Economic Lot size or Economic Order Quantity Model
Assumptions:
- The rate of demand for the item is deterministic and is constant D units per annum, independent of time.
- Production rate is infinite, i.e. production is instantaneous
- Shortages are not allowed
- Lead time is zero or constant independent of demand and the quantity ordered.
- The entire quantity is delivered as a single package (or production in a single run).
Objective:
To minimize the average annual variable cost.
Problem:
To determine when an order should be placed and how much quantity should be ordered.
The annual variable costs for this problem are two types –
- ordering or set-up cost and
- Inventory holding cost.
As Q is the order quantity and D is the annual demand, the number of orders per years will be D/Q. Therefore, the annual ordering cost will be = A.D/Q …….. (1)
Properties of EOQ model and Sensitivity Analysis
In the above nodal, various parameters are used such as demand (D), inventory carrying charges factor ®, ordering or set-up cost (A). These parameters are estimated and though they are assumed to be known, in real life what we have is an estimated value which may be different than real value for various reasons.
For this reason it is important for practical purposes to test the results of the EQQ model and find how sensitive the results are to the changes in various parameters.
The sensitivity can be explored in various ways. Let the “true” rate of demand is D, “ true” value of order cost is A, “ true” value of inventory holding cost is r and “true” value 9of unit purchase cost or production cost is v. Then the “true” optimal value of order quantity (Q*) will be,
In case when shortage costs are infinitely high (i.e. when shortages are not allowed) b = ¥ and eqn. 17 will reduce to
This is same as equation (6), i.e. optimal order quantity for the E0-model. This is obvious since the EOQ model assume that no shortages are allowed which imply that the shortage are infinite the basic inventory models are given below for easy understanding of the concept as well as to enable one solve the day to day Inventory problems too as far as determining the Economic Order Quantities, Time for ordering etc., .are concerned
The Classical Model
Corporate goals and strategies may sometimes conflict with EOQ. Measuring performance solely by inventory turns is one of the most prolific mistakes made in the name of inventory management. Many companies have achieved aggressive goals in increasing inventory turns only to find their bottom line has shrunk due to increased operational costs.
EOQ is essentially an accounting formula that determines the point at which the combination of order costs and inventory carrying costs are the least. The result is the most cost effective quantity to order. In purchasing this is known as the order quantity, in manufacturing it is known as the production lot size.
The Inputs
While the calculation itself is fairly simple the task of determining the correct data inputs to accurately represent your inventory and operation is a bit of a project. Exaggerated order costs and carrying costs are common mistakes made in EOQ calculations. Using all costs associated with your purchasing and receiving departments to calculate order cost or using all costs associated with storage and material handling to calculate carrying cost will give you highly inflated costs resulting in inaccurate results from your EOQ calculation
As you prepare to undertake this project keep in mind that even though accuracy is crucial, small variances in the data inputs generally have very little effect on the outputs. The following breaks down the data inputs in more detail and gives insight into the aspects of each.
Expressed in units, this is generally the easiest part of the equation. You simply input your forecasted annual usage.
Order Cost.
Also known as purchase cost or set up cost, this is the sum of the fixed costs that are incurred each time an item is ordered. These costs are not associated with the quantity ordered but primarily with physical activities required to process the order.
For purchased items, these would include the cost to enter the purchase order and/or requisition, any approval steps, the cost to process the receipt, incoming inspection, invoice processing and vendor payment, and in some cases a portion of the inbound freight may also be included in order cost. It is important to understand that these are costs associated with the frequency of the orders and not the quantities ordered
Associating actual costs to the activities associated with order cost is where many an EOQ formula
runs afoul. Do not make a list of all of the activities and then ask the people performing the activities “how long does it take you to do this?” The results of this type of measurement are rarely even close to accurate. I have found it to be more effective to determine the percentage of time within the department consumed performing the specific activities and multiplying this by the total labor costs for a certain time period (usually a month) and then dividing by the line items processed during that same period.
For the most part, order cost is primarily the labor associated with processing the order, however, you can include the other costs such as the costs of phone calls, faxes, postage, envelopes, etc.
Carrying cost
Also called Holding cost, carrying cost is the cost associated with having inventory on hand. It is primarily made up of the costs associated with the inventory investment and storage cost. For the purpose of the EOQ calculation, if the cost does not change based upon the quantity of inventory on hand it should not be included in carrying cost. In the EOQ formula, carrying cost is represented as the annual cost per average on hand inventory unit. Below are the primary components of carrying cost.
Interest: If you had to borrow money to pay for your inventory, the interest rate would be part of the carrying cost. If you did not borrow on the inventory, but have loans on other capital items, you can use the interest rate on those loans since a reduction in inventory would free up money that could be used to pay these loans. If by some miracle you are debt free you would need to determine how much you could make if the money was invested.
Insurance: Since insurance costs are directly related to the total value of the inventory, you would include this as part of carrying cost.
Taxes: If you are required to pay any taxes on the value of your inventory they would also be included.
Storage Costs: Mistakes in calculating storage costs are common in EOQ implementations. Generally companies take all costs associated with the warehouse and divide it by the average inventory to determine a storage cost percentage for the EOQ calculation. This tends to include costs that are not directly affected by the inventory levels and does not compensate for storage characteristics. Carrying costs for the purpose of the EOQ calculation should only include costs that are variable based upon inventory levels.
Since storage costs are generally applied as a percentage of the inventory value you may need to classify your inventory based upon a ratio of storage space requirements to value in order to assess storage costs accurately.
There are situations where you may not want to include any storage costs in your EOQ calculation. If your operation has excess storage space of which it has no other uses you may decide not to include storage costs since reducing your inventory does not provide any actual savings in storage costs. As your operation grows near a point at which you would need to expand your physical operations you may then start including storage in the calculation.
Other costs that can be included in carrying cost are risk factors associated with obsolescence, damage, and theft. Do not factor in these costs unless they are a direct result of the inventory levels and are significant enough to change the results of the EOQ equation.
Variations
There are many variations on the basic EOQ model. I have listed the most useful ones below.
- Quantity discount logic can be programmed to work in conjunction with the EOQ formula to determine optimum order quantities. Most systems will require this additional programming.
Additional logic can be programmed to determine max quantities for items subject to spoilage or to prevent obsolescence on items reaching the end of their product life cycle.
Your safety stock calculation may take into account the order cycle time that is driven by the EOQ. If so, you may need to tie the cost of the change in safety stock levels into the formula.
Implementing EOQ
There are primarily two ways to implement EOQ. Both methods obviously require that you have already determined the associated costs. The simplest method is to set up your calculation in a spreadsheet program, manually calculate EOQ one item at a time, and then manually enter the order quantity into your inventory system. Whichever method you use you should make sure to follow the following steps:
Test the formula. Prior to final implementation you must test the programming and setup. Run the
EOQ program and then manually check the results using sample items that are representative of the variations of your inventory base.
Project results: You’ll need to run a simulation or use a representative sampling of items to determine the overall short-term and long-term effects the EOQ calculation will have on warehouse space, cash flow, and operations. Dramatic increases in inventory levels may not be immediately feasible, if this is the case you may temporarily adjust the formula until arrangements can be made to handle the additional storage requirements and compensate for the effects on cash flow. If the projection shows inventory levels dropping and order frequency increasing, you may need to evaluate staffing, equipment, and process changes to handle the increased activity.
Maintain EOQ. The values for Order cost and Carrying cost should be evaluated at least once per year taking into account any changes in interest rates, storage costs, and operational costs. A related calculation is the Total Annual Cost calculation. This calculation can be used to prove the EOQ calculation. Total Annual Cost = [(annual usage in units)/(order quantity)(order cost)]+{[.5(order quantity)+(safety stock)]*(annual carrying cost per unit)}. This formula is also very useful when comparing quotes where vendors offer different minimum order quantities, price breaks, lead times, transportation costs.
Use it! The EOQ calculation is “Hard Science”, if you have accurate inputs the output is the most cost-effective quantity to order based upon your current operational costs. To further increase inventory turns you will need to reduce the order costs. E-procurement, vendor-managed inventories, bar coding, and vendor certification programs can reduce the costs associated with processing an order.
Equipment enhancements and process changes can reduce costs associated with manufacturing set up. Increasing forecast accuracy and reducing lead times which result in the ability to operate with reduced safety stock can also reduce inventory levels.
Maintaining inventory through counting, placing orders, receiving stock and so on takes personnel time and costs money. When there are limits on these resources, the logical move is to try to use the available resources to control inventory in the best way. In other words, focus on the most important items in inventory.
Any inventory system must specify when an order is to be placed for an item and how many units to order. Most inventory control situations involve so many items that it is not practical to model and give thorough treatment to each item. To get around this problem, the ABC classification scheme divides inventory items into three groupings: high dollar volume (A), moderate dollar volume (B) and low dollar volume (C). Dollar volume is a measure of importance; an item low in cost but high in volume can be more important than a high-cost item with low volume.
ABC Classification: If the annual usage of items in inventory is listed according to dollar volume, generally, the list shows that a small number of items account for a large dollar volume and that a large number of items account for a small dollar volume.
The ABC approach divides this list into three groupings by value: A constitutes roughly the top 15% of the items, B items the next 35%, and C items the last 50%. Segmentation may not occur always so neatly. The observation, though, is to try to separate the important from the unimportant. Where the lines actually break depends on the particular inventory under question and on how much personnel time is available.
ABC analysis provides a mechanism for identifying items which will have a significant impact on overall inventory cost whilst also providing a mechanism for identifying different categories of stock that will require different management and controls When carrying out an ABC analysis, inventory items are valued (item cost multiplied by quantity issued/consumed in period) with the results then ranked. The results are then grouped typically into three bands. These bands are called ABC codes.
ABC codes
“A class” inventory will typically contain items that account for 80% of total value, or 20% of total items.
“B class” inventory will have around 15% of total value, or 30% of total items.
“C class” inventory will account for the remaining 5%, or 50% of total items.
ABC Analysis is similar to Praetor the “A class” group will typically account for a large proportion of the overall value but a small percentage of the overall volume of inventory.
The ABC classification process is an analysis of a range of objects, such as finished products, items lying in inventory or customers into three categories. It’s a system of categorization, with similarities to Pareto analysis, and the method usually categorizes inventory into three classes with each class having a different management control associated:
A – outstandingly important; B – of average importance; C – relatively unimportant as a basis for a control scheme.
Each category can and sometimes should be handled in a different way, with more attention being devoted to category A, less to B, and still less to C.
Popularly known as the “80/20” rule ABC concept is applied to inventory management as a rule of-thumb. It says that about 80% of the Rupee value, consumption wise, of an inventory remains in about 20% of the items.
This rule , in general , applies well and is frequently used by inventory managers to put their efforts where greatest benefits , in terms of cost reduction as well as maintaining a smooth availability of stock, are attained.
The ABC concept is derived from the Pareto’s 80/20 rule curve. It is also known as the 80-20 concept. Here, Rupee / Dollar value of each individual inventory item is calculated on annual consumption basis.
Thus, applied in the context of inventory, it’s a determination of the relative ratios between the number of items and the currency value of the items purchased / consumed on a repetitive basis.
10-20% of the items (‘A’ class) account for 70-80% of the consumption
the next 15-25% (‘B’ class) account for 10-20% of the consumption and
the balance 65-75% (‘C’ class) account for 5-10% of the consumption
‘A’ class items are closely monitored because of the value involved (70-80% !).
High value (A), Low value (C), intermediary value (B)
20% of the items account for 80% of total inventory consumption value (Qty consumed X unit rate)
Specific items on which efforts can be concentrated profitably
Provides a sound basis on which to allocate funds and time
A,B & C , all have a purchasing / storage policy – “A”, most critically reviewed , “B” little less while
“C” still less with greater results.
ABC Analysis is the basis for material management processes and helps define how stock is managed. It can form the basis of various activity including leading plans on alternative stocking arrangements (consignment stock), reorder calculations and can help determine at what intervals inventory checks are carried out (for example A class items may be required to be checked more frequently than c class stores
Inventory Control Application: The ABC classification system is to grouping items according to annual issue value, (in terms of money), in an attempt to identify the small number of items that will account for most of the issue value and that are the most important ones to control for effective inventory management. The emphasis is on putting effort where it will have the most effect.
High value (A), Low value (C) , intermediary value (B)
A Items: These Items are seen to be of high Rupee consumption volume. “A” items usually include 10-20% of all inventory items, and account for 50-60% of the total Rupee consumption volume.
B Items: “B” items are those that are 30-40% of all inventory items, and account for 30-40% of the total Rupee consumption volume of the inventory. These are important, but not critical, and don’t pose sourcing difficulties.
C Items: “C” items account for 40-50% of all inventory items, but only 5-10% of the total Rupee consumption volume. Characteristically, these are standard, low-cost and readily available items.
ABC classifications allow the inventory manager to assign priorities for inventory control. Strict control needs to be kept on A and B items, with preferably low safety stock level. Taking a lenient view, the C class items can be maintained with looser control and with high safety stock level. The ABC concept puts emphasis on the fact that every item of inventory is critical and has the potential of affecting, adversely, production, or sales to a customer or operations. The categorization helps in better control on A and B items.
In addition to other management procedures, ABC classifications can be used to design cycle counting schemes. For example, A items may be counted 3 times per year, B items 1 to 2 times, and C items only once, or not at all.
Suggested policy guidelines for A , B & C classes of items
| A items (High cons. Val) | B items (Moderate cons. Val) | C item (Low cons. Val) |
| Very strict cons. Control | Moderate control | Loose control |
| No or very low safety stock | Low safety stock | High safety stock |
| Phased delivery (Weekly) | Once in three months | Once in 6 months |
| Weekly control report | Monthly control report | Quarterly report |
| Maximum follow up | Periodic follow up | Exceptional |
| As many sources as possible | Two or more reliable | Two reliable |
| Accurate forecasts | Estimates on past data | Rough estimate |
| Central purchasing /storage | Combination purchasing | Decentralized |
| Max. efforts to control LT | Moderate | Min. clerical efforts |
| To be handled by Sr. officers | Middle level | Can be delegated |
How to do ABC Analysis / Classification
ABC analysis is a basic supply chain technique, often carried out by inventory controllers/materials managers, and is the starting point in Inventory control.
ABC classification is a system of categorization, with similarities to Pareto analysis and the method usually categorizes inventory into three classes with each class having a different management control associated.
Although different criteria may be applied to each category the typical method of “scoring” an inventory item is that of annual consumption value of said item (Qty consumed X Cost of item) with the result then ranked and then scored (A, B or C).
Classification may be specific to the industry but typically follows a 70%, 90%, 100% banding in that A class items represent 70% of the value, B class items fall between 70% and 90% of the annual value with C class the remaining.
In practical terms the complex high cost materials typically fall into the A class items, with the consumable, low cost (and typically fast moving) classed as C class.
How to carry out the actual analysis?
Carrying out ABC analysis is a bit tricky affair. What ultimately is done is to segregate all the inventory items into three categories viz. A, B & C.
ABC analysis can be done for any given data that has money value as the prime factor. For example classification of pending suppliers’ bills, items of an MRO or any type of inventory, expenditure over a period of time, customers with respect to sale value etc.
ABC Classification / Analysis of Inventory
The ABC classification process is an analysis of a range of objects, such as finished products, items lying in inventory or customers into three categories. It’s a system of categorization, with similarities to Pareto analysis, and the method usually categorizes inventory into three classes with each class having a different management control associated:
A – Outstandingly important; B – of average importance; C – relatively unimportant as a basis for a control scheme.
Each category can and sometimes should be handled in a different way, with more attention being devoted to category A, less to B, and still less to C.
Popularly known as the “80/20” rule ABC concept is applied to inventory management as a rule of-thumb. It says that about 80% of the Rupee value, consumption wise, of an inventory remains in about 20% of the items.
This rule, in general, applies well and is frequently used by inventory managers to put their efforts where greatest benefits, in terms of cost reduction as well as maintaining a smooth availability of stock, are attained.
The ABC concept is derived from the Pareto’s 80/20 rule curve. It is also known as the 80-20 concept. Here, Rupee / Dollar value of each individual inventory item is calculated on annual consumption basis.
Thus, applied in the context of inventory, it’s a determination of the relative ratios between the numbers of items and the currency value of the items purchased / consumed on a repetitive basis.
10-20% of the items (‘A’ class) account for 70-80% of the consumption
The next 15-25% (‘B’ class) account for 10-20% of the consumption and
The balance 65-75% (‘C’ class) account for 5-10% of the consumption
High value (A), Low value (C), intermediary value (B)
20% of the items account for 80% of total inventory consumption value (Qty consumed X unit rate)
Specific items on which efforts can be concentrated profitably
Provides a sound basis on which to allocate funds and time
A,B & C , all have a purchasing / storage policy – “A”, most critically reviewed , “B” little less while “C” still less with greater results.
ABC Analysis is the basis for material management processes and helps define how stock is managed. It can form the basis of various activity including leading plans on alternative stocking arrangements (consignment stock), reorder calculations and can help determine at what intervals inventory checks are carried out (for example A class items may be required to be checked more frequently than c class stores
Inventory Control Application: The ABC classification system is to grouping items according to
annual issue value, (in terms of money), in an attempt to identify the small number of items that will account for most of the issue value and that are the most important ones to control for effective inventory management. The emphasis is on putting effort where it will have the most effect.
A Items: These Items are seen to be of high Rupee consumption volume. “A” items usually include 10-20% of all inventory items, and account for 50-60% of the total Rupee consumption volume.
B Items: “B” items are those that are 30-40% of all inventory items, and account for 30-40% of the total Rupee consumption volume of the inventory. These are important, but not critical, and don’t pose sourcing difficulties
C Items: “C” items account for 40-50% of all inventory items, but only 5-10% of the total Rupee consumption volume. Characteristically, these are standard, low-cost and readily available items.
ABC classifications allow the inventory manager to assign priorities for inventory control. Strict control needs to be kept on A and B items, with preferably low safety stock level. Taking a lenient view, the C class items can be maintained with looser control and with high safety stock level. The
ABC concept puts emphasis on the fact that every item of inventory is critical and has the potential of affecting, adversely, production, or sales to a customer or operations. The categorization helps in better control on A and B items.
The XYZ analysis is a procedure of stock management in the management economics, with which on the basis empirical experiences, results are usually assigned to a classification by bill explosions or by the determination by variation and/or fluctuation coefficients of goods and articles concerning its turnover regularity (consumption and its predictableness).
- X constant consumption, fluctuations are rather rare
- Y stronger fluctuations in consumption, usually for trend-moderate or seasonal reasons
- Z completely irregular consumption
The XYZ analysis in the materials requirement Planning (materials requirements planning), in addition, in camp planning and in the calculation is used, frequently combined with the ABC analysis.
Bandings may be specific to the industry but typically follow a 70%, 90%, 100% banding in that X class items represent 70% of the stock value (although they may account for 20% number wise), Y class items fall between 70% and 90% of the annual stock value with C class the remaining. In practical terms the complex high cost materials typically fall into the X class items, with the consumable, low cost (and typically fast moving) classed as X class.
Not all stock is equally valuable and therefore doesn’t require the same management focus. The results of the XYZ analysis provide information that helps evaluate how each inventory part should be monitored and controlled. These controls are typically:
X class items which are critically important and require close monitoring and tight control – while this may account for large value these will typically comprise a small percentage of the overall inventory count.
- Y class is of lower criticality requiring standard controls and periodic reviews of usage
- Z class require the least controls, are sometimes issues as “free stock” or forward holding.
Classification of inventory in terms of XYZ is also quite strategic as It can form the basis of various activity including leading plans on alternative stocking arrangements (consignment stock), reorder calculations and can help determine at what intervals inventory checks are carried out (for example X class items may be required to be checked more frequently than Z class stores.
Based on the ABC and XYZ analysis there is another control mechanism, popularly known as AX control.
AX Control
What is the AX category of items of Inventory?
Inventory plays an important role for any organization as it blocks the working capital which otherwise would have earned the organization some money. While the need for having inventory can’t be denied for any running plant / machinery, its availability in controlled measures too is highly desirable. Control techniques such as ABC and XYZ analyses though done in different ways, try, at the same time, to get maximum control with little commitment of resources.
Inventory Control of Slow-Moving Items
As stated earlier, slow moving materials are those which are not regularly demanded and their movement off the shelf is very occasional, say once in six months or so. Generally slow moving items are quite expensive and therefore one has to first decide whether to keep them all in stock and if to keep them in stock then in what quantity further difficulty of slow moving parts is that initial over-buying decision could take years to remedy the situation due to rarely occurring demands.
Some Inventory Policies for Slow Moving Spares
We shall illustrate our approach to manage the inventory of slow moving items with spares inventory problem as a substantial percentage of spares come under the slow moving categories. Some of the strategies that could be possibly adopted for efficient inventory management of slow-moving spares are as
- If spares are required only at pre-specified time such as at the time of major scheduled maintenance for replacement, then it is better not to stock them but to place procurement order sufficiently well in advance, keeping lead times in mind, so that these arrive just in time when these are needed.
- If the part gives adequate warning of impending break down, then also the best policy is to place an order the moment we get the warning. Adequate warning refers to the case when the lead time required is less than the warning time. This shows that major improvements in slow moving inventory are possible by cutting down the lead times.
For inadequate warning spares we must keep the stock. Generally maximum stock level will be 1 or 2 and the (S-1, S) or one-for-one ordering policy is very useful. This means placing an order for one spare when one is consumed.
