Introduction

Christer and Goodbody (1980) introduced the two-cycle capital replacement model in order to consider decision-making in relation to an existing asset. This model improved upon the notion of modelling more idealized replacement scenarios with like-with-like replacement in perpetuity (Eilon et al, 1966) and Christer (1984), in further developing this model, provided an alternative to the parametric modelling of continuous technological improvement (Elton and Gruber, 1976). Christer and Goodbody's central ideas were to model the replacement decision conditional on the current age of the existing plant and to consider only a finite time horizon comprising the current operate-and-replace cycle of length K (time units) and the immediately following operate-and-replace cycle for the new equipment of length L. Christer and Scarf (1994) later described a robust version of the model that considered asset events with costs which are 'difficult to measure', for example, penalty costs associated with failure and delay, and applied this model to medical equipment. This two-cycle model is considered here in the context of asset replacement in an urban railway system. We recommend a modification to the two-cycle model. This recommendation is made on the basis of experience with the model when applied to asset replacement problems at the Mass Transit Railway Corporation Limited (MTRCL) of Hong Kong.

Asset replacement studies carried out in conjunction with MTRCL indicate that, typically, operating (revenue) costs increase only slowly, and that, furthermore, the operating costs of new technology may be lower, so that replacement of existing technology with new can bring a step-reduction in operating costs. We argue that traditional OR replacement models do not handle this kind of cost behaviour very well. When assets 'age' only slowly, it is not surprising that the economic life is non-finite. In this context, Scarf and Martin (2001) and Scarf and Hashem (2003) suggested to use a fixed horizon model, with at most two replacements over a fixed horizon of length h, rather than a model with a fixed number of cycles (such as the two-cycle Christer–Goodbody model). The fixed horizon model, which is simpler and closer to the standard model used in financial investment appraisal, provides a solution although end-of-horizon effects can be distorting. In this paper, we compare the fixed horizon model with the two-cycle model. This comparison suggests a modification to the two-cycle model leading to a model that is very closely related to the two-cycle model, is consistent with the fixed horizon model and hence standard financial investment models, and can be used to model asset replacement when revenue costs change only slowly.

In addition to modelling recommendations, we describe the asset replacement processes at MTRCL. The management systems that have been put into place in order to ensure appropriate and effective consideration of possible asset replacement requirements are presented and reviewed. The procedural issues of asset replacement and the asset replacement system methodology discussed in the paper are in part based on the current practise at MTRCL, Hong Kong, and in part upon developments within that organization through collaboration with academia. Key elements in the process include: information gathering—undertaking of asset replacement studies; the engineering evaluation of feasible replacement or refurbishment options; decision-making based upon criteria that are widely understood within the organization; the ability to update decisions as emerging factors arise; flexible accounting systems; and follow-through—monitoring of replacement implementation—and review.

In the following section, we describe the MTRCL network and the asset replacement procedure at MTRCL. We then make recommendations about management systems for asset management. In the second half of the paper, we discuss capital replacement models and, in particular, we compare the fixed horizon model of Scarf and Martin (2001) with the two-cycle model. The modified two-cycle model is introduced and these models applied to escalator and point-machine replacement problems at MTRCL. We discuss these particular asset replacement problems in the context of the modified two-cycle model and fixed horizon model, and make specific recommendations. Issues associated with 'hidden' costs that are difficult to determine but may influence decisions significantly are presented in detail. We also make general recommendations for the application of traditional OR models in capital replacement.

Note that while the term asset replacement is used in this paper, refurbishment of existing assets may be a valid option incurring capital expenditure. Such refurbishment can then be classed as a capital project in asset management and, in modelling and financial terms, is equivalent to replacement. Therefore, we interpret the term asset replacement as the appraisal of capital projects in asset management—this interpretation would then imply, in our opinion, that asset replacement also includes decisions regarding the overhaul of existing assets. In fact, for the escalators at MTRCL, one could interpret the project options variously as overhaul, refurbishment, retro-fitting, or replacement, and there is extensive engineering debate about their definitions. Simply, where a capital budget has been obtained for the implementation of a project relating to asset management, then we class such a project as 'asset replacement'. Throughout we use the term operating cost, but the models are applicable in their stated form when considering income generated by assets.

The MTRCL network

The MTRCL operates a heavily utilized metropolitan service in Hong Kong. The railway network comprises seven lines with 52 stations over a total route length of 87.7 km. Current daily weekday patronage amounts to 2.5 million passenger journeys. The system has been growing progressively since the first line started operation in 1979. The latest addition is the Disney Resort Line, opened in September 2005. A schematic map of the network is shown in Figure 1.

Figure 1.

Schematic map of the network of MTRCL, Hong Kong.

Full figure and legend (97K)

There is significant investment in asset replacement and refurbishment projects even though the rail network is relatively young. The current annual expenditure is HK$300 million and growing. Investment projects are typically driven by technical obsolescence and requirements for performance and functionality improvements. While a manufacturer's recommended asset life can trigger the consideration of asset replacement, they do not drive asset replacement per se. Maintenance contracts and, in particular, the renewal of maintenance contracts can be a powerful force for investment in existing assets. The asset replacement decision procedure at MTRCL includes key activities. The key activities and attributes of the process used include:

• Identification of asset lives based on the 'design life' stated at initial purchase.
• A number of key horizons triggering analysis and decision-making.
• Supported analysis of options by the line manager in conjunction with an Asset Replacement Manager.
• Study group formation to develop options and recommendations.
• A process for inclusion of justified projects into the capital and revenue (C&R) budget.

These activities and attributes are discussed in the following section.

Discussion of asset replacement procedures

In this section, we discuss those processes and procedures that ensure appropriate capital replacement decisions are made. The processes that we recommend here are based upon a comparison of existing approaches at MTRCL with best practice approaches in similar industries, and the identification of directions for improvement in these decision processes. The processes and procedures established by MTRCL in its asset replacement manual were reviewed during a detailed study conducted by the first two authors with MTRCL. The authors also investigated, in particular, escalator refurbishment. Key documents were reviewed, interviews were held with key personnel involved with the development of the case for refurbishment and the management of the trial refurbishment programme. In addition to the detailed review of the escalator refurbishment programme, a number of other asset replacement studies were considered including air circuit breakers on the urban line, depot 50 Hz track circuits, and urban line mark 1 point-machines—this latter problem is also considered in this paper.

A particularly interesting point that emerged from this investigation was that the duration of the decision itself was often significant—7 years and counting for the escalators, beginning with an asset replacement study in 1998 (Dwight, 1999), continuing with a review (Dwight, 2000), and the current study (Dwight and Scarf, 2005). Thus, just as the life of an asset can be notionally divided into phases (design, testing, production, use, scrap—for example, see Blanchard and Fabrycky, 1998), so the life of a decision (the decision life) comprises a number of phases: alert, investigation, decision, implementation, and review.

Alerting the organization to the need for a study

The first phase of an asset replacement decision is the alert in which the potential requirement for capital expenditure on an asset is made known within the organization. Ideally, an alert would then lead to the second phase of a decision life: a study or investigation of the asset and its function. A list of circumstances that gave rise to an alert would include: performance degradation; the ultimate technical life of the asset is imminent; asset support needs are set to interfere with service provision; asset support costs are higher than attainable with an alternative asset; immediate or higher level functions provided or supported by the asset are changing; and spares or other requirements for maintenance of the asset are unavailable. There need to be mechanisms in place to ensure that such circumstances give rise to alerts and that the list of circumstances is exhaustive. Achievement of such a diverse view of an asset comes in part from having set triggers based on measured values but will ultimately rely on the diligence and knowledge of those in charge of the assets.

Investigation of asset replacement

An alert should necessarily lead to a study of the asset. The need for a study must be predicted with sufficient lead-time to avoid loss of function due to lack of asset performance or to take advantage of emerging technology in a timely manner, and this will constrain the requirements of the alerting process. In an asset replacement study, we would initially expect to confirm that the alert justifies a study, and to carry out a functional analysis. This latter analysis would identify the existing asset function as perceived by the organization; establish its position in the functional hierarchy, along with the long-term need for, or variation in its function, and functional performance criteria for the function and the higher-level functions; and review the system asset design against the reviewed function and required functional performance. The study would then review the condition of all assets that together fulfil the established function against current and future technology, and also establish the project resources (costs, service downtime, etc).

Consideration should then be given to interactions with other assets and activities of the organization. There may be similar parts or other assets involved with the delivery of the higher level function or assets requiring the same access arrangements, which are candidates for replacement. Project sharing (executing distinct capital projects simultaneously to minimize disruption and cost or to add greater value) or other interesting asset management strategies such as cannibalization could be considered. Adoption of a systems view (Blanchard and Fabrycky, 1998) would allow these interactions to be considered systematically. One could consider whether a functional view of asset condition could be developed as opposed to the more traditional hardware view—for example, placing station assets within the context of the service provided by the railway station allows consideration of the vulnerability of the station to the projected asset performance relative to the projected functional requirement.

Engineering considerations would then typically determine a number of feasible options for replacement. This would lead to a number of 'challengers' for replacement of the 'defending' asset (Christer, 1988; Rogers and Hartman, 2005). Broad costs and consequences would need to be quantified for the different options.

Finally, the study should consider appropriate decision analysis. Guidance on likely decision outcomes has been developed by Dwight (1999), who discusses the concept of the expected decision given the attributes of the asset itself, Figure 2. This concept could be developed further to allow calibration of the scales presented in Figure 2.

Figure 2.

Indicative relationship between the technology utilized in the asset and the replacement decision (Dwight, 1999).

Full figure and legend (8K)

Making and implementing the decision

Good decision-making is predicated on good information and so the asset replacement study is fundamentally important. Ideally, net present value (NPV) and life cycle costing analysis of competing replacement options would inform the decision, along with sensitivity analysis to key decision drivers. However, generally, decision-makers should also focus on the value of an asset to the business, rather than on particular criteria which may carry different weight among the various players in the decision-making process. For example, engineers may focus on downtime, financial managers on cost. MTRCL, in particular, have developed a value-based score for all capital projects, which is based on the sums of weighted scores with respect to the major corporate business objectives of safety, profitability, customer service, work environment, environment, user benefit, and corporate image, with categorization of projects into particular value ratings. This is helpful for making broad value judgements about project release (funding of projects). It is expected that identifying asset criticality will further assist in making visible the importance of the asset and the proposed project to the business. Through a standard rating system, the relative importance to business outcomes can be judged.

During the implementation phase, the engineering management for a project will be considered in more detail. On implementation, care needs to be taken to ensure continuity in objectives, and that the decision can be reviewed as new factors and options emerge.

Reviewing the decision

Emerging factors and options may affect the ongoing validity of the decision to either replace or refurbish the asset. In the case where the business environment has changed, replacement that may not have been viable may then become viable. Benefits would result from a process that identified changed circumstances and triggered a review of current projects that might be susceptible to such a change. Rules for re-appraisal of existing factors in the light of emerging factors will be useful in avoiding unnecessary re-evaluation. It seems that as a new factor emerges, it is not sufficient to leave existing determinations (decisions to date) unchanged since an emerging factor may influence the consequences of earlier determinations. Where an emerging factor is thought to interact with existing factors, those factors that interact with an emerging factor may need to be revisited in a decision re-appraisal. For example, a number of options may have been considered and an option chosen. Suppose a new factor emerges: should the decision be re-appraised and if so, how? A stopping rule for decision-making would be useful—at what point do we conclude that enough factors and options have been considered and that sufficient information is available to make the decision? A formal decision follow-up process from budget approval up to execution is recommended.

For example, in the case of the escalators at MTRCL, initial investigation into asset replacement was taken as early as 1998. Since that time, the core values of the organization, its business environment, the contract terms for escalator servicing, and knowledge about individual escalator condition have changed. In the meantime, trial refurbishments have also been undertaken. Under these circumstances, there is a strong case for reviewing the original decision.

Furthermore, the drivers of replacement decisions may change over the decision life. For example, for the escalator replacement at MTRCL, during the decision life, there appeared to be a shift in justification for replacement from refurbishment issues to retrofitting for improved performance. One could argue that this may be due to a change from the management perspective to the engineering perspective that coincides with an initial decision for asset replacement made by managers and then handed over to engineers for practical implementation. This implies that in asset management best practice, one needs to review the decision at particular stages of its life, and consider, in particular, changes in the objectives.

Risk management of the decision

Much of the discussion above suggests that the decision itself needs to be risk-managed, whereby consideration is given to risks associated with, for example: new asset condition/life information; new replacement/refurbishment cost and impact information; and changes in functional requirements, value of money, corporation core value changes, or in emerging technology. Such changes in the environment during the decision life are inevitable given the time scale and cost of decisions. Such a 'decision-validity risk' process would focus on actions necessary during the decision life (identification and registration of decision drivers; examination of sensitivity of decision to drivers; identification of risks; staged implementation to allow revision of the decision, specification of information to be collected during implementation; establishment of timing for decision reviews).

Decision-validity risk would also make explicit the notion that sensitivity analysis should be more clearly a part of the process of the asset replacement study. Such sensitivity analysis should be utilized to explore the robustness of the decision and the implied values of the decision drivers, and should attempt to quantify customer service and the impact of other factors that are 'difficult to quantify'. For example, for a passenger transport organization, quantitative consideration of delays to passengers from both asset replacement and retention should be attempted in the decision process. This should include delays due to planned and unplanned service downtime. Quantitative consideration of other penalties of unplanned events (failures) should also be included, for example, passenger injury. Alternatively, a maximum tolerable injury frequency could be set as an additional requirement. Some effort could be made to establish a sensible cost of passenger delay or inconvenience, with the acceptance that such a conversion of customer service targets to a monetary value may not be accepted. Hence, it may be instructive to establish the cost that would alter a decision to replace or to retain an asset. Another approach that avoids this monetary conversion issue is to model the level of inconvenience separately to ensure it remained below some acceptable threshold. This form of sensitivity analysis can be applied generally.

The decision-validity risk approach should also require the identification during the decision life of the benefits of delayed replacement. Where technologies are changing or where intended use is evolving there may be an advantage in postponing decisions to replace assets. This could be done qualitatively, by asking the group proposing the replacement: if the replacement will take advantage of developing technology; if it coincides with other activities; and if it allows better response to changing functional requirements. The exploration of real-options theory could also be undertaken. This theory seeks to quantify the cost–benefit of delaying a decision using options pricing theory—waiting will make a decision to invest in a project less uncertain since more information about project costs may become available, but this has to be traded off against lost opportunity. The approach has been used most typically to consider large investment projects for example, Bowe and Lee (2004).

Key elements for robust replacement decision-making

In summary, we can list those elements that are necessary for robust decision-making:

• engineering know-how to investigate feasible asset solutions and implement the solution;
• an asset replacement approval process that prioritizes projects using appropriate criteria, with NPV calculations done to support decision-making that include all relevant costs of the various options and examine sensitivities;
• an open management structure that facilitates the airing of project appraisal;
• good data along with the resources to transform the data into a formal case for a solution to the asset replacement decision problem;
• provision of a process that allows easy reaction to changing weightings on objectives to take advantage of business conditions as they evolve;
• a method that allows quick reaction to emerging replacement needs that arise outside the normal approval cycle; mechanisms for re-appraisal and stopping rules for the consideration of emerging factors since a decision process is sequential in nature and decision lives may extend over long time periods;
• for assets that come along with a maintenance provider, a good relationship with the contractor 'based on trust';
• a strategic plan for asset replacement with long-, medium- and short-term plans, with easy entry to medium-term plans—this can be contrasted with an approach to the control of capital based upon making the replacement decision process difficult to navigate;
• the use of a working group to ensure that all key aspects of decisions are included; and
• a value-based approach using summary classifications that clearly define the importance of projects to the organization.

Review of capital replacement models

Early economic life models such as Eilon et al (1966) considered an idealized equipment replaced at age T, that is, replacement every T times units, in perpetuity. In this idealized framework, for T small, frequent replacement leads to high replacement or capital costs. Infrequent replacement (large T), on the other hand, results in high operating or revenue costs (assuming that operating costs increase with the age of equipment). Trading-off capital costs against revenue costs leads to an optimum age at replacement, T^*, the so-called economic life. The decision criterion is typically a total cost per unit time or an annuity (that annual payment necessary to meet C&R costs in perpetuity). The annuity has been called the rent by Christer (1984). In the case without discounting, the total cost per unit time, c(T), and the annuity are equivalent and

where m₀(t) is the operating cost rate and R is the replacement cost, and assuming no residual value. From Equation (1), it follows that T^* is the solution of

provided it exists. In its discrete time form, the total cost per unit time is

where m_0i is the operating cost in time period i. With a discount factor, , and discounting to year end, and residual value function S(T), the NPV of all future costs in perpetuity is

An objection to this criterion is that as 1, c_NPV(T). Consequently, we recommend the annuity or rent (the amount paid annually and in perpetuity that is necessary to meet the total discounted cost) given by

whence

Notice that as 1, c_rent(T)c(T), the total cost per unit time. The economic life can be obtained by minimizing c_rent(T), typically using a spreadsheet by considering a range of values of T.

The economic life model can be adapted to consider technological change in a number of ways. One can consider economic factors for new models of equipment (future operating costs) in a parametric fashion, specifying a model for technological change, which then implies operating cost functions, replacement cost and residual values for each replacement cycle into the future (Elton and Gruber, 1976). Alternatively, one can model replacement over a limited timescale, either by fixing the time horizon, or by fixing the number of replacement cycles. Christer (1984) did the latter and described a two-cycle model, which models the immediate replacement decision problem by considering existing plant as having age and age-related operating cost m_0i, and new plant as having operating cost m_1i. In its discrete form, the annuity for this model is

Here K and L are decision variables, with K modelling the time (from now) to replacement of the existing asset; K+L is the time to second replacement. The advantage of this model is that one only needs to estimate the operating cost of the existing and new assets (as functions of age), the capital cost for the new asset, R₁, and the age-related resale or residual value of new and existing assets, S₀,S₁, and estimation is more straightforward than for a parametric model of technological change.

In the financial appraisal of projects, a standard approach fixes the time horizon and determines the NPV of future costs over this horizon (eg Northcott, 1985). This fixed horizon model has been studied by Scarf and Hashem (2003) and its simplicity lends itself to application in complex contexts (eg Scarf and Martin, 2001). The annuity for this model can be derived from Equation (2) above simply by setting X=K and K+L=h, the length of the planning horizon, and then considering h as fixed. Hence, there is only one decision variable, X, the time to replacement. Given the possibility that X=h, that is, no replacement over the planning horizon, hence we retain the current asset, the annuity function has a discontinuity at X=h, and X^*=h implies that it is not optimal to undertake the (replacement) project. Furthermore, since the replacement at the end of the horizon has a fixed cost (with respect to the decision variable X), its inclusion or exclusion has no effect on the optimal time to replacement. It is natural not to include the replacement cost at the horizon-end since a standard financial appraisal approach would only account for revenue costs up to project execution, capital costs at project execution, subsequent revenue costs up to the horizon-end, and residual values. Including the replacement at h, on the other hand, allows cost comparisons with the two-cycle model and the associated rent, Equation (2). We take the former approach here however and the annuity is

Of relevance to the study undertaken at MTRCL is the behaviour of these models (2) and (3) when the operating costs are constant (or increasing only slowly). The behaviour is simplest to follow for the continuous time formulation when the discount factor is unity (no discounting) and residual values are zero. Under these circumstances, the cost per unit time (annuity) for the two-cycle model and the fixed horizon model become

and

respectively. From (4), we get dc_rent²(K, L)/dK=[L(m₀-m₁)-2R]/(K+L)². Thus, there is no K such that dc_rent²(K, L)/dK=0, but that dc_rent²(K, L)/dK>0 K^*=0 if L(m₀-m₁)>2R for any fixed L. Furthermore, dc_rent²(K, L)/dL=[K(m₁-m₀)-2R]/(K+L)², and so if m₀>m₁ (which is a necessary condition for dc_rent²(K, L)/dK>0) dc_rent²(K, L)/dL<0 and so L^* does not exist. However, in any practical implementation of the two-cycle model, one would bound L with some upper value l_max, say. Then, the optimal policy would be K^*=0 (L^*=l_max) if

We can consider a similar argument for the fixed horizon model. Thus, dc_rent^h(X)/dX=(m₀-m₁)/h, X<h and so dc_rent^h(X)/dX>0 if m₀>m₁. However, since c_rent^h(X) has a discontinuity at X=h, X^*=0 is optimal only if m₀>m₁ and c_rent^h(0)<c_rent^h(h). That is, if (R+hm₁)/h<m₀, that is, if

Thus, comparison of inequalities (6) and (7) shows that the two models have different properties in terms of the behaviour of optimal policy as a function of cost parameters. Thus, the two-cycle model is inconsistent with standard financial models. However, a simple modification to the model will correct this inconsistency. Simply, omit the replacement at the end of the second cycle. For the constant revenue case above, the rent becomes c_rent²(K, L)=(Km₀+R+Lm₁)/(K+L) and optimal policy would be K^*=0 (L^*=l_max) if l_max(m₀-m₁)>R, which is consistent with the fixed horizon model and hence with standard financial appraisal models.

However, the two-cycle model (two replacements) is consistent with the economic life model when operating costs are increasing and replacement is like-with-like (Scarf and Hashem, 2003). Thus, it would appear that the two-cycle model with its two replacements (at t=K and at t=K+L) is applicable for the case of increasing operating costs and that a modified two-cycle model with one replacement (at t=K only) for operating costs that are constant or increasing only slowly. This apparent paradox can be reconciled however. When operating costs are increasing only slowly, typically L^* does not exist. Furthermore, in practice we must constrain L (and K for that matter) such that Ll_max (as pointed out above) since numerically we can only search for L^* over a finite space. In constraining Ll_max under the two replacements formulation, we impose a replacement at l_max when in fact there should not be a second replacement since L^* does not exist. The modified two-cycle model does not have a replacement at l_max. This then suggests that the two-cycle replacement model should be modified in the following subtle way: if there does not exist an L such that c_rent²(K, L) has a minimum strictly within the search space, that is, within {(K, L) : 0<K<k_max, 0<L<l_max}, then, when determining that K which minimizes c_rent²(K, l_max), no replacement cost should be incurred at t=K+l_max. Thus, the model should be modified so that there is only one replacement. Otherwise, the 'cost hurdle' for replacement of the current asset will be set artificially high (inequality (6)). Thus, in all practical situations for which operating costs are increasing only slowly, one should use this modified two-cycle model or the fixed horizon model as a special case. Of course, replacement of an existing asset in these circumstances would only be contemplated if the operating cost (or functionality) of the new asset is significantly lower (or functionality higher). As stated earlier, these circumstances may occur in practice more frequently than supposed and may in fact be the norm, since existing assets, for which there exists more performance-efficient technology, may be ageing very slowly (eg electricity supply network components, Brint et al, 1998).

Using the fixed horizon model or equivalently using the modified two-cycle model with a finite search space may lead to significant end-of-horizon effects (since costs beyond the horizon end are ignored). Thus, time to first replacement will depend on h (or equivalently l_max). Choice of h (or l_max) will need to be considered carefully; in practice, the horizon may be specified by company policy on accounting methods and discounting may reduce those costs incurred in the distant future to a small or insignificant level. Furthermore, specification of the residual value may be problematic, particularly for non-movable assets with either constant or slowly changing operating revenue. This is because the market resale value of the asset is arguably zero. However, the residual value, as measured by the benefit of the function the asset performs rather than its value if sold, may be non-zero. In this case, company policy may prescribe a 'straight line' depreciation so that the residual value is proportional to the estimated asset life fraction remaining at replacement or horizon end. However, such an approach may be difficult to justify since the asset life is unknown and linearity is a strong assumption. One possible approach here would be to look at sensitivity to the parameters in a residual value model such as this, but there would be a number of parameters and this may become over-complex. An alternative would be to equate the residual value at the horizon-end to the cost–benefit of the replacement (whenever it took place) over the next m years. But this then amounts to extending the planning horizon from K+L to K+L+m or from h to h+m. This of course will lead to models the same as those considered at present but with longer horizons (or to a three-cycle model if a subsequent refurbishment is also considered). Thus, if one accepts that a two-cycle model is sufficient for modelling purposes, then, logically, consideration of residual values for a non-movable asset amounts to considering sensitivity to horizon length (either h or K+L, whichever model is used).

Later in the paper where we consider escalator replacement and track point-machines replacement at MTRCL, we principally use the modified two-cycle model, but also include for comparison, the fixed horizon model. Tax considerations are not included in the modelling since MTRCL has an outstanding tax allowance from previous major extensions. In general, taxation should be incorporated into the financial model depending on the circumstances of the organization and the nature of the local tax regulations, since tax benefits and payments are real cash flows and may affect financial decisions.

In modelling replacement problems, it is not necessary to restrict models to (at most) two replacement cycles. Other authors consider models with an unrestricted number of replacements (Bellman, 1955; Bean et al, 1994; Hartman, 2004). While the restriction that the two-cycle model, the modified two-cycle model and the fixed horizon model above imply may lead to sub-optimal replacement policies, we argue that for replacement problems with typical discount rates and planning horizons, the modelling of operation and replacement beyond the end of the second cycle has little effect on the time to first replacement, and it is the time to first replacement that is the issue of principal interest in practice.

Escalator replacement

Detailed consideration of escalator replacement strategy began in the late 1990s at MTRCL as the early escalators approached their design life of 20 years. The escalators themselves are seen as an integral part of the railway system for transportation of passengers and staff between station platforms and street level. Maintenance of escalators is generally outsourced to equipment suppliers due to the difficulty that alternative contractors have in obtaining proprietary spares. The original manufacturers can keep costs down as a result of the economy of scale that is achievable through maintaining equipment over a large number of client organizations. Currently, MTRCL operate of the order of 600 escalators and the annual maintenance contract price is approaching the HK$100 million. Escalator replacement is therefore a significant issue within the organization.

Studies undertaken at MTRCL have suggested that the economic life of escalators is of the order of 25 years but that, based on overseas experience, escalator life can be extended to up to 40 years. However, given that the corporation has a large fleet, a strategy has to be set to manage escalator maintenance and to deal with the replacement or refurbishment of older escalator assets. A key factor in this strategy is the approach of the organization to the re-negotiation of maintenance contracts and in particular to determine the scale of refurbishment of older assets and the level of major parts replacement and supply within the negotiated contract.

For the presentation of the modelling work in this paper, it is necessary to consider the asset management options open to the corporation in a simple manner. Studies were undertaken for two groups of escalators, Group A and Group B. The groups differed in that the management options available were different. For Group A, replacement, although crudely costed in this paper, was not really a viable option—economic costs were too high and disruption unacceptable given the duration of replacement work. Refurbishment by the original manufacturer, replacing worn parts, upgrading the control panel, and improving maintenance access and safety was being carefully considered by the corporation (MTRCL) as a viable strategy for managing the asset life. Cost savings could be achieved through a reduction in the annual maintenance contract price post-refurbishment. Thus, put simply, for the Group A escalators, the corporation were faced with the decision: continue with the current relatively higher-price maintenance contract or refurbish and benefit from a new relatively lower-priced maintenance contract. Other benefits would also accrue from refurbishment for both contractor and the corporation. For the contractor, improved access and safety for maintenance was part of the refurbishment package. For the corporation, up-grade of the control panel would result in fewer unplanned escalator stoppages due to the installation of a 'power-dip ride-through' function—this would increase passenger safety and decrease delays due to unavailability. Owing to the large size of the fleet, it was also necessary to consider the timing of the refurbishment since only a rolling programme of refurbishment could be considered. In fact, a constraint on the number of unavailable escalators at any one station at any one time and the duration of the refurbishment (8 weeks) meant that only some 38 escalators could be refurbished per year. For the Group B escalators, the corporation were also considering refurbishment using different contractors. Thus, in the analysis presented later, we consider some five asset management options:

• 'do nothing'—continue with high-price maintenance contract;
• 'refurb'—renew worn parts, retro-fit new control box and proceed with lower-price maintenance contract;
• 'delay refurb'—delay refurbishment for up to n years;
• 'replace'—a full replacement option with nominal costs included for comparison purposes;
• 'rival refurb'—refurbishment carried out by a contractor other than the original equipment manufacturer, along with on-going maintenance contract with this competitor.

The costs of refurbishment (per escalator) in the present study were obtained from initial quotations from the respective manufacturers: these are HK$629K for a Group A escalator and, in the case of Group B, HK$662K for refurbishment by the manufacturer and HK$760K for refurbishment by a competitor. Ongoing annual maintenance contract costs (per escalator) are: HK$88K for Group A pre-refurbishment; HK$69K for Group A post-refurbishment; HK$62K for Group B pre-refurbishment; HK$50K for Group B post-refurbishment; HK$69K for Group B post-refurbishment with competitor to manufacturer. Prior to refurbishment for both the Group A and Group B, the cost of replacement of major parts is in addition to the annual maintenance contract and major parts are replaced on the basis of condition. For the Group A post-refurbishment, the annual maintenance contract includes replacement of major parts at no extra cost, and for the Group B if the refurbishment and subsequent maintenance contract is with the competitor, then again replacement of major parts is included. For refurbishment by the original equipment manufacturer, the cost of replacement of major parts carries an additional contingency of HK$13K per annum. This explains why the maintenance contract costs are lower for the Group B with the manufacturer. Given that we might expect major parts to be replaced somewhat less frequently than dictated by their recommended lives, we introduce a cost parameter to model such life-extension—this is the effective life factor, . =1 implies that major parts are replaced at a frequency corresponding to their recommended life (eg, once every 25 years for the steps at a cost of HK$478K), and the replacement frequency ∝ 1/ (=2 implies replacement of steps once every 50 years). The cost of a replacement (HK$1700K) is a nominal figure and used mainly for crude comparison with refurbishment. In practice, replacement may cost significantly more than this.

The corporation recommend a discount rate of r=0.11—when used with the recommended projected inflation rate of i=0.05, this corresponds to an effective discount factor, , of 0.057 (1/(1+)=(1+i)/(1+r)). Integral to the refurbishment option is the up-grading of the escalator control box to allow 'power-dip ride-through'—this facility prevents unnecessary emergency stops caused by momentary power loss that can cause injuries to passengers. However, the effectiveness of the 'ride-through' facility is uncertain, hence we introduce another cost parameter, control box retro-fit effectiveness, which represents the percentage of passenger injuries due to power dips that would be prevented by up-grading of the control box at refurbishment. Also, for the purposes of sensitivity analysis, it is necessary to place a cost on an emergency stop due to a power dip. We call this the penalty cost of failure. Historic records of the number of such stops (approximately 0.5 stops per escalator per year) and the retro-fit effectiveness are used to calculate a total penalty cost (saving) per escalator per year post-refurbishment. Finally, we also consider another parameter that is difficult to quantify: the passenger delay cost due to refurbishment. This cost is based on an opportunity cost calculation (2.5 million passengers per day using 52 stations each with typically five exits, implies 10 000 passengers per exit per day; if closing an exit means a 30 s delay per passenger then this amounts to a total of 500 person-days over the 8-week refurbishment period; using an opportunity cost of HK$400 per person-day gives a total delay cost of HK$200K per escalator refurbishment).

All costs above are based on a typical short-rise escalator.

There was considerable discussion on how to model the residual value of an asset at replacement or at the horizon-end. MTRCL policy was to consider a linear depreciation. However, linear depreciation amounts to taking the residual value to be the 'book value' and this is not in the spirit of NPV analysis, which seeks to maximize organizational wealth (Northcott, 1985). Also, since consideration of residual value is equivalent to extending the planning horizon, as discussed in the previous section, it was decided that it would be sufficient to choose the horizon carefully to take account of the asset life post-refurbishment and to consider the sensitivity of the decision variable(s) to the horizon length. The asset life post-refurbishment was considered to be of the order of 20 years.

Initially, we compare the different replacement models and the optimum policy that follows from them. Sensitivity to the cost factors is then considered using the fixed horizon model, both for the Group A and Group B escalators. We do not make recommendations about optimal policy. We merely provide the results of an analysis that quantifies the influence of 'difficult to quantify' cost parameters such as passenger delay cost and penalty cost of failure. A number of other 'replacement' options are available to MTRCL such as accelerating the refurbishment to 28 days at a cost of HK$100K per escalator for all relevant options above, or selling the escalators back to the original equipment manufacturers with a long-term contract for payment per passenger journey, but we do not consider these further here.

Results

Model comparison

We begin the presentation of the results for the escalator replacement problem with a comparison of the replacement models themselves. In particular, we wish to compare the optimum decision that follows from each of the three models discussed earlier: the two-cycle model, the modified two-cycle model, and the fixed horizon model. This comparison is made in Tables 1, 2 and 3 for a range of penalty costs of failure and refurbishment delay costs. Note that both these costs are measured on a per event basis: per unscheduled stop for the penalty cost and per refurbishment for the delay cost. Other cost factors are as indicated in the table titles. From Tables 1 and 2, we can see that over the range of penalty costs and delay costs considered the modified two-cycle model and the fixed horizon model are in broad agreement as to optimal policy. On the other hand, Table 3 indicates that the optimum decision following from the two-cycle model and the fixed horizon model are not in agreement when the penalty cost is high and refurbishment delay cost is low—such values for these cost factors would tend to drive early replacement. This suggests that the imposition of a replacement at the end of the second cycle as in the two-cycle model has the effect of unreasonably extending the replacement times. This lends further support to the use of the modified two-cycle model for investigating escalator replacement issues in more detail.

Table 1 - Comparison of optimum policy for the modified two-cycle model and the fixed horizon model, with optima presented as a function of penalty cost and refurbishment delay cost.

Full table

Table 2 - Comparison of optimum policy for the modified two-cycle model and the fixed horizon model, with optima presented as a function of penalty cost and the refurbishment delay cost.

Full table

Table 3 - Comparison of optimum policy for the two-cycle model and the fixed horizon model, with optima presented as a function of penalty cost and the refurbishment delay cost.

Full table

In Table 4, we look at annuities for the modified two-cycle model and the fixed horizon model for a range values of the respective decision variables. Note that the annuities for the fixed horizon model lie on the diagonal indicated with shaded cells. This is because the fixed horizon model is equivalent to the modified two-cycle model with the additional constraint that K+L=h. These annuities are also presented in Figure 3a. Figure 3b shows the annuities for the two models in the case of no discounting—discounting has the effect of slightly extending the economic life (since the NPV of future costs are reduced) and this accounts for the small difference in optimum policy between the fixed horizon model and the modified two-cycle model in Figure 2a, X^*=1, K^*=4 (years).

Figure 3.

Annuities (HK$000s per escalator per year) for typical Group A escalator for modified two-cycle model with refurbishment at K years from now and operation for a further L years. Annuities for fixed horizon model with h=22 years also shown (X<22: bold, solid curve; X=22: ). Cost parameters as Table 4, except: (a) effective discount factor equals 0.06 (equivalent to inflation rate of approximately 0.05 and discount rate of 0.11) and (b) no discounting.

Full figure and legend (28K)

Table 4 - Annuities (HK$000s per escalator per year) for typical Group A escalator for modified two-cycle model with refurbishment at K years from now and again after a further L years.

Full table (83K)

Effect of cost parameters on refurbishment policy

The cost parameters in Table 4 and Figure 3 are held at intermediate values. For the escalator replacement problem, we were interested in the effect of these cost parameters on optimum policy. In Figure 4, we present annuities for a number of 'replacement' options as a function of each of the cost parameters. These replacement options correspond to those being considered by the company, with 'refurb' referring to immediate refurbishment (in year 1), and 'delay refurb' referring to refurbishment in year 10 (from time of study). Given the size of the fleet, and the constraint on the number of escalators that can be refurbished at any one time and the duration of refurbishment, we would expect the refurbishment programme to last some 15 years and therefore a significant proportion of the fleet would experience this kind of delay prior to refurbishment. Therefore, we include it as a particular policy for indicative purposes. We use the fixed horizon model here in order to make comparisons between annuities—this is because one would wish to compare the cost of different options over the same horizon. Equivalently, we could use the modified two-cycle model with the additional constraint K+L=h=22 (years), say.

Figure 4.

Annuities (per escalator) as a function of cost parameters for fixed horizon model, with h=22 years for various refurbishment/replacement options. Typical Group A escalator; refurbishment cost, HK$629K; replacement cost HK$1700K. (a) Annuity versus effective life parameter, (b) annuity versus penalty cost of failure, (c) annuity versus nominal discount rate, (d) annuity versus control box retro-fit effectiveness, (e) annuity versus cost of refurbishment delay, and (f) annuity versus horizon length, h. Cost parameter values when not varying set at: effective life, 1.5; penalty cost of failure, HK$50K; nominal discount rate, 0.11; control box retro-fit effectiveness, 75%; and refurbishment delay cost, HK$100K.

Full figure and legend (69K)

Figure 5 illustrates the sensitivity analysis for the Group B escalators for which a competitor refurbishment option was available. From Figures 4 and 5, we can see that optimum policy is certainly sensitive to these cost factors with the influence of cost parameters as expected. For example, increasing the delay cost makes refurbishment more expensive and so the annuity rises and makes refurbishment less desirable relative to the status quo. Conversely, for increasing penalty cost, refurbishment becomes more desirable. Other effects are as we would expect, although the discount factor effect is quite strong.

Figure 5.

Annuities (per escalator) as a function of cost parameters for fixed horizon model, with h=22 years for various refurbishment/replacement options. Typical Group B escalator; refurbishment cost, HK$662K; rival refurbishment cost HK$760K. (a) Annuity versus effective life parameter, (b) annuity versus penalty cost of failure, (c) annuity versus nominal discount rate, (d) annuity versus control box retro-fit effectiveness, (e) annuity versus cost of refurbishment delay, and (f) annuity versus drive replacement probability. Cost parameter values when not varying set at: effective life parameter, 1.5; penalty cost of failure, HK$50K; nominal discount rate, 0.11; control box retro-fit effectiveness, 75%; refurbishment delay cost, HK$100K; and drive replacement probability, 0.5.

Full figure and legend (69K)

Threshold values that lead to a step-change in the optimum policy (option) can be observed from these figures. Thus, while estimation of the penalty cost of failure, for example, may be difficult and contentious, the importance of its effect can be observed. This may then provide an incentive for further investigation of this parameter or discussion about whether its true value is above or below the threshold of policy change.

Point-machines replacement

Consideration of the asset management of point-machines on the urban line indicates that operating costs may also be near-constant, but that new technology provides a step change reduction in this cost. A replacement study for the fleet of point-machines on this line was triggered by unavailability of spares, and a number of options were being considered: in-house development of spares for existing machines (option 1, BR1); up-grade to mark 2 (option 2, BR2); and replacement with a new type of point-machine (option 3, VCC), which were in use on other more recently developed lines in the network. Estimates of maintenance costs for each machine were constant (based on known servicing costs and replacement of key components at specified frequencies). Translating these into costs for the fleet as a whole given a phased implementation of upgrade or replacement gave the operating costs in Figure 6. Failure data for machines in options 1 and 3 had been collected over a period of 5 years (Figure 7). Again these indicate non-increasing failure rates. Furthermore, these rates are approximately equal—this then makes the problem simpler since it is not necessary to quantify the penalty cost of failure. Figure 8 illustrates the sensitivity of the annuity for the fixed horizon model (and equivalently the modified two-cycle model with K+L=h) to the discount rate and the horizon length. For options 1 and 2, two replacement times are considered: immediate and delayed for 8 years (from 2000). Here, the optimum decision is straight forward in comparison to the escalator replacement problem. We include this example in order to illustrate, firstly, another case with non-increasing operating costs, and secondly, to demonstrate that the annuity is relatively insensitive to the choice of horizon—and less so than to the discount factor.

Figure 6.

Projected maintenance costs for fleet of BR mk1 point-machines under various replacement options.

Full figure and legend (15K)

Figure 7.

Number of delays due to point-machines per point-machine per year. Number of 1 min delays and 5 min delays shown. Target for 5 min delays is 0.1 per machine per year.

Full figure and legend (12K)

Figure 8.

Annuity (per machine) for point-machines replacement options as a function of: (a) discount rate (horizon, h=22 years) and (b) horizon (nominal discount rate, 0.11, equivalent to an effective discount rate of 0.06, approximately).

Full figure and legend (26K)

Discussion

For the escalator replacement problem, it appears that refurbishment is recommended only if one is prepared to recognize that the values of difficult to quantify cost parameters lie in a certain region. Thus, this type of analysis cannot strictly recommend a policy, it can merely evaluate the relationship between decision policies/variables and factors in the decision problem. It should act as a guide for the decision-maker, rather than a decision-maker itself. Thus, in financial appraisal of projects, rather than attempt to estimate the values of 'difficult to quantify' parameters and then determine optimal policy, the influence of these parameters on the decision should be quantified. In this latter approach, threshold values that lead to a step-change in optimum policy can be investigated and presented and the decision-maker can then consider whether they believe that such values are realistic within the context of the problem.

For the escalator replacement problem in particular, one could argue that the cost of differing options or policies will reflect the maintenance contractor's profit requirement, whatever the details of the arrangement, and therefore the costs of options would expect to vary very little. What can differ, however, is that some options may lead to lower risk (eg, where the contractor bears the cost of major parts' wear-out, which may be subject to significant uncertainty) and lower risk is certainly desirable from the point of view of the operator. On a more technical point, the operations imposed limit of 38 escalator refurbishments per year as the maximum tolerable is significant in defining the cost of the escalator refurbishment and retro-fitting programme, and therefore this parameter might have been explored in the life cycle cost modelling.

For modelling capital replacement decisions, we recommend use of the modified two-cycle model. With this model, it is appropriate to fix the length of the planning horizon, by setting K+L=h, when considering the influence of model parameters on the decision. This is because annuities and present values are then compared over the same timescale. Such an approach is equivalent to using the fixed horizon model. End of horizon effects will be small typically given the range of values of the discount factor that are used in practice. However, the horizon length should be chosen in accordance with the typical lifetime of the asset or assets, and the end-of-horizon effect should be investigated by using a range of possible horizon lengths. Once satisfied with the determination of model parameters it would then be sensible to revert to using the modified two-cycle model to look at the optimum values of decisions variables themselves. In this way, the effect of model parameters can be compared fairly with a fixed horizon, but that for the actual decision itself end-of-horizon effects may be minimized. While this modelling advice applies most strongly to the case in which equipment ages only slowly (constant or slowly increasing operating costs), we would argue that this is typical of practical applications and therefore we make these recommendations generally.

Note that we have been using the term replacement here, but one could argue that the models are also applicable to overhaul decisions. Replacements and overhauls have very similar characteristics and similar OR decision models are applicable to both situations. In fact, conceptually, the overhaul problem and the capital replacement problem are indistinguishable, although Christer (1984) uses different models for capital replacement and for overhaul.

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