Avi Giloni

Information Sharing in a Supply Chain Under ARMA Demand

In this paper we study how the time-series structure of the demand process affects the value of information sharing in a supply chain. We consider a two-stage supply chain model in which a retailer serves autoregressive moving-average (ARMA) demand and a manufacturer fills the retailers orders. We characterize three types of situations based on the parameters of the demand process: (i) the manufacturer benefits from inferring demand information from the retailers orders; (ii) the manufacturer cannot infer demand, but benefits from sharing demand information; and (iii) the manufacturer is better off neither inferring nor sharing, but instead uses only the most recent orders in its production planning. Using the example of ARMA(1,1) demand, we find that sharing or inferring retail demand leads to a 16.0% average reduction in the manufacturers safety-stock requirement in cases (i) and (ii), but leads to an increase in the manufacturers safety-stock requirement in (iii). Our results apply not only to two-stage but also to multistage supply chains.

Robust weighted LAD regression

The least squares linear regression estimator is well-known to be highly sensitive to unusual observations in the data, and as a result many more robust estimators have been proposed as alternatives. One of the earliest proposals was least-sum of absolute deviations (LAD) regression, where the regression coefficients are estimated through minimization of the sum of the absolute values of the residuals. LAD regression has been largely ignored as a robust alternative to least squares, since it can be strongly affected by a single observation (that is, it has a breakdown point of 1/n, where n is the sample size). In this paper we show that judicious choice of weights can result in a weighted LAD estimator with much higher breakdown point. We discuss the properties of the weighted LAD estimator, and show via simulation that its performance is competitive with that of high breakdown regression estimators, particularly in the presence of outliers located at leverage points. We also apply the estimator to several data sets. ets.

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

This article considers the problem of determining the value of information sharing in a multi-stage supply chain in which the retailer faces AutoRegressive Moving Average (ARMA) demand, all players use a myopic order-up-to policy, and information sharing can only occur between adjacent players in the chain. It is shown that an upstream supply chain player can determine whether information sharing is of any value directly from the parameters of the model for the adjacent downstream players order. This can be done by examining the location of the roots of the moving average polynomial of the model for the downstream players order. If at least one of these roots is inside the unit circle or if the polynomial is applied to a lagged set of the downstream players shocks, there is value of information sharing for the upstream player. It is also shown that under credible assumptions, neither player k−1s order nor player ks demand is necessarily an ARMA process with respect to the relevant shocks. It is shown that demand activity propagates in general to a process that is called quasi-ARMA, or QUARMA, in which the most recent shock(s) may be absent. It is shown that the typical player faces QUARMA demand and places orders that are also QUARMA. Thus, the demand propagation model is QUARMA in–QUARMA out. The presented analysis hence reverses and sharpens several previous results in the literature involving information sharing and also opens up many questions for future research.

Robust Analysis of Variance: Process Design and Quality Improvement

We discuss the use of robust Analysis Of Variance (ANOVA) techniques as applied to quality engineering. ANOVA is the cornerstone for uncovering the effects of design factors on performance. Our goal is to utilise methodologies that yield similar results to standard methods when the underlying assumptions are satisfied, but are also relatively unaffected by outliers (observations that are inconsistent with the general pattern in the data). We do this by utilising statistical software to implement robust ANOVA methods, which are no more difficult to perform than ordinary ANOVA. We study several examples to illustrate how using standard techniques can lead to misleading inferences about the process being examined, which are avoided when using a robust analysis. We further demonstrate that assessments of the importance of factors for quality design can be seriously compromised when utilising standard methods as opposed to robust methods.

The Conditional Breakdown Properties of Least Absolute Value Local Polynomial Estimators

Nonparametric regression techniques provide an effective way of identifying and examining structure in regression data. The standard approaches to nonparametric regression, such as local polynomial and smoothing spline estimators, are sensitive to unusual observations, and alternatives designed to be resistant to such observations have been proposed as a solution. Unfortunately, there has been little examination of the resistance properties of these proposed estimators. In this article, we examine the breakdown properties of local polynomial estimation based on least absolute values, rather than least squares. We show that the breakdown at any evaluation point depends on the observed distribution of observations and the kernel weight function used, and make recommendations regarding choice of kernel based on two different breakdown measures. The results suggest that the breakdown point at an evaluation point provides a useful summary of the resistance of the regression estimator to unusual observations.

Optimal Configurations of General Job Shops

In this paper we study the problem of minimizing the expected number of jobs in a single class general open queueing network model of a job shop. This problem was originally posed by Buzacott and Shanthikumar [2] and solved by them for a special case. We extend their work in this paper. We derive feasibility conditions that simplify the analysis of the problem. We show that the optimal configuration can be completely characterized when both the utilizations of the machine centers are high and there are a large number of servers at each machine center. We also derive conditions under which the optimization problem reduces to solving a concave or a convex program and provide conditions under which the uniform flow line and the symmetric job shop (or variants of these) are optimal configurations for the job shop.