Inventory Oscillations Research Articles

Modelling oscillations in the supply chain: the case of a just-in-sequence supply process from the automotive industry

Pervasive and ubiquitous oscillations, mapping the repetitive variation in time of a specific state, are well known as abundant phenomena in research and practice. Motivated by the success of oscillators in the modelling, analysis and control of dynamical systems, we developed a related approach for the dynamic description of supply chains. This paper aims to introduce a generic oscillator model for supply chains by the original application of oscillator equations. Therefore an established oscillator model for deductive modelling of supply chain echelons is used. With the help of coupled van der Pol oscillators, the dynamical interaction of an inventory system is described and applied to a real-life supply process in automotive industry. According to its reductionist approach only two differential equations are used to analyse a Just-in-Sequence supply process in car industry. Based on the fact that any oscillatory state can be reduced to the phase of the oscillation (phase reduction), a phase space map is generated. This compact visual reference of the supply process can act as the quantitative basis for an adaptive control mechanism during its operation. By delaying or accelerating the inventory oscillations of the supplier stock a detuned coupled supply process can be re-synchronised without changing the amplitude. An additional analysis of Hilbert transform is applied to determine the boundaries of phase-locking between the inventory oscillation phases, where the instantaneous phases are bounded. Furthermore parameters of the synchronisation threshold and the transient phases between synchronous and non-synchronous regimes have been investigated, supported by an Arnold tongue representation. The investigations show that with the help of a generic oscillatory model it is possible to measure and quantify phenomena of inventory dynamics in supply chains. Especially the analysis of synchronisation phenomena with the help of phase space and Arnold tongue representations foster developments of performance measurement in supply chain management.

Exploring the oscillatory dynamics of a forbidden returns inventory system

We present an analytical investigation of the intrinsic oscillations in a nonlinear inventory system where excessive inventory cannot be returned to the supplier. Mathematically this is captured by a non-negative constraint on the replenishment order. By studying the eigenvalues of the characteristic matrices of the system, the criteria for different types of dynamic behaviour (including convergence, periodicity, quasi-periodicity, chaos, and divergence) are derived. The upper and lower bounds of the order and inventory oscillations are found via a time-domain analysis. Our results are verified by bifurcation diagrams. We find that the closer the replenishment rule feedback parameters are to the convergence area, the milder the intrinsic oscillation of the system.

Risk analysis for cooperation policies benefits in reducing the bullwhip effect in a telecom supply chain

Supply chain demand is often prone to fluctuations and instability. Known as the 'bullwhip effect', small variations in end-item demand create order and inventory oscillations that amplify from a downstream site to an upstream site. Applying a risk analysis approach, and assuming the bullwhip phenomenon as a constant reality, this paper will present the profits or losses that can accrue from various corporation policies. The latter are based on planning, information sharing and stock-adjustment strategies adopted by the supply chain actors. The system considered for this research is a four-stage supply chain. To allow risk measures and analysis, a specific discrete-event-simulation system was developed.

Managing the order pipeline to reduce supply chain volatility

The bullwhip effect in particular, and supply chain volatility in general, has been the subject of much analytical and empirical investigation by researchers. One goal of this work has been to determine supply chain designs and policies that minimize volatility. Using a system dynamics approach, we use three distinct supply chain volatility metrics to compare the ability of two alternative pipeline inventory management policies to respond to a demand shock. The results indicate that no one policy dominates on all three metrics of supply chain volatility. A simplistic static pipeline policy minimizes the bullwhip effect and lessens the likelihood of on-hand inventory oscillations, while a more sophisticated dynamic pipeline policy may converge more rapidly to the new equilibrium. In addition, simulation results suggest that the dynamic policy provides better customer service through fewer stockouts and backorders.

Bullwhip effect and inventory oscillations analysis using the beer game model

This work examines the bullwhip effect generated and suffered by each level of a four-stage beer game supply chain when different demand scenarios are considered. The paper shows that the actors who generate lower bullwhip are those who suffer more from its effects. Moreover, a new definition of an inventory oscillations measure based on bullwhip definition is introduced. Finally the paper verifies that the new measure of inventory oscillations provides more information on supply chain performance than the bullwhip measure.

RISK ANALYSIS FOR COOPERATION POLICIES BENEFITS IN REDUCING THE BULLWHIP EFFECT

supply chain demand is often prone to fluctuations and instability. Known as the “Bullwhip effect”, small variations in end item demand create order and inventory oscillations that amplify from a downstream site to an upstream site. Applying a risk analysis approach, and assuming the bullwhip phenomenon as a constant reality, this paper will present the profits or losses that can accrue from various corporation policies. The latter are based on planning, information sharing and stock-adjustment strategies adopted by the supply chain actors. The system considered for this research is a four-stage supply chain. In order to allow risk measures and analysis a specific discrete-event-simulation system, was developed.

Analysis of stock management gaming experiments and alternative ordering formulations

AbstractThis paper investigates two different yet related research questions about stock management in feedback environments. The first purpose is to analyse the effects of selected experimental factors on the performances of subjects (players) in a stock management simulation game. In light of these results, our second objective is to evaluate the adequacy of standard decision rules typically used in dynamic stock management models and to seek improvement formulations. To carry out the research, the generic stock management problem is chosen as the interactive gaming platform. In the first part, gaming experiments are designed to test the effects of three factors on decision‐making behaviour: different patterns of customer demand, minimum possible order decision (‘review’) interval and, finally, the type of receiving delay. ANOVA results of these three‐factor, two‐level experiments show which factors have significant effects on 10 different measures of behaviour (such as max–min range of orders, inventory amplitudes, periods of oscillations and backlog durations). In the second phase of research, the performances of subjects are compared against some selected ordering heuristics (formulations). First, the patterns of ordering behaviour of subjects are classified into three basic types. Comparing these three pattern types with simulation results using different decision rules, we observe that the common linear ‘anchoring and adjustment rule’ can represent the smooth and gradually damping type of behaviour, but cannot generate the non‐linear and/or discrete ordering dynamics. Thus, several alternative non‐linear rules are formulated and tested against subjects' behaviour patterns. Some standard discrete inventory control rules (such as (s, S)) common in the inventory management literature are also formulated and tested. These non‐linear and/or discrete rules, compared with the linear stock adjustment rule, are found to be more representative of the subjects' ordering behaviour in many cases, in the sense that these rules can generate non‐linear and/or discrete ordering behaviours. Another major finding is the fact that the well‐documented oscillatory dynamic behaviour of the inventory is a quite general result, not just an artifact of the linear anchor and adjust rule. When the supply line is ignored or underestimated, large inventory oscillations result also with the non‐linear rules, as well as the standard inventory management rules. Furthermore, depending on parameter values, non‐linear ordering rules are more prone to yield unstable oscillations—even if the supply line is taken into account. Further methodological and experimental research questions are suggested. Copyright © 2004 John Wiley & Sons, Ltd.

A non-linear macro model of endogenous inventory oscillations

On the basis of intertemporal profit maximization behaviour of a firm, this study constructs a disequilibrium macroeconomic model with buffer stock inventories. It is demonstrated that endogenous inventory cycles can arise in the small (i.e. in a neighbourhood of the equilibrium point) as well as in the large. This study also examines the stability properties of the local cycles by calculating the stability index. Numerical simulations illustrate relations between local cycles and global cycles.

Ergodic chaos in inventory oscillations: An example

This study reveals the dynamic structure of a nonlinear Metzlerian inventory cycle model that can generate complex dynamics. As a first step, it focuses on how the rational behavior of the supply side is responsible for the emergence of complex inventory fluctuations. To this end, the supply side is constructed on the basis of intertemporal optimization representing the short-run profit maximizing behavior of a firm. On the other hand, the demand side is constructed to be as simple as possible (i.e. the linear expenditure function). The firm is assumed to have a piecewisely flexible inventory-expected sales ratio. The resultant inventory adjustment system becomes piecewise-linear. This study demonstrates that the inventory accumulation may follow a wide range of complex dynamics including stable cycles, window phenomenon and ergodic chaos. It also shows that various types of dynamic behavior depend on the relationship between the marginal propensity to consume and marginal propensity to invest. Thus it can be concluded that the source of such a wide spectrum of complex inventory dynamics is an interaction between demand and supply.

Economic Barometers and Economic Models

STATISTICS as a scientific method goes back to the seventeenth century when William Petty and others computed mortality ratios on the basis of church records of births and deaths. This arithmetic as it was then called became a method for discovering statistical regularities in human affairs. It was used for such practical purposes as the computation of life annuity tables. It was also used by theologians, as Peter Suessmilch, to prove the wisdom of God by demonstrating the astonishing regularities in the creation. Statistics as a scientific method and academic discipline has spread in these two hundred or two hundred and fifty years of history from application to political and social affairs to all fields of human endeavor. There is today no field of inquiry or art in which statistics as a method does not find some use or some occasional misuse. Every use of statistics assumes that certain magnitudes or relationships, found to exist at the time when the counting took place, will continue to exist. Therefore, the use of statistics is based on the assumption of some continuing regularity in human affairs. But how can we assume that any magnitudes or relationships ascertained for the past have any validity for the present or the future in a world in which explosive changes appear to drown out what regularity there may be? Rapid change and political turmoil appear to make questionable any conclusions for the future drawn from measurements of the past. In this paper I will deal with this problem in the field of economic statistics and, more specifically, in the field of business cycle statistics. Here is a question of great importance for modern life. Next to problems of individual freedom and responsibility and foreign policy there is hardly a question more important than that of maintaining the continued growth and stability of the economy with a minimum of government regulation. The importance of these objectives was officially recognized in the Employment Act of I946. The determination of policies designed to promote economic growth and stability depends largely on our ability to appraise the economic outlook. The economic outlook cannot be appraised simply by looking at the most recent statistics alone. Recent statistics show, for instance, that business activity has been contracting, and that the contraction has slowed down in April or May of this year (I954). These facts themselves do not tell us whether, henceforth, economic activity is likely to expand again or to continue to move sidewise or whether the contraction has only slowed down temporarily and is likely to continue later this year or next. The question is: How can we derive from statistics of the past conclusions for the future? Inventory oscillations of a few months' periodicity move around a cyclical curve of several years' periodicity which in turn moves along a secular trend line. For an effective anti-cyclical policy we need to know where we stand in the cycle and on the trend. We look to business cycle analysis and business cycle statistics for an appraisal of probabilities in economic development this is the minimum we need to have as guidance for a policy of economic stabilization.