Exact solutions to the supply chain equations for arbitrary, time-dependent demands

Warburton, Roger D.H.; Hodgson, Jonathan P.E.; Nielsen, Erland Hejn

doi:10.1016/j.ijpe.2013.10.015

Cited by 6 publications

(6 citation statements)

References 40 publications

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“…The bullwhip effect was first mentioned by Forrester [6–7]. Other studies, e.g., [8–10], contain data on inventory volatility describing a similar effect. Similarly, Sterman in his BeerGame [11], designed for teaching the theory of inventory management, shows the same phenomenon.…”

Section: Literary Reviewmentioning

confidence: 93%

Numerical Solution of the Inventory Balance Delay Differential Equation

Novotná

2015

International Journal of Engineering Business Management

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Inventory represents an essential part of current assets, which are typically characterized by their transience. This paper aims to outline a numerical solution of the inventory balance equation supplemented by an order-upto replenishment policy for a case in which the problem is described by a differential equation with delayed argument. The results are demonstrated on a specific example and the behaviour of the model is presented using a computer simulation. The results are graphically shown in the Maple system. The solution makes use of the theory of functional differential equations, especially the part dealing with differential equations with delayed arguments.

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Section: Literary Reviewmentioning

confidence: 93%

Numerical Solution of the Inventory Balance Delay Differential Equation

Novotná

2015

International Journal of Engineering Business Management

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“…Other more advanced methods, such as exact solutions, were considered by several authors (e.g. Warburton 2004Warburton et al 2014, but these solutions need to be more fully developed in the future.…”

Section: The Optimisation Of Decision Parameters In the Iobpcs Familymentioning

confidence: 99%

“…A complex Lambert W function in an exponential was derived to explain the sensitive relationship between production delay and inventory oscillation. The analytical solution demonstrated that proper selection of the system parameters is necessary in order to improve system performance based on three criteria: the time to recover the inventory drift, the WIP adjustment and demand smoothing Warburton et al (2014). also utilised an exact solution for the OUT policy under an arbitrary, time-variant and non-linear demand pattern.…”

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confidence: 99%

The extension and exploitation of the inventory and order based production control system archetype from 1982 to 2015

Lin

Naim

Purvis

2017

International Journal of Production Economics

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In 1994, through classic control theory, John, Naim and Towill developed the 'Automatic Pipeline, Inventory and Order-based Production Control System' (APIOBPCS) which extended the original IOBPCS archetype developed by Towill in 1982 ─ well-recognized as a base framework for a production planning and control system. Due to the prevalence of the two original models in the last three decades in the academic and industrial communities, this paper aims to systematically review how the IOBPCS archetypes have been adopted, exploited and adapted to study the dynamics of individual production planning and control systems and whole supply chains. Using various databases such as Scopus, Web of Science, Google Scholar (111 papers), we found that the IOBPCS archetypes have been studied regarding the a) modification of four inherent policies related to forecasting, inventory, lead-time and pipeline to create a 'family' of models, b) adoption of the IOBPCS 'family' to reduce supply chain dynamics, and in particular bullwhip, c) extension of the IOBPCS family to represent different supply chain scenarios such as order-book based production control and closed-loop processes. Simulation is the most popular method adopted by researchers and the number of works based on discrete time based methods is greater than those utilizing continuous time approaches. Most studies are conceptual with limited practical applications described. Future research needs to focus on cost, flexibility and sustainability in the context of supply chain dynamics and, although there are a few existing studies, more analytical approaches are required to gain robust insights into the influence of nonlinear elements on supply chain behaviour. Also, empirical exploitation of the existing models is recommended.

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“…System dynamics is traditionally concerned with the numerical solution to a given problem, that is, simulation based analysis, but in cases where the mathematical setup is relatively simple, analytic solutions are also a possibility [72,73]. System dynamics also utilizes econometrics in order to estimate the partial mechanisms that the system dynamics model consists of if sufficient data is available, although a fundamental conflict between system dynamics and econometrics has existed from the beginning.…”

Section: System Dynamics Thinkingmentioning

confidence: 99%

The Balanced Scorecard and the Strategic Learning Process: A System Dynamics Modeling Approach

Nielsen

2015

Advances in Decision Sciences

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The main purpose of this paper is to improve on the conceptual as well as the methodological aspects of BSC as a quantitative model by combining elements from traditional balanced scorecard (BSC) thinking with the Systems Thinking. This is done by combining short and long term aspects of measurements. The result is then used to build and construct a balanced scorecard model for strategic learning with the specific aim to maintain satisfied customers and motivated employees. Strategic planning, operational execution, feedback, and learning are some of the most important key features of any performance measurement model. This paper aims to address not only the conceptual domain related to BSC, that is, learning and system dynamics causality and feedback, but also the methodological domain concept of precision solved by differential equations. Our results show how a potential move from a static strategic vision map to a linked and dynamic understanding may be not fully realistic but very useful for learning purposes. The new knowledge obtained from the learning feedbacks fertilizes both decision discussion and decision-making and what may be required in order to move to the next level of BSC and system dynamics integration.

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Exact solutions to the supply chain equations for arbitrary, time-dependent demands

Cited by 6 publications

References 40 publications

Numerical Solution of the Inventory Balance Delay Differential Equation

Numerical Solution of the Inventory Balance Delay Differential Equation

The extension and exploitation of the inventory and order based production control system archetype from 1982 to 2015

The Balanced Scorecard and the Strategic Learning Process: A System Dynamics Modeling Approach

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