On the Bullwhip Avoidance Phase: supply chain collaboration and order smoothing

This paper provides an assessment of the impact of collaboration and smoothing replenishment rules on supply chain operational performance and customer service level. Three supply chain configurations (i.e. Traditional, Information Exchange and Synchronised) in which orders are generated by smoothing (S, R) inventory control policies are studied for different proportional controllers. A supply chain stress test is performed through a sudden and intense change in demand. A structured and extended supply chain assessment framework is adopted. The main conclusions of this paper are the following. (i) The impact of Supply Chain Collaboration on overall supply chain performance is greater than that of order smoothing. Order smoothing mitigates the bullwhip effect, but it may have a negative impact on customer service. Supply Chain Collaboration mitigates the bullwhip effect, provides inventory stability, limits lumpy orders and enhances customer service level. (ii) The negative effect on customer service level of order smoothing is almost eliminated in synchronised supply chains.     

Discontinuous variational time integrators for complex multibody collisions

The objective of the present work is to formulate a new class of discontinuous variational time integrators that allow the system to adopt two possibly different configurations at each sampling time t_k, representing predictor and corrector configurations of the system. The resulting sequence of configuration pairs then represents a discontinuous—or non‐classical—trajectory. Continuous or classical trajectories are recovered simply by enforcing a continuity constraint at all times. In particular, in systems subject to one‐sided contact constraints simulated via discontinuous variational time integrators, the predictor configuration is not required to satisfy the one‐sided constraints, whereas the corrector configuration is obtained by a closest‐point projection (CPP) onto the admissible set. The resulting trajectories are generally discontinuous, or non‐classical, but are expected to converge to classical or continuous solutions for decreasing time steps. We account for dissipation, including friction, by means of a discrete Lagrange–d'Alembert principle, and make extensive use of the spacetime formalism in order to ensure exact energy conservation in conservative systems, and the right rate of energy decay in dissipative systems. The structure, range and scope of the discontinuous variational time integrators, and their accuracy characteristics are illustrated by means of examples of application concerned with rigid multibody dynamics. Copyright © 2014 John Wiley & Sons, Ltd.     

Replica time integrators

This paper is concerned with the classical problem of wave propagation in discrete models of nonuniform spatial resolution. We develop a new class of Replica Time Integrators (RTIs) that permit the two‐way transmission of thermal phonons across mesh interfaces. This two‐way transmissibility is accomplished by representing the state of the coarse regions by means of replica ensembles, consisting of collections of identical copies of the coarse regions. In dimension d, RTIs afford an O(n^d) speed‐up factor in sequential mode, and O(n^{d + 1}) in parallel, over regions that are coarsened n‐fold. In this work, we restrict ourselves to the solution of the 3d continuous wave equation, for both linear and non‐linear materials. By a combination of phase‐error analysis and numerical testing, we show that RTIs are convergent and result in exact two‐way transmissibility at the Courant–Friedrichs–Lewy limit for any angle of incidence. In this limit, RTIs allow step waves and high‐frequency harmonics to cross mesh interfaces in both directions without internal reflections or appreciable loss or addition of energy. The possible connections of RTIs with discrete‐to‐continuum approaches and, in particular, with the transition between molecular dynamics and continuum thermodynamics are also pointed to by way of future outlook. Copyright © 2011 John Wiley & Sons, Ltd.     

Pitfalls of the relaxation time approximation: Hydrodynamic sound in a multicomponent Fermi liquid

When transport in a Fermi liquid is treated in the relaxation time approximation, the quasiparticle energy appearing in the local equilibrium distribution must have the form determined by the nonequilibrium distribution function. Sometimes this requirement is overlooked and the equilibrium quasiparticle energy is used. In applications to unpolarized normal³He the resulting error can be repaired by a simple rescaling of the relaxation rates 1/₁ by the Fermi liquid corrections 1+F ^l/(2l+1). The distinction between the two forms of the relaxation time approximation is thus of little consequence, and quantities independent of the relaxation time are entirely unaffected. We point out that more significant damage results from using this wrong relaxation time approximation in a multicomponent (or spin-polarized single-component) Fermi liquid. In particular, it is essential to use the correct form to derive the velocity of hydrodynamic sound, even though the incorrect form also satisfies all the conservation laws, and even though the sound velocity is independent of the relaxation time.     

Discrete (Legendre) orthogonal polynomials—a survey

The discrete (Legendre) orthogonal polynomials, (DLOP's) are useful for approximation purposes. This set of mth degree polynomials {P_m(K, N)} are orthogonal with unity weight over a uniform discrete interval and are completely determined by the normalization P_m(O, N) = 1. The authors are employing these polynomials as assumed modes in engineering applications of weighted residual methods. Since extensive material on these discrete orthogonal polynomials, and their properties, is not readily available, this paper is designed to unify and summarize the presently available information on the DLOP's and related polynomials. In so doing, many new properties have been derived. These properties, along with sketches of their derivation, are included. Also presented are a representation of the DLOP's as a product of vectors and matrices, and an efficient computational scheme for generating these polynomials.     

Stockout propagation and amplification in supply chain inventory systems

We investigate the existence and magnitude of stockout propagation and stockout amplification in the context of supply chain inventory systems. Stockout amplification is a stage-to-stage increase in overall stockout rates. Stockout propagation is the tendency for stockout at one node to instigate a stockout at a neighbouring node and is conceptually related to the idea of cascading failures in physical systems, such as electrical power grids. We study these concepts in both upstream (‘supply side’) and downstream (‘demand side’) directions in the context of normal operating conditions for an adaptive R, S (periodic, order-up-to) inventory policy. We build a simulation model of a 5-stage serial supply chain that experiences normally distributed customer demands and gamma distributed lead times. We find that stockout propagation exists, but contrary to conventional wisdom, it occurs in the upstream direction. There is little indication that stockout propagation is occurring to any significant degree in the downstream direction. We also find stockout amplification occurring in the upstream direction in scenarios where more aggressively adaptive inventory parameter updating is performed. We discuss implications of this work in the areas of supply chain inventory modelling, ordering decisions, safety stock determination, and the use of adaptive inventory policies.     

Model simplification of stable discrete‐time systems by the squared magnitude Padé approximation

Abstract

A squared magnitude Padé approximation technique is presented for the model simplification of stable discrete‐time systems. The simplification is started from the squared magnitude function M(e^jTω ) =G(e^jTω )G(e^–jTω ), where G(z) is the z‐transfer function of a given high order discrete‐time system. The method is fully computer‐oriented and leads to a satisfactory approximation while preserving stability and minimum‐phase characteristics.     

Evaluation of the Micropolar elasticity constants for honeycombs

Summary The Micropolar and Lamè constants for a circular cell polycarbonate honeycomb are calculated using a finite element representation of the honeycomb microstructure. A hexagonally packed, circular cell, honeycomb sheet with a rigid circular inclusion was numerically analyzed under uniaxial tension. Micropolar Elasticity was found to be the best continuum representation of the discrete honeycomb. This conclusion was arrived at by matching the strain field in the discrete honeycomb with that predicted by a micropolar elastic continuum representation of the honeycomb. The minimum ratio of inclusion radius a to cell diameter d, for the honeycomb to be approximated accurately as a continuum was between 16 and 20. A radius of 20d and 32d showed a near perfect approximation to a continuum.     

Optimizing the admission time of outbound trucks entering a cross-dock with uniform arrival time by considering a queuing model

Cross-docking is a supply-chain strategy that can reduce transportation and inventory costs. This study is motivated by a fruit and vegetable distribution centre in Tehran, which has cross-docks and a limited time to admit outbound trucks. In this article, outbound trucks are assumed to arrive at the cross-dock with a single outbound door with a uniform distribution (0,L). The total number of assigned trucks is constant and the loading time is fixed. A queuing model is modified for this situation and the expected waiting time of each customer is calculated. Then, a curve for the waiting time is calculated. Finally, the length of window time L is optimized to minimize the total cost, which includes the waiting time of the trucks and the admission cost of the cross-dock. Some illustrative examples of cross-docking are presented and solved using the proposed method.     

Intermittent estimation of stationary time series

Let {X _n } _n=0 ^∞ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation ofX _n+1 based on the observations,X _i , 0≤i≤n in a strongly consistent way. Bailey and Ryabko proved that this is not possible even for ergodic binary time series if one estimates at all values ofn. We propose a very simple algorithm which will make prediction infinitely often at carefully selected stopping times chosen by our rule. We show that under certain conditions our procedure is strongly (pointwise) consistent, andL ₂ consistent without any condition. An upper bound on the growth of the stopping times is also presented in this paper.     

Picklist generation algorithm with order-consolidation consideration for split-case module-based fulfilment centres

This paper serves as an initial study on order-consolidating time for a module-based order-picking system. In this system, items are stored in modules, and order picking is performed in waves that comprise more than one customer order. Picked items from multiple modules are conveyed to the packaging department for sortation based on customer orders. The order-consolidating time is the main focus as well as the performance measure in this paper. Order-consolidating time is the time difference between the arrival time of the first and the last item at the packaging department that belong to the same customer order. We proposed a heuristic control strategy, namely a pick-list generation algorithm, which will reduce the order-consolidating time. We named our proposed algorithm the push algorithm, which is an improvement algorithm. The push algorithm is compared with the basic algorithm to evaluate its performance. This comparison is extended under different environment settings to provide a robust conclusion. The experimental results indicate that the proposed algorithm consistently out-performs the basic algorithm in every tested environment with at least 17% improvement.     

A discrete‐time multiqueue‐multiserver system with time‐division multiplexed services and non‐zero walktime

Abstract

This paper presents results for an N‐queue system which receives services from M equal‐speed servers under time division multiplexed manner. When served, each customer consumes fixed service time and departs. One practical constraint imposed is the non‐zero walktime consumed by a server when it undertakes the transition of its service from one queue to another. Two types of inputs, synchronous and asynchronous, are considered in this paper.     

A space–time coupled p-version least-squares finite element formulation for unsteady fluid dynamics problems

This paper presents a p-version least-squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled. The dimensionless form of the differential equations describing the problem are first cast into a set of first-order differential equations by introducing auxiliary variables. This permits the use of C° element approximation. The element properties are derived by utilizing p-version approximation functions in both space and time and then minimizing the error functional given by the space–time integral of the sum of squares of the errors resulting from the set of first-order differential equations. This results in a true space–time coupled least-squares minimization procedure. A time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step. The space–time coupled p-version approximation functions provide the ability to control truncation error which, in turn, permits very large time steps. What literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space–time coupled approach. For non-linear problems the non-linear algebraic equations resulting from the least-squares process are solved using Newton's method with a line search. This procedure results in a symmetric Hessian matrix. Equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance. The generality, success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection–diffusion and Burgers equations. The results are compared with the analytical solutions and those reported in the literature. The formulation presented here is ideally suited for space–time adaptive procedures. The element error functional values provide a mechanism for adaptive h, p or hp refinements. The work presented in this paper provides the basis for the extension of the space–time coupled least-squares minimization concept to two- and three-dimensional unsteady fluid flow.     

Longitudinal relaxation time for dilute quantum gases

We calculate the longitudinal relaxation timeT ₁ for a polarized spin-1/2 Fermi gas, in zero magnetic field, for conditions of temperatureT and densityn such that Boltzmann statistics are valid. Our results show generally thatT ₁ is independent of polarization of the gas. At highT, where the thermal wavelength is small compared to the scattering lengtha, T ₁ is proportionalT ^1/2, while at lowT, such that is greater thana, T ₁ is proportional toT ^–1/2.T ₁ thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. Physical arguments show that the existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of the expected temperature dependence we calculateT ₁ numerically, via the distorted-wave Born approximation, for the case of a gas interacting via a hard core. We also computeT ₁ for a spin-1/2 Bose gas, which also shows a minimum.     

An algorithm for discrete Chebyshev linear approximation with linear constraints

We describe a dual linear programming algorithm for solving the discrete Chebyshev (or l_∞) approximation problem subject to any type of linear constraints. The numerical results provided here indicate that the present algorithm is an efficient extension of the Barrodale and Phillips Chebyshev algorithm, to which it reduces in the absence of constraints.     

Stability and accuracy analysis of a discrete model reference adaptive controller without and with time delay

Adaptive control techniques can be applied to dynamical systems whose parameters are unknown. We propose a technique based on control and numerical analysis approaches to the study of the stability and accuracy of adaptive control algorithms affected by time delay. In particular, we consider the adaptive minimal control synthesis (MCS) algorithm applied to linear time‐invariant plants, due to which, the whole controlled system generated from state and control equations discretized by the zero‐order‐hold (ZOH) sampling is nonlinear. Hence, we propose two linearization procedures for it: the first is via what we term as physical insight and the second is via Taylor series expansion. The physical insight scheme results in useful methods for a priori selection of the controller parameters and of the discrete‐time step. As there is an inherent sampling delay in the process, a fixed one‐step delay in the discrete‐time MCS controller is introduced. This results in a reduction of both the absolute stability regions and the controller performance. Owing to the shortcomings of ZOH sampling in coping with high‐frequency disturbances, a linearly implicit L‐stable integrator is also used within a two degree‐of‐freedom controlled system. The effectiveness of the methodology is confirmed both by simulations and by experimental tests. Copyright © 2009 John Wiley & Sons, Ltd.     

Compression and localization of an atomic cloud in a time dependent optical lattice

We analyze a method of compressing a cloud of cold atoms by dynamic control of a far off-resonance optical lattice. We show that by reducing the lattice spacing either continuously or in discrete steps while cooling the atoms with optical molasses large compression factors can be achieved. Particle motion in the time-dependent lattice is studied numerically using a three-dimensional semiclassical model. Two experimentally realistic models are analyzed. In the first we continuously vary the lattice beam angles to compress atoms initially in a Gaussian distributed cloud with standard deviation of 250 µm into a single site of a two-dimensional lattice of area A ～ 35 × 35λ², with λ the wavelength of the lattice beams. This results in an optical depth for an on-resonant probe beam >80 which is an increase by a factor of about 1800 compared to the uncompressed cloud. In the second approach we use a discrete set of lattice beam angles to decrease the spatial scale of the cloud by a factor of 500, and localize a few atoms to a single lattice site with an area A ? λ².