Rogue seasonality in supply chains: an investigation and a measurement approach

Purpose – Shukla et al (2012) proposed a signature and index to detect and measure rogue seasonality in supply chains, but which however, were not effectively validated. The authors have sought to investigate rogue seasonality using control theory and realistic multi echelon systems and rigorously validate these measures, so as to enable their application in practice. Design/methodology/approach – Frequency domain analysis of single echelon and simulated four echelon Beer game system outputs are used in the investigation, with the simulation incorporating realistic features such as non-linearities from backlogs and batching, hybrid make to order-make to stock ordering system and the shipment variable. Lead time, demand process parameters, ordering parameters and batch size are varied in the simulation to rigorously assess the validity of the index. Findings –The signature based on the cluster profiles of variables, specifically whether the variables cluster together with or away from exogenous demand, was validated. However, a threshold for the proportion of variables that could be clustered with exogenous demand and the system still being classified as exhibiting rogue seasonality, would require to be specified. The index, which is derived by quantifying the cluster profile relationships, was found to be a valid and robust indicator of the intensity of rogue seasonality, and which did not need any adjustments of the kind discussed for the signature. The greater effectiveness of the frequency domain in comparison to time for deriving the signature and index was demonstrated. Practical implications – This work enables speedy assessment of rogue seasonality in supply chains which in turn ensures appropriate and timely action to minimize its adverse consequences. Originality/value – Detailed and specific investigation on rogue seasonality using control theory and Beer game simulation and rigorous validation of the signature and index using these methods

Sensing endogenous seasonality in the case of a coffee supply chain

Rogue seasonality, or endogenously generated cyclicality (in variables), is common in supply chains and known to adversely affect performance. This paper explores a technique for sensing rogue seasonality at a supply chain echelon level. A signature and index based on cluster profiles of variables, which are meant to sense echelon-level generation and intensity of rogue seasonality, respectively, are proposed. Their validity is then established on echelons of a downstream coffee supply chain for five stock keeping units (SKUs) with contrasting rogue seasonality generation behaviour. The appropriateness of spectra as the domain for representing variables, data for which is daily sampled, is highlighted. Time-batching cycles which could corrupt the sensing are observed in variables, and the need to therefore filter them out in advance is also highlighted. The knowledge gained about the echelon location, intensity and time of generation of rogue seasonality could enable timely deployment of specific mitigation actions

Detecting disturbances in supply chains: the case of capacity constraints

Purpose – The ability to detect disturbances quickly as they arise in a supply chain helps to manage them efficiently and effectively. This paper is aimed at demonstrating the feasibility of automatically, and therefore quickly detecting a specific disturbance, which is constrained capacity at a supply chain echelon. Design/Methodology/approach – Different supply chain echelons of a simulated four echelon supply chain were individually capacity constrained to assess their impacts on the profiles of system variables, and to develop a signature that related the profiles to the echelon location of the capacity constraint. A review of disturbance detection techniques across various domains formed the basis for considering the signature based technique. Findings – The signature for detecting a capacity constrained echelon was found to be based on cluster profiles of shipping and net inventory variables for that echelon as well as other echelons in a supply chain, where the variables are represented as spectra. Originality/value– Detection of disturbances in a supply chain including that of constrained capacity at an echelon has seen limited research where this study makes a contribution

Rogue seasonality detection in supply chains

Rogue seasonality or unintended cyclic variability in order and other supply chain variables is an endogenous disturbance generated by a company’s internal processes such as inventory and production control systems. The ability to automatically detect, diagnose and discriminate rogue seasonality from exogenous disturbances is of prime importance to decision makers. This paper compares the effectiveness of alternative time series techniques based on Fourier and discrete wavelet transforms, autocorrelation and cross correlation functions and autoregressive model in detecting rogue seasonality. Rogue seasonalities of various intensities were generated using different simulation designs and demand patterns to evaluate each of these techniques. An index for rogue seasonality, based on the clustering profile of the supply chain variables was defined and used in the evaluation. The Fourier transform technique was found to be the most effective for rogue seasonality detection, which was also subsequently validated using data from a steel supply network

Weak Disorder in Fibonacci Sequences

We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1-epsilon, but follow a different recursion rule with a small probability epsilon. We focus on the weak disorder limit and obtain the Lyapunov exponent, that characterizes the typical growth of the sequence elements, using perturbation theory. The limiting distribution for the ratio of consecutive sequence elements is obtained as well. A number of variations to the basic Fibonacci recursion including shift, doubling, and copying are considered.Comment: 4 pages, 2 figure

Kinetics of Heterogeneous Single-Species Annihilation

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A-->0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d>2, and in a phenomenological Smoluchowski theory which is applicable in d<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.Comment: TeX, 18 page

Power-law velocity distributions in granular gases

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.Comment: 11 pages, 9 figure

Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments: (i) non-magnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(v) ~ exp(-|v|). This behavior is consistent with kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.Comment: 4 pages, 3 figure

Data mining: a tool for detecting cyclical disturbances in supply networks.

Disturbances in supply chains may be either exogenous or endogenous. The ability automatically to detect, diagnose, and distinguish between the causes of disturbances is of prime importance to decision makers in order to avoid uncertainty. The spectral principal component analysis (SPCA) technique has been utilized to distinguish between real and rogue disturbances in a steel supply network. The data set used was collected from four different business units in the network and consists of 43 variables; each is described by 72 data points. The present paper will utilize the same data set to test an alternative approach to SPCA in detecting the disturbances. The new approach employs statistical data pre-processing, clustering, and classification learning techniques to analyse the supply network data. In particular, the incremental k-means clustering and the RULES-6 classification rule-learning algorithms, developed by the present authors’ team, have been applied to identify important patterns in the data set. Results show that the proposed approach has the capability automatically to detect and characterize network-wide cyclical disturbances and generate hypotheses about their root cause

Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\geq 2$.Comment: 15 pages, 3 figures; v2: addition of two new reference