Nonlinear dynamical systems and inventory management

Pinder, Jonathan P.

doi:10.1002/(sici)1099-1468(199601)17:1<27::aid-mde725>3.0.co;2-b

Cited by 6 publications

(8 citation statements)

References 20 publications

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“…Inventory management is an important part of enterprise organisation and management activities. A class of nonlinear inventory management systems is as follows [2]:…”

Section: Nonlinear Inventory Management Model Descriptionmentioning

confidence: 99%

“…Whenr > qs/(1 − s) 2 , at the fixed point p 0 , system (2) is stable. When r � qs/(1 − s) 2 , system (2) is at the bifurcation point.…”

Section: Equilibrium Stability Analysismentioning

confidence: 99%

“…Over the past few decades, chaos and its applications have attracted remarkable consideration in a variety of fields, including chemistry, ecology, and economy [1]. An economics management system is a typical discrete chaotic system, which has widely concerned scientists [2][3][4][5][6][7][8]. In 1993, Stiles and Levy proposed the concept of chaotic strategic management in [3].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics Analysis and Fractional-Order Approximate Entropy of Nonlinear Inventory Management Systems

Lei

2021

Mathematical Problems in Engineering

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Inventory management is complex nonlinear systems that are affected by various external factors, including course human action and policy. We study the inventory management model under special circumstances and analyse the equilibrium point of the system. The dynamics of the system is analysed by means of the eigenvalue trajectory, bifurcations, chaotic attractor, and largest Lyapunov exponent diagram. At the same time, according to the definition of fractional calculus, the fractional approximate entropy is used to analyse the system, and the results are consistent with those of the largest Lyapunov exponent diagram, which shows the effectiveness of this method.

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“…Inventory management is an important part of enterprise organisation and management activities. A class of nonlinear inventory management systems is as follows [2]:…”

Section: Nonlinear Inventory Management Model Descriptionmentioning

confidence: 99%

“…Whenr > qs/(1 − s) 2 , at the fixed point p 0 , system (2) is stable. When r � qs/(1 − s) 2 , system (2) is at the bifurcation point.…”

Section: Equilibrium Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics Analysis and Fractional-Order Approximate Entropy of Nonlinear Inventory Management Systems

Lei

2021

Mathematical Problems in Engineering

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“…The previous researches [2][3][4][5][6][7][8][9][10][11] have shown that complex nonlinear dynamics behaviours, e.g., chaos/ hyperchaos, can occur in the production-distribution system represented by the beer game model. The nonlinear factors come mainly from the nonlinear coupling of several oscillating feedback produced by the feedback structures among different decision-making entities, multiple inventory levels, time lag, etc., as well as the non-negativity [10,12,13] and piecewise-linearity [14] in ordering/dispatching decision-making. The chaos complex dynamics behaviours have been observed in multilevel series supply chain inventory systems [15][16][17], production-recycling system [18] and customer-supplier systems [19][20][21][22] more simple than the beer game model.…”

Section: Introductionmentioning

confidence: 99%

Effect of Ordering Policies on Complex Dynamics Behaviours in a Discrete-Type Manufacturing Industry Supply Chain System

Wang

2018

Chin. J. Mech. Eng.

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The beer game model is a typical paradigm used to study complex dynamics behaviours in production-distribution systems. The model, however, does not accord with current practical supply chain system models in discrete-type manufacturing industry, which are generally composed of retailers, distributors, manufacturers with internal supply chain, and suppliers. To describe how ordering policies influence the complex dynamics behaviour modes and operating cost in a general discrete-type manufacturing industry supply chain system, a high dimension piecewiselinear dynamics model is built for the supply chain system. Five kinds of ordering policy combination are considered. The distribution of both the largest Lyapunov exponent of effective inventory and average operating cost per cycle is obtained by simulation in a policy space. The simulation shows that for the general discrete-type manufacturing industry supply chain system, the upper chaotic corners emerge besides the lower chaotic corners in the policy space expressing the distribution of system behaviour mode, and that the ordering policies at each supply chain node as well as their combination have very significant effect on the topology of the distribution of both system behaviour mode and operating cost in the policy space. We find that chaos is not always corresponding to high cost, and the "chaos amplification" is not completely relevant to the "cost amplification".

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“…Brock, Dechert and Scheinkman, 1987;hereafter BDS). The evidence is mixed, and empirical assessments of nonlinear behaviour include Frank and Stengos (1988b) for macroeconomic aggregates, Scheinkman and LeBaron (1989) for stock returns, Bajo-Rubio et al (1992) for exchange rates, and Pinder (1996) for inventory management.…”

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confidence: 99%

Nonlinear Dynamics in Expectations: An Empirical Study

Resende

2000

Bulletin of Econ Res

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The paper investigates whether expectations data are consistent with nonlinear dynamics possibly involving deterministic chaos. Survey data on exchange rate expectations for four different currencies over one-week and one-month prediction horizons are considered. The evidence indicates that one cannot neglect the possibility of nonlinear dynamics underlying the erratic behaviour of expectation data, even though the evidence in that respect is not overwhelming. I. INTRODUCTIOǸChaos' has become a familiar word in economics, encompassing different patterns of nonlinear behaviour. The concept of deterministic chaos indicates, for example, the possibility of simple nonlinear difference equations or systems of differential equations which generate apparently erratic behaviour in spite of a deterministic underlying model. More precisely, Brown (1995) outlines three fundamental characteristics of chaos: (a) irregular periodicity; (b) sensitivity to initial conditions, and (c) a lack of predictability. The aforementioned characteristics can appear in different theoretical settings, for example, in the context of growth theory (e.g. Bernhabib, 1996). General surveys appear in Frank 167 Instituto de Economia, Universidade Federal do Rio de Janeiro Ã The author acknowledges Swarna Dutt and Dipak Ghosh for kindly providing the dataset used in the present paper. Comments from an anonymous referee were useful in improving the presentation of the paper. The usual caveats apply.

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Nonlinear dynamical systems and inventory management

Cited by 6 publications

References 20 publications

Dynamics Analysis and Fractional-Order Approximate Entropy of Nonlinear Inventory Management Systems

Dynamics Analysis and Fractional-Order Approximate Entropy of Nonlinear Inventory Management Systems

Effect of Ordering Policies on Complex Dynamics Behaviours in a Discrete-Type Manufacturing Industry Supply Chain System

Nonlinear Dynamics in Expectations: An Empirical Study

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