1. Quantity Discount Economic Order Quantity (EOQ) Analysis Tools
This topic will cover the generic version of the Quantity Discount Economic Order Quantity (EOQ) Analysis tools developed by the Army Communications-Electronics Life Cycle Management Command (C-E LCMC) Systems Analysis Division. Unlike the version, linked to data in the Army Commodity Command Standard System (CCSS), the generic version of the tool is available to any requestor at no cost. The concepts behind the Quantity Discount EOQ Analysis tool and its importance will be introduced.
The Quantity Discount EOQ analysis tool is best used for the re-procurement of existing items. It may also be used during production to analyze production buys.
The generic version of the Quantity Discount EOQ analysis tool can be obtained by sending an request to
Bernard Price
Certified Professional Logistician

2. Why Use Range Quantity Discount EOQ Analysis Tools?
Quantity Discounts Commonly Applied
Improved Decision Making with Better Information
Saves $ - Purchases Item Quantity Meeting Demands at the Lowest Total Ownership Cost
Commodity Independent
Generic Version Usable by All
This chart addresses the objective of the Quantity Discount Analysis Tools. All model versions improve best value decision making with better information. Also, all model versions are commodity independent. Both Quantity Discount EOQ Analysis model versions help to save money by determining the purchase quantity of items meeting re-procurement requirements at the lowest Total Ownership Cost (TOC). The CCSS version interfaces with the Army CCSS to obtain much of its input data. The generic tool version is not tied to the Army CCSS for its data and therefore can be used by both Government and Industry.
The objective of the Quantity Discount Pricing Evaluation model is to use bidder proposed range and quantity prices to determine the likely buy quantities of items over the length of the contract being solicited competitively. This helps to quickly and accurately estimate the purchase costs for items during the source selection.

3. NSN 5999-01-269-5573 (CCA) Quantity Discounts
Vendor Quantity
1 – 29
60 & UP
Unit Cost
$24,484
$ 7, 059
$ 6, 553
Purchase of 10 CCAs = 10 x $24, = $244,840
Purchase of 30 CCAs = 30 x $7,059
= $211,770
This Mobile Subscriber Equipment (MSE) Circuit Card Assembly (CCA) provides a good example to show how quantity discounts offer the opportunity to buy more items and pay less for the them. The range and quantity pricing on this chart was actually offered. The great disparity between the unit costs of the first two vendor ranges makes this savings opportunity readily apparent. In this example, we can buy 30 CCAs for about $33 thousand less than buying 10 CCAs.

4. Non-Recurring Buy Procurements
Unit Cost
$24,484
$ 7, 059
$ 6, 553
Vendor Quantity
1 – 29
60 & UP
Economic Purchase Quantities
1 - 8
60 & UP
Non-recurring demand procurements for a specific buy quantity is only handled by the generic version of the Quantity Discount EOQ Analysis model. When a specific purchase quantity is desired, the upper limit buy quantities for each pricing range can be computed to determine economic purchase quantities. If the quantity needed is not in the range of economical purchases, purchasing the lowest economic quantity in the next pricing range will save money. For the MSE CCA example, a buy quantity would be in the first range only when the quantity of items needed never exceeds eight. An informed buyer would save money and purchase 30 CCAs whenever 9 to 29 CCAs are needed because the total purchase of 9 items exceeds the total purchase cost of 30 items. Likewise, when at least 56 CCAs are needed, the informed buyer would purchase 60 or more. A smaller range of savings opportunity exists when a small unit cost decrease is offered in the next higher range.
Buy 30 When Need 9-29
Buy 60 When Need 56-59

5. Recurring Demand Procurements
Requirement: 60 Demands Per Year Forecast
Alternatives:
Buy 5 monthly = 5 x 12 x $24,484 = $1,469,040
Buy 30 twice = 30 x 2 x $7,059 = $423,540
Buy 60 once = 60 x $6,553 = $393,180
Supply Chain Management and the purchase of secondary items in legacy or fielded systems generally deal with recurring demand procurements. Using the same MSE CCA example, this slide covers the potential impact of procurement alternatives with a forecasted procurement demand rate of 60 demands per year. The annual purchase costs of alternative buys in each quantity range are shown. If 5 items are bought monthly, a little less than $1.5 million will be spent in a year. If 30 items are bought twice a year, about $424 thousand will be spent. If 60 are bought once, about $393 thousand will be spent for the year.
Although the higher purchase quantity is typically better for higher demand rate items, the annual purchase cost savings tends to become less significant at lower demand rates. Also, when costs associated with holding extra inventory enters into the analysis to determine the lowest TOC buy quantity, results for the lower demand rate items tends to become less obvious.

6. Economic Order Quantity (EOQ)
Best Buy Quantity Dependencies:
Purchase Cost
Ordering Cost
Holding Costs
Procurement Demand Rate
Constraints/Adjustment Factors:
Minimum Reorder Cycles
Remaining Life
Shelf Life
Quantity Range for Unit Price
Delayed Reordering
Economic Order Quantities apply only to recurring demand procurements. When the EOQ is computed, there are other factors to consider beyond the purchase cost. The best buy quantity, which underpins inventory management, also depends on the cost incurred each time an order is placed, the cost to hold inventory and the procurement demand rate.
Constraints introduce additional complexities that affect the quantitative decision-making of the EOQ. Some constraints may be a minimum length of time between reordering, the remaining life or the shelf life of the item and the quantity range offered for a unit price. Another adjustment factor is caused by a delay in reordering after the reorder point quantity was reached because more items are purchased to compensate for the inventory asset quantity being below the reorder point quantity before placing an order.

7. Holding Cost Factors Storage Cost Loss or Pilferage
Investment Opportunity or Discount Rate
Obsolescence Rate
Disposal Cost (End of Life Application Only)
Factors contributing to inventory holding costs are shown on this slide. Storage costs usually depend on the cost of the storage facility needed and the item’s volume. The generic model will use a cost per item per year input. The loss or pilferage of stock is another holding cost factor. The lost investment opportunity or the net discount rate is another holding cost factor because money used to buy items for storage now, could have been used for other investments. The obsolescence rate is another holding cost factor. Obsolescence is dependent on the technology of the item and the item’s age. Since the worth of lost stock is related to the item’s cost and the investment cost and cost associated with obsolescent stock also depends on the item’s cost, their model inputs are in terms of the percent of the item cost per year. The disposal cost only comes into play when disposing excess stock. A negative disposal cost is its salvage value. The disposal cost depends on the content of the item and its potential to use elsewhere.
The Army Materiel Management Decision File in the Commodity Command Standard System (CCSS) contain values for each of the inventory holding cost factors as an annual percentage of the item purchase cost. For C-E LCMC commodity items, it uses a storage cost of 1%, a loss rate of 2%, an investment discount rate of 7% and the obsolescence rate after the item’s first year of introduction typically varies from 7% to 10%. Therefore, the inventory holding costs at C-E LCMC generally sum up to about 20% of the item cost per year.

8. Procurement Demand Rate
Procurement Demand Rate Does Not Include Demands for Repair
Repair Costs Less Than Replenishment Buys Causing Repairs to be Pursued Before Purchasing Items
Good Model Output Will Depend on Good Input
Procurement Demands
Demand Rate associated with Throwaway Items
Certain Unserviceable Repairable Item Demands:
Item Not Returned by User or Field for Higher Level Repair
Item Washed Out Because Repair is Not Economical
If Demand Rate Data Includes Repairs, apply User Return Rate and Washout Rate Factors to Estimate Replenishment Demand Rate
The demand rate applied in Quantity Discount EOQ analysis tools is the procurement demand rate. If the demand rate used includes repaired items that are not replaced, model outputs may not be correct. Any demands for items being repaired is not part of the procurement demand rate because repairing costs less than purchasing in this instance, which causes repairs to be pursued first to replenish wholesale level stock with a serviceable item.
Demands associated with Throwaway or Consumable items are procurement demands. Demands associated with Unserviceable Repair items are procurement demands only when the Unserviceable item is not returned by the User or Field to be repaired or when the item is Washed Out because repairing would not be economical.
If the demand rate data being collected include repairs, then factors applied to the total demand rate will estimate the procurement demand rate. These factors will be a User Return Rate, where 1 minus the User Return Rate percentage covers Unserviceable items not returned for repair and a Wash Out Rate that describes the percentage of the items not repaired for economical reasons.

9. Determining EOQ
Objective: EOQ is the quantity to buy with Minimum Total Cost
Total Cost = Purchase Cost + Ordering Cost + Holding Cost
Total Cost
EOQ
Unit Cost
This chart shows how the classical Economic Order Quantity (EOQ) is determined when there is one unit price as with CCSS. The EOQ is the quantity to buy which minimizes the total cost per item. The total cost is the sum of unit purchase cost, ordering cost and the cost to hold for that quantity. The slope of the holding cost is dependent on the item’s cost and its procurement demand rate which explains why the forecasted demand rate influences the EOQ. The minimum total cost per item is typically where the holding cost equals the ordering cost.
With the Army’s institutionalization of Multiple Year, Packaged Buy contracts and Ordering Officers, the cost to place an order has been significantly reduced. The application of a low ordering cost encourages the EOQ to be a small reorder quantity. This classical relationship is good if no quantity discounts are offered.
Holding Cost
Ordering Cost

10. Range Quantity Discount EOQs
When quantity discounts are considered, the lowest total cost constrained EOQ is not necessarily in lowest range when the cost to order is small. The dotted lines of the total cost per item curves extend into the lower ranges to show what the unconstrained results would be if suppliers offered their reduced prices at those smaller quantities. When the buy quantities for a unit price are unconstrained and the cost to order is small, the typical EOQ along the dotted lines will tend to be Range 1 quantities. However, to obtain the reduced prices offered, the minimum quantity associated with the quantity discount must be purchased. In this conceptual example, the best buy EOQ is at the start of Range 2 where the constrained total cost is minimum. This illustrates one key reason why the Quantity Discount EOQ Analysis Model results may differ from the classical EOQ recommended buy quantity.
Unconstrained EOQ
Constrained EOQ

11. Additionally Constrained EOQs
Range 1
Range 2
Range 3 A B
When minimum reorder cycle constraints are considered, the EOQ for a single priced item may shift to a larger quantity in the first range if the cost to order is small. This shift occurs when the procurement demand rate times the minimum reorder cycle time yields a quantity higher than the unconstrained EOQ. Additionally, when an order is placed with an inventory asset position below the reorder point, the classical EOQ may again shift to a larger buy quantity to compensate for placing the order late.
These constraints cause adjustments to the classical EOQ buy quantity, making the Quantity Discount EOQ Analysis Model even more valuable. In updating the previous slide’s conceptual example, the best buy EOQ at Point B is still at the start of Range 2 where the constrained total cost is still minimum. However, now the savings relative to the Range 1 recommendation at Point A became larger.
Unconstrained EOQ
Constrained EOQ

12. Generic Tool Version
Handles Quantity Discounts for Recurring & Non-Recurring Demand Buys
More Flexible than the Army Tool Version
Handles End of Life Purchase Alternatives
Within 2 Reorder Cycles
Best Combinations of 1 or 2 Buys Compared
Log Mod Version 4 with Help Files Covering All Inputs & Outputs
The generic tool version of the Quantity Discount EOQ Analysis model handles both recurring and non-recurring demand buys. The generic version model is more flexible than the Army CCSS model version to account for more realistic, item specific input data. Storage and disposal costs do not have to be related to the unit price of the item. The remaining life and obsolescence costs may now be related to technology advances in addition to the item’s age and cost. The Quantity Discount EOQ Analysis model also handles end of life purchases. An end of life purchase is defined as being within 2 reorder cycles of the remaining life. As alternatives, the model will consider one lifetime buy relative to some combinations of 2 purchases to determine the least total cost alternative.
The latest generic Quantity Discount EOQ Analysis tool version is called Log Mod Version 4. The tool contains help files explaining all the model inputs and outputs. This model is available for distribution electronically at no cost to both Government and industry.

13. Implementing Quantity Discount Analysis Tools
AR Permits Army to Determine Reqts. & Procure Quantity Discounts in lieu of EOQ
At CECOM, LRC MyNSN + Contains Tool with Web Based Tie to CCSS
AMSAA and TACOM Reviewed Methodology in Tool & Recommend AMC Usage
Air Force, Veterans Administration & DLA in Philadelphia Distributed Generic Version Tool
Army use of a Quantity Discount Analysis tool to determine procurement requirements due to quantity discounts in lieu of buying the classical Economic Order Quantity (EOQ) is permitted by Army Regulation The Army Commodity Command Standard System (CCSS) version of the Quantity Discount EOQ Analysis tool is within a larger web based tool that extracts and uses data from CCSS to perform analyses and provide reports.
The methodology used in the generic version tool was reviewed, tested and verified by two independent Army organizations. Additionally, the generic model version has been distributed to approximately 100 requestors. Positive feedback regarding further model distributions were volunteered by the Air Force, Veterans Administration and Defense Logistics Agency in Philadelphia.

14. Quantity Discount Source Selection Evaluation Tool
Applies Quantity Discount EOQ Model Computations to Determine Likely Item Buy Quantities & Contract Purchase Costs
Bidders Provide Quantity Ranges & Prices for each Potential Contract Year
Improves Range Quantity Pricing Flexibility
Will Likely Yield Lower Proposed Prices vs. Government Specified Quantity Ranges
The Quantity Discount Pricing Evaluation model is a tool that determines more accurate contract pricing in source selections. The model applies Quantity Discount EOQ model computations to determine the likely buy quantities and the contract purchase cost of each bidder for the secondary item NSNs being re-procured in a competitive solicitation.
The bidders have the flexibility to input their own range and quantity pricing for each potential contract year based on how they purchase or produce the items. Bidder provided range quantity pricing will likely yield a lower price than the Government specifying quantity ranges required to be priced to determine comparative source selection costs. Bidder pricing to their own economical procurement or production costs for items should be better for competition than proposing prices for the minimum quantity in buyer provided ranges to reduce their risk.

15. Quantity Discount Source Selection Evaluation Tool
Buyer Inputs
Low, High and Likely Demand Rates for Items
Weighting Factors for Demand Rates
Contract Length
Minimum and Maximum Reorder Cycles
Inventory Holding Costs
Simulates Buys for Items over Contract Life
Automatically Selects Lowest Cost EOQ Buys
Computes Weighted Average Total Cost to Buyer
The Government provides inputs for the low, high and likely demand rates for each item and the weighting factors associated with those demand rates. Although the likely demand rate will be given more weight, accounting for the other possible demand rates discourages bidders from gaming their pricing. The buyer also provides the length of the contract, the minimum and maximum reorder cycles if they apply, and inputs for the inventory holding costs.
After all the inputs are collected, the model simulates item buys over the contract life by automatically selecting the lowest cost EOQ buys for each demand rate. The final result is a computed weighted average total cost for all the items within the solicitation over the potential contract life.

16. Conclusion Saves Money
Improves Acquisition & Inventory Management Decision Making
Determines & Compares Lowest Total Ownership Cost Buy
Provides Common Evaluation Baseline with More Accurate Source Selection Pricing
Distributed & Available for Widespread Use
Has Received Positive Feedback
In summary, usage of the Quantity Discount models helps to improve acquisition and inventory management decision making. The tools determine the lowest total ownership cost buy.
The source selection version tool provides a flexible, common evaluation baseline that more accurately determines the total cost of contract bids with Quantity Discount pricing. The generic model version has been distributed and is available for widespread use at no cost. The tool has also received positive feedback from objective reviews and can help its users to save money.
Saves Money

17. Now, some screens of a demonstration using the generic version of the Quantity Discount Economic Order Quantity Analysis Tool will be shown. The first screen to pop up asks whether the user wants to select Help, which defines and describes every input and output in the model, or Run the Analysis Tool. Running the analysis tool was selected for the demonstration.

18. The first run to be demonstrated shows the input screen for a non-recurring demand buy of the Mobile Subscriber Equipment (MSE) Circuit Card Assembly (CCA). A quantity of 15 items was inputted as being needed. After filling in the price and quantity range inputs, the EOQ Recommendation button was selected to make the computations.

19. The output screen for this non-recurring demand buy is now shown
The output screen for this non-recurring demand buy is now shown. The best purchase cost and economic upper range purchase quantities for each range are shown in the cost comparison portion. Below this, a quantity of 30 is outputted as the lowest cost purchase order quantity and its corresponding purchase cost of $211,770 is also displayed in the Quantity/Cost Calculator. If desired, the quantity of 30 can be replaced in the Quantity/Cost Calculator by any positive, integer number and the purchase cost corresponding to the new inputted quantity will appear.

20. The second run demonstration shows the input screen for a recurring demand buy of the MSE CCA. Inputs for the constraints, holding cost factors, and forecasted demand rate of the item are needed when recurring demands are analyzed. A demand rate of 2 per month, which is the same as 24 items per year, was inputted for this run. After selecting the EOQ button, the output screen for these inputs will be shown.

21. The output screen for the recurring demand buy is shown on this slide
The output screen for the recurring demand buy is shown on this slide. For the monthly replenishment rate of 2, a comparison of the total annual costs associated with the Economic Order Quantity (EOQ) in each range is shown in the upper portion. The EOQ with the least total annual cost is displayed as 30 items. The information in the middle portion shows that a buy quantity of 30 will last for 15 months before needing to make another buy.
The bottom portion has the Quantity/Cost Analyzer. A breakout of the total cost over this 15 month period shows its purchase cost, ordering cost and holding cost contributions to the total cost. If desired, the quantity of 30 can be replaced in the Quantity/Cost Calculator by any positive, integer number.

22. For this screen, an input of 60 items was made in the Quantity/Cost Analyzer at the bottom to see its impact. The annual cost, months of time before the next buy, and the total cost breakdown associated with the buy quantity of 60 is displayed. The results show that a buy of 60 items would last for 30 months before needing another buy and the cost breakout for the 30 month timeframe is outputted. The optimization portions above the analyzer remains the same.

23. The final demonstration run shows the same input screen for the MSE CCA recurring demand buy. However, an order is now being placed where the inventory asset position is 5 items below the Reorder Point. After selecting the EOQ button, the output screen for these inputs will be shown.

24. The top portion of the output screen first shows the optimal results for each range without considering the present inventory asset position. The middle portion shows that the most cost effective purchase quantity is 60 items when considering the inventory asset position is 5 items below the reorder point. 5 of the 60 items purchased gets us back up to the reorder point and the additional 55 items are to cover the recurring demands. The lower portion contains the Quantity/Cost Analyzer. It shows that a buy quantity of 60 will last for 27.5 months and it breaks out its purchase cost, ordering cost and holding cost contributions to the total cost. The very bottom shows that if 30 items were bought twice, its total cost over the same 27.5 month time frame would be $457,635. The two buys of 30 is $3,435 more than buying the 60 items in one purchase.
If you let me know that you want a free copy of the Quantity Discount/EOQ Analysis Tool, a zip file will be electronically mailed to each requestor.

25. Inventory Quantity Buildup
IMPACTED BY
LEAD-TIME
INVENTORY ELEMENTS
INV REQUIREMENT
ON ORDER QTY*
ON-HAND QTY
INSURANCE / RESERVE STOCK X NO
SAFETY LEVEL STOCK X YES
RECEIVE ORDER
ADMINISTRATIVE LEAD TIME X YES
PRODUCTION LEAD TIME X YES
REORDER POINT
RE ORDER QUANTITY ECONOMIC ORDER QUANTITY X NO
REQUIREMENT OBJECTIVE
UNFUNDED INSURANCE / RESERVES X NO
ECONOMIC RETENTION X NO
MAX RETENTION LIMIT
EXCESS TO DISPOSAL
When replenishing consumable stock, an order is supposed to be placed when the amount of inventory stock on-hand plus the amount of future stock on-order drops down to the reorder point quantity. The Economic Order Quantity (EOQ) is desired to be the minimum total ownership cost purchase quantity. The EOQ highlighted on this chart replenishes inventory from Order Receipt to the Requirement Objective Quantity.
The reorder point starts by covering any Insurance or Reserve Stock initially placed at the wholesale supply level to cover critical contingencies like war, which causes a surge in demands for the item. Safety Level stock is needed to cover the variability in demand rates and Procurement Lead Time variability. The Procurement Lead Time is the sum of the Administrative Lead Time (ALT) and Production Lead Time (PLT). The ALT is the buyer’s response time covering the time from when the order is required to when the procurement contract is placed plus the time to process the received shipment into stock. The PLT is the seller’s response time from when the contract order is placed to when the customer receives the procured item shipment.
The portion of this chart higher than the Requirement Objective quantity occurs when the on-hand and on-order stock exceeds this requirement. This stock may be retained to cover reserve stock that originally was not funded. Extra stock may also be retained when it is economically smart to hold the extra stock to preclude buying more items in the far future. The maximum retention limit is where the holding cost for the excess quantity equals the potential purchase cost. Quantities in stock above the maximum retention limit should be sent to disposal.
* ON-ORDER QUANTITIES ARE NOT IN INVENTORY