Effect of Change in Demand, Cost Estimates and Lot Sizes on EOQ

For people among us, who are not aware of sensitivity analysis, it is a technique for systematically changing crucial parameters to determine the effects of change.

Considering the factors involved in EOQ estimation, when we substitute different values into numerator or denominator of the formula, different results may arise.

Change in Demand Rate

When demand rises, Lot size shall also increase. But in smaller proportions then actual demand.

Change in the Setup Cost or Ordering Cost

An increase in setup costs causes an increase in EOQ as well and vice versa.


Change in the Holding Cost

This relationship is inversely proportional. If holding cost of an item increases, EOQ decreases. Conversely a decrease in holding cost will allow us to have increased lot sizes. Larger lot sizes are justified by lower handling costs.

How to Calculate EOQ

Considering that all the assumptions discussed in previous post to calculate EOQ are being satisfied, a cycle begins with Q units held in inventory, which happens when a new order is received. During the cycle, on-hand inventory is consumed at a constant rate because demand is known with certainty. As the lead time is a constant, a new lot can be ordered so that inventory falls to 0 precisely when the new order is received.

Formula for calculating EOQ (Q*) is as follows:

Where 

D = annual demand (units per year)

S = cost of ordering or setting up one lot (in currency)

H = cost of handling one unit in inventory for a year

EOQ: Economic Order Quantity

When we know about the challenges faced by an inventory controller or manager, we know that he/she has to face conflicting pressures to keep inventories low enough to avoid excess inventory holding costs but high enough to reduce the frequency of orders and setups

In order to balance these conflicting pressures and determining the best cycle inventory level for an item, we have to find the EOQ (Economic Order Quantity), which minimizes the annual handling costs as well as ordering costs. But yet again, we have to make certain assumptions in this imperfect world to calculate a deadly accurate economic order quantity.

Those assumptions are as follows:

1- Demand rate being constant and known with certainity
2- We do not have to limit lot sizes due to transportation capacity problems
3- Only, inventory holding costs and setup costs are incorporated in calculations.
4- Items don't really have to be interdependent. Which means if more than 1 item is ordered, no additional benefit is obtained while ordering to the same supplier.
5- There is no uncertainty in lead time.

I personally think that very few real world scenarios offer above 5 assumptions. Therefore, EOQ may be taken as very first step in approximation of lot sizes, even when any one or two of the above assumptions don't really apply.

80 20 Rule or Pareto's Concept

80-20 Rule is also known as Pareto's Concept. It may be simply stated as 80% of the activity is caused by 20% of the factors. Therefore, allowing managers to attack 80% of the problems.

This was proposed by an Italian scientist named Vilfredo Pareto in nineteenth  century. His work focused on the inequalities in data and he proposed that most of an "activity" is caused by relatively "few" of its factors.

Pareto Chart drawn during ABC Analysis, is a bar chart on which the "Percentage of Items" is plotted in along the x-axis and "Percentage of Dollar Value" is plotted against the y-axis.

A conceptual diagram of ABC Analysis using Pareto Chart is as follows:

Also, Below is a Pareto Chart generated through a computer program computing results of ABC Analysis. As you can see below, 2 factors are used:
1- Annual Cumulative Sales on Y-Axis
2- Cumulative Number of Items on X-Axis

In order to download an excel template developed by American Society for Quality, please click on the following link:
Download Excel File

How to Classify Items During ABC Analysis and Inventory Reduction Measures

In my previous post, I briefly defined ABC analysis and a general concept as to how much of Class A, B, and C items may constitute in the inventory.

An analyst can classify items into ABC through calculating dollar usage. Dollar usage is calculated by multiplying the annual demand rate by dollar value (cost) of a particular item.

After ranking items according to dollar usage and creating "Pareto Chart" (Which I will share in my next posts to come. If its urgent, you can search wikipedia for Pareto Chart.), the analyst may look for natural changes in slope.

And after classifying the items appropriately, a manager may direct that class A items be reviewed daily/frequently to reduce the average lot size and keep inventory records current.

In the same way, Class C items can be observed under loose control. Although stockouts of Class C can be as lethal as that of A, but the inventory holding costs of Class C items tend to be low as compared to Class A items. Which allow a manager to increase safety stocks, have larger lot sizes while ordering etc.

ABC Analysis and Critical Inventory Items

ABC Analysis may be defined as follows:
ABC Analysis is the process of dividing items into three classes according to their dollar usage so that managers can focus on items that have the highest dollar value.

The goal of this analysis is to identify the inventory levels of Class A items and allow the management to control them tightly by using levers as discussed in the previous post. These are the items which normally account for 20% of the inventory items but 80% of the dollar usage. Similarly, Class B items account for 30% of the inventory but 15% of the dollar usage. Finally, 50% of the rest of the inventory is categorized as Class C which only accounts for remaining 5% of the dollar usage.

What may be Your Options to Reduce Inventory Prudently?

So you are a manager and you are in search of cost-effective ways to reduce inventory?
We term these tactics as levers for reducing inventory.

Cycle Inventory/Pipeline Inventory
The primary lever is to reduce the lot size. JIT (Just in Time) Systems use extremely small lot sizes. But again, making only changes in Q (Lot Size) and neglecting other modifications of business processes can result in devastating scenarios. For example, setup cost can shoot visibly, leading us to use secondary levers.

1- Streamline methods of placing orders and making setups, so that costs proportionate to decrease Q may also be reduced

2- Increase Repeatability; it may include flexible automation, one worker - multiple tasks concepts or group technology, devoting resources to a product exclusively.

Safety Stock Inventory
The primary lever to reduce safety stock inventory is to place orders closer to the time when they must be received. But this approach can lead to undesirable customer service scenarios and stockouts. Four secondary levers can be used in this case:

1- Improve demand forecast so that there may be little surprises through using judgments or statistical tools available (we will discuss about them in times to come)

2- Cut lead times through using efficient sources of transportation. Also local alternate suppliers can also be used to cut lead times exponentially.

3- Suppliers can be reliable if demand forecast may be shared with them.

4- Always keeping an account of capacity cushion and labor buffers (cross-trained workers)

Anticipation Inventory
The primary lever to reduce anticipation inventory is to simple match demand rate with production rate (in vendor/manufacturer communication)
Secondary levers may be as follows to reduce anticipation inventory

1- Add new products with different demand cycles.

2- Provide off-seasonal promotional campaigns

3- Offer seasonal pricing plans

Classification of Inventory

Classification of inventory is very critical.
It is probably easy for us to classify inventory in context to how it is created. Although, it is almost impossible for an inventory manager to physically classify an inventory. But conceptually it is very important for him to know as in what phase the inventory lies at a particular point in time to reduce the overheads involved.

Cycle Inventory
The portion of total inventory that varies directly with lot size is called cycle inventory. Determining how frequently to order, and in what quantity, is called lot sizing. Following principles apply.

1- The lot size, typically termed as Q, varies directly with the elapsed time between orders. If a lot is ordered every five weeks, the average lot size must equal five weeks' demand.

2- The longer the time between orders for a given item, the greater the cycle inventory must be.

To calculate average cycle inventory, once an order or lot is received, cycle inventory drops to 0 (minimum). However, at the time of placing an order, cycle inventory is at its maximum. Average cycle inventory is the average of above mentioned two extreme states of ordering.

Average Cycle Inventory = (Q + 0)/2

When the demand rate is constant and uniform, you can take help of above formula. But, if you are unsure of growing demand, you can check if Q (lot size) multiplied by 1.5 satisfies your demand needs.

In case of uncertain growing demand, Average Cycle Inventory = ((Qx1.5) + 0)/2

Safety Stock Inventory
Safety stock inventory protects against uncertainties in demand, lead time, and supply. Safety stocks are desirable when suppliers fail to deliver the desired quantity on the specified date with acceptable quality or when manufactured items have significant amounts of scrap or rework. Safety stock inventory ensures that operations are not disrupted.

Anticipation Inventory
Inventory used to absorb uneven rates of demand or supply, which businesses often face, is referred to as anticipation inventory. Uneven future demands are always anticipated up to certain extent. And due to anticipation, managers always have an account of anticipation inventory. Specially in case of seasonal demands.

Pipeline Inventory
Pipeline inventory consists of items for which orders have been placed but not yet received in warehouse.
It can be calculated as follows:
Pipeline Inventory = Demand during Lead time (DL)  x Lead Time (L)

Are You in Favor of High Inventories? We Know You Have the Right Reasons

Customer Service
High inventory levels speed delivery and improve on-time delivery. Ofcourse, it reduces the potential of stock outs and backorders, which are key concerns of wholesalers and retailers.
Stockouts is termed as a situation when an item typically stocked isn't available to satisfy a demand, the moment it occurs.
Backorder is a customer's order which is not fulfilled. And customer may wait for one backorder, but next time that particular customer may take its business somewhere else, resulting in a potential loss of credibility of business, and sales ofcourse.

Ordering and Setup Cost
Each time a company places an order to its vendors, ordering costs incur. For instance, when we place an order, we have to go though following process.
Financial Charges:
(Online Transaction Charges, Bank Instrument Charges)
Postal/Communication Cost:
(In case of unavailability of advanced internet technologies at both sides to speed up and ease communication.
Transportation Cost:
Moving stocks from one place to another require transportation and labor and this is quite the same, directly proportionally to the number of orders placed.

More Discounts Enjoyed
Some professionals feel that purchasing bulk inventory will put them in a competitive position to bargain on discounts offered from vendors.And high inventory costs can be marginalized through bargaining for more discounts while purchasing.

Reduced Payments to Suppliers
If a company learns that its vendors are going to increase prices for certain items in near future. It can place a bulk order to reduce the future payments to its suppliers.

Detail of Costs Involved in Inventory Holding

Opportunity Cost
Financing inventory is always achieved through either investment or a loan from any financial institution. Interest or opportunity cost, whichever is greater, usually is the largest component of holding cost, often as high as 15 percent.
For instance, a pharmaceutical distributor may obtain a loan to finance inventory of its vendors at an annual interest rate of more then 12 percent annually or it may forgo an opportunity to invest in stocks or saving scheme at expected return rate of 11 to 13 percent annually.

Storage and Handling Costs
Inventory takes up space and it requires labor to frequently move inventory from one place to another as per demand. These costs may incur when a company or business rents space on either long term or short term basis. And up to some extent  there is some kind of opportunity cost involved with a rented or leased premises to store and take care of inventory.


Taxes, Insurance and Shrinkage
High inventory levels lead to more taxes. And shrinkage takes 3 forms normally. Theft or inventory. Discounting Inventory sale values owing to business pressures. Deterioration through physical spoilage or damage results in loss of inventory or shrinkage.

What are the Costs Associated with Holding Inventories?

Inventory holding cost is the variable cost of keeping items on hand, including interest and handling, taxes, insurance, and shrinkage. When the companies change their inventory levels, holding cost also changes. Typically holding cost of an item ranges from 20 to 40 percent of its value.
Suppose that a company's holding cost is 30 percent. If the average value of total inventory is 20 percent of the sales, the average annual cost to hold inventory is 6 percent - 0.30x0.20 of total sales. This cost is sizable in terms of gross profit margins, which often are less then 10 percent. And it creates a lot of pressure for trimming inventories to increase the gross profit margins.

What is the Real Challenge About?

Real challenge is not to pare inventories to the bone to reduce costs or to have plenty around to satisfy all demands, but to have the right amount to achieve the competitive priorities for the business most efficiently.