This document discusses an alternative approach to managing economic order quantity (EOQ) based on the ordering cost to interest rate ratio (O/I ratio) rather than the actual ordering and holding costs. It shows that as long as the O/I ratio remains the same, the calculated EOQ, expected number of orders per year (E(O)), and expected average inventory (E(I)) will be the same regardless of the specific ordering cost and interest rate used. The author believes this indicates that the actual costs are not critical inputs. The document presents examples calculating EOQ and the system-wide statistics E(O) and E(I) for different items under different O/I ratios to demonstrate this approach.

1. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
1
Eventhe most casual studentof InventoryManagement ismostlikely familiarwiththe conceptof
EconomicOrderQuantity. EOQ isa balancingact betweenthe costsincurredto “place orders”verses
the cost incurredto “holdthe inventory”. The literatureis repletewithexamples. The twokeyinputsto
the formulaare:1) the cost to orderparts, calledorderingcostoradministrationcost,and 2) the cost to
holdinventory,whichisusuallyexpressedasapercentage of the cost of an item perannum– i.e. an
interestrate.
Mr. D is nota proponentof the standardprocess usuallyassociatedwithEOQ – where numbersusually
setby accounting. Thisis because Mr. D was alwaysskeptical of the costestimates forthe “ordering
cost” and “holdingcost”as they were profferedbythe accountants. Thispaperwill show thatthese
costs are not critical to EOQ management,andwill presentanalternate approachto manage the
process.
First, itis necessary toreview the EOQformula:
Given: O = orderingcost/order
D = annual demand
C = itemcost
I = annual interestrate
EOQ = √2𝑂𝐷/𝐶𝐼 whichcan be rewritten
EOQ = √2𝐷/𝐶 *√ 𝑂/𝐼 whichcan be rewritten
EOQ = √2𝐷/𝐶 *√ 𝑅 where Ris the ratioof orderingcostto interestrate.
It isclear fromthe formulathat anytime the ratioof the orderingcostto the interestrate isthe same
(the O/Iratio),the EOQ for an itemwill evaluate tothe same number. Table 1A illustratesthis. The EOQ
for an itemiscalculated atfour differentsetsof costs. The O/Iratio isthe same forall entries,therefore
the EOQs calculate tothe same number.
Item
Annual
Demand 250
Item Cost $10.00
Ordering
Cost
Interest
Rate O/I Ratio EOQ
Number
of
Reorders
Per Year
@ EOQ
Holding
Cost Per
Year @
EOQ EOQ2
Number
of
Reorders
Per Year
@ EOQ2
Holding
Cost Per
Year @
EOQ2 EOQ3
Number
of
Reorders
Per Year
@ EOQ3
Holding
Cost Per
Year @
EOQ3
$100.00 40.00% 250.0 111.8 2.2 $559.02 112.0 2.2 $560.00 112.0 2.2 $560.00
$50.00 20.00% 250.0 111.8 2.2 $559.02 112.0 2.2 $560.00 112.0 2.2 $560.00
$25.00 10.00% 250.0 111.8 2.2 $559.02 112.0 2.2 $560.00 112.0 2.2 $560.00
$10.00 4.00% 250.0 111.8 2.2 $559.02 112.0 2.2 $560.00 112.0 2.2 $560.00
Table 1A -EOQ at Four Cost Estimates

2. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
2
Note:EOQ2 isthe EOQ roundedupto the nexthigherinteger. Thisisnecessarysince itisnotpossible
to ordera fractional item. Roundingupispreferredsince manyhigh-cost/low-volume items could
calculate toan EOQ of zeroif simple roundingisused. EOQ3isthe smallerof EOQ2 or the item’sannual
demand. The purpose of thisisto preventthe systematicorderingof a multi-yearquantityof parts. It
was deemedpreferable in Mr.D’s businesstohave the inventoryplannersperformamanual overrideto
procure parts that coveredmultiple yearsof demand. Mr.D has seenotherrestrictions onthe
calculationof EOQ,and theywill ultimatelyhave animpacton the managementof EOQ - viathe
calculationof EOQ3.
Of course,eventhoughthe EOQsfromTable 1A evaluate tothe same numberthe cost curvesare not
the same,as showinTable 1B.
Item
Annual
Demand Item Cost
250 $10.00
Order
Cost $100.00 $50.00 $25.00 $10.00
Interest
Rate 40% 20% 10% 4%
Order
Quantity
Total
Cost1
Total
Cost2
Total
Cost3
Total
Cost4
10 $2,520.00 $1,260.00 $630.00 $252.00
20 $1,290.00 $645.00 $322.50 $129.00
30 $893.33 $446.67 $223.33 $89.33
40 $705.00 $352.50 $176.25 $70.50
50 $600.00 $300.00 $150.00 $60.00
60 $536.67 $268.33 $134.17 $53.67
70 $497.14 $248.57 $124.29 $49.71
80 $472.50 $236.25 $118.13 $47.25
90 $457.78 $228.89 $114.44 $45.78
100 $450.00 $225.00 $112.50 $45.00
110 $447.27 $223.64 $111.82 $44.73
120 $448.33 $224.17 $112.08 $44.83
130 $452.31 $226.15 $113.08 $45.23
140 $458.57 $229.29 $114.64 $45.86
150 $466.67 $233.33 $116.67 $46.67
160 $476.25 $238.13 $119.06 $47.63
170 $487.06 $243.53 $121.76 $48.71
180 $498.89 $249.44 $124.72 $49.89
190 $511.58 $255.79 $127.89 $51.16
200 $525.00 $262.50 $131.25 $52.50
210 $539.05 $269.52 $134.76 $53.90
220 $553.64 $276.82 $138.41 $55.36
230 $568.70 $284.35 $142.17 $56.87
240 $584.17 $292.08 $146.04 $58.42
250 $600.00 $300.00 $150.00 $60.00
Table 1B - EOQ Total Cost Curves for Four Sets of Cost
$0.00
$500.00
$1,000.00
$1,500.00
$2,000.00
$2,500.00
$3,000.00
0 50 100 150 200 250
TotalCost
Order Quantity
EOQ Total Cost
Total Cost1
Total Cost2
Total Cost3
Total Cost4

3. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
3
Table 1C showsthe EOQ data foran item where the calculatedEOQisgreaterthan the item’sannual
demand. Note howEOQ3 islowerthanthe EOQ,as itwas setequal tothe item’sannual demand.
Mr. D’s preferredvariable fordoingEOQmanagementisEOQ3.
Item
Annual
Demand 100
Item Cost $1.00
Ordering
Cost
Interest
Rate O/I Ratio EOQ
Number
of
Reorders
Per Year
@ EOQ
Holding
Cost Per
Year @
EOQ EOQ2
Number
of
Reorders
Per Year
@ EOQ2
Holding
Cost Per
Year @
EOQ2 EOQ3
Number
of
Reorders
Per Year
@ EOQ3
Holding
Cost Per
Year @
EOQ3
$100.00 40.00% 250.0 223.6 0.4 $111.80 224.0 0.4 $112.00 100.0 1.0 $50.00
$50.00 20.00% 250.0 223.6 0.4 $111.80 224.0 0.4 $112.00 100.0 1.0 $50.00
$25.00 10.00% 250.0 223.6 0.4 $111.80 224.0 0.4 $112.00 100.0 1.0 $50.00
$10.00 4.00% 250.0 223.6 0.4 $111.80 224.0 0.4 $112.00 100.0 1.0 $50.00
Table 1C -EOQ at Four Cost Estimates
This“O/I ratioquirk”in the EOQ formulaiswhy Mr. D believes the “actual”orderingcostandinterest
rate are not critical to the EOQ formula. Intuitively toMr.D, it seemedlogical thatwhenatenfold
difference inthe orderingcostandinterestrate will resultin the same EOQfor an item, those costs
seemtobe irrelevant. Perhapsadifferentapproachto EOQ isnecessary – a systemoriented approach.
Considerthe inventory systemas a whole. Everyinventorysystemisinacurrentstate that Mr. D calls
State(S). Thisstate hasas its inputs (1) the orderingcostand interestrate (reallythe O/Iratio),(2) the
demandforeach item, and(3) the standard cost data foreach item.
The outputstatistics foreach itemare the EOQ plus twootherstatistics:e(o) - the expectednumberof
orders to be generatedinayear,and e(i) - the expected average inventory dollars. Forthe itemin
Table 1A these valuesare:
e(o) = Demand/EOQ= 250 / 111.8 = 2.2 orders/yr
e(i) = ½EOQ*Cost= (111.8/2) * $10.00 = $559.02
This paperwill alsocalculate e(o2) &e(i2),pluse(o3) &e(i3) –the expectedvaluesbaseduponthe
EOQ2 andEOQ3 values.
At the systemlevel thereare twostatisticsof interest: the total numbersof ordersexpectedtobe
generated –denotedasE(O) - whichisthe summationof the e(o) forall stockeditems. Likewise,the
total inventorygenerated -E(I) - isthe summationof the e(i) forall stockeditems. These twosystem-
wide statisticsare the critical measuresinthe EOQmanagementprocess: The E(O) estimates howmuch
work (cost) will be requiredtoprocessthe orders, andthe E(I) estimates how muchinventorywill be
required. DittoforE(O2) & E(I2), andE(O3) & E(I3).

4. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
4
Note:Lower case e(o) & e(i) are meanttodenote the expectedvaluesforaparticularitem. Uppercase
E(O) & E(I) are meantto denote expectedvaluesforthe complete system.
Considerthe systemof five itemsinTable 2A. Forthe entire system,the State(S) value of E(O) is 15.7
and the value of E(I) is$3920.72 – baseduponan O/I ratioof 250. In otherwords, forthis system we
wouldexpecttolaunch a total of 15.7 replenishmentordersinayearand have an average inventory
level due toEOQof $3920.72.
Ordering
Cost
Interest
Rate O/I Ratio
$10.00 4.00% 250
Item
Number
Annual
Demand ItemCost EOQ e(o) e(i) EOQ2 e(o2) e(i2) EOQ3 e(o3) e(i3)
Pn1 1000 $0.33 1230.9 0.8 $203.10 1231 0.8 $203.12 1000 1.0 $165.00
Pn2 250 $10.00 111.8 2.2 $559.02 112 2.2 $560.00 112 2.2 $560.00
Pn3 200 $25.00 63.2 3.2 $790.57 64 3.1 $800.00 64 3.1 $800.00
Pn4 100 $100.00 22.4 4.5 $1,118.03 23 4.3 $1,150.00 23 4.3 $1,150.00
Pn5 25 $500.00 5.0 5.0 $1,250.00 5 5.0 $1,250.00 5 5.0 $1,250.00
Sum 15.7 $3,920.72 15.5 $3,963.12 15.7 $3,925.00
E(O) E(I) E(O2) E(I2) E(O3) E(I3)
Table 2A - EOQ for Five Test Parts @ O/I ratio 250
The exact same results canbe achievedwhenotherorderingcostandinterestratesare used – as long
as the O/I ratioremainsat 250.
We can choose to go to an alternate State(S’)byusingadifferentO/IratiosshowninTable 2B.
Ordering
Cost
Interest
Rate O/I Ratio
$15.00 5.00% 300
Item
Number
Annual
Demand Item Cost EOQ e(o) e(i) EOQ2 e(o2) e(i2) EOQ3 e(o3) e(i3)
Pn1 1000 $0.33 1348.4 0.7 $222.49 1349 0.7 $222.59 1000 1.0 $165.00
Pn2 250 $10.00 122.5 2.0 $612.37 123 2.0 $615.00 123 2.0 $615.00
Pn3 200 $25.00 69.3 2.9 $866.03 70 2.9 $875.00 70 2.9 $875.00
Pn4 100 $100.00 24.5 4.1 $1,224.74 25 4.0 $1,250.00 25 4.0 $1,250.00
Pn5 25 $500.00 5.5 4.6 $1,369.31 6 4.2 $1,500.00 6 4.2 $1,500.00
Sum 14.3 $4,294.94 13.8 $4,462.59 14.1 $4,405.00
E(O) E(I) E(O2) E(I2) E(O3) E(I3)
Table 2B - EOQ for Five Test Parts @ O/I Ratio 300

5. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
5
Before continuing,itisimportanttounderstandhow the O/Iratioimpacts the EOQ,the E(O),and the
E(I).Table 3 shows the calculateddata foran itemat twentydifferentO/Iratios.
Annual Demand
Fixed Ordering Cost Fixed Interest Rate
O/I Ratio
Interest
Rate @
Fixed
ordering
cost
Ordering
Cost @
Fixed
Interest
Rate EOQ
25 100.00% $2.50 35.4
50 50.00% $5.00 50.0
75 33.33% $7.50 61.2
100 25.00% $10.00 70.7
125 20.00% $12.50 79.1
150 16.67% $15.00 86.6
175 14.29% $17.50 93.5
200 12.50% $20.00 100.0
225 11.11% $22.50 106.1
250 10.00% $25.00 111.8
275 9.09% $27.50 117.3
300 8.33% $30.00 122.5
325 7.69% $32.50 127.5
350 7.14% $35.00 132.3
375 6.67% $37.50 136.9
400 6.25% $40.00 141.4
425 5.88% $42.50 145.8
450 5.56% $45.00 150.0
475 5.26% $47.50 154.1
500 5.00% $50.00 158.1
Table 3 - O/I Ratio Impact on EOQ
250
10.00%$25.00
Item Cost
$10.00
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
E
O
Q
O/I Ratio
EOQvs O/I ratio
As the O/Iratio increases one of twothingsishappening: eitherthe interestrate isdecreasing, orthe
orderingcostis increasing. Inbothcases,itis cheapertoholdinventoryinlieuof orderingmore often,
so as the O/I ratioincreasesthe EOQsalsoincrease.Asthe EOQ increasesthe E(O) decreases
(Demand/EOQ). AsEOQincreasesthe E(I) increase (1/2of EOQ). Ditto forE(O2) & E(I2) andE(O3) &
E(I3).
Afterunderstandingthatthe O/Iratio isthe drivingforce inthe calculationof EOQ, the correct
managementquestion thenbecomes:“Whatisthe correct O/Iratio forthe business”?(Not“Whatare
the correct orderingcostand interestrate”?) Fortunately, the questioniseasytoanswersince
alternative statesforthe systemare easytodetermine.

6. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
6
By wayof illustratinghow the O/IratioimpactsE(O) andE(I),Table 4 shows twenty O/Iratioalternatives
for the systemof the five testitemsfromTable 2A, and plotsthe variablesE(O) vs.E(I).
O/I Ratio E(O) E(I) E(O2) E(I2) E(O3) E(I3)
25 49.6 $1,240 44.5 $1,394 44.5 $1,394
50 35.1 $1,753 32.0 $1,953 32.0 $1,953
75 28.6 $2,147 27.3 $2,259 27.3 $2,259
100 24.8 $2,480 22.7 $2,734 22.7 $2,734
125 22.2 $2,772 21.2 $2,906 21.2 $2,906
150 20.2 $3,037 19.8 $3,105 19.8 $3,105
175 18.7 $3,280 17.7 $3,502 17.7 $3,498
200 17.5 $3,507 16.9 $3,644 17.0 $3,628
225 16.5 $3,720 16.1 $3,828 16.2 $3,800
250 15.7 $3,921 15.5 $3,963 15.7 $3,925
275 15.0 $4,112 14.2 $4,341 14.4 $4,293
300 14.3 $4,295 13.8 $4,463 14.1 $4,405
325 13.8 $4,470 13.4 $4,584 13.7 $4,518
350 13.3 $4,639 13.1 $4,693 13.4 $4,618
375 12.8 $4,802 12.2 $5,059 12.5 $4,975
400 12.4 $4,959 11.9 $5,167 12.3 $5,075
425 12.0 $5,112 11.6 $5,282 12.0 $5,183
450 11.7 $5,260 11.5 $5,335 11.9 $5,228
475 11.4 $5,404 11.3 $5,455 11.7 $5,340
500 11.1 $5,545 10.6 $5,807 11.0 $5,685
Table 4 - O/I Ratio Alternatives For Five Test Parts
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0
E(I)
E(O)
E(I)vs E(O)
Giventhatthe State(S) forthe systemof five testpartshasan E(O) of 15.7 and an E(I) of $3920.72, the
questionis:“Cana State(S’) be foundthatwill betterfitthe businessneeds”? The answeris“Most
likely”. Ascanbe seenfromthe graph inTable 4, the options available(alternate State(S’)) are very
clear. Any of the combinationsof E(O) andE(I) onthe response curve are possible.
The choice of an alternate O/Iratiocouldbe as simple aschoosingone fromthe table based on
experience and“gutfeel”,orperhapsbaseduponrestraintsfromthe current businessclimate.
Latter it will be shownhowtolookat the alternativesandchoose whichscenariobestmeetsthe
businessneeds,viaasimple financial analysis.
Table 5 shows the applicationof the O/I ratio ina real worldsituation. The graphin Table 5 is the plot
of E(O3) vs.E(I3) for 20 differentO/Iratioscenarios. The datain Table 5 is froma service partsinventory
of more thanfifteen thousand items.
O/I Ratio E(O) E(I) E(O2) E(I2) E(O3) E(I3)
25 112,802 $2,820,047 94,147 $3,926,346 95,709 $3,911,773
50 79,763 $3,988,149 69,263 $5,019,715 71,411 $4,980,873
75 65,126 $4,884,465 57,615 $5,891,349 60,184 $5,823,494
100 56,401 $5,640,094 50,670 $6,610,132 53,571 $6,510,819
125 50,447 $6,305,817 45,621 $7,279,041 48,808 $7,144,666
150 46,051 $6,907,676 41,908 $7,879,603 45,334 $7,710,009
175 42,635 $7,461,143 39,035 $8,428,014 42,674 $8,220,663
200 39,881 $7,976,297 36,661 $8,938,463 40,492 $8,692,330
225 37,601 $8,460,141 34,722 $9,408,897 38,727 $9,122,865
250 35,671 $8,917,771 33,076 $9,849,476 37,240 $9,523,104
275 34,011 $9,353,037 31,611 $10,284,460 35,920 $9,917,711
300 32,563 $9,768,929 30,324 $10,706,889 34,768 $10,298,486
325 31,286 $10,167,824 29,215 $11,097,664 33,786 $10,646,282
350 30,148 $10,551,649 28,230 $11,469,202 32,920 $10,975,318
375 29,125 $10,921,995 27,289 $11,859,172 32,092 $11,321,630
400 28,200 $11,280,188 26,491 $12,205,449 31,401 $11,623,099
425 27,358 $11,627,351 25,735 $12,551,534 30,749 $11,923,432
450 26,588 $11,964,446 25,053 $12,883,819 30,163 $12,210,726
475 25,879 $12,292,299 24,404 $13,218,936 29,605 $12,500,570
500 25,223 $12,611,633 23,827 $13,532,524 29,118 $12,767,003
Table 5 - O/I Ratio Alternatives for a Service Parts Business
$0
$2,000,000
$4,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
$14,000,000
20,000 40,000 60,000 80,000 100,000
InventoryDollars
Number of Orders/Year
E(O3)vs. E(I3)

7. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
7
Afterseeingthischart,the questionthen becomes:“Woulditbe bettertohave more ordersand have
lessinventoryorvice versa”?
To reiterate,thatdecisionisoftendrivenbybusinessconditions. If the “goldoffice”ispushingfora
reductionin inventory, itmaynotbe advisable tochoose anO/Iratio that increasesinventory. Onthe
otherhand,if the numberof ordersexceedsthatcapacityof the manpoweravailabletocomplete the
workrequired,thenanincrease ininventory(reductioninorders) maybythe bestchoice.
Mr. D, inhisquartercenturymanaginginventory,experiencedsix majorcyclesof inventorychange.
Three were causedbyuppermanagementsettingnew ROA goals,andthree were causedby large
businessdownturns.
In the three caseswhere the ROA goalswere increased,Mr.D’s decision logicindeterminingthe
“correct O/Iratio” was this:“Inventory isa factorin ROA,butthe laborexpensefor the increased
ordering of partsis not. Therefore,the prudentaction is to reduceinventory atthe expenseof labor
costs”. The practical upshotof thatlogicwas that Mr. D useda lowerO/Iratio to drive a lower
inventory. (Service levelsandsafetystockwere alsochanged,butthat’snot the subjectof thispaper.)
As those ROA managementobjectivescame andwent, service level relatedissuesusuallyfollowed in
theirwake andinventorywastypicallyincreased toimprove service. Itwasthenthat Mr. D wentback
to a higherO/Iratio,and the EOQ quantitieswere increased.
Businessdownturnswerehandledmuch inthe same way. As inventorybalancesare usually the target
of managementfocusduringhardtimes, Mr.D’s goal wasto keepthe numberof ordersgenerated ata
constantlevel byreducingthe EOQs. When the businessrecoveredthe EOQswere increased.
The salientissue of these real lifeexamplesisthat Mr. D didnot give a hootabout the “real”cost of
orderingpartsand the cost of holdinginventory. He knew whathis currentState(S) wasand he knew
that the new State(S’) required more orlessinventory. Ipso facto,he hadtouse a differentO/Iratio.
The underlyingorderingcostandinterestrate didnotchange - whatevertheywere. Those costswere
justnot relevanttothe objective athand.
As a side note,when Mr.D came to hisfirstinventorymanagement position EOQlogicwasnotused to
setorder quantities. Orderquantitieswere determinedbaseduponitemcost –expensive partsordered
more oftenthancheap parts. When Mr. D firstimplemented EOQlogichisgoal wasto keepthe E(O)
aboutthe same as ithad beenunderthe oldprice stratifiedlogic. Once again, Mr. D didnotconsider
the “real” costsusedinthe EOQ formula. He justchose an O/I ratiothat resultedin the E(O) forthe new
State(S’) beingalmostidentical tothe E(O) forthe old State(S). The resultwasthat the E(I) for the EOQ
processwassubstantiallylowerthanthe E(I) forthe price stratified logic.
If your process doesnot permit you to ignore the costs factors that drive the EOQ process thenitis at
thispointthat the “real”orderingcost andholdingcostbecome important. Replenishmentorders
require manpowertoplace andto receive intostock. LargerEOQs require more moneytoacquire and,
if the current warehouse doesnothave sufficient additional storage capacity, mayrequirethe spending
of capital onnewfacilities. Fortunately,these business decisions canbe more easilymade by the use of
O/Iratio, as the nexttable will show.

8. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
8
Table 6A showsa simple costanalysis of the O/Iratios alternatives fromTable 5. Inessence,itisthe
EOQ analysisatthe systemlevel –comparingorderingcostversesinventory holdingcost. Table 6A is
baseduponEOQ3 and its resultingE(O3) &E(I3).
Stockroom
Labor
Rate/Hr
Stockroom
Order
Process
Rate/Hr
Planning
Labor
Rate/Hr
Planning
Order
Process
Rate/Hr Interst Rate
Ordering
Cost per
Order
Financial
O/I Ratio
$30.00 6 $40.00 20 7.00% $7.00 100
O/I Ratio E(O3) E(I3)
Planning
Ordering
Cost
Stockroom
Receiving
Cost
Inventory
Holding
Cost Total Cost
25 95,709 $3,911,773 $191,417 478,544 $273,824 $943,785
50 71,411 $4,980,873 $142,823 357,057 $348,661 $848,541
75 60,184 $5,823,494 $120,368 300,920 $407,645 $828,933
80 58,669 $5,963,335 $117,339 293,347 $417,433 $828,120
84 57,565 $6,068,370 $115,130 287,826 $424,786 $827,743
85 57,301 $6,094,911 $114,602 286,504 $426,644 $827,749
86 57,007 $6,125,209 $114,015 285,036 $428,765 $827,815
87 56,729 $6,155,431 $113,459 283,646 $430,880 $827,985
88 56,447 $6,185,508 $112,894 282,234 $432,986 $828,113
89 56,193 $6,212,663 $112,386 280,964 $434,886 $828,236
90 55,920 $6,244,194 $111,839 279,598 $437,094 $828,531
100 53,571 $6,510,819 $107,143 267,857 $455,757 $830,757
106 52,219 $6,676,884 $104,439 261,097 $467,382 $832,917
107 52,037 $6,700,167 $104,074 260,186 $469,012 $833,272
108 51,820 $6,729,235 $103,640 259,099 $471,046 $833,785
125 48,808 $7,144,666 $97,616 244,040 $500,127 $841,783
150 45,334 $7,710,009 $90,667 226,669 $539,701 $857,037
175 42,674 $8,220,663 $85,349 213,372 $575,446 $874,168
200 40,492 $8,692,330 $80,983 202,458 $608,463 $891,904
225 38,727 $9,122,865 $77,454 193,636 $638,601 $909,691
250 37,240 $9,523,104 $74,480 186,199 $666,617 $927,296
275 35,920 $9,917,711 $71,840 179,599 $694,240 $945,679
300 34,768 $10,298,486 $69,537 173,841 $720,894 $964,272
325 33,786 $10,646,282 $67,573 168,932 $745,240 $981,745
350 32,920 $10,975,318 $65,841 164,602 $768,272 $998,715
375 32,092 $11,321,630 $64,184 160,461 $792,514 $1,017,159
400 31,401 $11,623,099 $62,802 157,006 $813,617 $1,033,426
425 30,749 $11,923,432 $61,497 153,743 $834,640 $1,049,880
450 30,163 $12,210,726 $60,326 150,814 $854,751 $1,065,890
475 29,605 $12,500,570 $59,210 148,025 $875,040 $1,082,275
500 29,118 $12,767,003 $58,236 145,589 $893,690 $1,097,515
Table 6A - EOQ3 Financial Cost Analysis for Optimal O/I Ratio
$300,000
$400,000
$500,000
$600,000
$700,000
$800,000
$900,000
$1,000,000
$1,100,000
$1,200,000
0 50 100 150 200 250 300 350 400 450 500
TotalCost
O/I Ratio
Total Cost vs O/I Ratio
In thisanalysisthere are twotouchpointsthat addto orderingcost:whenthe inventory plannerreviews
an ordersuggestionandreleasesittoproduction/purchasing,andwhenthe orderisreceivedandputto
stock. Analysisof thisprocess hasshownthatan inventoryplannercanreview 20 ordersperhour and
the labor rate for planningis$40.00 per hour. Stockroompersonnel canreceive andstocksix ordersper
hour and stockroomlabor rate is $30.00 perhour. The combinationof the orderingcostsandrates
resultsinan individual ordercostof $7.00 per order. The cost of borrowingmoneyissevenpercent.
The analysiscalculateshowmanyman-hoursof time will be neededtoplanandreceive the E(O3) and
whatthose hours will costinwages,plushow muchmoneyininterestwill be spentonthe E(I3). The
total cost is plottedagainstthe O/Iratio.
Baseduponthisanalysis, the optimal O/I ratio for this businessis 84. Note thatthe orderingcostof
$7.00 perorder and7% interestrate usedinthisanalysis resultsin afinancial O/Iratioof 100.
As an FYI,for the EOQ2, E(O2) and E(I2) values,the optimal O/Iratioisalso84. Mr. D was surprisedat
this,as he expectedthe EOQ3logicto have more impacton the final EOQ.

9. EOQ and the O/I Ratio- A System approach to EOQ Management.
April 30, 2011
9
By wayof closingthe loop,Table 6B showsthe same analysisbasedonthe fractional EOQ. Note that
the optimal O/Iratiofor thisanalysisis100 – the same as the O/I ratiofor the orderingcostto interest
rate usedinthisfinancial analysis. Of course,usingEOQisnonsensical,asitisimpossible toorderan
iteminfractional quantities.
Stockroom
Labor
Rate/Hr
Stockroom
Order Process
Rate/Hr
Planning
Labor
Rate/Hr
Planning
Order
Process
Rate/Hr Interst Rate
Ordering
Cost per
Order
Financial
O/I Ratio
$30.00 6 $40.00 20 7.00% $7.00 100
O/I Ratio E(O) E(I)
Planning
Ordering
Cost
Stockroom
Receiving
Cost
Inventory
Holding
Cost Total Cost
25 112,802 $2,820,047 $225,604 564,009 $197,403 $987,016
50 79,763 $3,988,149 $159,526 398,815 $279,170 $837,511
75 65,126 $4,884,465 $130,252 325,631 $341,913 $797,796
88 60,124 $5,290,877 $120,247 300,618 $370,361 $791,227
89 59,785 $5,320,854 $119,570 298,924 $372,460 $790,954
90 59,452 $5,350,663 $118,904 297,259 $374,546 $790,709
99 56,685 $5,611,822 $113,370 283,425 $392,828 $789,623
100 56,401 $5,640,094 $112,802 282,005 $394,807 $789,613
101 56,121 $5,668,224 $112,242 280,605 $396,776 $789,623
125 50,447 $6,305,817 $100,893 252,233 $441,407 $794,533
150 46,051 $6,907,676 $92,102 230,256 $483,537 $805,896
175 42,635 $7,461,143 $85,270 213,176 $522,280 $820,726
200 39,881 $7,976,297 $79,763 199,407 $558,341 $837,511
225 37,601 $8,460,141 $75,201 188,003 $592,210 $855,414
250 35,671 $8,917,771 $71,342 178,355 $624,244 $873,942
275 34,011 $9,353,037 $68,022 170,055 $654,713 $892,790
300 32,563 $9,768,929 $65,126 162,815 $683,825 $911,767
325 31,286 $10,167,824 $62,571 156,428 $711,748 $930,747
350 30,148 $10,551,649 $60,295 150,738 $738,615 $949,648
375 29,125 $10,921,995 $58,251 145,627 $764,540 $968,417
400 28,200 $11,280,188 $56,401 141,002 $789,613 $987,016
425 27,358 $11,627,351 $54,717 136,792 $813,915 $1,005,424
450 26,588 $11,964,446 $53,175 132,938 $837,511 $1,023,625
475 25,879 $12,292,299 $51,757 129,393 $860,461 $1,041,611
500 25,223 $12,611,633 $50,447 126,116 $882,814 $1,059,377
Table 6B - EOQ Financial Cost Analysis for Optimal O/I Ratio
$300,000
$400,000
$500,000
$600,000
$700,000
$800,000
$900,000
$1,000,000
$1,100,000
0 50 100 150 200 250 300 350 400 450 500
TotalCost
O/I Ratio
Total Cost vs O/I Ratio
In summary,because of the “quirk”inthe EOQ formulathe actual orderingcostand interestrate are not
critical to the EOQ formula.
They may be important,at the systemlevel,whendecidingwhichO/Iratioismostcost effective.
Theyalsomay not be importantinthe managementof EOQat all.
Well there itis:one more tasty entrée inMr. D’s smorgasbordof ideas. Take whatyou want,andleave
the rest.
Contact Mr. D at MisterD@windstream.net
Optimize EOQ
OptimizingEOQ
Alternate EOQ