Inventory Control

The Economic Order Quantity (EOQ) formula is derived by setting the derivative of the total cost function to zero. It is calculated as: $EOQ = \sqrt{\frac{2DS}{H}}$ where $D$ is the annual demand, $S$ is the setup or ordering cost per order, and $H$ is the annual holding cost per unit.

The Reorder Point (ROP) determines when to place an order. It is calculated based on the demand during the lead time: $ROP = d \times L$ where $d$ is the daily demand and $L$ is the lead time in days. If demand is uncertain, safety stock is added to this value.

ABC Analysis is a classification technique based on the Pareto Principle (80/20 rule). It categorizes inventory into three groups: Class A (high annual dollar volume, roughly 15% of items but 70-80% of value), Class B (medium value), and Class C (low value, high volume).

Management focus should be highest for Class A items, requiring frequent cycle counting and tight control, while Class C items can be managed with simpler, less frequent oversight.

The Q-System is ideal for high-value items where stockouts are costly, as it provides constant visibility. However, it requires more sophisticated record-keeping and technology.

The P-System is more convenient for administrative purposes or when multiple items are ordered from the same supplier. It is often used for low-value items (Class C) where the cost of constant monitoring outweighs the benefits.

Unit Consistency: Always ensure that demand ($D$) and holding cost ($H$) are in the same time units. If demand is annual, the holding cost must also be expressed as an annual cost per unit. If $H$ is given as a percentage, multiply it by the unit cost ($C$) to get the dollar value.

Lead Time Alignment: When calculating the Reorder Point, ensure the daily demand ($d$) and lead time ($L$) use the same time units (e.g., days). If the lead time is in weeks, convert demand to a weekly rate.

Total Cost Components: Remember that the basic EOQ model focuses on minimizing variable costs (ordering and holding). The actual cost of the items themselves is only included in the total cost calculation if there are quantity discounts involved.

Sanity Check: If an answer for EOQ results in a very small number for a high-demand item, or vice versa, re-check your square root and multiplication steps. EOQ should logically balance the two cost curves.

Ignoring Safety Stock in Average Inventory: A common mistake is calculating average inventory as simply $Q/2$. While this is true for the basic EOQ model, if safety stock ($SS$) is present, the average inventory level is actually $(Q/2) + SS$.

Confusing Setup and Unit Costs: Students often mistake the cost of the item ($C$) for the ordering cost ($S$). $S$ is the administrative cost to place the order, regardless of how many units are in that order.

Assuming Constant Demand: In reality, demand is rarely perfectly constant. The EOQ model provides a baseline, but managers must adjust for seasonality and trends which the basic formula does not account for.