Lead Time Demand Distribution Research Articles

An inventory model: What is the influence of the shape of the lead time demand distribution?

In this paper the influence of the shape of the lead time demand distribution is studied for a specific inventory model which is described in a preceding paper by Heuts and van Lieshout [4]. This continuous review inventory model uses as lead time demand distribution a Schmeiser-Deutsch distribution (S-D distribution) [9]. In a previous paper [4] an algorithm was given to solve the decision problem.

A comparison of several approximations to the lead time demand distribution

Several distributions have been used for approximating the lead time demand distribution in inventory systems. We compare five distributions, the normal, the logistic, the lognormal, the gamma and the Weibull for obtaining the expected number of back orders, the reorder levels to have a given protection and the optimal order quantity, reorder levels in continuous review models of ( Q, r) type. The normal and the logistic distributions are inadequate to represent the situations where the coefficient of variation (the ratio of the standard deviation to the mean) of the lead time demand distribution is large. The lognormal, the gamma and the Weibull distributions are versatile and adequate; however the lognormal seems to be a viable candidate because of its computational simplicity.

The truncated normal–gamma mixture as a distribution for lead time demand

AbstractA central problem in inventory control concerns the statistical description of total demand during the lead time between placement and receipt of an order. Since both the demand per unit time and the lead time are random variables, the distribution of lead time demand is formulated as a mixture. In application, one or both components of the mixture are often assumed to be normally distributed despite their nonnegativity. In practice, this assumption is taken to imply that a normal curve, truncated at zero, is a valid description. Several approximations to the true tail area probabilities (given truncation) are examined. In turn, this leads to an improved and simpler expression for the normal–gamma mixture. Some numerical results are also presented.

An Analysis of Air Force EOQ Data with an Application to Reorder Point Calculation

One of the important uses of an EOQ item's distribution of lead time demand is to set its reorder point. This paper shows that a realistic model of observed demand patterns can be chosen from the compound Poisson family of distributions. Actual historical data from several U.S. Air Force bases are analyzed using the geometric-Poisson and constant-Poisson distributions. The control discipline is order quantity, reorder point with continuous review. The service level is based on percent of demand supplied during lead time and is consistent with current USAF methodology. The reorder point is based on independent calculations and no attempt is made to jointly optimize the order quantity and reorder point. Lead time is assumed to be known and constant.

The logarithmic poisson gamma distribution: A model for leadtime demand

AbstractThis paper considers an inventory system in which demand occurrences arise according to a stationary Poisson process, demand sizes at each occurrence follow a logarithmic distribution, and leadtimes are random variables with the gamma distribution. Both the exact and approximate distribution for leadtime demand are derived and computations are performed which compare the approximation to the exact distribution. The results have application to both repairable and consumable item inventory systems.

The Sensitivity of Inventory Decisions to the Shape of Lead Time-Demand Distribution

Abstract This paper studies the effects of the shape of the lead-time-demand (ltd) distribution on some basic inventory decisions. We found that the shape of the ltd distribution significantly affects the reorder point, stock-out risk, and expected lost sales of an inventory item. In the continuous-review(Q, R) model, the shape of the ltd distribution significantly affects the shortage cost component of the cost function; however, in most inventory systems, the shortage cost component accounts for a very small proportion of the system's total cost. Therefore the shape of the ltd distribution has little effect on the optimum (Q, R) solutions. We then discuss the implications of these findings.

Determining the Reorder Point, Protection Level and Lead Time Demand of an Inventory Item

It is obvious that an inventory item's lead time demand is affected by the length of the lead time as well as the actual demand on each day during the lead time. In a situation where the lead time and the daily demand are both stochastic, the probability distribution of an item's lead time demand is then determined by the probability distributions of the item's daily demand and lead time. This article presents a computationally simple method for determining the lead time demand's probability distribution from estimations of the item's daily demand and lead time probability distributions; no restriction is placed on the distribution forms of the daily demand, the lead time and the lead time demand. After obtaining the lead time demand distribution, this article illustrates the computation of “reorder points” and “protection levels” for an inventory item.

Stock Control with Two Suppliers and Normal Lead Times

This paper helps practitioners to compute the mean and variance of the lead time demand distribution when two suppliers are used simultaneously to replenish stock of a single item. The lead times of each supplier are assumed to be normally distributed and two replenishment orders are placed, one with each supplier, at the same time. The results indicate that the reorder level required to give a specific probability of no stock-out during replenishment is lower when using two suppliers simultaneously. Tables have also been prepared to help practitioners determine the minimum sizes of replenishment orders when two suppliers are used and replenishment orders are placed at the same time.

Using MRP and EOQ/Safety Stock for Raw Materials Inventory Control: Discussion and Case Study

The MRP and EOQ safety stock model approaches are reviewed relative to raw materials inventory control. Useful methods for developing order quantities, lead time demand distributions, and other parameters are presented. Ways to use and combine these approaches are considered. In conclusion, a case study in chemical process operation is presented.

The Numerical Generation of Lead Time Demand Distributions for Inventory Models

This paper presents a general method for computing a lead time demand distribution from the basic distributions of order quantity, orders per unit time, and lead time. These distributions are specified numerically and can therefore be derived directly from historical data.

Sensitivity of the (Q, R) inventory model to penalty cost parameter

AbstractThis paper treats an approximate continuous review inventory model with backlogging of excess demand and stochastic leadtime. The major result derived is that the behavior of the optimal order size with respect to the shortage cost parameter is determined solely by the “conditional mean residual life” function corresponding to the leadtime demand distribution. Some minor results and illustrative examples are also included.

ON LEAD TIME DEMAND DISTRIBUTIONS

ABSTRACTA key factor in establishing inventory policy for an item is the procurement lead time demand distribution (LTDD). Demand during lead time is a random variable if at least one of the components‐length of lead time, order intensity, and order size‐is a random variable. This paper discusses the problem of estimating the functional form of the LTDD for various combinations of the component random variables, using the method of generating functions. Since a normal approximation will often be used in practice, expressions are also given for the mean and variance of the LTDD for the various cases.