Methodology to determine the optimal replacement age of … · 2009-08-26 · METHODOLOGY TO DETERMINE THE OPTIMAL REPLACEMENT AGE OF MOBILE MINING MACHINES 297 Introduction Background

METHODOLOGY TO DETERMINE THE OPTIMAL REPLACEMENT AGE OF MOBILE MINING MACHINES 297

Introduction

BackgroundThe management and maintenance of mining machinery,especially in underground applications, is a difficult task. Inaddition to this, the costs associated with running andmaintaining a trackless fleet are significant. The costsincreases resulting from older machines are not wellunderstood or quantified, and hence accumulate a largeproportion of hidden as well as direct costs. This is due to anumber of reasons, namely:

• The complex nature of the machines where numerousand various components exist, and are interrelated

• The way information is recorded and the type ofinformation recorded

• The nature of the mining cycle does not easily allowone to determine the impact of an unreliable machine.

A range of additional costs associated with oldermachines is derived from unquantifiable trends andintangible benefits (to be discussed under ‘replacementfactors’.

In addition to this, it is understood that in a number ofmining houses there is no justified or standardized approachin determining the optimal machine life, which wouldprovide the basis for effective machine replacementprogrammes. This leads to an array of shortcomings,namely increased lifecycle costs, increased downtime (andhence productivity losses) and, given the current supplyproblems, an extremely long lead time for replacementmachines. These challenges are compounded by the capitalplanning and budgeting process employed by many mines,where capital application is required annually, and for thenext year.

In partnering with customers to develop solutions used toimprove their customers business, Sandvik has responded tocurrent market demands, in initiating an analysis of this. Astudy into current replacement methods used in the miningindustry, similar industries and appropriate methodsavailable was undertaken. From this, with input from AngloPlatinum and on-site maintenance personnel, a model wasformulated.

ObjectivesThe model has more specific objectives which are toprovide a simple guideline to:

• Predict machine replacements ( for capital motivation,capital planning, and to facilitate machine replacementprograms)

• Optimize lifecycle costs, and • Provide a basis for benchmarking sites.

Due to the complexity and diversity of all Sandvikmachines, used to mine PGM’s, namely bolters, drill rigs,trucks, dozers and loaders, the aim was for a replacementapproach, but the model has been specifically developedbased on the fundamentals of the loaders.

Replacement environmentThe machine replacement topic has initiated a wide varietyof debate from many schools of thought, and withoutcarefully scoping the replacement environment, one canrender results inappropriate if not meaningless. Hence, in anattempt to create a manageable task and providerepresentative results, a specific environment in which thereplacement would take place has been described in Figure 1.

NUROCK, D. and PORTEOUS, C. Methodology to determine the optimal replacement age of mobile mining machines. Third International PlatinumConference ‘Platinum in Transformation’, The Southern African Institute of Mining and Metallurgy, 2008.

Methodology to determine the optimal replacement age ofmobile mining machines

D. NUROCK and C. PORTEOUS

Sandvik Mining

Fleet management of mobile machinery in the mechanized mining environment is essential to theeconomic exploitation of an orebody. Due to the complex nature of the machines and theenvironment in which they operate, effectively managing such a fleet proves to be a challengecurrently not fully understood or addressed by mining houses. With constant pressures onincreasing production figures and cutting costs, in addition to the global strain on machine leadtimes, the management of trackless equipment has become a top priority. A study was undertakenby Sandvik, with input from Anglo Platinum, in an effort to provide a solution to their customers.The aim was to provide a tool to determine the optimal time to replace a machine based on actualdata, using lifecycle cost calculations and the theory of vehicle replacement given a specificcustomer environment. The factors affecting this decision were determined, quantified andinputted into a model, which can calculate the optimal replacement age of a machine. Theobjective of such was to provide an indication of the most economical point to replace a givenmachine in a given environment in order to extract the most value for the mine. This can be usedto plan and motivate capital expenditure as well as optimize machine operating costs.

text:Paper 73 Nurock 9/26/08 2:51 PM Page 297

APLATINUM IN TRANSFORMATION298

It looks at the:• Life of mine (LOM)—if machine life exceeds the life of

mine, machine replacements are not viable(alternatively rebuild/remanufacture or rental optionsare preferable here or a business case should beconducted to determine the viability of running the oldmachines)

• Machine availability—where no replacement machineexists at the end of a current machine’s life, clearly areplacement option is not an alternative, and the above-mentioned options should be considered

• Machine cost: revenue—where information exists,other analysis tools using cost benefit analysis orpayback type methods could be used

• CAPEX (capital expenses) or OPEX (operatingexpenses) Sensitivity—if a mine wishes to optimize (oris sensitive to) CAPEX, through lower capital costalternatives, other options need to be explored otherthan new machine replacements. It is important to keepin mind that this is generally at the expense of OPEX.On the other hand, a mine may aim to optimize itsOPEX (at the expense of a higher CAPEX). It ispremise on which this model is based

• Equipment needs—it is recommended that priormachine replacements are planned, and the productionparameters are checked to determine if in fact newmachines are required.

It is under these conditions in which the replacementmodel described in this paper is best suited.

Current methodsAn investigation was carried out to determine how themining houses currently use relevant information todetermine the replacement lives of their trackless mobilemachinery. It was evident that, in most cases, eithersimplistic assumptions or experienced estimates were usedand in some instances purely reactive planning occurs.

A number of applicable methods exist, either in theory orin practice, and the challenge is to adapt these methods andformat this information into a useable, valuable andapplicable medium.

The most applicable methods are listed below. • Cost per ton trends—this uses the total machine costs

divided by the number of tons a machine produces. It isbased on the principle that as a machine ages, therunning costs increase and as the availability of themachine decreases, the tons are reduced, henceincreasing the cost per ton. The minimum cost per tonis the optimal replacement point. In a sense this usesthe similar methodology of a cost-benefit or paybackanalysis and is very appropriate since the purpose of themachine is to produce tons, thereby, using this measureas a financial indicator. However information about thetons produced is required and often not available

• Equivalent annuity (EA)—this method looks at thecash flows associated with the machine and the times inwhich they are incurred. It uses the time value ofmoney to be able to compare different timingalternatives. It then calculates the total value or cost ofan alternative (a replacement age) and equates this to anannuity. Annuities of different alternatives can now becompared, on the same basis, and the lowest annuityrepresents the lowest cost option. This method is verypowerful and is an accepted asset appraisal method,although it is commonly not easily understood andhence accepted

• Theory of vehicle replacement—this is a well-knowntheory and is based on the trade-off of decreasingcapital cost and increasing running costs with the age ofa vehicle. A point exists where the total cost is aminimum, which indicates the optimal replacementage.

The model developed uses a combination of all the abovemethods, based on the available information and with theaim of providing a simple guideline to determining theoptimal replacement age.

Model developmentInitially, due to the fact that the machines are physicalassets, the first step is to establish the design life of themachine. However, this proves a futile exercise since:

• Machines can be repaired or rebuilt several times toprolong life

• The maintenance philosophy, methods, expertise andeffectiveness affect the life and operation of many ofthe parts and hence the whole machine

• Different maintenance conditions, operating conditions,practices and environmental factors also affect the lifeof the machine.

As a result of these factors, it was decided that theeconomic life of the machine would be the best measure.This type of approach, although initially consideredillogical, is consistent with the aim of business—to makemoney; hence looking at the economics of the machine

Figure 1. Environment applicable to the optimal replacementinterval



replacement decision is a business decision. However, notoverlooking the nature of the problem at hand, the modelneeds adequately to take into account the above-mentionedfactors. Following the identification of the key factors thatinfluence the replacement decision, these need to bequantified in order to be translated into an economicdecision.

A number of factors exist that need to be included in thereplacement decision, some of which are relatively simpleto calculate and others which prove somewhat moredifficult. Some of the reasons include the fact that theparameters themselves can be difficult to quantify, over andabove the lack of data, quality of these data or the format ofthe data available. A challenge in developing an appropriatemodel is to retrieve and use realistic and representative datain the absence of accurate quantitative information. The aimis to quantify the causes—factors influencing thereplacement decision. This can be done by looking at theeffects that are assumed to be representative of the causes,in this case the costs of running machines and the machineavailability. Figure 2 expands on these pertinent factors; theimportance of such a step in the model development is thejustification for the primary inputs to the model, namelyrunning costs and availability. These parameters are easilyaccessible due to the reporting system used by Sandvik onsite, where they maintain the customer’s machines.

The advantages of using these figures are borne out bythe fact that these are actual figures, hence representing sitespecific and machine specific influencers. This yields adistinct advantage in that the information is realistic andrepresentative, although limitations could exist wherehistorical data are required in order for decisions to bemade. This could constrain the replacement modelling life,machine type or site. Another disadvantage associated withusing historical data is that only retrospective planning canbe done. What this means is that one a machine has beenoperating and accumulated data, one can look at the trendsand see when the machine was suppose to be replaced. Itcannot account for changes that have occurred for example,an improvement in roadways, maintenance practices,operating practices, etc. However, this still contributestowards the aim in that it provides a general idea orguideline from which to predict machine lives and can beseen as a starting point.

A note of caution must be made when using anddeveloping such models; as obvious as it may seem, thequality of the outputs depends completely on the quality ofthe input information.

Replacement factors

Operating costsOperating costs include maintenance costs, consumablesand labour. Due to the nature of the reporting system, themaintenance cost and availability data are inputted inintervals of 1 000 hours. It follows that the model usesanalyses in 1 000 hour intervals. As previously discussed,the maintenance costs are the actual parts costs, excludingthe cost of parts used for damages. The consumables arebased on inputs and assumptions. Ground engaging tools(GET) and tyres are excluded since is it assumed that theseare independent of age and hence will merely shift thecurve up, but will have little effect on identifying theoptimal replacement age. Labour is based on standardvalues used in Sandvik maintenance contracts, based onlabour compliments where man:machine ratios are used.

The reduction in machine availability with age, entails anincrease in maintenance labour time. This has beenincluded in the model and is based on the availability trend.

Financing costsThe capital cost of the machine has a significant role indetermining the machine life since this cost is spread overthe life of the machine. The model caters for a simple inputof the purchase price of the machine. However, to maintaina simple useable model, the cost of capital has beenexcluded. The cost of capital is the cost incurred infinancing the machine. By virtue of the methodologyapplied, the depreciation is taken into account, by spreadingthe capital cost of the machine over its life. When one looksat different replacement alternatives, the machine cost isdivided by the number of hours for that interval, and henceis a representation of the depreciation. The tax shield is abenefit from tax where the capital cost is converted to anexpense (through depreciation), this reduces the company’snet income and hence reduces the tax payable. This isbasically the company tax rate multiplied by thedepreciation value.

The effect of tax shield on the replacement decisionKeeping in mind the aim of the model, which is to generatea simple guideline to indicate the optimal replacementperiod, the tax shield was assumed inconsequential. Withdiffering alternatives of machine lives, the financial cost(through depreciation) is spread over different time periods.This results in depreciation values being incurred both at adifferent rate and in a different time period for eachreplacement alternative. Inevitably the total capital cost ofthe machine is depreciated and a tax benefit is gained, thetiming of which plays a role. An analysis was carried out inorder to determine the effect of this role on the replacementdecision and hence to determine if the initial assumptionwas correct.

The model uses a methodology, explained under the‘Model methodology’ section, to determine the costsassociated with each alternate replacement interval, themost optimal point being termed the optimal replacementinterval (ORI). In the tax shield analysis, the average costper each replacement alternate interval was calculatedbased on no tax advantage and compared to the intervalcosts where the tax shield has been included. Figure 3shows the trends and relationships of the data. This figurefurther shows that the average cost is lower when gainingthe tax advantage and that both curves follow the sametrend, as expected. Looking at the differences in the twocurves, it is apparent that the discrepancy between them is

Figure 2. Cause and effect diagram


Figure 4. Trend of ORI gradient

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highest for smaller replacement intervals where differencesreach 28%. This is in direct correlation with the actual taxshield where the company tax rate is 29%—which isslightly discounted to account for the time the machineneeds to accumulate its 1 000 hours. The difference dropsto 6% and is on average 15%. However, these differencesdo not play a part in changing the ORI, the ORI in bothinstances equating to 11 000 hours based on the giveninputs.

Changing differences in the curves indicates variations inthe shape of the curves, which could favour earlierreplacement ages if the ORI is marginal and the tax shieldhas been accounted for. To determine the impact ofincluding the tax shield, on marginal cases, one can look atthe change in the shape of the ORI themselves anddetermine how this would affect marginal cases. Oneapproach to quantify the shape of the curve is by looking atthe derivative of the curve—generally calculated from theformula of the function. However, to keep it simple, we willuse the derivative analogy by looking at the gradients. Thefirst derivative of a curve indicates the direction of thecurve. If the gradient is positive this indicates an upwardsloping curve where an increase in the dependant variableresults in an increase in the independent variable. This isshown in Figure 4. As expected, the gradients are negativesince the average cost per hour decreases as thereplacement interval increases, driven by the financial costof the machine. After the curve reaches the minimum point

(here at 11 000 hours) it becomes positive as the averagecosts per hour start increasing. However, this tells us littleabout the steepness of the curve, which is the aspect thatinfluences the marginal ORI. The steepness of the curve ismeasured by the second derivative, which is the gradient ofthe gradient of the initial curve. There is no clear trend tothese points so to get an estimate of the nature of therelationship, a linear trend line has been fitted. A largergradient implies that a change in the independent variable(the replacement interval) results in a larger change in thedependant variable (R/h) and hence results in a lessmarginal outcome. In a situation like this, marginal resultsare not preferable since the outcome of one scenario is onlyslightly better or worse than its next best alternative, whichincreases the risk of allowing marginal (and assumedinsignificant) factors playing a larger role on the decision.Looking at the equations of the trend lines shown in Figure 5, it can be seen that the gradient of the ORI notincluding the tax shield (≈ 8) is greater than the gradient ofthe ORI with tax shield (≈ 5) meaning that the ORI (notincluding the tax shield) is less marginal and hence a betteroption. These results are not notably different but allow oneto justify the exclusion of the tax shield in the model.

Availability costsThe production loss associated with an unreliable orunavailable machine is by no means insignificant.However, this is a tricky aspect to deal with since (a) it is

Figure 3. The effect of tax shield on ORI



difficult to equate the effect on production of one machinebeing down and (b) the production loss is not lost forever, itis merely transferred later in time. Even though thisdefinitely has a cost associated with it and will affect theproject’s NPV. In absence of a more applicable approach,this production loss, termed availability cost, will beincluded based on a number of factors. These are: themachine’s production rate, the machine’s averageutilization percentage, the machine’s effectiveness, the

basket price of the commodity being extracted, the dilutionand recovery, and most importantly, for purposes of themodel, the machine’s availability.

Other factorsA number of intangible and non quantifiable factors exist,which have not been included in the model, due to theirnature. These include factors such as:

• Decrease in utilization of older machines• Increase in damages on older machines• Benefit due to technological advantages in machine

performance, maintainability, consumption andoperator comfort.

AssumptionsIn order to achieve the aim of the model, a number ofassumptions have been made, some of which are based onhistory and experience whereas others simplify the model toa manageable proportion. The list is fairly detailed and isnot conducive to the aim of this paper and has hence beenomitted. The nature of the assumptions deal with the trendsof machine availability, utilization, inflation, metal priceforecasting, consumable costs, intangible benefits, etc.

Model methodologyThe methodology used in the model uses the cost per hourto determine the optimal replacement life. This incorporatesthe fundamentals from the theory of vehicle replacement inthat is uses the lifecycle costs, which are driven by thecapital and running cost parameters and the timingadvantage of equivalent annuity by applying discountingfactors to future cash flows. The resulting outcome issimilar to the cost per ton analysis. It achieves this througha number of steps, which are indicated in Figure 5, asimplified and easy to follow flow diagram.

• The basic principles of this methodology are based onderiving input parameters for operating costs,availability costs and financial costs per 1 000 hourintervals (Figure 6)

• In order to account for the risk and cost of money forfuture cash, a discounting factor is applied based on theannual utilization. The time value of money is aconcept which is widely known, and the application ofthis can be found in numerous sources and hence is notaddressed in this paper Figure 5. The optimal replacement interval methodology

Figure 6. Cost per interval


Figure 7. Cumulative costs


• Since using the data in the raw form tells us little andcan be very erratic, due to expensive componentchange-outs for example, these costs are thencumulated (Figure 7). This cumulative cost representsthe lifecycle cost of the machine up until that stage inits life

• This cumulative cost is then divided by the number ofhours accumulated (its life) for different life scenarios(Figure 8)

• The results of this yield a cost per hour, whichrepresent the average costs over the life of the machine.

• This can be compared to the alternate life options andthe lowest cost per hour is the optimal replacementinterval.

Figure 9 shows the drivers of cost for each replacementinterval and as expected, for small replacement intervals thecapital cost of the machine is predominant and for longerreplacement intervals, the availability and operating costsbecome more prominent.

An exercise was carried out to compare the outcomes ofthe optimal replacement interval (ORI) methodology versusan equivalent annuity model and the results werecomparable. This has been done for a number ofalternatives based on real data. A simple example has beenprepared to show how each methodology works and toshow the comparison between the two. The details of thisexercise are seen in Table I and a graph has been plotted inFigure 10. From this figure it is clear that the samerelationship between the ORI and EA exists. In thisinstance, the EA life was 4 000 hours and the ORI life is 5000 hours. This acts as a confirmation of the applicabilityof the ORI.

Outcomes of the modelBased on a test case, the figures have been generated andact as an example of what the model outputs. It gives anindication of the relative cost per hour values for eachreplacement alternative from which the minimum can befound. Further investigation will determine the difference invalue lost by prolonging the life of the machine and itsimpact on NPV. In this instance the ORI was 11 000 hours.This model can easily be run for a number of machines on asite to determine the average, economically optimal lifeexpected from machines on that site. In addition to this, themodel can be used to compare machines on different sitesby running the model for a number of machines.

Sensitivity analysisTo reduce the risk associated with inaccurate or sensitiveinputs, a sensitivity analysis was conducted. Consideringthe nature and environment of the inputs, and theirinclusion in the model in terms of the calculations, anumber aspects were identified as being the risk factors andhence the reason for sensitivity analysis. These are

• Commodity price (which affects the cost ofavailability)

• Capital cost of the machine • Discount rate • Annual utilization (since this affects the timing of cash

flows).The sensitivity analysis was done using the optimal

replacement interval as the dependent variable. In additionto this, sensitivity analysis was also carried out looking atthe changes on the cost per hour. There are a number ofreasons for including the cost per hour:

• the replacement age is discrete, i.e occurring only in1 000 hour interval, and if an input is changed thecorresponding output may not change, whereas the costper hour is more sensitive and will show the differencei.e it reflects the marginal cost

• additionally since this output is more sensitive, it canbe used to verify mechanisms in the model and in thesensitivity analysis.

Figure 8. Optimal replacement interval



As expected one can see the discrete nature of thereplacement ages in Figure 11, which shows no clearmeasure of relative sensitivity. The graph shows an increasein replacement life with a decrease in capital cost — since ahigher capital cost would warrant a longer life in order tojustify this. The same trend is seen for the discount rate.With a higher discount rate, future values are discountedmore heavily and so their impact is reduced, indicatinghigher running and availability costs in the future are lesssignificant. Replacement age remains fairly stable with achange in annual utilization. However with a very highutilization, it appears the life is extended, assumed to be asa result of the lower effect of discounting, since with a high

utilization the time periods are much smaller. Additionally,as expected, the higher the availability cost, the lower themachine life, due to a large cost associated with machinedowntime, which increases with age and hence does notjustify longer lifetimes.

Figure 12 shows sensitivity relative to cost per hour. Ascan be seen, this is less discrete than the replacement lifesensitivity figure. It is clear from this graph that the capitalcost and availability are the most sensitive parameters. Withan increase in availability and capital costs, the whole costper hour curve increases, hence the cost per hour at theoptimal replacement age is higher. It can further be seenthat as discount rate increases cost decreases since costs are

Figure 9. Breakdown of costs

Table IORI vs. EA calculations

Year 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Age 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Capital cost R2,000 R- R- R- R- R- R- R- R- R- R-Maintenance cost R- R50 R75 R100 R125 R150 R175 R200 R225 R250 R275 Availibility cost R- R100 R200 R300 R400 R500 R600 R700 R800 R900 R900 Total costs per period 2000 150 275 400 525 650 775 900 1025 1150 1175PV factor 1 0.9712859 0.9433962 0.9163074 0.8899964 0.864441 0.8396193 0.8155103 0.7920937 0.7693494 0.7472582NPV for the period 2000 154.43445 291.5 436.53472 589.89 751.93105 923.0374 1103.6034 1294.0389 1494.7695 1572.4151Total NPC 2000 2154.4345 2445.9345 2882.4692 3472.3592 4224.2902 5147.3276 6250.931 7544.9699 9039.7394 10612.155

EA factor 1 1.9712859 2.9146821 3.8309895 4.7209859 5.5854269 6.4250462 7.2405565 8.0326502 8.8019996 9.5492577EA amount 2000 1092.9082 839.1771 752.40853 735.51568 756.3057 801.13473 863.3219 939.28775 1027.0098 1111.3067ORI 200000 2.1544345 1.2229672 0.9608231 0.8680898 0.844858 0.8578879 0.8929901 0.9431212 1.0044155 1.0612155

Figure 10. ORI vs EA


Figure 11. Sensitivity analysis (replacement age)

Figure 12. Sensitivity analysis (cost per hour Age)


now discounted by a larger amount: the higher the discountrate, the smaller the present value (PV) factor and hence thesmaller the cost of the day.

Application of the modelThe model has been run on for number of load-haul-dumpLHDs) on one particular site. Figure 13 shows the optimalreplacement aes for each machine and their correspondingcost per hour. Based on the inputs, the estimated ORIs arein the range of 9000–15000 , with an average of 12 000hours. These numbers are thought to be very representative

of these machines in their specific environment. This typeof analysis can be used to determine the average machinelife and hence put together a planned replacement schedulefor a site. Other uses for this type of analysis can be tocompare the same machine type on different sites and tocompare the ORIs to the current machine ages, as can beseen in Figure 14. In this case, it is clear that all themachines are over their ORI and essentially are destroyingvalue for the mine. However, from an analysis like this it isdifficult to calculate exactly how much money is beingwasted, in present value terms. This is a topic for futurework.

Figure 13. ORI and cost per hour for a fleet



ConclusionThis model provides a simple tool to determine theeconomically optimal replacement ages of machines ondifferent sites in any given environment. Although theapproach used is applicable to a range of machine types, themodel was based on low profile loaders. The machine agesoutputted from the model range from 9 000–15 000 hours.This is based on a fleet of low profile 5 ton LHDs mining aplatinum orebody. From observations and discussions withpersonnel, these figures are considered very reasonable andrepresentative. The outcomes of the model are retrospectivein that this was the optimal replacement life of the machinesin the given the environment, which can provide a basis forfuture forecasts. Due to the nature and set-up of the model,machine analyses on a variety of machine models and on arange of sites is possible, but constrained to the historicaldata available.

AcknowledgementsIdeas and observations have been taken from anddiscussions have been underway with a number of peoplerelevant to this topic, they include:

• Seppo Tolonen, [Wa Technologies Oy. FinnishMaintenance Management Consultant]

• Economic Life Model, Leon Kruger, De Beers• Optimal Replacement Model, Wain Chaplain, –

Sandvik.

References

OWEN, R. Fleet Replacement Best Practices.Fleet Management Conference and Equipment Show,Mercury Associates Inc. 2007.

Lifecycle Cost Analysis article in E News: Energy DesignResources.

LAURIA, P. When vehicle replacement budgets shrink,Fleet Financials Publication, July/August 2002,Mercury Associates Inc.

LAURIA, P. Pay me now or Pay me later, Inc.500Publication, July 2005,

YANKOVICH, T. Fleet Efficiency Study for The City ofTyler, Texas, April 2003, Conducted by MercuryAssociates Inc.

Holistic Asset Management, 2004 Urban Water Council,US Conference of Mayors, Redoak Consulting

VORSTER, M. A Machine Replacement Strategy,Construction Equipment Article, July 2005.

SKIPPER, G.C. Numbers Tell the Tale, ConstructionEquipment Article, December 2006

Figure 14. ORI vs Current machine lives

Danielle Nurock Systems Engineer, Sandvik

Following graduation from Wits University as an Industrial Engineer, Danielle started work as partof a team who’s purpose is to improve mine productivity. As a systems engineer her involvemententailed optimzation of mining processes and impact on business, application of production costmodels and dynamic simulations. She is currently involved in a number of projects with role ofproject facilitator and manager, using her systems approach. Development of benchmark andprocess optimization tools. Development of machine replacement tool.




Methodology to determine the optimal replacement age of … · 2009-08-26 · METHODOLOGY TO DETERMINE THE OPTIMAL REPLACEMENT AGE OF MOBILE MINING MACHINES 297 Introduction Background

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