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A survey of inventory holding cost assessment and safety stock allocation.


Inventory holding cost (IHC) and safety stock inventory (SSI) are critical to the effective management of inventory, and their quantification has impact at the highest levels of many manufacturing and service industries. This study demonstrates the necessity of accurately measuring and monitoring IHC. It is further demonstrated that knowledge of the underlying statistical pattern of supply and demand variations can significantly improve forecasting and impact the appropriate the levels of safety stock inventory in a variety of industries.


Controlling inventory is a fundamental purpose of supply-chain design for manufacturers. The key driver to the success of just-in-time (JIT) manufacturing is the minimization of work-in-process (WIP) inventory. This WIP inventory is minimized through an efficient matching of the manufacturing process and the rate of supply of component parts. Lean manufacturing systems are designed to minimize supply variability, both internally and externally, thereby minimizing concerns associated with inventory holding cost (IHC), and safety stock inventory (SSI) for raw materials and WIP. However, most businesses that carry inventory are unable to take advantage of the lean manufacturing concept. This concept is most applicable for firms who either mass produce make-to-stock finished goods or supply such firms. A prime example of this would be an automobile manufacturer and its first level suppliers. Most other firms are faced with the task of quantifying the costs associated with holding inventory, and deriving meaningful safety stock estimates for each particular product. For that reason, it is important for the remainder of firm types (even non-manufacturing firms) to give a diligent analysis to IHC and SSI, two very important elements of inventory management.


Inventory holding cost (IHC) is the variable cost of keeping inventory on hand, and is a combination of the costs associated with opportunity costs, storage, taxes, insurance, shrinkage, and other variables. Typically, the IHC is expressed as a percentage of the value of an item, which betrays that there may be a "fudge factor" associated with the IHC. In truth, few ultimately know its true value. Assigning a set percentage to IHC assumes that the IHC is linearly proportional to the amount of inventory held, when the rate itself very well may decay (or increase) with increasing quantities. In fact, IHC may change from one accounting period to the next. Failure to accurately determine IHC and use this cost to make decisions fails to recognize that inventory can represent one-third to one-half of a company's assets. A company with a 36% IHC will pay for the inventory twice in slightly more than two years: once to purchase it, and a second time to carry it for about 25 months. Hence, it seems problematic that nearly one half of companies do not use IHC to make their inventory management decisions. The IHC affects profitability, and may affect a company's business plan in terms of make-buy, or make-to-order/make-to-stock, as well as other top-level decisions (IOMA, Dec. 2002).


A part of the holding cost should include the actual cost of the item, and in many ways, it does. Cost of capital (opportunity cost) is the main component of holding cost that considers the item cost. In fact, the calculation of holding cost should ideally be divided between the price-dependent and quantity-dependent components, namely:

Inventory Holding Cost (Price, Quantity) = Cost(Price) + Cost(Quantity)

This quantity cost would include the allocations from overhead that affect all physical inventory to one extent or another. However, in practice, most stocking strategies do not incorporate the cost of the item; and as a result, expensive items are stocked the same way as cheap ones.

Calculating holding costs differs from industry to industry, but a general method can be illustrated from the used vehicle sales sector. In calculating holding cost, the following should be ascertained:

The average inventory for a period = [I.sub.avg];

The inventory floor plan rate, which is the cost of capital = R;

The average inventory at a particular point in time = [I.sub.cur]

The average monthly fixed overhead = OH;

The average time that an item remains in inventory before sale = T.

Once these quantities are known, then the following calculations can be made:

Daily Interest Cost Per Unit

[C.sub.Int] = ([I.sub.avg]R/365)/[I.sub.cur]

Daily Fixed Overhead Cost Per Unit

[C.sub.OH] = (OH/30)/[I.sub.cur]

Daily Holding Cost Per Unit DHC = [] [C.sub.OH]

Inventory Holding Cost Per Unit IHC = DHC x T

In this example, the hidden costs of damage, shrinkage, and opportunity cost are not included. In a survey conducted by Inventory Management Report, Harding (2005) noted the following factors in determining IHC:

* Scrap, obsolescence, shrinkage, and inventory losses;

* Facility overhead cost and storage;

* Inventory and handling personnel;

* Inventory-handling capital equipment;

* Rework and repair of inventory; and

* Other business-specific factors.

Harding further elaborates that IHC can be divided into fixed and variable components; the variable factors depending upon the dollar value of the inventory. She mentions that the fixed factors may change with volume, but will usually do so in a step-function manner. Variable cost factors include

A. Cost of money. This is the interest rate of borrowed money, or, in the absence of loans, the rate that could be earned if the money were invested

B. Inventory taxes

C. Insurance

D. Obsolescence reserve

A holding cost that is given as a percentage of the value of inventory usually comprises only variable costs. Fixed cost factors include: Storage space (in square feet); Capital equipment; and Personnel

These fixed costs fluctuate with inventory volumes, but can be expressed as a rate based on average inventory levels. Depending on the industry, fixed costs may contribute just as much to IHC as variable costs. Additional cost factors may be used, depending on the type of inventory being stored. Two that Harding mentions are secondary quality costs, and computation costs. Secondary quality costs are incurred when re-inspecting inventory which is easily damaged, or has a short shelf-life. Computation costs are incurred when there is a substantial investment in inventory tracking systems. When all of the relevant costs of inventory are properly calculated, the true value of IHC can be 50% or more of the value of the inventory. An additional component of fixed overhead would include utilities such as electricity, heat, refrigeration, etc. as appropriate to the type of inventory. It is important to realize that these and other external and internal factors for a firm may fluctuate, and can therefore change the holding costs from one period to the next. Forecasting these changes is also important to assigning a meaningful IHC.

Halskau (2003) discusses the impact of postponed payments and discounts on the inventory holding cost. Essentially, these both serve as discounts to the IHC, and accurately calculating them will usually change the value of the EOQ. An application of this would evaluate two purchasing offers, one with no interest and no payments for a certain period, and the other with a price discount. He then provides instructions and formulae that would help to determine which offer has the most favorable impact on cost.


Safety stock inventory (SSI) is excess inventory that is maintained to avoid the costs associated with uncertain supply and demand. These costs can include lost revenues from stock-outs and production delays due to depletion of necessary components.

The amount of safety stock inventory (SSI) that a firm invests in is a measure of the relative uncertainty of the product demand, component supply, or both. Where demand and supply are constant (JIT systems), SSI is minimized. Most manufacturing firms exhibit variable demand and fairly determinable supply. Agricultural and fishing type firms, on the other hand exhibit fairly predictable demand, but uncertain supply in the form of rainfall, catch amounts, etc. Safety stocks of these different industry types have manifested themselves in items on the shelf, silos of grain, fish farms, and frozen foods.

Supply and demand can be described by statistical distributions, of which there are many (normal, chi-square, Gumbel, etc.). Therefore, in order to quantify the safety stock of a product, which is a function of the distribution of its supply and demand, it is necessary to understand the statistical nature of both supply and demand separately, since they may exhibit different behaviors.

Supply planning executives at Schering-Plough HealthCare (IOMA, April 2003) use a methodology called "statistical safety stock" in order to estimate the SSI. Statistical safety stock "attempts to quantify each factor of variability and place a value based on probability and desired service levels." In calculating the SSI, Schering-Plough managers use information related to the product life cycle of finished goods, and forecasting based on tracking the stock-keeping units (SKU's). Four variables that are essential to the Schering-Plough method are:

* The variance of demand;

* The desired service level;

* The lead time for replenishment; and

* The reliability of the supplier or manufacturing process.

These last two items measure the variability of supply. Schering-Plough uses the standard formula for calculating the safety stock, namely,

Service Level Factor x (Square Root [weekly demand variance x lead time in weeks]), or

SS = z [[sigma].sub.L] = z [square root of [[sigma].sup.2.sub.t] L (3)

The Schering-Plough group uses several methods to determine demand variance. One method is to evaluate forecast variability, which is the variance between actual demand and forecasted demand. A second method is to calculate the variance of customer orders. The Schering-Plough methodology applies statistical models using products classified according to ABC analysis, which classifies products based on their relative importance and dollar value. In addition to ABC classifications, the model also classifies products based on their demand characteristics (lumpy, seasonal, mature, new, etc.). The Schering-Plough group found that for their calculation of statistical safety stock, forecast variability (variance) is usually the most important factor. Although service level was only the second most important factor, it is interesting to note that the group used another statistical model to examine different scenarios in order to evaluate the tradeoffs between the investment in inventory and customer service. Evaluating such tradeoffs is essential to establishing a meaningful service level, rather than a "rule of thumb" value. In their safety stock study, the Schering-Plough managers demonstrated that high service levels on the more costly, low-volume inventory caused an inventory investment that was disproportionately higher than the increases in customer service. This challenges the conventional wisdom that tends to overestimate service levels for expensive items. Alternatively, assigning higher service levels to low-cost, high-volume inventory does not significantly impact overall inventory levels. It seems from this analysis that the service level for an item should be assigned based on the relative demand of the item (variance), and that demand rather than cost should drive the ABC analysis. Using ABC stratification has been shown in other studies to reduce inventory levels by 33% over methods that maintain the same inventory levels for all items.

BASF Corporation (IOMA, May 2003) has developed a process that enables them to assess and respond to the ever-changing demand landscape through active management and forecasting. The system that BASF has designed consists of six stages:

1. Kickoff Meeting

2. Review "As Is"

3. Design "To Be"

4. Pilot "To Be"

5. Roll Out "To Be"

6. Handoff Project

BASF treats each improved planning management process as if it were a new product, assigning managers, budgets, and post-implementation audits to each one. This process highlights the fact that demand variance is central to the determination of safety levels and SSI.

A poll among inventory managers (IOMA, December 2002) showed that one of the key strategies used to reduce inventory investment was ABC analysis, where products were categorized based primarily on turnover rate and other measures of demand. Such categorizations resulted in significant reductions in inventory costs. A corollary practice that is suggested is "adopting a variable customer service level approach for different inventory segments." This technique involves categorizing products based on their demand, then adjusting the service level of each segment based on demand. In addition to reducing inventory investment, this practice has also significantly improved forecasting accuracy in some cases.

Talluri and Gardner (2004), analyzed the supply and demand variability in the computation of ISS. These findings are presented in Table 1.

Table 1 shows that no static amount of safety stock is appropriate across an enterprise. Each quadrant describes different combination of supply and demand, which may also imply a different combination of statistical distributions. Even though the figure shows [F.sup.-1.sub.s] as the "Inverse Normal," it could just as easily be the inverse of some other less convenient distribution. Quadrant I represents JIT manufacturing, where supply and demand in the manufacturing setting are both matched. Quadrant II might represent a fishing or farming enterprise, with stable demand, but unpredictable supply. Quadrant III represents most firms, namely exhibiting random demand and fairly reliable suppliers. It seems that these safety stock computations are fairly simple to determine, yet many firms resort to industry averages and fudge factors in establishing these critical values.


A key component to determining the amount of safety stock necessary is choosing the appropriate service-level policy, which is the probability that an out of stock condition will be observed during an inventory cycle. An inventory cycle is the period between receipt of an order and the receipt of the subsequent order. The higher the service level, the higher the SSI. It is essential that the service level be properly selected, since unnecessarily high service levels result in large excesses of inventory, thereby increasing IHC. Low service levels expose the firm to the costs that SSI is intended to prevent. Service level and SSI are related in the equation for safety stock, given below:

SS = z [[sigma].sub.i] (1)

Where z is a function of the service level under conditions of normally distributed demand, and F L is the standard deviation of the demand during lead time. Once [[sigma].sub.L] is determined, then selecting z becomes a simple task of determining how frequently (in terms of order cycles) the firm is willing to risk running out of inventory. While the determination of service level for a particular item is arbitrary, studies have shown that properly evaluating the SSI alone can lead to service level improvements (IOMA, 2003, 2004).


The standard technique used to minimize total inventory costs is the economic order quantity (EOQ), which is the lot size that minimizes the sum of holding and ordering costs. Although the ideal assumptions underlying the EOQ generally do not hold, the theoretical value itself is the most helpful estimate available for optimizing inventory levels. These assumptions include: uniform demand; no constraints on lot sizes; no other relevant costs beyond holding and ordering; and no uncertainty in lead time or supply. The EOQ is related to the total cost for inventory, and is expressed by the following equation:

EOQ = [square root of 2DS/H] (2)

Where D is the annual demand, S is the ordering cost for a single lot, and H is the annual unit holding cost. Since H is in the denominator, decreasing its value justifies increasing on-hand inventory. However, an accurate calculation of IHC will include previously omitted costs, and will tend to increase H, thereby reducing the EOQ.


If all supply and demand variability for a particular product were known, then the holding cost for inventory could be optimized. An important technique to reduce inventory costs is to reduce supply variability by including suppliers in demand planning activities. This leads to improved lead times, and can result in up to 25% lower inventory carrying costs. This is possible because the uncertainty of lead times is normally hedged by an increased safety stock, which has the associated carrying cost. In Fig. 1, eliminating the lead time variability reduces the amount of SSI by a factor of [square root of [R.sup.2][s.sup.2.sub.L]]. Sharing reliable demand information with suppliers is a hallmark of lean manufacturing systems, but there is no reason why firms across all sectors cannot use this powerful tool to achieve reductions in the "flab" of excess inventory.

The usual demand forecast for a product is made using models based on time series methodologies and previous demand data. This method, however, creates problems in cases of very low-demand, expensive items. Caterpillar Logistics Technology Services LLC has developed two techniques to deal with slow-moving inventory (IOMA, May 2004). The first technique uses the Poisson distribution to forecast the interaction with customers and the time between orders, instead of a time series of quantity demanded. According to Caterpillar, this method works extremely efficiently for slow-moving inventory. The second Caterpillar technique is used in the replenishment process, and is also based on the Poisson distribution. Caterpillar uses the historical time between orders to forecast the next order, and then delays the purchase of the replacement until close to that date. This method dramatically reduces the inventory costs for slow-moving items, while maintaining the desired service level.


Inventory holding cost (IHC) and safety stock inventory (SSI) are critical to the effective management of inventory, and their quantification has impact at the highest levels of many manufacturing and service industries. The measurement of the economic order quantity (EOQ) is impacted by the IHC. Even though the effect of the IHC upon the EOQ is smoothed by taking its square root (Equation 2), nothing smoothes out its impact when it is drastically underestimated and applied to an unnecessary excess of inventory. It is evident from the studies presented that IHC should be painstakingly measured, and routinely monitored for accuracy, especially in an economy that shows as many macroeconomic swings as have been exhibited in recent years. Safety in SSI means knowing the up-to-date variability of supply and demand, as these are the key components to formulating SSI. Since not all demand and supply distributions are alike, knowing the underlying statistical pattern of these variations have been shown to significantly improve forecasting and the levels of inventory in every kind of industry. Armed with these lessons of analysis, inventory managers should demonstrate more expertise in defining actual values for these quantities, and less reliance upon age-old, arbitrary estimates.


Halskau, Oyvind, (2003). EOQ Models for Postponed Payments of Stored Commodities. International Journal of Physical Distribution & Logistics Management, 33( 8), 686-700.

Harding, Mary Lu, (2005). What's Your Inventory Carrying Cost, and Why Don't You Know It? IOMA: Inventory Management Report January, 2.

Harris, Terry: (2004). Finding & Fixing Faulty Inventory Stocking Strategies. IOMA: Inventory Management Report, February, 2.

IOMA: Inventory Management Report (2003). Statistical Model Sets Correct Safety Stock at Schering-Plough, April,. 6.

IOMA: Financial Executives News (20020. APICS Warns Inventory Carrying Costs Far Too High at Most Cos. December, 6.

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IOMA: Inventory Management Report (2004). How to Reduce Inventory through Safety Stock & Lot-Size Optimization. October, 1.

IOMA: Supplier Selection & Management Report (2004). Why Buyers Need To Calculate The ''Real'' Cost Of Carrying Inventory. July, 1.

Krajewski, L.J., & Larry P. Ritzman, (2005). Operations Management: Processes and Value Chains. Seventh Edition, Upper Saddle River, N J: Pearson Prentice-Hall.

Noland, Tony: (2004). Hold the Holding Costs. Ward's Dealer Business October, 10.

Talluir, S., Cetin, K. & A.J. Gardner, (2004). Integrating Demand and Supply Variability into Safety Stock Evaluations. International Journal of Physical Distribution & Logistics Management, 31(1), 62-69.

J. E. Holsenback, Francis Marion University

Henry J. McGill, Francis Marion University
Table 1. Different Inventory Models and Safety
Stock Formulations

 Lead Time

Demand Constant Variable

Constant I II
 No Safety Stock [R.sub.L] = RL

 [[sigma].sub.L] = [square
 root of [R.sup.2]

 SS = [F.sup.-1.sub.s] (CSL)

Variable III IV
 [R.sub.L] = RL [R.sub.L] = RL

 [[sigma].sub.L] = [square [[sigma].sub.L] = [square
 root of [[sigma].sup.2. root of [[sigma].sup.2.
 sub.R]L] sub.R]L + [R.sup.2]

 SS = [F.sup.-1.sub.s] (CSL)


R = Average Demand per period

L = Average Lead-Time for Replenishment

[R.sub.L] = Reorder Point

SS = Safety Stock
[[sigma].sub.R] = Standard Deviation of demand per

[s.sub.L] = Standard Deviation for lead time

[F.sup.-1.sub.s] = Inverse Normal

CSL = Cycle Service Level
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Author:Holsenback, J.E.; McGill, Henry J.
Publication:Academy of Accounting and Financial Studies Journal
Geographic Code:1USA
Date:Jan 1, 2007
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