Safety stock

Last updated

Safety stock is a term used by logisticians to describe a level of extra stock that is maintained to mitigate risk of stockouts (shortfall in raw material or packaging) caused by uncertainties in supply and demand. Adequate safety stock levels permit business operations to proceed according to their plans. [1] Safety stock is held when uncertainty exists in demand, supply, or manufacturing yield, and serves as an insurance against stockouts.

Logistics management of the flow of resources

Logistics is generally the detailed organization and implementation of a complex operation. In a general business sense, logistics is the management of the flow of things between the point of origin and the point of consumption in order to meet requirements of customers or corporations. The resources managed in logistics may include tangible goods such as materials, equipment, and supplies, as well as food and other consumable items. The logistics of physical items usually involves the integration of information flow, materials handling, production, packaging, inventory, transportation, warehousing, and often security.


A stockout, or out-of-stock (OOS) event is an event that causes inventory to be exhausted. While out-of-stocks can occur along the entire supply chain, the most visible kind are retail out-of-stocks in the fast-moving consumer goods industry. Stockouts are the opposite of overstocks, where too much inventory is retained.


Safety stock is an additional quantity of an item held in the inventory to reduce the risk that the item will be out of stock. It acts as a buffer stock in case sales are greater than planned and/or the supplier is unable to deliver the additional units at the expected time.

With a new product, safety stock can be used as a strategic tool until the company can judge how accurate its forecast is after the first few years, especially when it is used with a material requirements planning (MRP) worksheet. The less accurate the forecast, the more safety stock is required to ensure a given level of service. With an MRP worksheet, a company can judge how much it must produce to meet its forecasted sales demand without relying on safety stock. However, a common strategy is to try to reduce the level of safety stock to help keep inventory costs low once the product demand becomes more predictable. That can be extremely important for companies with a smaller financial cushion or those trying to run on lean manufacturing, which is aimed towards eliminating waste throughout the production process.

Material requirements planning (MRP) is a production planning, scheduling, and inventory control system used to manage manufacturing processes. Most MRP systems are software-based, but it is possible to conduct MRP by hand as well.

Lean manufacturing or lean production, often simply "lean", is a systematic method for the minimization of waste within a manufacturing system without sacrificing productivity, which can cause problems. Lean also takes into account waste created through overburden and waste created through unevenness in work loads. Working from the perspective of the client who consumes a product or service, "value" is any action or process that a customer would be willing to pay for.

The amount of safety stock that an organization chooses to keep on hand can dramatically affect its business. Too much safety stock can result in high holding costs of inventory. In addition, products that are stored for too long a time can spoil, expire, or break during the warehousing process. Too little safety stock can result in lost sales and, in the thus a higher rate of customer turnover. As a result, finding the right balance between too much and too little safety stock is essential.

Reasons for keeping safety stock

Safety stocks are mainly used in a "make-to-stock" manufacturing strategy, which is employed when the lead time of manufacturing is too long to satisfy the customer demand at the right cost/quality/waiting time.

The main goal of safety stocks is to absorb the variability of customer demand. Indeed, production planning is based on a forecast, which is (by definition) different from the real demand. By absorbing these variations, safety stock improves the customer-service level.

Production planning border area between business management, engineering, industrial engineering, and computer science in particular, the economic

Production planning is the planning of production and manufacturing modules in a company or industry. It utilizes the resource allocation of activities of employees, materials and production capacity, in order to serve different customers.

Creating a safety stock will also prevent stockouts from other variations, like an upward trend in customer demand.

A market trend is a perceived tendency of financial markets to move in a particular direction over time. These trends are classified as secular for long time frames, primary for medium time frames, and secondary for short time frames. Traders attempt to identify market trends using technical analysis, a framework which characterizes market trends as predictable price tendencies within the market when price reaches support and resistance levels, varying over time.

Safety stock is used as a buffer to protect organizations from stockouts caused by inaccurate planning or poor schedule adherence by suppliers. As such, its cost (in both material and management) is often seen as a drain on financial resources that results in reduction initiatives. In addition, time-sensitive goods such as food, drink, and other perishable items could spoil and go to waste if held as safety stock for too long. [1] Various methods exist to reduce safety stock; these include better use of technology, increased collaboration with suppliers, and more accurate forecasting. [2] [3] In a lean supply environment, lead times are reduced, which can help minimize safety stock levels, thus reducing the likelihood and impact of stockouts. [4] Due to the cost of safety stock, many organizations opt for a service level-led safety stock calculation; for example, a 95% service level could result in stockouts, but is at a level that is acceptable to the company. The lower the service level, the lower the requirement for safety stock.

Service level measures the performance of a system. Certain goals are defined and the service level gives the percentage to which those goals should be achieved. Fill rate is different from service level.

An enterprise resource planning system (ERP system) can also help an organization reduce its level of safety stock. Most ERP systems provide a type of production planning module. An ERP module such as this can help a company develop highly accurate and dynamic sales forecasts and sales and operations plans. By creating more accurate and dynamic forecasts, a company reduces its chance of producing insufficient inventory for a given period, thus should be able to reduce the amount of safety stock required. [1] In addition, ERP systems use established formulas to help calculate appropriate levels of safety stock based on the previously developed production plans. While an ERP system aids an organization in estimating a reasonable amount of safety stock, the ERP module must be set up to plan requirements effectively. [5]

Enterprise resource planning refers to the corporate task of optimizing the existing resources in a company

Enterprise resource planning (ERP) is the integrated management of core business processes, often in real-time and mediated by software and technology.

Inventory policy

The size of the safety stock depends on the type of inventory policy in effect. An inventory node is supplied from a "source" which fulfills orders for the considered product after a certain replenishment lead time. In a periodic inventory policy, the inventory level is checked periodically (such as once a month) and an order is placed at that time as to meet the expected demand until the next order. In this case, the safety stock is calculated considering the demand and supply variability risks during this period plus the replenishment lead time. If the inventory policy is continuous policy (such as an order point-order quantity policy or an order point-order up to policy) the inventory level is continuously monitored and orders are placed with freedom of time. In this case, safety stock is calculated considering the risk of only the replenishment lead time. If applied correctly, continuous inventory policies can lead to smaller safety stock whilst ensuring higher service levels, in line with lean processes and more efficient overall business management. However, continuous inventory policies are much harder to implement, so most of the organisations using traditional planning processes and tools opt for periodic inventory policy.

Methods for calculating safety stocks

Reorder point method with demand and lead time uncertainty for type I service

A commonly used approach calculates [6] [7] the safety stock based on the following factors:

Assuming that demand during successive unit time periods are independent and identically distributed random variables drawn from a normal distribution, the safety stock can be calculated as: [9]


The reorder point can then be calculated as:

The first term in the ROP formula is the average demand during the lead time. The second term is the safety stock. If the lead time is deterministic, i.e. , then the ROP formula is simplified as .

Issues with this approach

No universal formula exists for safety stock, and application of the one above can cause serious damage. [12] [13] It makes several implicit assumptions:

  • The assumption that demand is a succession of independent normal random variables: First, real demand cannot be negative. If the ratio of standard deviation to mean is quite high, this will skew the distribution (compared to the normal distribution), leading to consistent overestimation of safety stock by this formula. Second, and more importantly, demand is often influenced by external random factors which persist for more than one time period, so that the successive demands are not independent. With a very large number of sources (for example, consumers of a central retail warehouse), that may not be an issue[ clarification needed ], but otherwise it is (for example, for a manufacturer that supplies these retail warehouses)
  • The use of average and standard demand assumes it is constant. For seasonal demand (for example high in summer, low in winter), the formula will consistently produce stock outs in summer and waste in winter. Similar errors apply for demand that grows or declines. That does not invalidate the formula, but it influences the parameters to be input into the formula in each time period.
  • Lead time is extremely hard to quantify in complex manufacturing and/or purchase environment, which has become the norm in global supply chains that span many independent partners. In practice, lead time is estimated by a rule of thumb that hardly improves on estimating safety stock with a rule of thumb. Even when lead time is correctly quantified, the formula assumes supply (production and purchase) is statistically constant, which is not always the case.

Type II service

Another popular approach described by Nahmias [14] uses the standardized unit loss integral L(z), given by:

Where is cumulative distribution function for the standard normal. Let β be the proportion of demands met from stock (service level), Q the order quantity and σ the standard deviation of demand, then the following relationship holds:

In this case, the safety stock is given by:

and the expected number of units out of stock during an order cycle is given by σL(z). [15]

See also

Related Research Articles

Normal distribution probability distribution

In probability theory, the normaldistribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

Pauli matrices Matrices important in quantum mechanics and the study of spin

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. Usually indicated by the Greek letter sigma, they are occasionally denoted by tau when used in connection with isospin symmetries. They are

In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open. In real analysis, measurable functions are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable.

Electrical resistivity and its converse, electrical conductivity, is a fundamental property of a material that quantifies how strongly it resists or conducts the flow of electric current. A low resistivity indicates a material that readily allows the flow of electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a 1 m × 1 m × 1 m solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

Rayleigh distribution

In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. It is essentially a chi distribution with two degrees of freedom.

In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.

In econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model. For forecasting, combining ARIMA and ARCH models could be considered. For instance, a hybrid ARIMA-ARCH model was examined for shipping freight rate forecast.

The Mundell–Fleming model, also known as the IS-LM-BoP model, is an economic model first set forth (independently) by Robert Mundell and Marcus Fleming. The model is an extension of the IS-LM model. Whereas the traditional IS-LM model deals with economy under autarky, the Mundell–Fleming model describes a small open economy. Mundell's paper suggests that the model can be applied to Zurich, Brussels and so on.

In complexity theory, the Karp–Lipton theorem states that if the Boolean satisfiability problem (SAT) can be solved by Boolean circuits with a polynomial number of logic gates, then

Capacity planning is the process of determining the production capacity needed by an organization to meet changing demands for its products. In the context of capacity planning, design capacity is the maximum amount of work that an organization is capable of completing in a given period. Effective capacity is the maximum amount of work that an organization is capable of completing in a given period due to constraints such as quality problems, delays, material handling, etc.

Bullwhip effect Effetto Forrester

The bullwhip effect is a distribution channel phenomenon in which forecasts yield supply chain inefficiencies. It refers to increasing swings in inventory in response to shifts in customer demand as one moves further up the supply chain. The concept first appeared in Jay Forrester's Industrial Dynamics (1961) and thus it is also known as the Forrester effect. The bullwhip effect was named for the way the amplitude of a whip increases down its length. The further from the originating signal, the greater the distortion of the wave pattern. In a similar manner, forecast accuracy decreases as one moves upstream along the supply chain. For example, many consumer goods have fairly consistent consumption at retail but this signal becomes more chaotic and unpredictable as the focus moves away from consumer purchasing behavior.

Supply-chain optimization is the application of processes and tools to ensure the optimal operation of a manufacturing and distribution supply chain. This includes the optimal placement of inventory within the supply chain, minimizing operating costs. This often involves the application of mathematical modelling techniques using computer software.

In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the parameters of the model. The SABR model is widely used by practitioners in the financial industry, especially in the interest rate derivative markets. It was developed by Patrick S. Hagan, Deep Kumar, Andrew Lesniewski, and Diana Woodward.

Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst % of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution.

Generalized Pareto distribution

In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location , scale , and shape . Sometimes it is specified by only scale and shape and sometimes only by its shape parameter. Some references give the shape parameter as .

Truncated normal distribution

In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above. The truncated normal distribution has wide applications in statistics and econometrics. For example, it is used to model the probabilities of the binary outcomes in the probit model and to model censored data in the Tobit model.

The reorder point (ROP) is the level of inventory which triggers an action to replenish that particular inventory stock. It is a minimum amount of an item which a firm holds in stock, such that, when stock falls to this amount, the item must be reordered. It is normally calculated as the forecast usage during the replenishment lead time plus safety stock. In the EOQ model, it was assumed that there is no time lag between ordering and procuring of materials. Therefore the reorder point for replenishing the stocks occurs at that level when the inventory level drops to zero and because instant delivery by suppliers, the stock level bounce back.

The base stock model is a statistical model in inventory theory. In this model inventory is refilled one unit at a time and demand is random. If there is only one replenishment, then the problem can be solved with the newsvendor model.


  1. 1 2 3 Monk, Ellen and Bret Wagner. Concepts in Enterprise Resource Planning. 3rd Edition. Boston: Course Technology Cengage Learning, 2009.
  2. The IOMA Handbook of Logistics and Inventory Management By Bob Donath, Institute of Management and Administration (Ioma), Institute of Management & Administration
  3. S. P. Meyn, 2007. Control Techniques for Complex Networks Archived 2008-05-13 at the Wayback Machine , Cambridge University Press, 2007.
  4. A Stitch in Time: Lean Retailing and the Transformation of Manufacturing By Frederick H. Abernathy
  5. Rooney, C., & Bangert, C. (2001, April). Developing the Right Approach to Requirements Planning Under ERP. Adhesives Age, 44(4), 49. Retrieved November 19, 2008, from Corporate ResourceNet database.
  6. Ronald H.Ballou, Business Logistics/Supply Chain Management, Fifth Edition
  7. Piasecki, Dave. "Optimizing Safety Stock". Retrieved May 23, 2011.
  8. "R Glossary". Retrieved 2013-07-03.
  9. "deci_2396.tex" (PDF). Retrieved 2013-07-03.
  11. W. J. Hopp, M. L. Spearman, Factory Physics, 3rd ed.
  12. Baudin, Michel (2012-02-12). "Safety Stock: Beware of formulas" . Retrieved 2015-06-30.
  13. Hou, Billy (2014-01-29). "Four Common Pitfalls of Safety Stock". OPS Rules. Retrieved 2015-06-30.
  14. Steven Nahmias, Production and Operation Analysis, Irwin 1989
  15. Ronald H. Ballou, Samir K. Srivastava, Business Logistics: Supply Chain Management, Pearson Education, 2007