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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.

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.

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 investigate the behavioral operations effect in production inventory decision of supply chain consisting of one manufacturer and one buyer, and analyze how the unfairness concerns impact the decision of production inventory in a supply chain system.

First, a model without the buyer’s unfairness concern is established; then, advantage unfairness concern and disadvantage unfairness concern behavior of buyer are taken into account in the production inventory system. The authors analyze how advantage unfairness concern and disadvantage unfairness concern impact the optimal decisions and channel coordination.

The result shows several important conclusions. First, the buyer’s optimal ordering quantity and expected utility show opposing trend when the buyer has advantage unfairness concern. Second, the stronger bargaining power of the manufacturer results in an increasing buyer’s optimal ordering quantity under the advantage unfairness concern case, but decreasing under the disadvantage unfairness concern case. Third, the supply chain production-inventory can be coordinated under advantage unfairness concern case, but cannot be coordinated under disadvantage unfairness concern.

The study can provide to practitioners with important implications that when the vendor or the buyer in supply chain wants to make the decision of inventory replenishment, taking unfairness concerns into account will lead to different results. Therefore, to effectively improve the operations performance of supply chain, partners of the supply chain should not only care about their own interest, but also need to consider the fairness concern of the other partner, reflecting the cooperation consciousness of supply chain management.

This paper contributes to the new field of creative management–behavioral operations, offering managerial implications for the decision and optimization of supply chain production-inventory problem.

A production‐inventory system based on a model proposed by Axsäter is examined with the purpose of understanding the dynamic properties of the model.

The information flow concept is discussed and a dynamic analysis using a system simplification approach is carried out to achieve an understanding of the dynamic behaviour of the system. Finally, the information flow is examined and analysed from a hierarchical perspective.

The model is extended to include an order decision rule and a production unit and it is shown that the extended model has the capability to represent the dynamics of a number of different system management principles. The three different model instances of base stock, kanban and material requirements planning character are analysed.

Dynamic modelling of production‐inventory and supply chain models are usually analysed at an aggregate level not involving any complex relations of materials or capacities. In this paper, this line of research is merged with an approach based on multiple information channels using matrix representation and it is shown how a system simplification approach can be used for this purpose.

To provide an overview of how a number of frequently used smoothing‐based forecasting techniques can be modelled for use in dynamic analysis of production‐inventory systems.

The smoothing techniques are modelled using transfer functions and state space representation. Basic control theory is used for analysing the dynamic properties.

A set of expressions are derived for the smoothing techniques and dynamic properties are identified.

Dynamic properties are important in many applications. It is shown that the different smoothing techniques can have very different influences on the dynamic behaviour and therefore should be considered as a factor when smoothing parameters are decided on.

Dynamic behaviour of production‐inventory systems can be analysed using control theory based on, e.g. transfer functions or state space models. In this paper a set of models for five common smoothing techniques are analysed and their respective dynamic properties are highlighted.

While numerous mathematical models of production‐inventory systems have been developed and are in operation there is no commonly accepted approach to guide the professional in managing the system effectively and comprehensively. A higher proportion of these models are not readily acceptable as they are strictly technical and canonical in form and content. This article attempts to develop a hybridised information system while recognising the existing operational problems and planning for the accommodation of change. The attempt here has been specifically to derive some factual premises to facilitate professionals to develop meaningful insights into the solution process.

Due to uncertainty in supply chains caused by the coronavirus disease 2019 (COVID-19), organizations are adjusting their supply chain design to address challenges faced during the pandemic. To safeguard their operations against disruption in order quantities, supply chain members have been looking for alternate suppliers. This paper considers a two-level supply chain consisting of a manufacturer and two suppliers of a certain type of components required for the production of a finished product. The primary supplier (supplier A) is unreliable, in the sense that the quantity delivered is usually less than the ordered quantity. The proportion of the ordered quantity delivered by supplier A is a random variable with a known probability distribution. The secondary supplier (supplier B) always delivers the order in its entirety at a higher cost and can respond instantaneously. In order for supplier B to respond instantaneously, the manufacturer is required to reserve a certain quantity at an additional cost. Once the quantity received from the main supplier is observed, the manufacturer may place an order not exceeding the reserved quantity.

A mathematical model describing the production/inventory situation of the supply chain is formulated. The model allows the determination of the manufacturer's optimal ordering policy.

An expression for the expected total cost per unit time function is derived. The optimal solution is determined by solving a system of nonlinear equations obtained by minimizing the expected total cost function.

The proposed model can be used by supply chain managers aiming at identifying various ways of handling the uncertainty in the flow of supplies across the chain.

This proposed model addresses a gap in the production/inventory literature.

The implementation of the Japanese inventory control system, Kanban, in a production line, reduces Work‐in‐Process (WIP) inventory without affecting production or sales, though there is a point at which the reverse becomes true. The hypothesis that Kanban policy would reduce total WIP inventory without affecting production/sales at all was tested under two environmental conditions, cyclical demand and constant growth demand, by means of a simulated model, and also showed that under cyclical demand, frequent starts and stops in the line due to use of all the Kanban cards will produce eventual growth in all inventories, if not rectified. It is hoped that further research will develop a sufficently comprehensive model to facilitate the implementation of such a materials handling system.

The purpose of this paper is to compare the effectiveness of the Buy-and-Hold (BNH), Fee-for-Service (FFS), and Direct-to-pharmacy (DTP) agreements for the US pharmaceutical industry and its individual participants. There have been mixed responses to these agreements and the industry is currently under debate as to which contract would be best for the industry and its individual participants. The question is answered by comparing the agreements and settling the industry debate regarding the impact of these distribution agreements.

The model features multi-period production-inventory planning with time varying parameters in a decentralized setting. Under each distribution agreement, mathematical programming models are formulated to determine the profit maximizing production, inventory, and ordering decisions for the manufacturer and the wholesaler in a finite time horizon. The applicability of the model in the US pharmaceutical industry using real-world data is demonstrated.

It is shown that the DTP agreement always outperforms the BNH and FFS agreements. Furthermore, the DTP agreement is flexible because it allows the manufacturer and the wholesaler to split the additional profit in an arbitrary way. The findings reveal that the DTP agreement can improve total profit by about 0.08 - 1 percent (relative to FFS) and 5 percent (relative to BNH).

Considering the size of the pharmaceutical industry, efficient distribution agreements are imperative. Unfortunately, the existing literature provides insufficient guidance to help managers make this important decision. This knowledge gap is addressed in literature, and provides important insight for practitioners on what agreement is most beneficial for this industry.