**Basic Inventory Models**

Basic Fixed order Quantity Model

The simplest node in this category is when all aspects of the situation are known with certainty. If the annual demand for a product is 1,000 units, it is precisely 1,000-not 1,000 plus or minus 10 percent. In addition, the setup costs and holding costs are known and constant. Although the assumption of complete certainty is rarely valid, it provides a good starting point for our coverage of inventory models. The Iced-order-quantity model attempts to determine both the specific point, R, at which an order will be placed and the size of that order,.Q. The order (or reorder) point, R, is always a specified number of units actually in inventory. The solution to a fixed-order quantity model may stipulate something like this: When the number of units of inventory ~n hand drops to 36. place an order for 57 more units.Exhibit 16.2 and the discussion about deriving the optimal order quantity are based on the following assumptions of the model:

• Demand for the product is known, constant, and uniform throughout the period.

• Lead time (L). which is the time from ordering to receipt, is constant.

• Price per unit of product is constant (no quantity discounts).

• Ordering or setup costs are constant.

• All demands for the product are known with certainty; thus. there are no back orders or stock outs,

• There is no interaction with other products

The next step is to find that order quantity, Q, for which total cost is a minimum. In Exhibit 16.3, the total cost is minimum at the point where the slope of the total cost curve is zero. Using calculus, the appropriate procedure involves taking the first derivative of total cost with respect to Q (which is the slope) and setting this equal to zero. For the basic model considered here. the calculations to obtain the economic order quantity (EOQ) would be as

follows: