Replacement model

Replacement Model in Operations Research

1. REPLACEMENT THEORY
Prof.P.D.Devan
AsstProfessor
Department of Mechanical Engineering
KumaraguruCollege of Technology
Coimbatore

2. Replacement Model
Theproblemofreplacementariseswhenanyoneofthe
componentsofproductiveresources,suchasmachinery,buildingand
mendeterioratesduetotimeorusage.
Ex:
Amachine,whichispurchasedandinstalledinaproductionsystem,duetousage
someofitscomponentswearoutanditsefficiencyisreduced.
Abuildinginwhichproductionactivitiesarecarriedout,mayleavecracksin
walls,roofetc,andneedsrepair.
Aworker,whenheisyoung,willworkefficiently,asthetimepassesbecomesold
andhisworkefficiencyfallsdownandaftersometimehewillbecomeunableto
work.

3. Efficiency Vs Time
At the beginning the operating efficiency id 95% and it is reduced to 50% at final
stage.
When the efficiency is too low its not advisable to use the facility further, as the
maintenance cost will be very high and unit production cost also will increase.
Hence the replacement of the facility is due at this stage.

4. Decision Types
We may decide whether to wait for complete failure of the item .
The expensive item may be considered individually to decide whether we should
replace now or, if not, when it should be reconsidered for replacement.
Whether the item is to be replaced by similar type of item or by different.
The main objective of replacement is to help the organization for maximizing
its profit or to minimize the cost.

5. Failure Mechanism of Items
Nature of
Failure
Gradual
Progressive
Retrogressive
RandomSudden

6. Gradual Failure
As the life of the machine increases or due continuous usage, due to wear and tear of
components of the facility, its efficiency deteriorates due to which the management
can experience.
a)Progressive Increase in maintenance expenditure or operating costs,
b)Decreased productivity of the equipment
c)Decrease in the value of the equipment (resale value) of the equipment/facility
decreases.
Ex: Automobile, Machine Tool

7. Sudden Failure
Theitemsultimatelyfailsuddenlyafteraperiodoftime.
Thelifeoftheequipmentcannotbepredictedandissomesortofrandomvariable
Theperiodbetweeninstallationandfailureisnotconstantforanyparticulartype
ofequipmentbutwillfollowsomefrequencydistribution

8. Progressive Failure
In this case probability of failure increases with the increase in life of an item.
Ex: Electrical bulbs and computer components

9. Retrogressive failure
Someitemswillhavehigherprobabilityoffailureinthebeginningoftheirlife,
andasthetimepasseschancesoffailurebecomesless.
Thatistheabilityoftheitemtosurviveintheinitialperiodoflifeincreasesits
expectedlife.
Ex:Newlyinstalledmachinesandnewvehicles

10. Random Failure
Constant probability of failure is associated with items that fail from random
causes such as physical shocks, not related to age.
In such cases all items fail before aging has any effect.
Ex: Vacuum Tubes

11. Stages of Maintenance

12. Costs Associated with Maintenance
Purchase or Capital Cost (C)
Salvage value / Scrap value / Resale value / Depreciation (S)
Running costs including maintenance, Repair and Operating costs

13. Types of Replacement Problems
Replacement of items that deteriorate with time (value of money not changing
with time)
Replacement of items that deteriorate with time (Value of money changing with
time)
Replacement of items that fail suddenly (individual and group replacement
policies)
Staff Replacement

14. General Approach to Replacement Problem
The information necessary to formulate optimum replacement policy is:
(i) Objective assessment of the probability of the item failing at a particular point
of time
(ii) Assessments of the cost of replacement in terms of:
(a) Actual cost of the item,
(b) Direct costs of labourinvolved in replacement,
(c) Costs of disruption in terms of lost production, lost orders etc.,

15. Replacement of items that deteriorate with time
(Value of money not changing with time)
Certainequipment/partsaredeteriorategraduallywithrespecttotime.
Afteracertainperiodtheefficiencyoftheitemwillreduceandmaintenancecost
increases.
Thentheolditemmustbereplacedbynewone.
Ex:Automobilepartwearoutwithageandtheownerneedstoreplacetheold
partatsuitabletimebyanewone

16. Costs to be Considered
Capital/Purchase cost =(C)
Scrap value after ‘t’ years= S(t)
Operating cost at time ‘t’ = M(t)
Optimal replacement period = n
Depreciation cost
Operating cost
Optimal replacement period is corresponding to which the minimum average cost

17. Replacement of items that deteriorate with time
(Value of money changing with time)
Thisproblemiscomplicatedasthemoneyvaluechangeswithtime.Thiscanbe
dealtundertwodifferentconditions:
(a)Themaintenancecostgoesonincreasingwithusageorageortimeandthen
wehavetofindoutoptimumtimeofreplacingtheitem.Herethevalueofmoney
decreaseswithaconstantratewhichisknownasitsdepreciationratioor
discountedfactor.
(b)Ifabusinessmantakesaloanforacertainperiodatagiveninterestrateand
agreestopayitinanumberofinstalments,thenwehavetofindthemostsuitable
periodduringwhichtheloanwouldberepaid.

18. Replacement of items that fail suddenly
Therearecertainitemsorsystemsorproducts,whoseprobabilityoffailure
increaseswithtime.Theymayworkwithdesignedefficiencythroughouttheirlife
andiftheyfailtoacttheyfailsuddenly.
Thenatureoftheseitemsistheyarecostlytoreplaceatthesametimeandtheir
failureaffectthefunctioningofentiresystem.
Forexample,resistors,componentsofairconditioningunitandcertainelectrical
components.Ifwedonotreplacetheitemimmediately,thenlossofproduction,
idlelabour;idlerawmaterials,etcaretheresults.Itisevidentfailureofsuch
itemscausesheavylossestotheorganization.

19. Individual Replacement Policy
Thispolicystatesthatreplacetheitemsoonafteritsfailure.Herethecostof
replacementwillbesomewhatgreaterastheitemistobepurchasedindividually
fromthesellerasandwhenitfails.
Fromthetimeoffailuretothereplacement,thesystemremainsidle.Morethan
that,astheitemispurchasedindividually,thecostoftheitemmaybemore.
Incase,thecomponentortheitemisnotavailableinthelocalmarket,wehaveto
getitfromotherplaces,wheretheprocurementcostmaybehigherforindividual
purchase.
Ex:Bearinginamachine

20. Group Replacement Policy
Iftheorganizationhasgotthestatisticsoffailureoftheitem,itcancalculatethe
averagelifeoftheitemandreplacetheitembeforeitfails,sothatthesystemcan
workwithoutbreak.
Inthiscase,alltheitems,eventheyareingoodworkingcondition,arereplacedat
astipulatedperiodascalculatedbytheorganizationbyusingthegroup
replacementpolicy.
Incaseanyitemfails,beforethecalculatedgroupreplacementperiod,itis
replacedindividuallyimmediatelyafterfailure.Hencethispolicyutilizesthe
strategyofbothindividualreplacementandgroupreplacement.
Ex:StreetLights,ElectronicPartsandetc

21. THANK YOU