Effective Lead Time Research Articles

Analysis of production and inventory systems when orders may cross over

This paper is concerned with the analysis of periodic-review order-up-to inventory systems with backorders in which stochastic replenishment order crossovers may be observed, i.e., where it is possible that orders arrive in a different sequence to that in which they were issued due to high stochastic lead time fluctuations. This may be the case whenever sequentially placed orders are processed on parallel replenishment systems with independent stochastic processing times, and multiple orders may be open at the same time. Following the widespread tendency in the manufacturing industry to reduce order sizes and thus increase order frequency while parts and materials are replenished from distant sources, these conditions are nowadays met in many real-world processes. Such systems typically use regular order intervals, e.g. to enable joint replenishment of various item positions. In this paper, the concept of effective lead times is elaborated as a methodological basis for analyzing periodic replenishment processes that may exhibit order crossover. It is compared with the existing concept of outstanding orders. Based on this, formulae are developed to give an exact analysis of three essential performance indicators of a periodic-review order-up-to inventory system with independent stochastic lead times.

Quasi-Biweekly Mode and Its Modulation on the Diurnal Rainfall in Taiwan Forecasted by the CFS

Abstract The occurrence of diurnal afternoon convection in Taiwan undergoes substantial modulation from tropical intraseasonal oscillations in the western North Pacific, including the quasi-biweekly (QBW) mode. By analyzing surface station observations and the Climate Forecast System (CFS) Reanalyses (CFSR), as well as the NCEP CFS version 2 (CFSv2) reforecast data over 18 summers from 1993 to 2010, it was found that the QBW mode plays a significant role in the formation of episodic diurnal convection. When the cyclonic circulation of the QBW mode is located west of Taiwan, followed by an anticyclonic circulation to the east, Taiwan's diurnal convection activity tends to intensify and persists for about 4–7 days. Synoptically, this situation reflects the enhanced subtropical anticyclone leading to fair weather conditions and increased monsoon southwesterly winds moistening the lower troposphere, all of which are conducive to thermally induced diurnal convection in Taiwan. The opposite situation tends to suppress the diurnal convection activity for a sustained period of time. Based upon this synoptic linkage, an empirical relationship between the precipitation diurnal amplitude and low-level circulation fields of the CFSv2 is derived. It was found that the CFSv2 forecast exhibits an effective lead time ranging from 16 to 24 days for the QBW mode and, subsequently, diurnal convection episodes in Taiwan.

Short-term ensemble streamflow forecasting using operationally-produced single-valued streamflow forecasts – A Hydrologic Model Output Statistics (HMOS) approach

Summary We present a statistical procedure for generating short-term ensemble streamflow forecasts from single-valued, or deterministic, streamflow forecasts produced operationally by the U.S. National Weather Service (NWS) River Forecast Centers (RFCs). The resulting ensemble streamflow forecast provides an estimate of the predictive uncertainty associated with the single-valued forecast to support risk-based decision making by the forecasters and by the users of the forecast products, such as emergency managers. Forced by single-valued quantitative precipitation and temperature forecasts (QPF, QTF), the single-valued streamflow forecasts are produced at a 6-h time step nominally out to 5 days into the future. The single-valued streamflow forecasts reflect various run-time modifications, or “manual data assimilation”, applied by the human forecasters in an attempt to reduce error from various sources in the end-to-end forecast process. The proposed procedure generates ensemble traces of streamflow from a parsimonious approximation of the conditional multivariate probability distribution of future streamflow given the single-valued streamflow forecast, QPF, and the most recent streamflow observation. For parameter estimation and evaluation, we used a multiyear archive of the single-valued river stage forecast produced operationally by the NWS Arkansas-Red River Basin River Forecast Center (ABRFC) in Tulsa, Oklahoma. As a by-product of parameter estimation, the procedure provides a categorical assessment of the effective lead time of the operational hydrologic forecasts for different QPF and forecast flow conditions. To evaluate the procedure, we carried out hindcasting experiments in dependent and cross-validation modes. The results indicate that the short-term streamflow ensemble hindcasts generated from the procedure are generally reliable within the effective lead time of the single-valued forecasts and well capture the skill of the single-valued forecasts. For smaller basins, however, the effective lead time is significantly reduced by short basin memory and reduced skill in the single-valued QPF.

JIT delivery with stochastic lead time

We examine the effect of stochastic lead times on Just-in-Time (JIT) delivery. We find that with stochastic lead times there is a possibility of order crossover, and what order crossover does is to transform the original lead times into effective lead times, which is an AR(1) process that is an autoregressive process of Order 1. The mean of this process is the same as the mean of the original lead time, but its variance could be much smaller. The implication is that when we consider order crossover in the analysis, the cost could be less than otherwise (but never less than that with deterministic lead times). The literature on JIT with stochastic lead times has never considered order crossover, which produces the effective delivery times (EDT). Here, we demonstrate some important properties of the EDT: that it is a Cauchy sequence, and hence it converges; that it is an AR(1) process; and that it stochastically dominates the parent lead time distribution.

Adaptive lead time quotation in a pull production system with lead time responsive demand

In this paper, a single-stage single-class kanban controlled manufacturing system is considered, where the problem is quoting accurate lead times for orders that are generated by an MRP system. Order release mechanism as in classical MRP is sensitive to the changes in the lead time according to the concept of lead time syndrome. The objective is to establish a cost effective lead time quoting procedure. The problem is modeled as a two-dimensional Markov chain, and it is solved explicitly by using matrix geometric techniques. Comparative analysis is done between static and dynamic lead time quoting procedures, and significant cost benefits of the dynamic procedure are shown under various scenarios. Guidelines for setting design parameters such as the number of kanbans and the frequency of updating the lead time are provided through numerical tests.

The impact of stochastic lead time reduction on inventory cost under order crossover

We use exponential lead times to demonstrate that reducing mean lead time has a secondary reduction of the variance due to order crossover. The net effect is that of reducing the inventory cost, and if the reduction in inventory cost overrides the investment in lead time reduction, then the lead time reduction strategy would be tenable. We define lead time reduction as the process of decreasing lead time at an increased cost. To date, decreasing lead times has been confined to deterministic instances. We examine the case where lead times are exponential, for when lead times are stochastic, deliveries are subject to order crossover, so that we must consider effective lead times rather than the actual lead times. The result is that the variance of these lead times is less than the variance of the original replenishment lead times. Here we present a two-stage procedure for reducing the mean and variance for exponentially distributed lead times. We assume that the lead time is made of one or several components and is the time between when the need of a replenishment order is determined to the time of receipt.

A mirror-image lead time inventory model

The production-operations literature is rife with the inventory model where the demand rate, D, is iid, but where the lead time, L, is deterministic. Here we present a mirror-image lead time model where the reverse is true; that is, where D is deterministic and L is iid. This lead time model is interesting: first, it is subject to order crossover; second, because of order crossover, the optimal order cycle and order quantity could be smaller; and third, the optimal cost incurs inventory savings due to the reduction in the variance of the lead times in crossover situations. We perform this analysis in the context of three inventory reorder point, order quantity models that differ only in the characterisation of the shortage cost. These are Model 1 that uses the shortage cost per stockout occasion; Model 2 with the shortage cost per unit short; and Model 3, where the shortage cost is per unit short per unit time. Also, we develop response surfaces (for the normal approximation) for the optimal cost, C*, the optimal order quantity, Q*, and the optimal safety stock factor, , in terms of the problem parameters (ordering cost per order, holding cost per unit per unit time, the particular shortage cost, and the standard deviation of the parent lead time). However, we find that the normal approximation is good in Model 1 and adequate for Model 3. For Model 2, the normal approximation understates the cost, because of the large penalties associated with the long right tail of the distribution of the demand during the effective lead time when the parent lead time is exponentially distributed. Nevertheless, the normal approximation could serve to provide a bound for the total cost and could be more convenient, albeit biased slightly upward in the case of Model 3 and significantly downward in the case of Model 2 than a straightforward simulation of the problem.

Earthquake early warning system in southern Italy: Methodologies and performance evaluation

We investigate the effect of extended faulting processes and heterogeneous wave propagation on the early warning system capability to predict the peak ground velocity (PGV) from moderate to large earthquakes occurring in the southern Apennines (Italy). Simulated time histories at the early warning network have been used to retrieve early estimates of source parameters and to predict the PGV, following an evolutionary, probabilistic approach. The system performance is measured through the Effective Lead‐Time (ELT), i.e., the time interval between the arrival of the first S‐wave and the time at which the probability to observe the true PGV value within one standard deviation becomes stationary, and the Probability of Prediction Error (PPE), which provides a measure of PGV prediction error. The regional maps of ELT and PPE show a significant variability around the fault up to large distances, thus indicating that the system's capability to accurately predict the observed peak ground motion strongly depends on distance and azimuth from the fault.

Multi-time scale stream flow predictions: The support vector machines approach

Effective lead-time stream flow forecast is one of the key aspects of successful water resources management in arid regions. In this research, we present new data-driven models based on Statistical Learning Theory that were used to forecast flows at two time scales: seasonal flow volumes and hourly stream flows. The models, known as Support Vector Machines, are learning systems that use a hypothesis space of linear functions in a Kernel induced higher dimensional feature space, and are trained with a learning algorithm from optimization theory. They are based on a principle that aims at minimizing the generalized model error (risk), rather than just the mean square error over a training set. Due to Mercer's condition on the kernels the corresponding optimization problems are convex and hence have no local minima. Empirical results from these models showed a promising performance in solving site-specific, real-time water resources management problems. Stream flow was forecasted using local-climatological data and requiring far less input than physical models. In addition, seasonal flow volume predictions were improved by incorporating atmospheric circulation indicators. Specifically, use of the North-Pacific Sea Surface Temperature Anomalies (SSTA) improved flow volume predictions.

On continuous review stock control with multiple suppliers and non-negative lead times with special emphasis on erlang distribution

This paper develops formulae for the moments of the effective lead time in the context of multi-sourcing when the individual lead times have non-negative support unlike the normal distribution. A formula for the distribution of effective lead time provides easy computational method for the mean and variance as well as any other moments. We provide exact formulae for the mean and variance of the effective lead time in the case of individual lead times having Erlang distribution. Computations are illustrated using a numerical example.

Multistage Inventory Management with Expediting

After reformulating Clark and Scarf's (1960) classical serial multi-echelon model so that the lead time between adjacent echelons is one week (period), the option to expedite between each resulting echelon is added. Thus, each week requires a decision to be made at each echelon on how many units to expedite in from the next upstream echelon (to be received immediately) and how many to regular order (to be received in one week), with the remainder detained (left as is). The model can be interpreted as addressing dynamic lead time management, in which the (remaining) effective lead time for each ordered unit can be dynamically reduced by expediting and/or extended. Use of Clark and Scarf's (1960) idea of echelon stocks reduces a complex, multidimensional stocking problem to the analysis of a series of one-dimensional subproblems. What are called top-down base stock policies, which are readily amenable to managerial interpretation, are shown to be optimal. Myopic policies are shown to be optimal in the stationary, in1nite horizon case. The results are illustrated numerically.

Cycle time reduction by improved MRP-based production planning

The important practical problem of planning the production of large assemblies employing an MRP-based system is considered. The objective is to produce products on-time, with minimal cycle time and low work-in-process costs. The approach is based on the determination of accurate lead-time estimates and on the introduction and use of lead-time offsets in the solution methodology. An effective Lead-time Evaluation and Scheduling Algorithm (LETSA) is employed that can perform detailed backward scheduling of operations belonging to a large assembly on a given facility with an objective of minimizing the cycle time. A scaling procedure is used to account for capacity sharing effects by multiple products in a common facility. These scaled lead-time estimates are then employed by an MRP-based system to release work-orders on the shop-floor. The effectiveness of these lead-times and lead-time offsets are evaluated by simulating production using the MRP generated order release times and verifying on-time completion of the multiple assemblies in the common facility. Numerical experiments are presented to validate the performance of the approach. Optimized batch sizes for minimal work-in-process (WIP) costs can also be obtained using LETSA. Thus, the important objectives of minimizing cycle time for on-time delivery and minimizing schedule costs can be accomplished simultaneously.

Analysis of a dual sourcing inventory model with normal unit demand and Erlang mixture lead times

We consider an inventory model where two suppliers are used concurrently to replenish one stock item. The unit demand is assumed to be normally distributed and the supplier lead times are mixtures of Erlang distributions. The lead time distributions need not be identical. This paper presents closed form expressions to evaluate the means and variances of the effective lead times, the probability of no stockout at a fixed reorder level and the potential lost sales. When the lead times are not identical, at a comparable service level, it is possible to achieve a lower average stock level by using unequal order splits. Several data sets are used in the paper to illustrate the method.

Comments on “A Climatology of Significant Winter-Type Weather Events in the Contiguous United States, 1982–94”

Branick (1997) presents results from a sophisticated national winter weather climatology study and suggests possible applications to operational forecasting. We at the National Weather Service’s Hydrometeorological Prediction Center (NWS’s HPC) appreciate the author’s efforts and agree with and support many of the author’s findings and recommendations. We also look forward to the possibility of accessing this database and applying it to the HPC’s winter weather forecast program. We concur with the author’s recommendations regarding the need for a standardized method for reporting winter weather, something meteorologists at the HPC have desired for some time. A standardized reporting system [e.g., the suggested use of local storm reports (LSRs) by all NWS offices] would be invaluable for supporting real-time and poststorm forecast verification, responding to frequent media queries, and preparing and issuing HPC’s operational storm summaries, as well as poststorm research and case studies. We also strongly agree on the importance of and the need for effective long lead time forecasts (greater than 12 h) of winter weather. In section 5, the author states, ‘‘if NCEP is to provide effective [winter weather] guidance to WFOs, it will be necessary to establish guidance products that cover lead times of 12–24 h.’’ We agree that long lead time is extremely important. This statement, however, may leave readers with the impression that no winter weather guidance currently exists. In fact, forecasts of heavy snow, which the author points out accounted for 80% of the reports in the sample and deems the ‘‘dominant hazard,’’ have been issued for a number of years by HPC for lead times beyond 12 h. The HPC, in part formerly the Weather Forecast Branch of the National Meteorological Center, issues two 12-h forecasts that indicate the potential for heavy

Evaluating Re-order Levels and Probabilities of Stockout during a Lead Time for Some Stock-Control Models

When several suppliers are concurrently used to replenish one stock item, it is often of interest to compute the mean and the variance of the effective lead time, i.e., the minimum of all lead times. However, in many cases, especially with non-identical lead time distributions, these quantities do not have closed form expressions and their calculation can be complicated. Difficulty in computation also arises in evaluating demand during lead time, even if there is only one supplier. This paper presents a numerical integration method using Gaussian quadrature to evaluate the effective lead time mean and variance, re-order level and the probability of stockout during the effective lead time. The Gaussian quadrature rules are easy to implement and several data sets are used in the paper to demonstrate the method.

DUAL SOURCING COST-OPTIMIZATION WITH UNRESTRICTED LEAD-TIME DISTRIBUTIONS AND ORDER-SPLIT PROPORTIONS

Abstract Among recent studies considering the splitting of an order among several suppliers (i.e., in “multiple sourcing”), one group considered only the favorable effect of multiple suppliers on the effective lead time demand and required safety stock, but its effects on the annual order and holding cost components have been ignored. Another group that considers the effect of using two suppliers on all relevant cost components imposes severe restrictions on the suppliers' lead-time distributions as well as the proportion of order-split between the suppliers. Our primary purpose is to present easily-solvable decision models for minimizing the sum of annual holding and ordering costs with two suppliers, subject to a maximum allowable stockout risk; restrictions on lead-time distributions and order-split proportion are completely eliminated. Solving these models gives the optimal total order quantity, reorder point and proportion of split between the two suppliers. Numerical results from our models reveal s...

Estimating Moments of the Effective Lead Time for a Stock Control Model with Independent Normal Lead Times

Estimating Moments of the Effective Lead Time for a Stock Control Model with Independent Normal Lead Times

Estimating Moments of the Effective Lead Time for a Stock Control Model with Independent Normal Lead Times

In multiple sourcing, replenishment orders for one stock item may be placed at the same time with several suppliers. In order to determine the re-order level and the size of the buffer stock, we then need to estimate the mean and variance of the effective lead time, i.e. the smallest of the lead times. Previous work on this topic has assumed that the mean and variance are either known or may be estimated from large samples, but the number of observations typically available is small. This paper presents a Bayesian approach to the problem when the lead times are independent and normally distributed, although it is shown that the method may be used in more general circumstances. The computational procedures are described and illustrated with an example.

Estimating Moments of the Effective Lead Time for a Stock Control Model with Independent Normal Lead Times

Estimating Moments of the Effective Lead Time for a Stock Control Model with Independent Normal Lead Times

Reducing Inventory Costs and Choosing Suppliers with Order Splitting

Splitting orders among several suppliers is a common business practice. Two earlier studies pointed out that, when splitting an order between two suppliers, the major benefit in inventory-related costs is in the reduction of stockouts due to the reduction of the effective lead time and the effective lead time demand. This conclusion implies that, among several suppliers, one should select the two suppliers with the lowest average lead times. In contrast, our study shows that: (i) an important benefit is in the reduction of average inventory; (ii) this benefit can only be realized when one selects a second supplier with a ‘suitably’ larger average lead time than the first supplier - a strategy that contradicts the selection rule implied by the earlier studies. Therefore, there is an economic trade off between this benefit and the more well-known benefit of lower lead time demand achieved by using suppliers with the lowest average lead times.