# Finding the Optimal Inventory Level

Determining the right amount of inventory to hold falls under the topic of Inventory Forecasting, Demand Forecasting, and Economic Order Quantity. Whether you work for a manufacturer, a distributor or a retailer at some point you are going to have to determine the optimal amount of inventory you want to order. You have to start by defining the level of service you are willing to accept and then try to minimize your inventory costs.

If you are new to these topics I suggest reading our intro article titled “What is Inventory Management?” to get your feet wet.

Let’s start by defining a few terms:

• Forecasting: Attempting to guess the amount of inventory that will be demanded by the customer sometime in the future.
• Mean: Average amount of inventory demanded in a given period of time (Year, Quarter, Week, etc.)
• Uncertainty: A statistical measurement of the range of inventory that might be demanded

At this point in inventory management we begin to use statistics. Statistics is an important part of inventory management and is crucial for making the right inventory level decisions. If you hate math, I suggest checking out some of the inventory management software options that we have reviewed over on our review page here that can basically do all of these calculations for you behind the scenes.

Single Period Inventory Forecasting

Let’s assume that we are company that purchases our products (orders inventory) at the beginning of a time period and is attempting to guess how much inventory will be needed. This is called single period inventory forecasting. We also have to assume that at the end of this pre-defined period of time we will either have to scrap the inventory left over, sell it at a discount, or return it to the manufacturer for a rebate.

An common example of this type of forecasting occurs for fashion retailers who purchase inventory at the beginning of a season (summer, winter, spring, fall) and then discount the items at the end of each season.

It turns out that this is a very common problem in inventory management, and is typically solved by what is called the newsvendor problem or the newsboy problem. You can read the entire newsvendor model article on wikipedia, however I will give you the basic rundown here.

To make the best guess possible in this single period scenario we will need to know several values ahead of time. In addition to the Mean and Uncertainty defined above we will need the following values:

•  Cost of Overstocking: The per item cost of not selling an item by the end of the period. Usually written as the cost paid for the item minus the salvage cost of the good at the end of the period (discounts, rebates, etc.)
• Cost of Understocking: This can be thought of as missed opportunity. The profit the company could have earned if they could have sold one more unit. For example, if there is a stockout and the customer is unable to purchase the item, what would have been the profit on that item.

To find the mean and the uncertainty, you will have to use basic statistics and look at the sales (demand) of previous time periods. You can easily calculate these values using an excel sheet to compare the average quantity demanded over previous periods and then ask excel to tell you the standard deviation of those averages. If you do not know how to use excel to calculate these values using your own inventory numbers, I suggest looking into one of the many inventory management software tools that can do it for you.

However, using the four values of Cost of OverstockingCost of UnderstockingMean and Uncertainty (which is also called standard error; calculated by taking the standard deviation divided by the square root of the number of measurements in your data) we can determine the best guess for the optimal amount of inventory to forecast.

•  Inventory Forecasting Calculator (Excel Tool)

Multiple Period Inventory Forecasting

After single period inventory forecasting things get a lot more complicated. To do each of these topics justice, we have divided them into several digestible articles. To delve more into these topics check out the Advanced Inventory Management article that covers the following topics:

• Multiple Period Inventory Forecasting
• Economic Order Quantity
• Base Stock Inventory Model
• Period Review Inventory Model

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