in the present study. The taxonomy will help provide researchers with a clear understanding of the structure of the subject areas and help in identifying areas where research has been carried out and the subject areas where gaps exist for future research to proceed. The present study also provides an overview of the methodological rigor of SCM research in India and points out some of the limitations that researchers should avoid in future studies.

This study aims to examine the interrelationship between resilience, robustness and bullwhip effect using an inventory- and order-based production control system being subjected to operational disruption in the customer demand process.

Control engineering techniques and simulation are employed for the supply chain dynamics study.

The results show that resilience and robustness are two conflicting performance characteristics and therefore, a tradeoff can be established between them. It is also observed that improvement in resilience and reduction of bullwhip effect can be achieved simultaneously through a proper selection of control parameters.

The work establishes a relationship between the resilient behavior of a supply chain and bullwhip effect.