Mr. D developed a three-step process to optimize service levels for inventory parts at his company. The process involved 1) calculating initial service levels based on order volume and modifying it based on cost, 2) tweaking the overall service level through iterations to reach a target, and 3) combining data for all parts and selecting iterations to reach the target aggregate service level. This iterative process usually took two to three runs to optimize the service level program. Later, Mr. D implemented a normal distribution approach he learned from a book that significantly reduced safety stock levels over his previous method.

1. How to Optimize Service Levels
1
It iswell understoodthatservice level isabigfactor inthe amountof stock an inventorysystemwill
generate. Higherservice levelsmean more safety stockisrequiredtomeetthose goals. Itis,therefore,
incumbentonthe inventorymanagerto optimizesafetystock andgetthe mostout of the inventory
investment. Asthe architectof Sundstrand’sservice partsinventory system,Mr.D realizedthisearlyon
inhis tenure. Thispaperdescribes how Mr.D attackedthisissue.
Mr. D’sinitial approachwasfairly simple. Mr. D believed thatthe partwiththe highestnumberof
customerordersshouldhave the highestservice level andthe partwiththe lowestnumberof orders
shouldhave the lowest. Mr.D also believed thatlow costitemsshouldhave higherservicelevelsthen
highcost items. So, Mr. D developedathree stepprocessforoptimizing service level.
1. Calculate aninitial service level baseduponcustomerordervolume.
2. Modifythe initial servicelevel upordownbasedona costmatrix.
3. Addor subtract a constant quantitytotweakthe overall service level tothe target value.
Thiswas an iterative process,andusually required twotothree tweakstothe service level programto
getthe aggregate service level settothe targetedvalue.
The logicof Step2 was determinedbyastructural analysis andwaspart of the tweakingdone between
program runs. The maximumallowableservicelevel foranyitemwas99% and the minimumwas50%.
The overall aggregate service levelforall partsvariedovertime tofitthe businessneeds,butwas
usuallybetween90and 95 percent. Mr. D usedthismethodforalmosttwenty years.
In 2005, Mr. D was given a copyof Dr. Craig Sherbrooke’sbook OptimalInventoryModeling of Systems.
Mr. D was impressed bythe Doctor’s methodof optimizingsafetystocks.However, Mr.D believed that
the Poisson approachthe Doctor had usedwasgoingto be intractable forany large populationof parts.
To avoidthis issue withthe Poissonprocess Mr.D appliedanormal distributionapproachand
implemented thisnewmethod in2005. The reductioninsafetystockover Mr. D’s previousmethod
was significant. However, Mr.D warns that thismethodisextremelybiasedagainsthighcostitems,and
may raise the level of “back-ordereddollars”toan unacceptable level.

2. How to Optimize Service Levels
2
Let’s getright to the rat killing. The optimization logicis reallyquite simple –goingfromzeropiecesof
safetytosome maximumnumberof pieces, we calculatehow muchservice level improvementeach
additional pieceof safetystock produces, andthenquantifythatimprovementin termsof the costto
buythat piece of stock – what Dr. Sherbrooke called “bangforthe buck”. Table 1A is the “bang forthe
buck” data fora sample item.
Part
Number
Descrip-
tion Unit Cost
Annual
Number CO
Average
Monthly
Number CO
Sigma of
Monthly
Number CO
Annual
Quantity
Ordered
Average
Monthly
Quantity
Ordered
Sigma of
Monthly
Quantity
Ordered
Lead Time
in Days
PN1 Bearing $108.32 121 10.1 3.2 766 63.8 18.7 154
4
5
Units SS Per
Iteration
MaxN for
CO
Sigma @ Lt
Monthly CO MaxN for QTY
Sigma @ Lt
Monthly Qty AOQ
6 1 20 7.3 101 42.3 6.3
7
A B C D E F G H I J K
Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Cumulative
Increase in
Number of
Orders
Serviced
Cumulative
Bang for Buck
10 0 0 50.00% 60.5000 0.0 0.0
11 1 1.0 55.41% 5.41% 67.0518 6.5518 0.0096 6.5518 0.0096
12 2 2.0 60.73% 5.32% 73.4834 6.4317 0.0094 12.9834 0.0095
13 3 3.0 65.85% 5.12% 79.6814 6.1979 0.0090 19.1814 0.0093
14 4 4.0 70.70% 4.85% 85.5446 5.8632 0.0086 25.0446 0.0091
15 5 5.0 75.20% 4.50% 90.9894 5.4448 0.0079 30.4894 0.0089
16 6 6.0 79.30% 4.10% 95.9530 4.9636 0.0072 35.4530 0.0086
17 7 7.0 82.97% 3.67% 100.3950 4.4419 0.0065 39.8950 0.0083
18 8 8.0 86.20% 3.22% 104.2971 3.9022 0.0057 43.7971 0.0080
19 9 9.0 88.98% 2.78% 107.6623 3.3652 0.0049 47.1623 0.0076
20 10 10.0 91.33% 2.35% 110.5112 2.8489 0.0042 50.0112 0.0073
21 11 11.0 93.29% 1.96% 112.8787 2.3675 0.0035 52.3787 0.0069
22 12 12.0 94.88% 1.60% 114.8102 1.9314 0.0028 54.3102 0.0066
23 13 13.0 96.16% 1.28% 116.3570 1.5468 0.0023 55.8570 0.0063
24 14 14.0 97.17% 1.00% 117.5730 1.2160 0.0018 57.0730 0.0059
25 15 15.0 97.94% 0.78% 118.5115 0.9385 0.0014 58.0115 0.0056
26 16 16.0 98.53% 0.59% 119.2224 0.7110 0.0010 58.7224 0.0054
27 17 17.0 98.97% 0.44% 119.7512 0.5288 0.0008 59.2512 0.0051
28 18 18.0 99.29% 0.32% 120.1372 0.3860 0.0006 59.6372 0.0048
29 19 19.0 99.52% 0.23% 120.4139 0.2767 0.0004 59.9139 0.0046
30 20 20.0 99.68% 0.16% 120.6085 0.1946 0.0003 60.1085 0.0044
Table 1A - Bang for Buck Data for PN1
Note that the blue numbersandlettersare the row and cell numbers fromthe Excel table. Toenhance
the explanation of the process,the calculations done in the analysis willbe shownasExcel formulas.
Data definitions:
Part Number– The itemnumberof the detail part. These part numbershave beenchangedtoprotect
the innocent,butthey are actual itemsfroma real service partsbusiness.
Description– The nomenclature of the item.
UnitCost – The standard unitcost of the item.

3. How to Optimize Service Levels
3
Annual NumberCO – The forecastnumberof customerordersexpectedinthe next12months. If a
forecastforthis statisticisnotavailable historical datacanbe usedinitsstead,or can be usedto“ratio
out” an estimate baseduponthe forecastof quantity versesthe historical quantitysold.
Average Monthly NumberCO – The forecastannual numberof customerorders dividedby12.
Sigma of MonthlyNumber CO – The standarddeviation of the forecastmonthlynumberof customer
orders.
Annual Quantity Ordered– The quantity forecasttobe soldinthe next12 months.
Average Monthly Quantity Ordered- The forecastquantitydividedby12.
Sigma of MonthlyQuantity Ordered – The standarddeviationof the monthlyforecastquantity.
Lead Time inDays – The procurementormanufacturingleadtime forthe item.
AOQ – The average orderquantity:
= total quantityordereddividedbynumberof orders.
=H3/E3
Sigma @ Lt Monthly CO – The standarddeviationof the numberof customer ordersoverthe full lead
time. BasicStatisticsshowhowto calculate this fromthe sigmaof the monthlydata.
= (standarddeviationof monthly numberof orders) *Sqrt(lead-time/30)
= G3*SQRT(K3/30)
MaxN for CO – The highestnumberof safetystockunitsthatwill be calculatedforthisitem.
= the 99th percentileof the normal distribution
= ROUNDUP(NORMINV(0.99,0,G6) + 2,0)
UnitsSS PerIteration – The numberof unitsof safetystockeach iterationof the analysis.
Thisanalysiswill doamaximumof 20 iterations,sodivideMaxN by20, but thiscannot be lessthan1.
See Table 1C for an example where thisnumberisgreaterthan1.
= MAX(F6/20,1)
The processto optimize aggregate service level isasfollows:
Step 1 – Start at zero unitsof safetystock - “Iteration0”.
We knowfrominventorytheorythat anitemwithnosafetystock will achieve a50% service level.
Therefore,the expectedannualnumberof customersorders coveredata 50% service level is½the
annual orderquantity. ForPN1 this is 60.5 orders.
Step2 – Addone iterationof safetystock.Repeatuntil maximumlimitreached.
Calculate the expectedservice level:
For PN1,one iterationis one piece of safetystock. This will produce aservice levelof:
SL = NORMDIST(C11,0,$G$6,TRUE) = 55.41% foriteration1

4. How to Optimize Service Levels
4
Calculate the expectednumberoforders servicedfor the current iteration:
ENOS = D11*$E$3 = 55.41 * 121 = 67.05 foriteration1
Calculate the increase in numberof orders servicedoverthe last iteration:
INOS= F11-F10 = 67.05 – 60.5 = 6.55 for iteration1 overiteration0
Calculate the cost to achieve thisincrease in orders serviced– the bang for the buck.
B4B = G11/ ($C$3*$E$6*$K$6)
B4B = (increase innumberordersserviced) /(costof inventoryinvested)
B4B = 6.55 / (unitcost* Unitsperiteration* AOQ)
= 6.55 / (108.32 * 1 * 6.3)
= 0.0096
In simple words,the investmentof 1unitof safetystockforthisitemincreasedthe numberof
ordersservicedby6.55. Dividingthe increase inorders bythe costof inventoryinvestment
shows howmanyadditional orderswere servicedperdollarof inventoryinvestment. Note that
since safetystocksare calculatedbaseduponthe quantitysold,notthe numberof customer
orders,the investmentneedstobe scaledbythe average orderquantity. Therefore,forthis
firstpiece of safetystockforPN1 an additional .0096 orderswere servicedforeachdollarof
cost spentonthe “piece”of stock.
Calculate the cumulative increase in orders servicedfromzero safetystock to this iteration.
CINOS =I10+G11
Calculate the cumulative Bang for the buck.
CB4B =I11/ ($C$3*C11*$K$6)
The logicinfavorof usingcumulative dataisthatwe cannot sell the (N+1)thunitof safety stock
until we firstsell the Nthunit. Therefore, we calculate the cumulativebenefitandcost as the
level of safetystockincreases. Mr.D chose to use the cumulative bangforbuckin his service
level optimization process.
Tables1B through1F showthe analysisforfive additional items (atthe endof the discussion). Note
howPN5 islowcost and the bang for the buckin large. PN2 isveryexpensive andhasa verylow bang
for the buck.
Step 3 – Combine the datafor all items andpickthe bestcost levels. Keepincludingthe bestiterations
until the targetaggregate service level isobtained.
Table 2A is the concatenationof the data forall the items. The table issortedby‘Bang forBuck’ from
largestto smallest.

5. How to Optimize Service Levels
5
Total
Number
of CO
Target
Aggregate
Service
Level
400 95.00%
Item
Number Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Total System
Orders
Serviced
System
Service
Level
Begin 50.00% 200.00 0.00 200 50.00%
PN4 1 1 69.76% 19.76% 11.85897 3.35897 0.07734 203.36 50.84%
PN6 1 1 84.83% 34.83% 2.54502 1.04502 0.07703 204.40 51.10%
PN4 2 2 84.97% 15.21% 14.44408 2.58512 0.05952 206.99 51.75%
PN5 1 1 59.20% 9.20% 33.74560 5.24560 0.03768 212.23 53.06%
PN3 6 8.4 77.72% 3.97% 149.23091 7.62407 0.00784 320.05 80.01%
PN1 6 6 79.30% 4.10% 95.95302 4.96360 0.00724 325.01 81.25%
PN3 7 9.8 81.33% 3.60% 156.15103 6.92012 0.00712 331.93 82.98%
PN1 7 7 82.97% 3.67% 100.39495 4.44193 0.00648 336.38 84.09%
PN3 8 11.2 84.55% 3.22% 162.33159 6.18057 0.00636 342.56 85.64%
PN1 8 8 86.20% 3.22% 104.29715 3.90220 0.00569 346.46 86.61%
PN4 5 5 99.52% 1.44% 16.91779 0.24473 0.00564 346.70 86.68%
PN3 9 12.6 87.38% 2.83% 167.76323 5.43164 0.00559 352.14 88.03%
PN5 9 9 98.19% 1.32% 55.96883 0.75254 0.00541 352.89 88.22%
PN1 9 9 88.98% 2.78% 107.66233 3.36518 0.00491 356.25 89.06%
PN3 10 14 89.82% 2.45% 172.46023 4.69700 0.00483 360.95 90.24%
PN1 10 10 91.33% 2.35% 110.51119 2.84886 0.00415 363.80 90.95%
PN6 3 3 99.90% 1.88% 2.99698 0.05626 0.00415 363.86 90.96%
PN3 11 15.4 91.90% 2.08% 176.45691 3.99667 0.00411 367.85 91.96%
PN1 11 11 93.29% 1.96% 112.87872 2.36753 0.00345 370.22 92.55%
PN3 12 16.8 93.65% 1.74% 179.80321 3.34630 0.00344 373.57 93.39%
PN5 10 10 99.00% 0.81% 56.43197 0.46314 0.00333 374.03 93.51%
PN3 13 18.2 95.08% 1.44% 182.56009 2.75688 0.00284 376.79 94.20%
PN1 12 12 94.88% 1.60% 114.81017 1.93145 0.00282 378.72 94.68%
PN3 14 19.6 96.25% 1.16% 184.79500 2.23491 0.00230 380.95 95.24%
PN1 13 13 96.16% 1.28% 116.35696 1.54679 0.00226 382.50 95.62%
PN5 11 11 99.48% 0.47% 56.70204 0.27007 0.00194 382.77 95.69%
PN3 15 21 97.18% 0.93% 186.57774 1.78274 0.00183 384.55 96.14%
PN1 14 14 97.17% 1.00% 117.57300 1.21603 0.00177 385.77 96.44%
PN2 7 7 99.91% 0.28% 9.99135 0.02757 0.00000 398.39 99.60%
PN2 8 8 99.98% 0.07% 9.99829 0.00694 0.00000 398.40 99.60%
Table 2A - Bang for Buck All PN
Some lines have been hidden to save space
Some lines have been hidden to save space
The processof selectingwhichiterationstochoose issimple. Startat the top, whichis the itemthat
givesthe bestbangfor the buck,and workdownuntil the targetedsystemservice level isachieved.
Then,go back through all the iterationsthatwere includedandchoose the lastone foreach item.
For thisexample,usingthe “BangforBuck” criteria,the aggregate service level isachievedafter
includingiteration14for PN1. Includingthisiterationbringsthe servicelevel to95.24%. All iterations
afterthisone are ignored. The lastiterationforall the itemsare highlightedinyellow,exceptforPN2
whichhad noiterationsselectedbefore the targetsystemservice levelwasachieved. Inthisexample
Mr. D has allowedthe servicelevel foriterationstoexceed his99% highlimit. Each inventorymanager
shouldmake theirowndecisionabouthow highaservice level anyitemshouldhave.

6. How to Optimize Service Levels
6
Table 2B isthe analysisbaseduponthe “Cumulative BangforBuck”.
Total
Number
of CO
Target
Aggregate
Service
Level
400 95.00%
Item
Number Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Cumulative
Bang for
Buck
Total System
Orders
Serviced
System
Service
Level
Begin 50.00% 200.00 0.00 200 50.00%
PN4 1 1 0.6976 0.1976 11.8590 3.3590 0.0773 203.36 50.84%
PN6 1 1 0.8483 0.3483 2.5450 1.0450 0.0770 204.40 51.10%
PN5 5 5 0.8778 0.0537 50.0319 3.0588 0.0309 231.51 57.88%
PN5 6 6 0.9187 0.0410 52.3677 2.3358 0.0286 233.85 58.46%
PN4 7 7 0.9999 0.0008 16.9975 0.0137 0.0280 233.86 58.47%
PN6 4 4 1.0000 0.0010 2.9999 0.0030 0.0276 233.87 58.47%
PN5 7 7 0.9484 0.0296 54.0577 1.6900 0.0262 235.56 58.89%
PN5 8 8 0.9687 0.0203 55.2163 1.1586 0.0240 236.71 59.18%
PN6 5 5 1.0000 0.0000 3.0000 0.0001 0.0221 236.71 59.18%
PN5 9 9 0.9819 0.0132 55.9688 0.7525 0.0219 237.47 59.37%
PN5 10 10 0.9900 0.0081 56.4320 0.4631 0.0201 237.93 59.48%
PN5 11 11 0.9948 0.0047 56.7020 0.2701 0.0184 238.20 59.55%
PN5 12 12 0.9974 0.0026 56.8513 0.1492 0.0170 238.35 59.59%
PN3 1 1.4 0.5506 0.0506 105.7134 9.7134 0.0100 248.06 62.02%
PN3 13 18.2 0.9508 0.0144 182.5601 2.7569 0.0068 377.29 94.32%
PN1 12 12 0.9488 0.0160 114.8102 1.9314 0.0066 379.22 94.80%
PN3 14 19.6 0.9625 0.0116 184.7950 2.2349 0.0065 381.45 95.36%
PN1 13 13 0.9616 0.0128 116.3570 1.5468 0.0063 383.00 95.75%
PN2 7 7 0.9991 0.0028 9.9913 0.0276 0.0001 398.39 99.60%
PN2 8 8 0.9998 0.0007 9.9983 0.0069 0.0000 398.40 99.60%
Table 2B - Cumulative Bang for Buck All PN
Some line have been hidden
Some line have been hidden
Some line have been hidden

7. How to Optimize Service Levels
7
Table 3 comparesthree methods – Mr. D’s oldmethod,the Bang forBuck method,andthe Cumulative
Bang for Buckmethod.
Item Number
Number
of CO
Service
level
1990
Method
Orders
Serviced
1990
Method
Service
level
Bang 4
Buck
Method
Orders
Serviced
Bang 4
Buck
Method
Service
Level
Cum.
Bang 4
Buck
Method
Orders
Serviced
Cum.
Bang 4
Buck
Method
Sigma of
Qty over
Lead
Time Unit Cost
Safety
Stock @
1990
Method
Safety
Stock @
Bang 4
Buck
Method
Safety Stock
@ Cum.
Bang 4 Buck
Method
Pn1 121 96.17% 116.4 94.88% 114.8 94.88% 114.8 42.3 $108.32 $8,109.99 $7,480.67 $7,480.67
Pn2 10 75.00% 7.5 50.00% 5.0 50.00% 5.0 2.6 $10,351.50 $18,436.62 $0.00 $0.00
Pn3 192 96.48% 185.2 96.25% 184.8 96.25% 184.8 680.9 $10.21 $12,577.68 $12,375.54 $12,375.54
Pn4 17 91.12% 15.5 99.52% 16.9 99.99% 17.0 7.1 $10.70 $102.85 $197.41 $276.37
Pn5 57 95.25% 54.3 98.19% 56.0 99.74% 56.9 132.9 $4.09 $907.48 $1,138.94 $1,518.58
Pn6 3 63.67% 1.9 99.90% 3.0 100.00% 3.0 2.9 $4.07 $4.19 $37.00 $61.67
Total 400 380.8 380.5 381.5 $40,138.80 $21,229.56 $21,712.84
Average 95.20% 95.12% 95.36%
Table 3 - System Service Level Analysis
It can be seen fromTable 3 that the biggestcontributortothe reductioninsafetystockisitem PN2,
whichisveryexpensive andwentfroma75% to 50% service level. Mr.D’s experience leadshimto
believethatthisitem will be onthe expeditelistatthe endof the month wheneveryone ischasing
sales,soperhapsa 50% service level isnotappropriate. Minimumservice levelsare anotherissue each
managermust take intoconsideration.
Mr. D has developed,justasafunexercise,a“twosided”optimization. Inthisprocess partscan have a
service levelof lessthan50%. PN2wouldprobablyfit these criteria. However,since the Sundstrand
service-partssystemneverallowedthe service levelstobe lessthan50% he neverimplementedthe two
sidedprocessina real worldenviron. The PoissonmethodusedbyDr.Sherbrooke mayallow service
levelstobe optimizedatless than50%. This maybe problematicformostinventorysystems.
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 if youhave anyquestions.

8. How to Optimize Service Levels
8
Part
Number
Descrip-
tion Unit Cost
Annual
Number CO
Average
Monthly
Number CO
Sigma of
Monthly
Number CO
Annual
Quantity
Ordered
Average
Monthly
Quantity
Ordered
Sigma of
Monthly
Quantity
Ordered
Lead Time
in Days
PN2 Rotor $10,351.50 10 0.8 0.6 13 1.1 0.7 468
4
5
Units SS Per
Iteration
MaxN for
CO
Sigma @ Lt
Monthly CO MaxN for QTY
Sigma @ Lt
Monthly Qty AOQ
6 1 8 2.2 9 2.6 1.3
7
A B C D E F G H I J K
Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Cumulative
Increase in
Number of
Orders
Serviced
Cumulative
Bang for Buck
10 0 0 50.00% 5.0000 0.0 0.0
11 1 1.0 67.28% 17.28% 6.7276 1.7276 0.0001 1.7276 0.0001
12 2 2.0 81.46% 14.19% 8.1464 1.4187 0.0001 3.1464 0.0001
13 3 3.0 91.03% 9.57% 9.1031 0.9567 0.0001 4.1031 0.0001
14 4 4.0 96.33% 5.30% 9.6329 0.5298 0.0000 4.6329 0.0001
15 5 5.0 98.74% 2.41% 9.8738 0.2409 0.0000 4.8738 0.0001
16 6 6.0 99.64% 0.90% 9.9638 0.0899 0.0000 4.9638 0.0001
17 7 7.0 99.91% 0.28% 9.9913 0.0276 0.0000 4.9913 0.0001
18 8 8.0 99.98% 0.07% 9.9983 0.0069 0.0000 4.9983 0.0000
Table 1B - Bang for Buck Data for PN2

9. How to Optimize Service Levels
9
Part
Number
Descrip-
tion Unit Cost
Annual
Number CO
Average
Monthly
Number CO
Sigma of
Monthly
Number CO
Annual
Quantity
Ordered
Average
Monthly
Quantity
Ordered
Sigma of
Monthly
Quantity
Ordered
Lead Time
in Days
PN3 Nut $10.21 192 16.0 4.4 13061 1088.4 274.9 184
4
5
Units SS Per
Iteration
MaxN for
CO
Sigma @ Lt
Monthly CO MaxN for QTY
Sigma @ Lt
Monthly Qty AOQ
6 1.4 28 11.0 1587 680.9 68.0
7
A B C D E F G H I J K
Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Cumulative
Increase in
Number of
Orders
Serviced
Cumulative
Bang for Buck
10 0 0 50.00% 96.0000 0.0 0.0
11 1 1.4 55.06% 5.06% 105.7134 9.7134 0.0100 9.7134 0.0100
12 2 2.8 60.04% 4.98% 115.2712 9.5578 0.0098 19.2712 0.0099
13 3 4.2 64.86% 4.82% 124.5252 9.2541 0.0095 28.5252 0.0098
14 4 5.6 69.45% 4.59% 133.3417 8.8165 0.0091 37.3417 0.0096
15 5 7.0 73.75% 4.30% 141.6068 8.2651 0.0085 45.6068 0.0094
16 6 8.4 77.72% 3.97% 149.2309 7.6241 0.0078 53.2309 0.0091
17 7 9.8 81.33% 3.60% 156.1510 6.9201 0.0071 60.1510 0.0088
18 8 11.2 84.55% 3.22% 162.3316 6.1806 0.0064 66.3316 0.0085
19 9 12.6 87.38% 2.83% 167.7632 5.4316 0.0056 71.7632 0.0082
20 10 14.0 89.82% 2.45% 172.4602 4.6970 0.0048 76.4602 0.0079
21 11 15.4 91.90% 2.08% 176.4569 3.9967 0.0041 80.4569 0.0075
22 12 16.8 93.65% 1.74% 179.8032 3.3463 0.0034 83.8032 0.0072
23 13 18.2 95.08% 1.44% 182.5601 2.7569 0.0028 86.5601 0.0068
24 14 19.6 96.25% 1.16% 184.7950 2.2349 0.0023 88.7950 0.0065
25 15 21.0 97.18% 0.93% 186.5777 1.7827 0.0018 90.5777 0.0062
26 16 22.4 97.90% 0.73% 187.9770 1.3993 0.0014 91.9770 0.0059
27 17 23.8 98.47% 0.56% 189.0577 1.0807 0.0011 93.0577 0.0056
28 18 25.2 98.90% 0.43% 189.8790 0.8213 0.0008 93.8790 0.0054
29 19 26.6 99.22% 0.32% 190.4932 0.6142 0.0006 94.4932 0.0051
30 20 28.0 99.45% 0.24% 190.9451 0.4519 0.0005 94.9451 0.0049
Table 1C - Bang for Buck Data for PN3

10. How to Optimize Service Levels
10
Part
Number
Descrip-
tion Unit Cost
Annual
Number CO
Average
Monthly
Number CO
Sigma of
Monthly
Number CO
Annual
Quantity
Ordered
Average
Monthly
Quantity
Ordered
Sigma of
Monthly
Quantity
Ordered
Lead Time
in Days
PN4 Seat $10.70 17 1.4 1.0 69 5.8 3.6 121
4
5
Units SS Per
Iteration
MaxN for
CO
Sigma @ Lt
Monthly CO MaxN for QTY
Sigma @ Lt
Monthly Qty AOQ
6 1 7 1.9 19 7.1 4.1
7
A B C D E F G H I J K
Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Cumulative
Increase in
Number of
Orders
Serviced
Cumulative
Bang for Buck
10 0 0 50.00% 8.5000 0.0 0.0
11 1 1.0 69.76% 19.76% 11.8590 3.3590 0.0773 3.3590 0.0773
12 2 2.0 84.97% 15.21% 14.4441 2.5851 0.0595 5.9441 0.0684
13 3 3.0 93.97% 9.01% 15.9752 1.5311 0.0353 7.4752 0.0574
14 4 4.0 98.08% 4.11% 16.6731 0.6979 0.0161 8.1731 0.0470
15 5 5.0 99.52% 1.44% 16.9178 0.2447 0.0056 8.4178 0.0388
16 6 6.0 99.90% 0.39% 16.9838 0.0660 0.0015 8.4838 0.0326
17 7 7.0 99.99% 0.08% 16.9975 0.0137 0.0003 8.4975 0.0280
Table 1D - Bang for Buck Data for PN4
Part
Number
Descrip-
tion Unit Cost
Annual
Number CO
Average
Monthly
Number CO
Sigma of
Monthly
Number CO
Annual
Quantity
Ordered
Average
Monthly
Quantity
Ordered
Sigma of
Monthly
Quantity
Ordered
Lead Time
in Days
PN5 Retainer $4.09 57 4.8 2.4 1940 161.7 73.5 98
4
5
Units SS Per
Iteration
MaxN for
CO
Sigma @ Lt
Monthly CO MaxN for QTY
Sigma @ Lt
Monthly Qty AOQ
6 1 12 4.3 312 132.9 34.0
7
A B C D E F G H I J K
Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Cumulative
Increase in
Number of
Orders
Serviced
Cumulative
Bang for Buck
10 0 0 50.00% 28.5000 0.0 0.0
11 1 1.0 59.20% 9.20% 33.7456 5.2456 0.0377 5.2456 0.0377
12 2 2.0 67.92% 8.72% 38.7158 4.9702 0.0357 10.2158 0.0367
13 3 3.0 75.75% 7.83% 43.1777 4.4619 0.0321 14.6777 0.0351
14 4 4.0 82.41% 6.66% 46.9730 3.7953 0.0273 18.4730 0.0332
15 5 5.0 87.78% 5.37% 50.0319 3.0588 0.0220 21.5319 0.0309
16 6 6.0 91.87% 4.10% 52.3677 2.3358 0.0168 23.8677 0.0286
17 7 7.0 94.84% 2.96% 54.0577 1.6900 0.0121 25.5577 0.0262
18 8 8.0 96.87% 2.03% 55.2163 1.1586 0.0083 26.7163 0.0240
19 9 9.0 98.19% 1.32% 55.9688 0.7525 0.0054 27.4688 0.0219
20 10 10.0 99.00% 0.81% 56.4320 0.4631 0.0033 27.9320 0.0201
21 11 11.0 99.48% 0.47% 56.7020 0.2701 0.0019 28.2020 0.0184
22 12 12.0 99.74% 0.26% 56.8513 0.1492 0.0011 28.3513 0.0170
Table 1E - Bang for Buck Data for PN5

11. How to Optimize Service Levels
11
Part
Number
Descrip-
tion Unit Cost
Annual
Number CO
Average
Monthly
Number CO
Sigma of
Monthly
Number CO
Annual
Quantity
Ordered
Average
Monthly
Quantity
Ordered
Sigma of
Monthly
Quantity
Ordered
Lead Time
in Days
PN6 Label $4.07 3 0.3 0.7 10 0.8 2.0 65
4
5
Units SS Per
Iteration
MaxN for
CO
Sigma @ Lt
Monthly CO MaxN for QTY
Sigma @ Lt
Monthly Qty AOQ
6 1 5 1.0 9 2.9 3.3
7
A B C D E F G H I J K
Iteration
Units of
Safety
Stock
Iteration
Service
Level
Delta in
Service
Level
Expected
Number of
Orders
Serviced
Increase in
Number of
Orders
Serviced
Bang for
Buck
Cumulative
Increase in
Number of
Orders
Serviced
Cumulative
Bang for Buck
10 0 0 50.00% 1.5000 0.0 0.0
11 1 1.0 84.83% 34.83% 2.5450 1.0450 0.0770 1.0450 0.0770
12 2 2.0 98.02% 13.19% 2.9407 0.3957 0.0292 1.4407 0.0531
13 3 3.0 99.90% 1.88% 2.9970 0.0563 0.0041 1.4970 0.0368
14 4 4.0 100.00% 0.10% 2.9999 0.0030 0.0002 1.4999 0.0276
15 5 5.0 100.00% 0.00% 3.0000 0.0001 0.0000 1.5000 0.0221
Table 1F - Bang for Buck Data for PN6
Optimizingservice level
Managing service level