# Operations Research: WHAT IS AN AVERAGE INVENTORY?

WHAT IS AN AVERAGE INVENTORY?

Before conceptualizing a simple inventory model, let us try to understand what is an average inventory?

The following assumptions about the acquisition of a single piece of inventory must be made in order to build the economic lot size inventory model.

• First, demand for the item is steady and known in advance to the decision maker.
• Second, the lead time, or the time it takes to acquire an item, is known. This is the time it takes between placing an order and receiving it into inventory.

Although the above said two assumptions are rarely true in the real world for inventory problems, they do allow us to build a simple model into which more realistic, complex aspects can be included.

The mean value of an inventory during a certain time period is called average inventory, and it differs from the median value of the same data set. A formula that estimates the worth or number of a certain commodity or collection of goods over two or more defined time periods is known as average inventory.

Let q be order size under the preceding assumptions, it can be shown in the following figure that the number of units in inventory is equal to q when each new order is practically received into inventory and that the inventory is gradually decreased until it becomes zero just at the point when the next order is received. Also, it is observed that the average inventory (q/2) is equal to one-half the number of units in the lot size.

As shown in the figure below the average inventory is effected by the order quantity and the number of orders per year (function of time). Moreover, each new order is received into inventory at exactly the time at which the previous order is decreased, resulting in no stock outs.

Question: PepperFry, a furniture selling company,  buys 2700 TV cabinets per order. What is the average inventory level, the company has to maintain?

Answer: Here q = 2700 units per order.

Average Inventory Level = q / 2 = 2700 / 2 = 1350 units