Given the significance of the benefits and costs associated with holding inventories, it is important that the firm efficiently control the level of inventory investments. A number of inventory control models are available that can help in determining the optimal inventory level of each item. These models range from the relatively simple to the extremely complex. Their degree of complexity depends primarily on the assumptions made about the demand or use for the particular item and the lead time required to secure additional stock. A related question involves the extent of control and the type of inventory model that should be applied to different inventory items. A technique called ABC inventory classification can be helpful in this regard.
The ABC inventory classification method divides a company’s inventory items into three groups. Group A consists of those items with a relatively large dollar value but a relatively small percentage of the total items, whereas group C contains those items with a small dollar value but a large percentage of the total items. Group B contains the items which are in between groups A and C. A typical result of an ABC analysis is that group A contains roughly 1 to 10 percent of the total number of items carried in inventory, but these items may represent as high as 80 to 90 percent of the total dollar value of the inventory. On the other hand, group C may contain about 50 percent of the total number of items, but these items may constitute less than 10 percent of the inventory’s total dollar value.
Group B contains the remaining items. Even though the actual cutoff between the groups is somewhat arbitrary, the ABC method provides management with information that can be used to determine how closely different inventory items should be controlled. As an example, consider the Toro Company, which manufactures lawn mowers. It purchases gasoline motors from another company for use in these mowers. Because of their cost, the motors might be classified as group A items. As a result, Toro management might determine the inventory costs associated with the motors and use a detailed model to calculate the economic order quantity. On the other hand, Toro might classify all nuts and bolts it uses as a group C item. As a result, the company’s policy on nuts and bolts might consist of little more than simply keeping an ample supply on hand.
In the “classic” inventory models, which include both the simpler deterministic models and the more complex probabilistic models, it is assumed that demand is either uniform or dispersed and independent over time. In other words, demand is assumed either to be constant or to fluctuate over time due to random elements. These types of demand situations are common in retailing and some service operations. The simpler deterministic inventory control models, such as the economic order quantity (EOQ) model, assume that both demand and lead times are constant and known with certainty. Thus, deterministic models eliminate the need to consider stockouts. The more complex probabilistic inventory control models assume that demand, lead time, or both are random variables with known probability distributions.
Basic EOQ Model
In its simplest form, the EOQ model assumes that the annual demand or usage for a particular item is known with certainty. It also assumes that this demand is stationary or uniform throughout the year. In other words, seasonal fluctuations in the rate of demand are ruled out. Finally, the model assumes that orders to replenish the inventory of an item are filled instantaneously. Given a known demand and a zero lead time for replenishing inventories, there is no need for a company to maintain additional inventories, or safety stocks, to protect itself against stockouts. The assumptions of the EOQ model yield the saw -toothed inventory pattern shown in.
The vertical lines at the 0, T1, T2, and T3 points in time represent the instantaneous replenishment of the item by the amount of the order quantity, Q, and the negatively sloped lines between the replenishment points represent the use of the item. Because the inventory level varies between 0 and the order quantity, average inventory is equal to onehalf of the order quantity, or Q/2. This model assumes that the costs of placing and receiving an order are the same for each order and independent of the number of units ordered. It also assumes that the annual cost of carrying one unit of the item in inventory is constant, regardless of the inventory level. Total annual inventory costs, then, are the sum of ordering costs and carrying costs.The primary objective of the EOQ model is to find the order quantity, Q, that minimizes total annual inventory costs.
Certainty Case of the Inventory Cycle
Algebraic Solution In developing the algebraic form of the EOQ model, the following variables are defined:
Ordering costs are equal to the number of orders per year multiplied by the cost per order, S. The number of orders per year is equal to annual demand, D, divided by the order quantity, Q. Carrying costs are equal to average inventory, Q/2,multiplied by the annual carrying cost per unit, C.
The total annual cost equation is as follows:Total costs = Ordering costs + Carrying costs
By substituting the variables just defined into, the following expression is obtained:Total costs = (Number of orders per year* cost of order) + (Average inventory*
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