3 Inventory Analysis

Learn how inventory supports operations, how its costs and service goals shape stocking decisions, and how to estimate reorder points and safety stock.

Why organizations hold inventory

Inventory analysis balances product availability against the cost and risk of holding stock. The objective is not to minimize inventory at all costs, but to keep the right items available where and when they are needed. Inventory can help keep production flowing and meet customer demand, while tying up capital and creating risks of aging or obsolescence.

Different inventory roles can overlap. For example, goods in transit are , while additional goods held beyond expected demand during transit can serve as .

Inventory costs and trade-offs

Inventory decisions involve four cost categories:

: The amount paid for goods, including relevant discounts.
: The administrative and operational cost of placing or preparing an order. Ordering more frequently usually increases this cost.
: The cost of keeping stock, including space, handling, insurance, damage, spoilage, obsolescence, and the opportunity cost of capital. Larger average stocks usually increase this cost.
: The consequences of not having stock when needed. These may include lost sales, backorders, production delays, expediting, and reduced customer confidence.

Reducing one cost can raise another. Larger orders may reduce the number of orders placed but increase average inventory. More can reduce shortages but raises . A sound policy weighs these trade-offs instead of treating low inventory as an end in itself.

Choose a meaningful service target

A service target needs to specify what “service” measures. is the proportion or probability of replenishment cycles with no stockout. A target of $95\%$ CSL means roughly $95$ out of $100$ cycles avoid any stockout; it does not mean that $95\%$ of units are filled.

is the share of total demand supplied immediately from available inventory. The measures are not interchangeable: a cycle can experience a stockout while still satisfying most of its demand. Higher service targets generally require more , so the target should reflect the consequences of shortages as well as inventory cost.

Set a reorder point

A is the inventory-position threshold that triggers replenishment. accounts for replenishment already in transit and is commonly calculated as:

\text{Inventory position} = \text{on-hand stock} + \text{on-order stock} - \text{backorders}

In a simple setting with steady demand and a fixed lead time, the reorder point is average demand during lead time plus :

\text{ROP} = \text{average demand during lead time} + \text{safety stock}

If average demand is $d$ units per day and lead time is $L$ days, expected demand during lead time is $dL$ . With no uncertainty, this expected demand is the reorder point. With uncertainty, is added to reduce the chance of running out before the order arrives.

Estimate under uncertainty

When demand during lead time is approximately normally distributed, a common CSL-based calculation uses the mean and standard deviation of that demand:

\text{Safety stock} = z\sigma_{LT}

\text{ROP} = \mu_{LT} + z\sigma_{LT}

Here, $\mu_{LT}$ is mean demand during lead time, $\sigma_{LT}$ is its standard deviation, and $z$ corresponds to the chosen CSL. For example, a one-sided $95\%$ target uses approximately $z=1.645$ . This is an approximation that assumes the distribution is reasonably represented by a normal curve.

If daily demand is independent from day to day, lead time is independent of demand, and lead time is measured in days, an approximate variance for demand during a random lead time is:

\sigma_{LT}^{2}=\mu_{L}\sigma_{d}^{2}+\mu_{d}^{2}\sigma_{L}^{2}

Here, $\mu_d$ and $\sigma_d$ are the mean and standard deviation of daily demand, while $\mu_L$ and $\sigma_L$ are the mean and standard deviation of lead time. The first term captures demand variation; the second captures lead-time variation. If lead time is fixed, the second term is zero.

These formulas rely on the stated assumptions. Correlated demand and lead time, seasonal patterns, or intermittent demand may require a different model.

Work through a reorder-point example

A shop sells an average of $20$ units per day, with a daily demand standard deviation of $6$ units. Supplier lead time averages $5$ days, with a standard deviation of $1$ day. Assuming independence:

Mean demand during lead time is $20\times5=100$ units.
Standard deviation during lead time is $\sqrt{5(6^2)+20^2(1^2)}\approx24.1$ units.
For a $95\%$ CSL, is approximately $1.645\times24.1\approx40$ units.
The reorder point is $100+40=140$ units.

The shop would reorder when its reaches about $140$ units. This is a planning estimate, not a guarantee: the actual outcome depends on whether demand and lead time behave as assumed.

Review inventory in practice

For each item and stocking location, review demand history and forecasts, actual supplier lead times, stockout records, on-hand and on-order balances, and the chosen service measure. Estimate demand during lead time rather than using average demand in an arbitrary period. Compare actual shortages and excess stock with the target, then update assumptions when demand patterns or supplier performance change.

A useful first analysis is to rank items by , calculated as annual demand multiplied by unit cost, and focus tighter review on items with the greatest financial impact. Also watch for slow-moving or aging stock, which can signal excess inventory or obsolescence.

Connect the decisions

Inventory supports production, customer availability, and protection from uncertainty, but it incurs purchasing, ordering, carrying, and shortage costs. A reorder point covers expected demand during replenishment lead time plus . depends on variability and the chosen service target; when demand or lead time is uncertain, estimate the distribution of lead-time demand and revisit assumptions as conditions change. Distinguish cycle service level from when setting and evaluating service goals.