Interpreting supply chain dynamics: A quasi-chaos perspective

doi:10.1016/j.ejor.2013.09.025

European Journal of Operational Research

Volume 233, Issue 3, 16 March 2014, Pages 566-579

https://doi.org/10.1016/j.ejor.2013.09.025 Get rights and content

Highlights

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The application of the chaos theory needs careful assessment or the conclusion can be misleading.
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Randomness is not chaos; quasi-chaos behavior interpreted as chaos may lead to erroneous decisions.
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Stochastic demand results in more quasi-chaos phenomena than deterministic demand results in chaos.
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Opposite sets of decision-making in inventory adjustments are needed under the stochastic and the deterministic settings.
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Understanding delicate interplay to better tackle problem correctly/more effectively at the demand or the supply end.

Abstract

Chaotic phenomena, chaos amplification and other interesting nonlinear behaviors have been observed in supply chain systems. Chaos can be defined theoretically if the dynamics under study are produced only by deterministic factors. However, deterministic settings rarely present themselves in reality. In fact, real data are typically unknown. How can the chaos theory and its related methodology be applied in the real world? When the demand is stochastic, the interpretation and distribution of the Lyapunov exponents derived from the effective inventory at different supply chain levels are not similar to those under deterministic demand settings. Are the observed dynamics of the effective inventory random, chaotic, or simply quasi-chaos? In this study, we investigate a situation whereby the chaos analysis is applied to a time series as if its underlying structure, deterministic or stochastic, is unknown. The result shows clear distinction in chaos characterization between the two categories of demand process, deterministic vs. stochastic. It also highlights the complexity of the interplay between stochastic demand processes and nonlinear dynamics. Therefore, caution should be exercised in interpreting system dynamics when applying chaos analysis to a system of unknown underlying structure. By understanding this delicate interplay, decision makers have the better chance to tackle the problem correctly or more effectively at the demand end or the supply end.

Introduction

Recent waves of product recalls that have taken place in the auto industry reaffirm the criticality of good supply chain management (SCM) to the competitiveness of companies. This is true because the demand and supply bases have become so connected and at the same time very dispersed globally. Various types of uncertainties originated from demand, design, production and delivery, as well as time delays and feedback between decision making and their effect render supply chain systems rather complicated. A case in point is a faulty design, a non-conforming manufacturing process or a failure in proper usage resulting in out-of-place floor mats or defective accelerator pedals, and eventually leads to a global product recall. Due to complex and dynamic characteristics, a seemingly insignificant change or deviation in system conditions such as the above-mentioned may usher the system into a chaotic state (Hwarng & Xie, 2008). Therefore, it is valuable to study the dynamics and intricate behaviors in a complex supply chain (Thomas, Kevin, & Rungtusanatham, 2001). By adopting a system dynamics approach with a complexity perspective, the intriguing nature of such systems can be better understood.

There have been considerable interests in applying chaos theories and tools in finance, economics and management studies (Lorenz, 1993), while limited studies in SCM. A majority of the literature is based on the beer distribution model, such as Mosekilde and Larsen (1988) on two- and three-dimensional chaotic attractors, Thomsen, Mosekilde, and Sterman (1992) on hyperchaotic and higher-order hyperchaotic phenomena, Sosnovtseva and Mosekilde (1997) on chaos-chaos intermittency, Larsen, Morecroft, and Thomsen (1999) on stationary periodic, quasi-periodic as well as chaotic and hyperchaotic dynamics, Laugesen and Mosekilde (2006) and Mosekilde and Laugesen (2008) on border-collision bifurcations. These studies focus on showing the existence and categories of chaotic/hyperchaotic behaviors and various modes exhibited in a supply chain system. They highlight the role of decision making, e.g., the decisions on the adjustment of the actual inventory and the supply line, in the cause of system chaos. To further understand the chaotic dynamics, Hwarng and Xie (2008) conducted a comprehensive study of a complex supply chain system modeling after the well-known beer distribution model (Sterman, 1989), under some known deterministic settings with deterministic demand processes such as a step function or a broad-pulse function. The simulation results indicate that supply chain factors (Cachon and Fisher, 2000, Chen et al., 2000, Lee et al., 1997a, Lee et al., 1997b, Sterman, 1989) such as decisions on adjustment of discrepancy between inventory and supply line, demand pattern, ordering policy, information sharing, lead time, and supply chain level, have direct impact on the chaotic behavior of inventory dynamics.

However, pure deterministic settings rarely exist in reality. In fact, the underlying structures of real-world data are typically unknown. Facing the situation with unknown demand processes, how should we interpret the result when applying the chaos theory to analyze historical data of which the underlying structure is unknown? Motivated by the theoretical limitation and practical utility, we investigate the impact of stochastic nature in demand on the system dynamics from a chaos perspective. A simulation model based upon the beer distribution model is developed to investigate system dynamics across all levels of the supply chain. Using the Lyapunov exponent (LE), we characterize the system dynamics in terms of inventory across all supply chain levels. The main idea is to ascertain the interplay of randomness and chaos and offer some insights into the practical utilities of the chaos analysis in complex supply chain systems.

The structure of the paper is organized as follows: Section 2 describes the model under study; Section 3 presents concisely the methods and tools that we will adopt in our analysis; Section 4 explains the simulation and experiment settings as well as results and analysis; Section 5 discusses a few key findings; Section 6 closes with conclusions.

Section snippets

The supply chain system

Various forms of the beer distribution model (for example, Chen & Samroengraja, 2009) have been studied since the beer distribution game was first developed at MIT in the 1960s. Researches have mainly focused on the supply chain system dynamics and its complexity. Analytical studies tend to focus on the inventory level or order quantity decisions. Though based on random demand processes (Cachon, 1999, Chen et al., 2000, Kim et al., 2006), they are not related to chaos dynamics. One typical

Chaos

Chaos is a phenomenon of disorderly-looking long-term evolution occurring in a deterministic nonlinear system (Williams, 1997) whereby its behavior is sensitively dependent on initial conditions, topological transition and density of periodic points (Devaney, 1989). More specifically, a system of chaos can be characterized by a number of distinct features including (1) non-randomness and nonlinearity; (2) apparent disorder: the motion of the variables looks disorganized and irregular; (3)

Simulation and results

To efficiently investigate the effects of demand type, demand process, and supply chain level on the chaos characteristics of the system dynamics, experimental settings are constructed according to the 24 scenarios coded in Table 4. As mentioned in Section 2.3, there are 1325 parameter combinations for each scenario. In other words, we will need to calculate the LEs for each of the time series generated from the 1325 parameter settings. The computation is to be repeated for all 24 scenarios.

Discussion

Noteworthy, the amplification is more pronounced under the stochastic demand type. The above results together with Fig. 10, Fig. 11 reaffirm the fact that stochastic demand processes do confound the system by inducing a higher level of quasi-chaos dynamics as characterized by the Lyapunov exponent.

It is also interesting to note the spread of the values of $R_{adj}^{2}$ . To some extent, $R_{adj}^{2}$ may serve as an indicator of the predictability of a model. Regions 3, 6, 7, and 8 have $R_{adj}^{2}$ close to or

Conclusion

Applications of chaos theories in supply chain management have been sparse in the literature. The premise for such studies is that the dynamics under study are subject to the influence of deterministic factors endogenously. Chaos, by definition, can only be characterized for dynamics that are free from random shocks. However, a supply chain system that is only subject to deterministic factors is rare in the real world. Nevertheless, in practice, chaos theories like other theories can be applied

Acknowledgments

The authors are grateful to the two referees for their valuable comments and suggestions.

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Production, Manufacturing and LogisticsInterpreting supply chain dynamics: A quasi-chaos perspective

Highlights

Abstract

Introduction

Section snippets

The supply chain system

Chaos

Simulation and results

Discussion

Conclusion

Acknowledgments

Physica D: Nonlinear Phenomena

Physica D: Nonlinear Phenomena

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

Computers & Operations Research

Physica D: Nonlinear Phenomena

Physica D: Nonlinear Phenomena

Physica D: Nonlinear Phenomena

The fast Fourier transform and its applications

Managing supply chain demand variability with scheduled ordering policies

Management Science

Supply chain inventory management and the value of shared information

Management Science

Quantifying the bullwhip effect in a single supply chain: The impact of forecasting, lead times, and information

Management Science

The stationary beer game

Production and Operations Management

An introduction to chaotic dynamical systems

Chaos and nonlinear dynamics: an introduction for scientists and engineers

Determining embedding dimension for phase-space reconstruction using a geometrical construction

Physical Review A

Simulation modeling & analysis

Production, Manufacturing and Logistics
Interpreting supply chain dynamics: A quasi-chaos perspective