The question of optimal inventory

The optimal size of inventories

Inventory management is tasked with determining the optimal level of stocks. For instance, delivery interruptions to customers can be avoided by having the appropriate inventories of a good on hand. Without such inventories, a company can lose business. On the other hand, the inventory levels should not be too high because they can tie up capital and create a financial burden for the company. The median stock level, safety stocks and order volume play a decisive role in inventory management.

Components of warehouse inventories

Components of inventories

An important component of the inventory is order quantity, with which storage supplies are replenished. The greater the order quantity or the lower the order placement, the larger the average stock level held in storage on the basis of order quantity. This is described as median inventory.
In determining the optimal order quantity, a typical conflict of interests in logistics has to be solved. This is because the amount of capital tie-up and storage costs depends on the size of the order. Set against these order variables, there are fixed order and fixed batch costs, which arise only once with each receipt of stock. These are the order costs that decrease proportionately as the order quantity rises. The classical order quantity formula for minimizing the sum of the two opposing costs is as follows:

Order volume formula

The total average inventory of a warehouse must be distinguished from the median inventory as it also comprises an additional minimum inventory level. If one could accurately foresee the demand for replenishment, the median inventory would also suffice to satisfy demand. The order quantity triggered at the order point would then arrive at the warehouse just at the end of the reorder period when the old inventory is depleted.
But the forecast demand curve (inventory depletion) frequently does not match the actual demand curve. In the same way, the actual delivery of the goods can take place before or after the planned delivery (incoming stock). Therefore, a safety stock has to be maintained. The median inventory level is therefore derived from stock replenishment when planned and actual demand match planned and actual reorder periods. The safety stock, in turn, results from uncertainties associated with the demand pattern and replenishment, which lead to warehouse retrieval and replenishment periods being missed.
To determine how much capital is tied up in the inventories, the stock levels during movement should also be considered along with the median stock. These are also called movement inventories, pipeline inventories or in-process inventories. They arise during the transport and transshipment of goods. Should transport and handling of an article from the factory to the distribution warehouse take two weeks and should 100 units of this article be sold from the distribution warehouse per week, the value of movement inventories would average 200 units [1, 2].

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