Setting Safety Stock Research Articles

Improved strategy for service level-based safety stock determination

Abstract An alternative strategy is proposed for setting safety stocks to achieve a fixed service level. The approach involves scheduling order releases earlier in the inventory cycle instead of carrying a fixed safety stock based directly on a stockout probability. It is shown that, when combined with a fixed reorder quantity, the alternative strategy results in lower expected carrying costs for a stationary probability distribution of lead time demand.

Determining Safety Stock in the Presence of Stochastic Lead Time and Demand

We consider the problem of setting safety stock when both the demand in a period and the lead time are random variables. There are two cases to consider. In the first case the parameters of the demand and lead time distributions are known; in the second case they are unknown and must be estimated. For the case of known parameters a standard procedure is presented in the literature. In this paper, examples are used to show that this procedure can yield results that are far from the desired result. A correct procedure is presented. When the parameters are unknown, it is assumed that a simple exponential smoothing model is used to generate estimates of demand in each period and that a discrete distribution of the lead time can be developed from historical data. A correct procedure for setting safety stocks that is based on these two inputs is given for two popular demand models. The approach is easily generalized to other models of demand. Safety stock calculation is simplified when certain normality assumptions are valid. Simulation results in the Appendix indicate when these assumptions about normality are reasonable.

A table for the calculation of safety stock

AbstractSafety stock is often calculated to accommodate a given service level (SL), where service is defined in some manner by the user. In this regard, the two favorite definitions of service are the percent of good cycles and the fraction of demand satisfied by off‐the‐shelf inventory.Judging from its increased appearance in the literature, especially in textbooks, the latter definition apparently is gaining in popularity. Unfortunately, this definition requires a little more effort to use. A procedure originally worked out by Brown (Brown's Method) shows how the calculations are to proceed. The partial expectation, E(z), is first calculated as a function of the expected lead time demand (μ), the standard deviation (σ) of lead time demand, and the required service level. Once E(z) is found, a table is consulted (Brown's Table) to determine z. Finally, the safety stock is calculated from the formula, zσ.There are several problems with using Brown's Table. First, z is given as the dependent variable rather than the independent variable, so the user has to search a bit to find the nearest pair of entries that straddle the required value of E(z). Then the user must perform an awkward interpolation, something many business students find very confusing.An additional problem with the table is that it is both sparse and inaccurate for high values of z. In fact, there are no entries at all for z 4.50, and there is only one significant digit of accuracy for z 3.93. Finally, Brown does not supply a computer program that calculates z directly from E(z). While this lack of a program is not important to the casual user of the tables, it can be important when one wishes to set safety stock levels automatically and internally by the computer.This article presents a new table, in which E(z) is the dependent variable rather than the independent variable. The computer program used to evaluate the entries yields solutions that are accurate to about fourteen decimal places. With this kind of precision the authors were able to extend Brown's Table to high values of z, while at the same time providing for virtually any number of significant digits. Incidentally, the entry density in this table is nonuniform (somewhat logarithmic) to accommodate usage over various orders of magnitude of z and E(z).The article also includes a simpler version of our computer program (single precision), which yields about four decimal place accuracy. The double precision program actually used is available on request, but it is somewhat complicated and depends on the computer used (the authors used a TRS‐80).

OPTIMAL SAFETY‐STOCK INVESTMENT THROUGH SUBJECTIVE EVALUATION OF STOCKOUT COSTS

ABSTRACTThis paper solves the problem of setting safety stocks by combining a subjective evaluation of the stockout‐cost function with the usual holding‐cost function. The technique given in this paper for estimating a decision maker's (DM's) disvalue function for stockouts is robust in terms of the shapes permissible for this function and allows for uncertainty on the part of the DM in expressing his/her trade‐offs. The estimation technique could be applied to situations other than the safety‐stock problem. We provide an optimization routine for the safety‐stock problem which is designed to operate in conjunction with the estimation technique. Safety‐stock levels are arrived at iteratively.

Safety Stocks in MRP—Systems with Emergency Setups for Components

Material Requirements Planning or Manufacturing Resource Planning (MRP) systems originally were designed for a deterministic environment. Often, however, demand for finished products is uncertain and some type of buffering mechanism is necessary to provide desired levels of service. When the schedule is replanned each period, as typically is done, variability of demand may manifest itself in the form of early or “emergency” production runs. Safety stock may serve to avert some or most of these emergency production runs. We have developed a heuristic algorithm which is shown to provide extremely good guidelines for setting safety stock levels.