INVESTMENT IN SETUP COST,LEAD TIME,AND DEMAND PREDICTABILITY IMPROVEMENT IN THE EOQ MODEL

We study an economic order quantity/reorder point (EOQ/ROP) model with stochastic demand and backorders where options of investing in reducing setup cost, lead time, and variance of demand forecast errors are available. The model is quite comprehensive relative to previous models since it simultaneously addresses the strategic decisions associated with these three investment opportunities as well as the tactical decisions of determining both the lot size and the safety stock. We develop a simple search procedure to obtain the optimal values of setup cost, lead time, variance of demand forecast errors, order quantity, and safety stock multiplier. Computational studies are performed to determine the sensitivity of the optimal solution of the model to changes in the model's parameters.     

Optimal Bandwidth Selection in Heteroskedasticity–Autocorrelation Robust Testing

This paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lag M=bT for some constant b∈(0, 1] and sample size T. It is shown that the nonstandard fixed‐b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small‐b limit distribution. We further show that, for typical economic time series, the optimal bandwidth that minimizes a weighted average of type I and type II errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long‐run variance estimator. A plug‐in procedure for implementing this optimal bandwidth is suggested and simulations (not reported here) confirm that the new plug‐in procedure works well in finite samples.     

A Data‐Driven Inventory Control Policy for Cash Logistics Operations: An Exploratory Case Study Application at a Financial Institution

A number of market changes are impacting the way financial institutions are managing their automated teller machines (ATMs). We propose a new class of adaptive data‐driven policies for a stochastic inventory control problem faced by a large financial institution that manages cash at several ATMs. Senior management were concerned that their current cash supply system to manage ATMs was inefficient and outdated, and suspected that using improved cash management could reduce overall system cost. Our task was to provide a robust procedure to tackle the ATM's cash deployment strategies. Current industry practice uses a periodic review system with infrequent parameter updates for cash management based on the assumption that demand is normally distributed during the review period. This assumption did not hold during our investigation, warranting a new and robust analysis. Moreover, we discovered that forecast errors are often not normally distributed and that these error distributions change dramatically over time. Our approach finds the optimal time series forecaster and the best‐fitting weekly forecast error distribution. The guaranteed optimal target cash inventory level and time between orders could only be obtained through an optimization module that was embedded in a simulation routine that we built for the institution. We employed an exploratory case study methodology to collect cash withdrawal data at 21 ATMs owned and operated by the financial institution. Our new approach shows a 4.6% overall cost reduction. This reflects an annual cost savings of over $250,000 for the 2,500 ATM units that are operated by the bank.     

THE APPLICATION OF A DYNAMIC FORECASTING MODEL WITH INVENTORY CONTROL PROPERTIES

This article summarizes the application of a forecasting model. Forecasts are made of monthly sales of products which do not change in style on an annual basis. The model is an exponential smoothing model. Adjustments of the parameters of the model are made whenever the average forecast error over the previous four periods is too large to be explained solely by unassignable causes. The efficiency gained in using the model is measured by the ratio of the standard deviation of the forecast errors to the standard deviation of sales. If this ratio is less than one, then the safety stock level that is carried for a given product can be reduced if sales are forecasted with the model and the standard deviation of the forecast errors is used to determine the safety stock level. The net effect is the reduction in the cost of carrying safety stocks. The results of the proposed model are also compared to a similar set of results generated from a basic, exponential model.     

Effect of forecast errors on rolling horizon master production schedule cost performance for various replanning intervals

Master production schedules are usually updated by the use of a rolling schedule. Previous studies on rolling schedules seem to form the consensus that frequent replanning of a master production schedule (MPS) can increase costs and schedule instability. Building on previous research on rolling schedules, this study addresses the impact of overestimation or underestimation of demand on the rolling horizon MPS cost performance for various replanning frequencies. The MPS model developed in this paper is based on actual data collected from a paint company. Results indicate that under both the forecast errors conditions investigated in this study, a two-replanning interval provided the best MPS cost performance for this company environment. However, results from the sensitivity analysis performed on the MPS model indicate that when the setup and inventory carrying costs are high, a 1-month replanning frequency (frequent replanning) seems more appropriate for both of the above forecast error scenarios.     

Outbreak-Based Giardia Dose–Response Model Using Bayesian Hierarchical Markov Chain Monte Carlo Analysis

Giardia is a zoonotic gastrointestinal parasite responsible for a substantial global public health burden, and quantitative microbial risk assessment (QMRA) is often used to forecast and manage this burden. QMRA requires dose–response models to extrapolate available dose–response data, but the existing model for Giardia ignores valuable dose–response information, particularly data from several well-documented waterborne outbreaks of giardiasis. The current study updates Giardia dose–response modeling by synthesizing all available data from outbreaks and experimental studies using a Bayesian random effects dose–response model. For outbreaks, mean doses (D) and the degree of spatial and temporal aggregation among cysts were estimated using exposure assessment implemented via two-dimensional Monte Carlo simulation, while potential overreporting of outbreak cases was handled using published overreporting factors and censored binomial regression. Parameter estimation was by Markov chain Monte Carlo simulation and indicated that a typical exponential dose–response parameter for Giardia is r = 1.6 × 10⁻² [3.7 × 10⁻³, 6.2 × 10⁻²] (posterior median [95% credible interval]), while a typical morbidity ratio is m = 3.8 × 10⁻¹ [2.3 × 10⁻¹, 5.5 × 10⁻¹]. Corresponding (logistic-scale) variance components were σ_r = 5.2 × 10⁻¹ [1.1 × 10⁻¹, 9.6 × 10⁻¹] and σ_m = 9.3 × 10⁻¹ [7.0 × 10⁻², 2.8 × 10⁰], indicating substantial variation in the Giardia dose–response relationship. Compared to the existing Giardia dose–response model, the current study provides more representative estimation of uncertainty in r and novel quantification of its natural variability. Several options for incorporating variability in r (and m) into QMRA predictions are discussed, including incorporation via Monte Carlo simulation as well as evaluation of the current study's model using the approximate beta-Poisson.     

Insights into neural-network forecasting of time series corresponding to ARMA(p,q) structures

Motivated by the lack of evidence supporting the conjecture that the back-propagation neural network (BPNN) is a universal approximator thus it can perform at least comparably to linear models on linear data, this study is designed to answer two primary research questions, namely, “how does the BPNN perform with respect to various underlying ARMA(p,q) structures?” and “how does the level of noise in the training time series affect the BPNN’s performance?” The goal is to understand better the modelling and forecasting ability of BPNNs on a special class of time series and suggest proper training strategies to improve performance. Using Box–Jenkins models’ performance as a benchmark, it is concluded that BPNNs generally performed well and consistently for time series corresponding to ARMA(p,q) structures. BPNNs’ ability to model and forecast is not affected by the number of parameters but by the magnitude of the coefficients of the underlying structure. Overall, BPNNs perform significantly better for most of the structures when a particular noise level is considered during network training. Therefore, a proper strategy is to train networks at a noise level consistent in magnitude with the time series’ sample standard deviation.     

Some Empirical Findings on Short-Term Forecasting: Technique Complexity and Combinations

The purpose of this research is to determine if prior findings that favor simple forecasting techniques and technique combinations hold true in a short-term forecasting environment, where demand data can be quite volatile. Twenty-two time series of daily data from a real business setting are used to test one-period ahead forecasts, the epitome of short-term forecasting. The time series vary systematically as to data volatility and forecast difficulty. Forecast accuracy is measured in terms of both mean absolute percentage error (MAPE) and mean percentage error (MPE).     

AN EVALUATION OF FORECAST ERROR IN MASTER PRODUCTION SCHEDULING FOR MATERIAL REQUIREMENTS PLANNING SYSTEMS.

Typical forecast-error measures such as mean squared error, mean absolute deviation and bias generally are accepted indicators of forecasting performance. However, the eventual cost impact of forecast errors on system performance and the degree to which cost consequences are explained by typical error measures have not been studied thoroughly. The present paper demonstrates that these typical error measures often are not good predictors of cost consequences in material requirements planning (MRP) settings. MRP systems rely directly on the master production schedule (MPS) to specify gross requirements. These MRP environments receive forecast errors indirectly when the errors create inaccuracies in the MPS. Our study results suggest that within MRP environments the predictive capabilities of forecast-error measures are contingent on the lot-sizing rule and the product components structure When forecast errors and MRP system costs are coanalyzed, bias emerges as having reasonable predictive ability. In further investigations of bias, loss functions are evaluated to explain the MRP cost consequences of forecast errors. Estimating the loss functions of forecast errors through regression analysis demonstrates the superiority of loss functions as measures over typical forecast error measures in the MPS.     

On vendor part delivery dates in a stochastic assembly system

This paper describes the development of a model for the determination of optimal mean part delivery dates in a stochastic assembly system for the objective of minimizing the expected cost of subassembly and part inventory. Parts are assembled at each station to a subassembly. The part delivery and processing times at assembly stations follow known probability distributions. An approximate solution technique based on the optimization of individual stations in isolation is developed. The approximation applies a correction factor, as a function of the variability in part delivery and processing time, cost parameters and number of stations, to the decisions from the single station solutions to compensate for interdependence between stations. Results indicate that this is an effective approach and yields good near-optimal solutions with very little computational effort. Insights regarding the effect of the type of distribution used, random processing times, variance of the distribution used and cost parameter values on part delivery dates are also reported.     

On variance amplification in a three-echelon supply chain with minimum mean square error forecasting

We analyse a three echelon supply chain model. First-order autoregressive end consumer demand is assumed. We obtain exact analytical expressions for bullwhip and net inventory variance at each echelon in the supply chain. All of the three supply chain participants employ the order-up-to policy with the minimum mean square error forecasting scheme. After demonstrating that the character of the stochastic ordering process observed at each level of the supply chain is mathematically tractable, we show that the upper stream participants have complete information of the market demand process. Then we quantify the bullwhip produced by the system, together with the amplification ratios of the variance of the net inventory levels. Our analysis reveals that the level of the supply chain has no impact upon the bullwhip effect, rather bullwhip is determined by the accumulated lead-time from the customer and the local replenishment lead-time. We also find that the conditional variance of the forecast error over the lead-time is identical to the variance of the net inventory levels and that the net inventory variance is dominated by the local replenishment lead-time.     

Uncertainty Importance Analysis Using Parametric Moment Ratio Functions

This article presents a new importance analysis framework, called parametric moment ratio function, for measuring the reduction of model output uncertainty when the distribution parameters of inputs are changed, and the emphasis is put on the mean and variance ratio functions with respect to the variances of model inputs. The proposed concepts efficiently guide the analyst to achieve a targeted reduction on the model output mean and variance by operating on the variances of model inputs. The unbiased and progressive unbiased Monte Carlo estimators are also derived for the parametric mean and variance ratio functions, respectively. Only a set of samples is needed for implementing the proposed importance analysis by the proposed estimators, thus the computational cost is free of input dimensionality. An analytical test example with highly nonlinear behavior is introduced for illustrating the engineering significance of the proposed importance analysis technique and verifying the efficiency and convergence of the derived Monte Carlo estimators. Finally, the moment ratio function is applied to a planar 10‐bar structure for achieving a targeted 50% reduction of the model output variance.     

Judgmental Forecasting: Cognitive Reflection and Decision Speed

This research analyzes how individual differences affect performance in judgmental time‐series forecasting. Decision makers with the ability to balance intuitive judgment with cognitive deliberation, as measured by the cognitive reflection test, tend to have lower forecast errors. This relationship holds when controlling for intelligence. Furthermore, forecast errors increase for very fast or very slow decisions. We provide evidence that forecast performance can be improved by manipulating decision speed.     

Replanning the Master Production Schedule for a Capacity-Constrained Job Shop

This research examines the use of both frozen and replanning intervals for planning the master production schedule (MPS) for a capacity-constrained job shop. The results show that forecast error, demand lumpiness, setup time, planned lead time, and order size have a greater impact on the mean total backlog, total inventory, and number of setups than the frozen and replanning intervals. The study also shows that a repetitive lot dispatching rule reduces the importance of lot sizing, and a combination of repetitive lot dispatching rule and single-period order size consistently produces the lowest mean total backlog and total inventory. The results also indicate that rescheduling the open orders every period produces a lower mean total backlog and total inventory when the forecast errors are large relative to the order sizes. This result suggests that the due date of an open order should be updated only when a significant portion of the order is actually needed on the new due date.     

A diagnostic analysis of the impact of forecast errors on production planning via MRP system nervousness

Abstract. The purpose of this paper is to examine the impact of forecast errors on the performance of a multi-product, multilevel production planning system via MRP system nervousness. The accuracy of forecasting methods was at one time a major concern of production scheduling and inventory control. However, with the advent of material requirements planning (MRP) systems, the significance of selecting an accurate forecasting method has diminished. Inaccurate forecast results are taken as a fact of life in production planning. Instead of attempting to develop an accurate forecasting method, efforts have been devoted towards providing an appropriate buffering method ai the master production schedule level or on the shop floor level to counteract fluctuations in demand. MRP is capable of rescheduling planned orders as well as open orders to restore the priority integrity after the disruptive changes of forecast errors occur. Nevertheless, excessive rescheduling may lead to a problem, generally referred to as system nervousness. This study investigates this problem by means of a computer simulation model. The results show that the presence of forecasi     

基于波动持续性的最优组合构建与分散化研究

构建恰当资产组合来减少风险, 是投资组合理论研究的重要目标.由于金融时间序列的波动往往会伴随着持续性特征, 该种特性会增大组合未来收益的风险.本文通过构建随机波动模型序列持续性最优投资组合模型, 以降低金融资产波动的持续性特征对组合收益波动的影响;并通过研究其分散化水平, 考察该投资组合构建方法的有效性与稳健性.研究发现:与均值方差的组合模型相比较, 序列持续性组合的风险分散化水平更好.此研究在资产组合选择方面, 具有较为重要的理论价值及实践意义.     

Quantifying costs of forecast errors: A case study of the warehouse environment

Our study evaluates the impact of forecast errors on organizational cost by simulating a labor-intensive warehouse environment using realistic cost data from a case study. Unlike past studies that measure forecast error in terms of forecast standard deviation, our study also considers the impact of forecast bias, and the complex interaction between these variables. Two cases of organizational cost curves are considered, with differing and asymmetric structures. Results find forecast bias to have a considerably greater impact on organizational cost than forecast standard deviation. Particularly damaging is a high bias in the presence of high forecast standard deviation. Although biasing the forecast in the least costly direction is shown to yield lower costs, sensitivity analysis shows that increasing bias beyond the optimum point rapidly increases costs. ‘Overshooting’ the optimal amount of bias appears to be more damaging than not biasing the forecast at all. Given that managers often deliberately bias their forecasts, this finding underscores the importance of having a good understanding of organizational cost structures before arbitrarily introducing bias. This finding also suggests that managers should exercise caution when introducing bias, particularly for forecasts that inherently have large errors. These findings have important implications for organizational decision making beyond the simulated warehouse, as high forecast errors are endemic to many labor-intensive organizations.     

Classic Dose‐Response and Time Postinoculation Models for Leptospira

Leptospirosis is a preeminent zoonotic disease concentrated in tropical areas, and prevalent in both industrialized and rural settings. Dose‐response models were generated from 22 data sets reported in 10 different studies. All of the selected studies used rodent subjects, primarily hamsters, with the predominant endpoint as mortality with the challenge strain administered intraperitoneally. Dose‐response models based on a single evaluation postinfection displayed median lethal dose (LD₅₀) estimates that ranged between 1 and 10⁷ leptospirae depending upon the strain's virulence and the period elapsed since the initial exposure inoculation. Twelve of the 22 data sets measured the number of affected subjects daily over an extended period, so dose‐response models with time‐dependent parameters were estimated. Pooling between data sets produced seven common dose‐response models and one time‐dependent model. These pooled common models had data sets with different test subject hosts, and between disparate leptospiral strains tested on identical hosts. Comparative modeling was done with parallel tests to test the effects of a single different variable of either strain or test host and quantify the difference by calculating a dose multiplication factor. Statistical pooling implies that the mechanistic processes of leptospirosis can be represented by the same dose‐response model for different experimental infection tests even though they may involve different host species, routes, and leptospiral strains, although the cause of this pathophysiological phenomenon has not yet been identified.