Inventories are materials stored, waiting for processing, or experiencing processing. They are ubiquitous in modern business. Observation of almost any company balance sheet reveals that a very significant part of its assets comprise inventories of raw materials, products within the production process, or finished products.

Because of their practical and economic importance, the subject of inventory control is a major consideration in many situations. Questions must be constantly answered as to when and how much raw material should be ordered, when a production order should be released to the plant, what level of safety stock should be maintained at a retail outlet, or how in-process inventory is to be maintained in a production process. These questions are amenable to quantitative analysis through the subject of inventory theory. The Inventory Add-in add-in embodies some of the mathematical results of inventory theory. The Inventory Add-in is part of the OM/IE collection of the Jensen add-ins. It is described at the website www.ormm.net.

This game simulates some of the stochastic systems considered by the add-in and the subject of inventory theory.

Inventories

We consider here an inventory holding a single product as illustrated in the figure below.

The figure might represent a raw material inventory. The flow out of inventory is a relatively continuous activity where individual items are placed into the production system for processing. To replenish the inventory, an order is placed to a supplier. After some delay time, called the lead-time, the raw material is delivered in a lot of a specified amount. At the moment of delivery, the rate of input is infinite and at other times it is zero. Whenever the instantaneous rates of input and output to a component are not the same, the inventory level changes. When the input rate is higher, inventory grows; when output rate is higher, inventory declines.

Usually the inventory level remains positive. This corresponds to the presence of on hand inventory. In cases where demand exceeds the available inventory customers must either wait or sales may be lost. When the customer is willing to wait, we show the shortage as a negative inventory value. We call this a backorder or shortage condition. A backorder is a stored output requirement that is delivered when the inventory finally becomes positive. Backorders are possible for some systems, while they are not for others. A finished product inventory, for example, may promise later delivery if a customer arrives to find no product available. The will generally be extra costs when inventory is backordered.

Alternatively, a customer with alternative suppliers may go elsewhere if he or she finds the inventory empty. This is called a lost sale. The inventory may go to zero, but will never be negative. The demands on the inventory that occur while the inventory level is zero are called lost sales. For most businesses, lost sales are bad. There is generally a cost of goodwill suffered by the disappointed customer. The cost is at least the value of the profit foregone from a lost sale.

The Game

This workbook has two games distinguished by whether backorders are allowed or not. For the games, time progresses in one week intervals. At the end of each week you must decide how much to order. The quantity ordered will be delivered after some lead time. Click one of the links below to go to the game that you would like to play.