Economic Ordering Quantities: A Practical Cost Reduction Strategy for Inventory
Management
By Todd Duell
Abstract
Inventory management is an important concern for all managers in all types of businesses. For companies that operate on relatively low profit margins, poor inventory management can seriously undermine the business. But, that’s not to say that companies with large profit margins can’t benefit from a practical cost reduction strategy for inventory management. The challenge isn’t to reduce inventories to the bone, to reduce costs, or to have plenty of stock available to satisfy all demands, but to achieve the right balance to meet your competitive priorities. There are several pressures for low and high inventories that have to be balanced to achieve the “optimal” inventory management strategy. Pressures for low inventories include, but are not limited to: holding costs, interest or opportunity costs, storage and handling costs, taxes, insurance, and shrinkage costs. Pressures for high inventories include, but are not limited to: customer service (backorders and stockouts), ordering costs, setup costs, labor and equipment utilization, transportation costs, and quantity discounts. One model above all, Economic Ordering Quantity (EOQ), provides the most practical cost reduction strategy for inventory management.
Pressures for Low Inventories
(1) Holding Cost: is the variable cost of keeping items on hand, including interest, storage and handling, taxes, insurance, and shrinkage. Companies usually state an item’s holding cost per period of time as a percentage of its value.
(2) Interest or Opportunity Cost: is the difference between the cost to obtain a loan and the opportunity of an investment promising an attractive return. This variable is typically the largest component of the holding costs.
(3) Storage and Handling Cost: is the opportunity cost associated with storage space that can be used more productively in some other way. Since inventory takes up space, companies usually express their storage costs in terms of cost per square foot. Costs may include lease or loan payments, maintenance, and utilities.
(4) Taxes, Insurance, and Shrinkage: more taxes are paid if end-of-year inventories are high and insurance on assets increase when there is more to insure. Shrinkage takes the form of theft, obsolescence, or deterioration through
expiration or damage. When the rate of deterioration is high, building large inventories may be unwise.
Pressures for High Inventories
(1) Customer Service: can speed delivery and improve on time deliveries. Having inventory available reduces the potential for stockouts and backorders. A stockout occurs when an item that is typically stocked is not available to satisfy the demand when it occurs. A backorder is a customer demand that cannot be filled when promised. Occasionally customers will wait, but in today’s fast paced internet enabled community, you will most likely loose the sale to your competitor. However, an even bigger problem will occur if this problem persists, the company will loose their reputation and good will.
(2) Ordering Cost: the cost to place each order (purchase requisition). For every item, the cost is exactly the same regardless of the size of the order. Utilizing e-commerce can help to streamline the order process and reduce the costs of placing orders by reducing the number of errors, amount of paperwork, and staffing requirements.
(3) Setup Cost: the cost involved in changing over equipment to produce a different product. It includes the labor and time to make the change, cleaning, and new tools. Setup cost is also independent of order size, so there is a pressure to order a large supply of the component and hold it in inventory.
(4) Labor and Equipment Utilization: by creating more inventory, management can increase the work-force productivity and facility utilization in three ways. (1) Placing larger, less frequent production orders reduces the setup costs. (2) Holding excess inventory reduces the chance of costly rescheduling of production orders because components were not available. (3) Building inventories improves resource stabilization when demand is cyclical or seasonal. The company uses the excess inventory produced during the slack periods to handle the extra demand during the peak periods to minimize the need for extra shifts, extra equipment, temporary workers, and overtime.
(5) Transportation Cost: can be reduced by having more inventory on hand. This minimizes the number of shipments that need to be expedited by more expensive modes of transportation. Combining orders or ordering larger lot sizes can also reduce the costs by providing quantity discounts and decreasing the shipping costs. In almost all situations, economies of scale can be used to negotiate large discounts that provide incentives for ordering larger quantities.
Economic Ordering Quantity Assumptions
Using the EOQ model provides the most practical cost reduction strategy for inventory management by minimizing the total amount of annual inventory Holding costs and Ordering costs. This approach to determining the EOQ is based of the following five assumptions:
(1) The demand rate for the item is constant (i.e. 100Kg/year) and known with relative certainty.
(2) There are no constraints on the size of the lot (i.e. material handling limitations).
(3) The only two relevant costs are the inventory holding cost and the fixed cost per lot for ordering or setup. (4) Decisions for one item can be made independently for
other items (i.e. there is no advantage for combining several different orders going to the same manufacturer).
(5) There is no uncertainty in the lead time or supply. The lead time is known with relative certainty. The amount received is exactly what was ordered and it arrives all at once rather than piecemeal.
At first glance, you might think that this is a really nice theory, but it doesn’t reflect the reality of your situation. In fact, different lot sizing approaches may need to be evaluated to reflect quantity discounts, uneven demand rates, expiration dates, or interaction between items. However, as the remainder of this white paper will show, EOQ is often the most reasonable first approximation of average lot sizes, even when one or more of the assumptions don’t quite apply.
EOQ Theory
When the EOQ assumptions are satisfied inventory
inventory, which happens when an order is received. During the cycle, the inventory is used at a constant rate. Since demand is known with relative certainty and the lead time is constant, a new lot of material can be ordered so that the inventory falls to 0 when a new lot is received.
The annual Holding cost for this amount of inventory, which increases linearly with Q, as Figure 2a shows, is calculated as:
Annual Holding Cost = (Average cycle inventory)(Unit holding cost)
The annual Ordering cost is calculated as:
Annual Ordering Cost or Setup Cost = (Number of orders/year)(Ordering or setup cost)
The average number of orders per year equals the annual demand divided by Q. For example, if 1000 units must be ordered each year and the average lot size is 200 units, 5 orders (1000/200 = 5) will be placed during the year. The annual ordering or setup cost decreases non linearly as Q increases, as shown in Figure 2b because fewer orders are placed. The total annual cost is the sum of the two cost components as shown in Figure 2c:
Total Cost = Annual Holding cost + Annual Ordering or Setup cost
or
Equation 1:
Where: Q = Lot Size, in units
H = Cost of holding one unit in inventory for one year (holding cost)
D = Annual demand in units per year
S = Cost of ordering or setting up one lot, in dollars per lot
Figure 2c also reveals that when the holding cost exceeds the ordering cost, we can immediately conclude that the quantity ordered is too large. Thus, a smaller quantity should be ordered to balance the holding cost and ordering cost. Conversely, if the ordering cost exceeds the holding cost, we can conclude that the quantity ordered is not large enough. Thus, a larger quantity should be ordered to balance the holding cost and ordering cost.
EOQ Reality
Applying calculus to the total cost formula (Equation 1), we can derive a more practical formula for EOQ that simultaneously minimizes the holding costs and ordering costs as shown in Figure 2c (Best EOQ).
Equation 2:
Where: D = Annual demand in units per year
S = Cost of ordering or setting up one lot, in dollars per lot
H = Cost of holding on unit in inventory for one year (holding cost)
Understanding the Effects of Changes
Since the EOQ model works best when the five assumptions are met, it’s important to understand what will happen if changes are made to critical parameters. Let’s
consider the effects of making changes to each of the parameters.
(1) Changes to the Demand Rate (D): Because D is in the numerator, the EOQ increases in proportion to the square root of the annual demand. Therefore, when demand rises, the lot size should also rise, but more slowly than the actual demand.
(2) Changes to the Setup Cost (S): Because S is in the numerator, increasing S increases the EOQ. Conversely, reducing S reduces the EOQ. This relationship explains why it is important to cut ordering costs and setup costs. When weeks of supply decline, inventory turns increase. When ordering costs and setup costs become trivial, a major impediment to small lot production is removed.
(3) Changes to the Holding Cost (H): Because H is in the denominator, the EOQ declines when the holding costs increase. Conversely, when the holding costs decrease, the EOQ increases. Thus, larger lot sizes are justified by lower holding costs.
(4) Errors in Estimating D, H, and S: Total cost is fairly insensitive to errors even when estimates are off by a large margin. The reason are that errors tend to cancel each other out and the square root reduces the effect of the error. Let’s look at an example of how this relationship works:
Example 1:
D = 936 units/year S = $45/order H = $15/year
Now that we know the EOQ, we can calculate the total cost from Equation 1:
Example 2: Let’s say we overestimate the holding costs from Example 1 by 2H, which is a 100% error:
Now that we know the new EOQ, we can calculate the total cost from Equation 1:
So although we introduced a 100% error into our holding cost estimate, the actual increase in total cost (from $1124 to $1590) is only 29%. This allows managers to deviate somewhat from the EOQ to accommodate supplier contracts or storage
(5) Errors in Estimating EOQ with Expiration Dates: EOQ assumes that you are consuming and producing “widgets” without expiration dates. This becomes a problem when the entire EOQ quantity of material will not be consumed before the material expires. Thus, leading to costly unused raw materials and in some cases extra handling and disposal costs. To compensate for expiration dates, we need to determine if the entire EOQ quantity of material will be consumed before the expiration date of the material. If the entire quantity will not be used, the EOQ needs to divided by the ratio of the number of days in the EOQ period divided by the number of days in the expiration date of the material (Equation 3).
Equation 3: EOQexp = EOQ ÷ [(Demand Period ÷ EOQ
Number of Orders) ÷ (Expiration Date)] Where: EOQ Number of Orders = Demand Amount ÷ EOQ Example 3: Given the following information, do we need to reduce the EOQ to compensate for the expiration date of the material?
EOQ = 13Kg
Demand Period = 30 Days EOQ Number of Orders = 0.1
Expiration Date of the Material = 180 Days
Start by determining the EOQ Period — how many days it will take to use up the entire raw material if the EOQ quantity is purchased.
30 Days ÷ 0.1 EOQ Number of Orders = 300 Days This is more than the number of days for the expiration date of the material. Thus, we need to adjust the EOQ based on the expiration date of the material using Equation 3.
EOQexp = 13 ÷ [(30 ÷ 0.1) ÷ (180)] = 7.8 Kg Thus, by taking into consideration the expiration date of the material when calculating the EOQ, we have just saved the company the cost of purchasing 5.2 Kg (13 Kg — 7.8 Kg = 5.2 Kg) of the raw material that won’t be consumed as well as the additional disposal cost.
Safety Stock and Reorder Point
The EOQ answers the important question: How much do we order? Another important question that needs to be answered is: When should we place the order? A reorder point (ROP) system is used to track the remaining inventory of an item each time a withdrawal is made to determine whether it is time to reorder. However, the problem facing all systems is that demand and lead times aren’t always predictable. Thus, safety stock levels also need to be determined to prevent stock-outs. Managers must weigh the benefits of holding safety stock against the cost of stock-outs. This is usually a function of how critical the material is to the manufacturing process and the lead time to order, receive, test, inspect, and release materials. To weight the risk of a stock out, you can use the Normal
probability function to assign the desired probability of not running out of stock. For example, if you were to select a z value of 1.645 (90% from the Normal probability table), you are assuming that the risk of running out of stock during the lead time is 10% (100% — 90% = 10%). Higher values of z provide more safety stock. Lower values of z provide less safety stock.
To translate this policy into a specific safety stock level, we must know how the demand during the lead time is distributed. If demand varies little around the average, safety stock can be small. Conversely, if demand during the lead time varies greatly around the average, the safety stock must be large. Variability is measured with mean and variance. It is usually acceptable to assume that the demand during the lead time is normally distributed. Thus, safety stock is calculated by multiplying the risk (z) by the number of standard deviations from the mean (s ) by the square root of the lead time ( L).
Equation 4:
Where: z = Risk represented by the Normal probability s = Standard deviation of the demand
L = Lead time in days
Once you have determined the safety stock, the actual reorder point (ROP) can be calculated as the average demand (D) multiplied by the lead time (L) plus the safety stock.
ROP = DL + Safety Stock Equation 5:
L = Lead time in days
Example 4: If the demand for a buffer is 20 liters per week with a standard deviation of 5 liters and a lead time of 2 days for manufacturing, what is the safety stock and reorder point amount with a 90% risk level?
D = 20 liters per week = 20/7 = 2.8 liters per day s = 5 liters per day
L = 2 days z = 1.645 (90%)
Use Equation 4 to find the safety stock amount:
Safety Stock = 1.645 x 5 x 2 = 11.6 Liters Now that we know the safety stock amount, we can use Equation 5 to find the reorder point:
ROP = 2.8 x 2 + 11.6 = 17.2 Liters
The primary advantages of calculating the safety stock and reorder point with these methods are:
(1) The review frequency of each item may be individualized. Tailoring the review frequency to the item can reduce the total ordering and holding costs.
(2) Fixed lot sizes, if large enough, may result in quantity discounts. Physical limitations such as material handling methods, storage, preparation equipment, the time allotted for manufacturing, or validated manufacturing methods may
(3) Lower safety stock will results in a cost savings.
(4) Computerized systems can automatically monitor the reorder process when materials have dropped below the reorder point.
Summary
By utilizing the EOQ model, there are only two main costs to calculate, the holding cost and the setup or ordering cost. It is important to calculate these two costs accurately to ensure that you are optimizing your EOQ. To further optimize the EOQ, finding strategies to reduce the ordering and setup cost and/or holding cost is probably the best place to start. However, EOQ is just one part of the equation to create a cost reduction strategy for managing your inventory. You should always consider a cost-benefit-analysis of the pressures for low inventory versus the pressures for high inventory. Once these criteria are established, the risk for holding inventory can be weighed against the expiration data of the material, the safety stock and the reorder point can be established to hopefully prevent stock outs with a minimal impact on your overall cost to carry the inventory.
Formulations Pro Makes EOQ and ROP Easy to Manage
The first piece of information that you will need to know for the EOQ is the demand for your buffer and raw materials over a specified period of time. To make this process easy to use, the Formulations Pro database has a two step process (see Figure 3):
(1) Enter the Data: Enter the demand and cost information into the fields.
(a) Start/End: Enter the start and end date for the demand period of time.
(b) Lead Time: Enter the lead time for ordering and testing the material.
(c) Order or Setup Cost: Enter the order and setup costs. (d) Holding or Carrying Cost: Enter the holding or carry cost
per day.
Figure 3
Next, with the demand, lead time and cost figures,
Formulations Pro will help you to determine the economic
ordering and reorder point quantities.
(2) EOQ Recommendations: All the recommendations will be calculated for you to minimize your costs. All you have to do is enter the safety stock risk factor, desired order and reorder levels (Figure 4).
(a) The number of orders that will be placed on an annual basis will tell you how often you will need to place a new order.
(b) The total cost to carry the inventory takes into consideration the number of units ordered, the holding
and carrying cost, the demand, and the order and setup cost.
(c) The EOQ will tell you the amount to order to minimize your costs.
(e) The desired or actual order amount allows you to specify how much you will order or manufacture for each lot. This allows you to compensate with standardized order quantities which may be easier to order or manufacture.
(d) The EOQ taking into consideration the expiration date of the material will fine tune the EOQ recommendation for materials that will expire before they are consumed.
(f) The safety stock risk factor is used to compute the safety stock quantity.
(g) The safety stock amount is the calculated amount of safety stock needed to prevent a stock out during the lead time.
(h) The recommended reorder amount should be followed as closely as possible to maximize your ordering and production schedules. This value uses the average demand rate and compensates the reorder amount based on the lead time and safety stock. When the stock falls below this level it is time to place a new order.
(i) The desired or actual reorder amount lets you
the next manufacturing lot. This will help to prevent backorders and stockouts. As well, this allows you to compensate with safety stock for inconsistencies in supply or demand and production schedules.
Figure 4
In just 2 short steps, Formulations Pro can give you the competitive edge you need to implement a practical cost reduction strategy for inventory management. For further information about more advanced EOQ strategies or how
Formulations Pro can give your company the competitive edge
that you need please contact: Formulations Pro, Inc.
12608-36 Carmel Country Rd San Diego, Ca 92130
858-794-1530
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