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We focus on the inventory management of critical spare parts that are used for service maintenance. These parts are commonly characterised by a large variety, an intermittent demand pattern and oftentimes a high shortage cost. Specialized service parts models focus on improving the availability of parts whilst limiting the investment in inventories. We develop a method to forecast the demand of these spare parts by linking it to the service maintenance policy. The demand of these parts originates from the maintenance activities that require their use, and is thus related to the number of machines in the field that make use of this part (known as the active installed base), in combination with the part's failure behaviour and the maintenance plan. We use this information to predict future demand. By tracking the active installed base and estimating the part failure behaviour, we provide a forecast of the distribution of the future spare parts demand during the upcoming lead time. This forecast is in turn used to manage inventories using a base-stock policy. Through a simulation experiment, we show that our method has the potential to improve the inventory-service trade-off, i.e., it can achieve a certain cycle service level with lower inventory levels compared to the traditional forecasting techniques for intermittent spare part demand. The magnitude of the improvement increases for spare parts that have a large installed base and for parts with longer replenishment lead times.
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Forecasting Spare Part Demand using Service Maintenance Information
Sarah Van der Auweraera, Robert N. Boutea,b
aResearch center for Operations Management, Faculty of Business and Economics KU Leuven, Belgium
bTechnology & Operations Management Area, Vlerick Business School, Belgium
We focus on the inventory management of critical spare parts that are used for service maintenance. These
parts are commonly characterized by a large variety, an intermittent demand pattern and oftentimes a high
shortage cost. Specialized service parts models focus on improving the availability of parts whilst limiting
the investment in inventories. We develop a method to forecast the demand of these spare parts by linking it
to the service maintenance policy. The demand of these parts originates from the maintenance activities that
require their use, and is thus related to the number of machines in the field that make use of this part (known
as the active installed base), in combination with the part’s failure behaviour and the maintenance plan.
We use this information to predict future demand. By tracking the active installed base and estimating the
part failure behaviour, we provide a forecast of the distribution of the future spare parts demand during the
upcoming lead time. This forecast is in turn used to manage inventories using a base-stock policy. Through
a simulation experiment, we show that our method has the potential to improve the inventory-service trade-
off, i.e., it can achieve a certain cycle service level with lower inventory levels compared to the traditional
forecasting techniques for intermittent spare part demand. The magnitude of the improvement increases for
spare parts that have a large installed base and for parts with longer replenishment lead times.
Keywords: Inventory management, Forecasting, Spare parts, Service maintenance, Installed base
1. Introduction
In this paper we propose a forecast method for spare part demand by making use of information on
the maintenance operations. We address the following research questions: (1) How can we use information
from maintenance operations to generate forecasts, and (2) to what extent does this method improve the
inventory management of the spare parts, compared to more traditional forecast methods that only rely on
historical part demand to construct forecasts.
Efficient spare part management is indispensable for companies that increasingly offer services related
to the products they originally supply. Indeed, the after-sales activities (such as maintenance and repairs)
generate a more steady stream of revenue and can as such be an important source of profit (Auramo &
Accepted for publication by the International Journal of Production Economics (March 2019)
Ala-risku, 2005; Cohen et al., 2006). At the same time, challenges are associated with managing these
after-sales activities in a cost-effective way. The demand for spare parts, for instance, is very hard to
predict. When a critical part is requested and not available in stock, the company is not able to perform
the maintenance operation in time. This could jeopardize a client’s productivity, causing time delays and
high costs. To prevent part unavailability, companies keep stock buffers to deal with the uncertainty in part
demand. Keeping extra stock, however, can become costly when this is done for a large number of items, or
for expensive items. Efficient spare parts inventory management is thus an important but challenging task,
where the investment in inventories is to be traded off against the desired service levels.
1.1. Background and Motivation
Our research is inspired by an Original Equipment Manufacturer (OEM) in the compressed air, generator,
and pump industry who is currently facing these challenges. The OEM has service maintenance contracts
with its customers, in which they guarantee a pre-defined availability of spare parts. The OEM is thus
responsible for the maintenance of the machines installed at its customers. We refer to those assets as the
active installed base, i.e., the number of sold (installed) machines that haven’t been discarded, and can
generate spare parts demand either to replace failed components or for preventive maintenance. The OEM
currently manages over 250 000 different spare parts. The demand for approximately 40 000 of these parts
is currently forecasted using simple exponential smoothing (SES) and inventories are managed using a base-
stock policy. For the remaining 210 000 parts demand is too small (only one or two items per year) or
too little historical demand observations are available to keep the part in inventory. The company aims to
increase the part availability in the future, without unduly inventory investments. To date, the spare part
inventory is managed by the Service Logistics department. The Service Operations department, however,
who is in charge of the maintenance operations itself, is increasingly collecting data on its installed base, such
as machine survival and part reliability data. The Service Logistics department is therefore investigating
whether they can make use of this information to improve their spare part inventory management.
Managing spare part inventory is challenging, as many of them are characterised by an intermittent
demand pattern: many periods of zero demand interspersed by occasional non-zero demands (e.g., Boylan
& Syntetos, 2010). As standard forecasting techniques produce inaccurate results for these intermittent
demands, specific techniques have been developed, with Croston-based methods the most widely used (Cros-
ton, 1972; Syntetos et al., 2009a; Boylan & Syntetos, 2010; Bacchetti & Saccani, 2012). These techniques
are time-series based in the sense that rely on the assumption that future values of the demand series can
be predicted based on past demand, and no attempt is made to identify variables that influence the series
(Stevenson, 2012). We believe that we can use more detailed sources of information, such as reliability
characteristics and the maintenance policy, to generate forecasts, rather than merely looking at past demand
data. The amount of data collected and stored by companies increases, which makes the use of more sophis-
ticated data driven methods possible. These methods allow to capture the drivers of the demand, instead of
the observed demand alone.
1.2. Related Literature
There are a number of papers that discuss the use of installed base information for spare part demand
forecasting (see Van der Auweraer et al., 2019). The demand drivers that are most commonly discussed in
literature are the maintenance policy, which depicts when a part is replaced (e.g., Hu et al., 2015; Romeijnders
et al., 2012), the size and age of the installed base (e.g., Jalil et al., 2011; Kim et al., 2017; Stormi et al.,
2018), and the part failure probability (e.g., Barabadi, 2012; Si et al., 2017; Ritchie & Wilcox, 1977). Those
works tend to focus on only a specific subset of installed base information and the combination of these
different demand drivers is generally lacking. Moreover, the literature typically makes a distinction between
forecasting models for spare part demand for preventive maintenance (e.g., Hu et al., 2015; Romeijnders
et al., 2012; Wang & Syntetos, 2011; Wang, 2011) and forecasting demand for corrective maintenance (e.g.,
Hong et al., 2008; Jin & Liao, 2009; Kim et al., 2017; Minner, 2011; Stormi et al., 2018), sometimes also
referred to as reliability based forecasting. Both are rarely combined, however.
The literature on reliability based forecasting tends to focus on a specific phase in the product life cycle
(PLC) of the installed base, oftentimes the initial (e.g., Jin & Liao, 2009) or end-of-life (EOL) phase (e.g.,
Hong et al., 2008; Kim et al., 2017). By restricting the analysis to a specific PLC phase, simplifying model
assumptions can be made. For example, when the end-of-life phase is studied, potential expansion of the
installed base in the future can be neglected, which reduces the complexity of the forecasting problem.
However, these models are not applicable in the other life cycle phases and are in this way limited. In
addition, the majority of the methods makes restrictive distributional assumptions, for example on the
failure behaviour of the parts. Exceptions to this are Minner (2011) and the extension of his model by
Wu & Bian (2015). Their methods are applicable in every phase of the PLC and are not restrictive on
the distributional assumptions. Nonetheless, these approaches rapidly become complex and computationally
intensive because of their recursive nature, which renders them hard to apply in a practical setting.
When it comes to the benefit of using information from the service operations, we find that the proposed
methods in the literature generally show promising performance: they are capable to predict the actual
demand well and increase forecast accuracy. Nevertheless, their performance evaluation is typically decoupled
from inventory management and their impact on inventories and availability is rarely evaluated. This is in
contradiction to Syntetos et al. (2010), who state that forecasting performance in an inventory context should
always be evaluated with respect to its implications for stock control.
1.3. Our Contribution to the Literature
Our work contributes to the existing literature by offering a versatile forecast method that considers
a larger set of spare part demand drivers (in combination with each other) to construct the forecasts. It
incorporates information on the maintenance policy, which can be either corrective or preventive. Corrective
maintenance generates stochastic demand, whereas preventive maintenance interventions generate deter-
ministic demand, as they are known in advance. Our method also takes into account the evolution of the
active installed base over time, which can increase through the sales of new machines that are serviced and
decrease through the end-of-use of old machines. Finally, our method considers the part reliability, which
defines when a part in the installed base will fail and require a corrective replacement. We refer to this
collection of information used as Service Maintenance Information (SMI).
Our method is applicable throughout the full PLC, and is not tailored to one specific phase. Consequently,
there is no need for separate methods for the different PLC phases, and there is no need to identify the current
PLC stage. Moreover, it does not put restrictions on the probability distributions of the different model
components as it uses real data observations to generate its forecast. The method uses a statistical fit on the
historical part failures, and continuously improves this fit (“learns”) as more information becomes available.
The versatility of our method makes it applicable for a large variety of parts, regardless of the part specific
characteristics and without any distributional assumption.
We also consider the data requirements for our method to be amenable for implementation in a practical
setting. Our method requires data of historical machine sales and discards to track the evolution of the
installed base over time, a history of past part failures to estimate the part failure probability, and information
on past preventive maintenance actions on the installed machines together with the current preventive
maintenance schedule –if applicable.
The result of our forecast is an estimate of the distribution of the demand during the upcoming lead
time. This distribution can be used as an input for an inventory policy; we apply it to determine the optimal
base-stock policy to attain a pre-defined target service level. This way, we connect forecasting directly with
inventory management.
We find that our method has the potential to improve forecast accuracy and outperform the current
state-of-the-art forecasting procedures for intermittent demand. The proposed method is able to achieve a
higher inventory-service efficiency, especially when the installed base is large and lead times are long.
The paper is organised as follows: In Section 2 we introduce and describe our forecasting method. We
evaluate its performance in a numerical study, which we introduce in Section 3. The results of this numerical
tThe current point in time. t >0.
LThe replenishment lead time.
jThe machine age; t– time of machine installation. jt.
iThe part age; t– time of part installation. ij.
pi,j,t,L The probability of a demand occurring for a part of age i, installed in a machine of age j,
in the time interval (t, t +L].
j,t,L The conditional probability of a machine with age jto survive after the lead time L, esti-
mated at time t.
i,t,L The conditional failure probability of a part with age iin (t, t +L], estimated at t.
nij (t) The counted number of parts with age i, installed in machines with age j, at t.
Dt,L The demand forecast made at time tover lead time L.
NtThe size of the active installed base at time t.
λt+sThe estimated number of future machine sales occurring in period t+s, estimated at t.
s∈ {1, ..., L}.
TpThe lifetime of a part (time from replacement until failure)
TmThe economic lifetime of a machine (time from installation until discard)
fTp(θ) The probability distribution of the time until part failure.
fTm(θ) The probability distribution of the time until machine discard.
Table 1: Notations used.
study are discussed in Section 4. Section 5 concludes the paper.
2. Installed Base Forecasting for Future Service Part Demand
In this section we present our approach to use information on the maintenance operations to forecast
future spare parts demand. We distinguish between three main sources of information: (1) the maintenance
policy, (2) the size and age of the installed base, where we distinguish between the installation of the machine
and the installation of the part, and (3) the part reliability. These model components are explained in further
detail in the following sections. Table 1 presents the notation used.
The spare part demand forecast, b
Dt,L, is made at time tfor the upcoming replenishment lead time L.
This timeframe is denoted by the discrete time interval (t, t+L]. The lead time Lis considered deterministic,
and in our company example its value can range from a week to over five months. At time t, we estimate
the probability bpi,j,t,L that a part of age iinstalled in a machine with age jgenerates a demand in the
upcoming lead time L. Next, we monitor how many parts nij(t) of age iare installed in machines with
age j. The forecast b
Dt,L then consists of the sum of the demand probabilities for each of the parts in the
installed base. In the remainder of this section we first describe how the demand forecast is derived when
a corrective maintenance policy is in place (i.e., with only corrective replacements). Thereafter, in Section
2.6 we discuss the demand forecast in case a preventive maintenance policy applies (with corrective and
preventive replacements).
2.1. The Active Installed Base
The active installed base can be defined as the set of systems or products for which a company provides
after-sales services (Dekker et al., 2013). It is the active set of machines, which contain the part under study
and can generate a future demand for spare parts. This is the number of machines that has been sold to
customers and has not been discarded yet. A machine discard occurs when a customer ends the use of a
machine. We observe the active installed base at time tand note the age jof each active machine. The age
jof the machine is a discrete number and represents its time since installation.
Machines typically last longer than their parts, which are replaced upon failure of the part (or preven-
tively). Therefore, we also monitor the age iof the studied part in each installation, i.e., the time since the
last part replacement, or if the part has not been replaced yet, the time since installation. We explicitly
distinguish between part age and machine age, contrary to, for example, Kim et al. (2017), because a demand
occurs for a machine that is still active and experiences a failure, and machines can be discarded from the
active installed base before they have failed, which means they can no longer generate a spare part demand.
The part age is a discrete number, expressed in the same time unit as the machine age. Thus, the part age
is always smaller than or equal to the age of the machine in which it is installed: ij. The part age idrives
the part failure probability, and the machine age jdrives the machine survival probability.
Let Ntdenote the size of the active installed base at time t, which corresponds to the sum of the number
of parts nij (t) of age iinstalled in machines of age j, for each part-machine age combination at time t:
nij (t).(1)
As the installed base is monitored at each time t, we do not need to make assumptions on its evolution
over time, and its product life cycle behaviour is automatically captured.
In practical settings, monitoring the installed base implies keeping track of the machine sales and discards
to determine the size and age of the installed base, and of the maintenance interventions, i.e., the timing
of the corrective and preventive part replacements. As such, the company can determine nij (t) by simply
counting the number of parts of age i, installed in active machines of age j.
2.2. Demand Probability
Every part of age i, installed in a machine of age j, has a probability of being replaced in the upcoming
lead time, that is in the interval (t, t +L]. This probability is denoted by pi,j,t,L, which depends on both
the failure probability of the part, defined by the part age i, and the probability that the machine is not
discarded during the lead time, depending on the machine age j. The demand probability pi,j,t,L is therefore
defined by the product of (1) the failure probability of the part with age iin the interval (t, t +L], pp
which is independent of the machine age j, and (2) the survival probability of a machine with age j,pm
which is independent of the part age iand the part failure behaviour. Let Tpdenote the lifetime of a part
(time from replacement until failure) and Tmthe economic lifetime of a machine (from installation until
discard). We can then express pi,j,t,L as:
pi,j,t,L =P(Tpi+L|Tp> i)·P(Tm> j +L|Tm> j)
i,t,L ·pm
We estimate the probability of pi,j,t,L using an estimation of the part failure probability pp
i,t,L, and an
estimation of the machine survival probability pm
j,t,L, which are discussed next.
2.3. Machine Survival Probability
The machine lifetime Tmis stochastic, but we assume that machines installed at different points in time
have an identical lifetime probability distribution fTm. We consider machine lifetime independent of the
part lifetime. This implies that the lifetime of a machine solely depends on the machine age j, and not on
the age of the consisting parts nor the number of historical failures this machine has already experienced.
This independence seems a reasonable assumption if the machines are expensive relative to the parts (mix
of expensive and cheaper items). In that case, a machine will not be discarded if it experiences part failures,
but it will be repaired and parts will be replaced. This is in contrast to, for example, consumer electronics,
where the decision to discard the product is highly dependent on the number of historical failures of the
product and the customer’s willingness to repair (again) (Lu & Wang, 2015).
The probability at time tthat the machine is not discarded in the time interval (t, t +L] is defined by
j,t,L =R
Typically, fTm(θ) is not known by the service provider. However, when a company keeps track of the
evolution of its installed base over time, it can estimate fTm(θ), and consequently pm
j,t,L, using censored
observation data of the historical machine lifetime data.
2.4. Part Failure Behaviour
Without loss of generality, we assume there is no influence of different usages or the operating environment
on the failure probability distribution, and parts installed at different points in time have an identical
lifetime probability distribution fTp(θ). We consider parts that are non-repairable, i.e., need replacement
and generate a part demand upon failure. When replaced, we assume the part to be as-good-as-new.
Analogously to the probability of a machine discard, we determine for each of the parts in the active
installed base the conditional probability of failure during the upcoming lead time pp
i,t,L, given that the part
did not fail yet, and has reached age iat time t:
i,t,L =Ri+L
where fTp(θ) is the probability distribution of the time-to-failure.
In some cases, fTp(θ) can be estimated directly using data from, for example, stress testing. An alternative
would be to keep track of historical corrective and preventive replacements, in which case the company needs
to register the type of replacement with the associated part ages upon replacement, as well as the age of parts
which are still operational at the time of observation. Those part ages are in fact the part survival time.
For failed parts, the survival time is recorded as a non-censored observation. For preventively replaced parts
and parts which are still operational, this survival time is a lower bound; it is registered as a right-censored
observation. Moreover, for parts that did not fail but whose machine is no longer active, the part survival
time gets a lower bound as well. This way, a distribution can be fit and pp
i,t,L can be estimated. Because the
machine discards are implicitly taken into account in the estimate, pm
j,t,L is already included in the estimation
of the part failure probability pp
2.5. Lead Time Demand Forecast
To obtain the lead time demand forecast we first estimate the demand probabilities for the different part
age - machine age combinations in the installed base using an estimator of the part failure probability and
an estimator of the machine surivial probability:
bpi,j,t,L =bpp
i,t,L ·bpm
which we then multiply with the respective ni,j (t) to obtain the demand estimated at time tover the risk
period1L. The lead time demand forecast b
Dt,L then equals:
Dt,L =
nij (t)·bpi,j,t,L.(6)
In addition, we can also include the possibility of new machines sales that cause a part failure during
that same lead time. We acknowledge that in most cases the effect will be limited because the duration of
the lead time is typically smaller compared to the time to failure. The number of new installations during
the lead time can be estimated either by assuming a sales process, or by including projections from the
marketing department. The expected number of sales in period t+s(s∈ {1, ..., L}) is denoted by b
1Note that in a periodic review inventory policy, demand is forecasted over the risk period, which is defined by the lead time
plus the review period.
Each of the newly installed items has an associated demand probability of pi,j,t+s,Ls, where i=j= 0 as
both the part and machine have age zero upon installation. The forecasted part demand, estimated at time
tover L, is then given by:
Dt,L =
nij (t)·bpi,j,t,L +
s=1 b
In order to use the forecast as a decision input for an inventory policy we need to forecast the distribution
of the lead time demand. For each part in the installed base, the probability of demand is expressed by
bpi,j,t,L. The forecast of the probability distribution of the lead time demand at time t,b
P(Dt,L) is then
defined by a Poisson binomial distribution, i.e., a sum of independent Bernoulli random variables which may
have different expectations, namely bpi,j,t,L (Hong, 2013). Note that when the expectations, bpi,j,t,L, are equal
for all iand j, the Poisson binomial distribution boils down to a binomial distribution.
With an active installed base of size Ntat time tand the forecasted lead time demand probability at
time tfor part k, denoted as bpk(i.e., the corresponding pi,j,t,L for part k), k[1, Nt], we then have the
following forecast of the lead time demand probabilities:
P(Dt,L = 0) =
(1 bpa),
P(Dt,L =dt,L) = X
(1 bpb)!,
P(Dt,L =Nt) =
a=1 bpa,
with Znthe combinations of parts in the active installed base that can be selected from {1 ,2, . . . , Nt}for
which the total demand equals dt,L. For example, if we estimate the probability of demand to be equal to
two ( b
P(Dt,L= 2)), with an active installed base consisting of three parts (Nt= 3), then Znconstitutes all
the combinations of two part numbers that can generate a demand of two: Zn={(1,2),(2,3),(1,3)}.Ais
then the set of possible parts that effectively generate a demand (i.e., fail) in the subset of Zn, for example
A={1,2}, and Acis its complement: Ac={1 ,2, . . . , Nt} \A, in this case Ac= 3. In our example, we
would then obtain b
P(Dt,L = 2) = (bp1·bp2)·(1 bp3)+(bp2·bp3)·(1 bp1)+(bp1·bp3)·(1 bp2).
2.6. Preventive Maintenance Policy
Spare part demand not only originates from unscheduled corrective replacements (due to failures), but
also from preventive replacements. The latter stems from scheduled maintenance, aimed at preventing
Figure 1: Illustration of preventive replacements, with τ= 8 and Nt= 2.
failures by replacing parts before they fail. We assume that for both corrective and preventive maintenance
actions, spare parts replace the failed or worn parts.
Preventive maintenance can be time-based, i.e., a part is replaced every so many running hours or after
a certain calendar time, regardless of its condition, or inspection-based, where a part is inspected after a
certain time and it is decided upon whether to replace the part or not. Between two preventive replacements,
a breakdown might still occur, calling for a corrective replacement. When a time-based periodic replacement
policy is in place and the planned periodic maintenance interventions are not rescheduled due to intermediate
corrective interventions within the periodic maintenance interval, the preventive replacements generate a
deterministic demand stream. When such a preventive policy applies, we can exploit the knowledge about
planned maintenance, which is known as advance demand information, to predict its demand.
We denote τas the periodic maintenance interval, i.e., the calendar time between two preventive main-
tenance interventions. A larger interval τreduces the total number of preventive replacements but increases
the probability of an unplanned corrective intervention (if τapproaches , the preventive policy reduces to
a corrective policy). A short interval τ, however, does not fully utilise the part lifetime. The optimal length
of the maintenance interval τis the result of this tradeoff (e.g., Jardine & Tsang, 2013). In our work, we
consider the value of τas exogenously given.
The actual planning of the time-based periodic part replacement is based on the time since installation.
We define tj,P M as the time of the next periodic replacement of the part under study for a machine with
age j. As such, tj,P M equals the time of installation of the machine, (tj) , plus the smallest value that
is a multiple of the periodic maintenance interval and exceeding the machine age j. If we define Tas the
set {τ, 2τ, 3τ,. . . }, then tj,P M = (tj) + min{x|x T , x > j}. This is illustrated in Figure 1, where a
demand forecast is made at time 10, the installed base consists of two machines, installed at time 1 and 7
respectively, with τ= 8. At time t= 10, the age of the first installed machine equals 9 and the age of the
second installed machine equals 3. As such, t9,P M = (10 9) + 2 ×8 = 17 and t3,P M = (10 3) + 1 ×8 = 15.
If the lead time L= 7, the forecast for the preventive maintenance demand (during the lead time) at time
t= 10 equals 2.
The total number of replacements in the upcoming lead time Dt,L is at least as large as the number of
planned periodic replacements, that is, larger than or equal to:
Ik,tj,P M (9)
where Ik,tj,P M is an indicator function that equals one if for part k, installed in a machine with age j,
tj,P M (t, t +L], and zero otherwise. To account for discards we can correct Equation (9) with the number
of planned discards in (t, t +L].
When a preventive maintenance policy is in place, the demand originating from corrective replacements
during the lead time is forecasted by the probability that a part with age ifails during the lead time,
but prior to the periodic replacement, that is in the interval (t, min(tj,P M , t +L)]. Let πbe the age of
the part at the time of the periodic replacement or at the end of the lead time, whichever comes first:
π= min{i+ (tj,P M t), i +L}. Then:
i,j,t,L =Rπ
where fp(Tp) is the probability distribution of the time-to-failure, estimated based on censored failure ob-
servations. Remark that under a preventive policy the failure probability pp
i,j,t,L becomes dependent on the
machine age, as it determines the timing of the periodic replacement.
The forecasted distribution of the total part demand for both preventive and corrective replacements in
the upcoming lead time is then given by:
P(Dt,L =
Ik,tj,P M + 0) =
(1 bpa),
P(Dt,L =
Ik,tj,P M +dt,L) = X
(1 bpb)),
P(Dt,L =
Ik,tj,P M +Nt) =
a=1 bpa.
3. Numerical Study
We set up a simulation experiment to illustrate the benefits of our forecasting method using Service
Maintenance Information (SMI). The prime benchmark method in our study is the Syntetos-Boylan Ap-
proximation (SBA) method discussed by Syntetos & Boylan (2005). Hasni et al. (2018) show in a recent
study the potential outperformance of this method compared with bootstrapping techniques for intermittent
demand, and as such advocate the value of the SBA method as a benchmark. In addition, we compare
with simple exponential smoothing (SES) (e.g., Brown, 1963; Gardner, 2006), as this method is often used
in industry and also by the OEM which motivates our research. We first discuss the design of the simu-
lation experiment (Section 3.1), and then we address the performance evaluation of the forecast methods
throughout the product life cycle (Section 3.2).
3.1. Experimental Design
We make the following assumptions for every period t(where tequals one week) in our simulation
experiment. First, machines containing the part under study are sold to customers. They become operational
immediately after the sales have occurred. We assume new sales occur following a Poisson process with rate
λ, although it is possible to use any kind of sales process. We consider two different machine installation
rates λ={0.25; 1.25}installations per week. To mimic the product life cycle, we distinguish three stages in
the sales process. We let the expected sales be λ/2 in the first 240 weeks, λin the next 400, and again λ/2
in the final 160 weeks (until the sales end).
Second, when machines terminate their life, they no longer generate a spare part demand. We assume a
random machine survival probability and use an exponential distribution with parameter 1/ρto model the
time to discard, but any type of distribution can be included (exponentially distributed machine survival has
been used by for example Gharahasanlou et al., 2016; Hong et al., 2008; Hu et al., 2015; Kim et al., 2017;
Liu & Tang, 2016; Stormi et al., 2018). The average lifetime of a machine in our simulation experiment is
set to ρ= 720 weeks.
Third, maintenance is performed and parts are replaced. The time to failure probability distribution can
take any shape, although in a realistic setting it is positive and typically skewed to the right. Examples
are the lognormal distribution, the exponential distribution, or the Weibull distribution. We opt to use the
latter in this study, with scale and shape parameters αand β, as suggested by Barlow & Hunter (1960).
We consider two different part failure properties α={336; 480}and β=1.5, assuming a machine operates
continuously (24/7). The scale and shape parameter of the part failure behaviour, αand β, are not affected
by the product life cycle, as they are independent of the life cycle of the installed base. The preventive
maintenance interval is considered exogenous, and is set to τ= 2/3α.
Fourth, the installed base record is updated by monitoring and counting the parts in active machines
with its respective ages iand j. And fifth, a demand forecast for the upcoming lead time is made. The lead
time Lvaries from 1 to 20 weeks. We set the smoothing constants for the SES and SBA forecast methods
equal to γ= 0.1, which is common practice for intermittent demand. As such, we investigate 80 scenarios
Parameter Values
λ{0.25; 1.25}per week
α{336; 480}
ρ720 weeks
τ2/3 α
Table 2: Parameter settings of the numerical experiment.
Figure 2: Illustration of the link between the PLC of a machine, the installed base evolution, and the spare part demand per
period, together with the timings of the simulation experiment (Adapted from Dekker et al., 2013).
with parameter values inspired by the OEM and summarised in Table 2.
3.2. Performance Evaluation for Different PLC Phases
We evaluate the model performance by registering the forecast accuracy, the achieved cycle service level,
and the average per period inventory holdings, in the three life cycle phases (initial, mature, and end-of-life).
Although the forecast method is identical in each of the three, we distinguish the performance evaluation in
these life cycle phases because the dynamics of spare part demand are related to those of the demand for
machines (Dekker et al. 2013). Figure 2 illustrates the connection between the product life cycle and spare
part demand. For the initial phase, we assume no previous knowledge on the part failure behaviour exists.
We can thus only start to make an estimate about the parameters of the part failure probability in this phase
as soon as the first demand occurs. From then on, the model is periodically updated, i.e. we re-estimate
the failure behaviour based on new observations. We evaluate the model performance in the initial phase
during the first 240 weeks, starting with the first machine installation in week 1. The SBA method is also
initialised in this initial phase as proposed by Teunter & Duncan (2009). In the mature phase, we observe
the model performance from week 400 to 640, and in the EOL phase we observe week 1360 until week 1600.
Initial phase Mature phase EOL phase
λ α (1)
0.25 336 1.02 0.04 97.85 1.1 0.27 83.15 1.08 0.25 87.06
480 1.01 0.01 98.69 1.07 0.22 88.69 1.05 0.18 90.66
1.25 336 1.1 0.26 89.1 1.55 0.51 39.77 1.4 0.47 49.88
480 1.05 0.15 93.61 1.32 0.45 56.32 1.27 0.42 61.92
Table 3: Descriptive demand statistics for β= 1.5 and ρ= 720 weeks: (1) The average per period demand size, when demand
occurs (ADS), (2) the coefficient of variation of the per period demand size (CV), and (3) The average percentage of periods
with zero demand (APZ).
Figure 3: Example of a spare part demand time series, for λ= 1.25, α= 480, β= 1.5 and ρ= 720.
The performance of the methods is measured for every scenario in 100 simulation runs. Table 3 reports
some descriptive demand statistics for the different scenarios, which shows the variety in demand patterns
in the different scenarios: (1) The average demand size, when demand occurs (ADS), (2) the coefficient
of variation of the demand size, when it occurs (CV ), and (3) the average percentage of weeks with zero
demand (AP Z). Figure 3 provides an example of a demand pattern for λ= 1.25, α= 480, β= 1.5, ρ= 720,
and the EOL phase starting after 800 weeks.
4. Results and Discussion
We first discuss the performance of our proposed method when only corrective maintenance is in place.
We focus both on forecast accuracy (Section 4.1) as well as inventory implications (Section 4.2). Thereafter,
Initial phase Mature phase EOL phase
0.25 336 0.002 0.009 -0.004 0.005 0.061 -0.005 -0.001 -0.012 0
480 0.002 0.002 -0.005 0.004 0.059 0.003 -0.001 -0.012 0.001
1.25 336 0.011 0.062 -0.012 0.025 0.075 0.005 -0.009 0 0.004
480 0.007 0.037 -0.009 0.016 0.059 -0.003 -0.007 -0.008 0.003
Table 4: Mean Error (ME) measured in the different PLC phases. The lowest absolute value for each scenario and PLC phase
is shaded. Additional parameter values: β= 1.5 and ρ= 720 weeks.
Initial phase Mature phase EOL phase
0.25 336 0.162 0.159 0.163 0.446 0.44 0.435 0.392 0.383 0.381
480 0.128 0.126 0.132 0.364 0.36 0.356 0.326 0.319 0.317
1.25 336 0.361 0.36 0.358 0.99 0.981 0.966 0.86 0.848 0.836
480 0.271 0.269 0.272 0.781 0.771 0.762 0.72 0.709 0.701
Table 5: Root Mean Square Error (RMSE) measured in the different PLC phases. The lowest value for each scenario and PLC
phase is shaded. Additional parameter values: β= 1.5 and ρ= 720 weeks.
we discuss the performance of our method when a preventive maintenance policy is in use (Section 4.3).
4.1. Forecast Accuracy
We use the classic measures to evaluate forecast accuracy: Mean error (ME), and Root Mean Square
Error (RMSE). We do not include relative-to-the-series measures, such as the mean average percentage error,
because the actual demand (and thus the denominator in these forecast accuracy measures) is oftentimes
zero in intermittent demand patterns (Syntetos & Boylan, 2005). The results for the one-period-ahead ME
and RMSE are presented in Table 4 - 5. Our method using Service Maintenance Information is denoted as
SMI and is benchmarked against the Syntetos-Boylan approximation (SBA) and simple exponential smooth-
ing (SES).
We find that the SMI method outperforms SES and SBA in the mature and EOL phase according to
both forecast accuracy measures, although the difference is limited. The SMI method is outperformed in the
initial phase of the PLC by SBA, but the difference is again very small.
We also observe that the SMI method tends to overestimate demand slightly in the initial phase, resulting
in a small negative ME. Given the large amount of zero values in the initial phase (between 89.1% and 98.69%
of the periods have zero demand), SES and SBA have a higher forecast accuracy in this phase.
Figure 4 shows the forecasting performance of the SMI and SBA methods for one particular scenario in the
mature phase. The SMI method, indicated by the dotted line, anticipates the increase in demand, whereas
the SBA method (the dashed line) lags behind. Moreover, the SBA method is very reactive whenever
a demand occurs, whereas the SMI methods provides a more stable forecast. Although not displayed in
Figure 4, similar behaviour can be observed in the EOL phase, where the SBA method tends to lag behind
Figure 4: The forecasting performance of SBA and SMI compared to the actual demand, for λ= 1.25, α= 480, β= 1.5 and
ρ= 720 in the mature phase.
on the decreasing trend in demand and consequently overestimates demand. This is also indicated by the
negative ME for SBA (and SES) in this phase.
4.2. Inventory Implications
In addition to the forecast performance, we also measure the impact of our SMI forecast method on the
inventory holdings. We use a periodic order-up-to-level (T, S ) policy, which is often used in an intermittent
demand context (e.g., Eaves & Kingsman, 2004; Sani & Kingsman, 1997; Syntetos & Boylan, 2006; Syntetos
et al., 2009b). At the end of the review period T, the demand forecast is estimated and the optimal order-
up-to-level Stis determined to satisfy a target service level. A replenishment order is placed to raise the
inventory position up to the level St.
We consider the inventory review period Tto be one week. During a week the following sequence of events
occurs: receive orders (placed L+1 weeks ago) at the beginning of the week, observe demand throughout
the week, forecast future demand (at the end of the week), evaluate the inventory position, and place a new
order if necessary.
The order-up-to level Stis optimised to meet a target cycle service level (CSL), which is the target
fraction of cycles in which demand can be delivered from stock. In our experiment, we attempt to meet a
CSL of respectively 70%, 80%, 85%; 90%, 95%, and 99%. Backorders can be carried forward. We use Eq. (8)
to define the forecasted lead time demand distribution, b
P(Dt,L =x), for the SMI method under corrective
Figure 5: Example of a cumulative lead time demand distribution at t= 600, when a corrective maintenance policy is in place,
with λ= 0.25, α= 336, β= 1.5, ρ= 720, L= 6 weeks and T= 1 .
maintenance. As such, Stis the smallest integer value that satisfies
x=0 b
P(Dt,L =x).(12)
Figure 5 illustrates the forecasted lead time demand distribution for the scenario with λ= 0.25, α= 336,
L= 6, T= 1, at time t= 600, where a corrective maintenance policy is in place. For a target service level
of 70% and 99%, the required base-stock level equals 2 and 6 respectively.
To determine the order-up-to-level when the SES and SBA forecast methods are used, it is necessary to
make an assumption on the underlying demand distribution (Syntetos et al., 2009a). We follow the approach
of Babai et al. (2012), Syntetos & Boylan (2006), and Syntetos et al. (2015) to approximate the lead time
demand by a Negative Binomial Distribution (NBD). The NBD is defined by a mean and a variance, which
can be defined based on the forecasts. The mean of the distribution is estimated by the lead time (+ review
period) demand forecast. The variance is constructed by the associated smoothed mean squared error (MSE),
MSEt,T +L, with a smoothing constant ηof 0.25 (Babai et al., 2012; Pennings & Dalen, 2017; Syntetos et al.,
MSEt,T +L=η(b
Dt(T+L),T +L
+ (1 η)MSEt1,T +L,(13)
where Diis the demand occurring in period i. The NBD assumes the variance to be larger than the mean.
Figure 6: Tradeoff between the achieved CSL and the average inventory levels, averaged over all scenarios, when a corrective
maintenance policy is in place.
When this assumption is not met, Sani & Kingsman (1997) show that the variance can be set equal to 1.1
times the mean. The order-up-to level for a target CSL is calculated as the corresponding quantile of the
lead time (plus review period) demand distribution.
We investigate the tradeoff between the achieved CSL and the average per period inventory levels nec-
essary to attain this CSL. Figure 6 presents this tradeoff curve over all scenarios, life cycle phases, and lead
times, and shows how the SMI method outperforms SES and SBA. As the tradeoff curve associated with the
SMI method lies consistently above the frontier of SES and SBA, using the SMI forecast method results in
lower average inventory holdings than SES and SBA, for the same service level. Likewise, it yields a higher
service level for the same inventory holdings.
If we look into more detail, we can observe differences in performance between the PLC phases (Figure 7).
In the initial phase (Figure 7a), the SMI method is outperformed for most CSL targets by SBA and SES.
As indicated by the ME, SMI overestimates demand in the initial phase, and consequently reaches high
CSLs with more inventory than necessary. SES and SBA, on the contrary, underestimate the demand in
the initial phase according to the ME, resulting in lower inventory levels. Because of the highly sporadic
nature of demand in the initial phase (89 to 98% of periods without demand) SES nonetheless reaches the
target CSLs of 70%, and 80%. For a target CSL over 95%, however, the SMI method outperforms SES and
SBA in the initial phase, achieving a higher CSL with lower inventory levels. In the mature and EOL phase
(a) Initial phase (b) Mature phase
(c) EOL phase
Figure 7: Tradeoff between the achieved CSL and the average inventory levels in the different PLC phases, averaged over all
scenarios, when a corrective maintenance policy is in place.
(Figures 7b-7c), the SMI method outperforms SES and SBA consistently. In the EOL phase (Figure 7c) we
observe that for a target CSL of 99%, the SMI average inventory levels are 41% lower compared to SBA,
and 56% lower relative to SES.
In both the mature and EOL phase, we observe that the efficiency gains of the SMI method are higher for
longer lead times and a large installed base. Figure 8 illustrates the efficiency curves for the EOL phase for
short (L=1) and long (L=20) lead times, and small (λ=0.25) and large (λ=1.25) installed base sizes. The
gap between the SMI method and the SBA and SES method increases when Lincreases. The SMI method
anticipates the demand, whereas SBA and SES lag behind. This lagging effect increases when lead times
are longer. Figure 8 also shows how the outperformance of the SMI method augments when the size of the
installed base increases. In this case, SMI has more information available to generate its forecasts.
(a) λ=0.25, L=1 (b) λ=0.25, L=20
(c) λ=1.25, L=1 (d) λ=1.25, L=20
Figure 8: Tradeoff between the achieved CSL and the average inventory levels in the EOL phase, for different values of lead
time and installed base size, with α=366, β=1.5, and ρ=720.
Similar behaviour can be observed in the mature phase, as illustrated in Figure 9. Here, we present the
results for three different lead time scenarios (L=1, L=8, and L=20), when λ=1.25 and α=480. The SMI
method outperforms SBA and SES in terms of efficiency, and the difference in performance increases with a
longer lead time.
4.3. Preventive Maintenance
When a periodic preventive replacement policy is in place the SES and SBA methods can be applied in
two ways: Either we can use them to forecast all demand (both for corrective and preventive replacements),
as is often done in practice. Or the methods can be applied to only forecast the stochastic part of the demand,
i.e., the demand for corrective replacements, and separate it from the demand for preventive replacements,
(a) L=1 (b) L=8
(c) L=20
Figure 9: Tradeoff between the achieved CSL and the average inventory levels in the mature phase, for different lead time
values, with λ=1.25, α=480, β=1.5, and ρ=720.
Figure 10: Tradeoff between the achieved CSL and the average inventory levels, averaged over all scenarios, when a preventive
maintenance policy is in place.
which is known some time in advance (see also Poppe et al., 2017). We refer to the former methods as SES
and SBA, and to the latter methods as SES PM and SBA PM.
Figure 10 shows the inventory-service tradeoff curve of SES, SBA , SES PM and SBA PM compared with
our SMI method, averaged over all scenarios, life cycle phases, and lead times. It illustrates how SES PM
and SBA PM (continuous lines) outperform their counterparts which do not include the advance demand
information (dashed lines). The SMI method outperforms all methods.
Looking at the different lifecycle phases, we find that in the initial phase (Figure 11a) the SMI method
only outperforms the other forecast methods for high target CSLs. This was also observed when a corrective
maintenance policy was in place (Figure 7a). In the mature and EOL phase (Figure 11b and 11c) the SMI
method outperforms SBA and SES, even when advance demand information of the preventive replacements
is taken into account in their forecasts (SES PM and SBA PM).
5. Conclusions
In this paper we present a method to forecast spare part demand which incorporates information on the
service maintenance operations that drive spare part demand. The main idea behind our approach is that
spare part demand is generated by part failures and equipment maintenance, which is useful information to
predict future demand. We consider a larger set of spare part demand drivers (in combination with each
other) than the existing literature to construct the forecasts: information on the (evolution of the) active
installed base, the part reliability, and the maintenance policy to forecast future spare part demand.
We provide a forecast of the distribution of the future spare parts demand during the upcoming lead
(a) Initial phase (b) Mature phase
(c) EOL phase
Figure 11: Tradeoff between the achieved CSL and the average monthly inventory levels in the different PLC phases, when a
preventive maintenance policy is in place.
time, rather than a point forecast. This distribution is in turn used to manage inventories; We apply it to
determine the optimal a base-stock policy to attain a pre-defined target service level. This way, we connect
forecasting directly with inventory management.
Our approach is intuitively appealing and straightforward, which can facilitate its implementation in
practice. Additionally, our method is applicable throughout the full product life cycle of the installed
machines, which means there is no need to use different methods for each of the PLC phases, and there is
also no need to identify each PLC stage. Moreover, it can be applied both when both a corrective and a
preventive maintenance policy apply, and it is not dependent on predefined probability distributions.
A numerical simulation experiment shows its improvement potential compared to the current best-in-
class forecast methods that do not take this service maintenance information into account. Our method is
capable to achieve higher cycle service levels with lower inventories in the mature and end-of-life phase of
the machines, and its improvement potential is larger when the installed base is relatively large, and when
lead times are longer.
The main challenge to implement our method is the collection of accurate data. Our method requires
keeping track of historical machine sales and discards to monitor the evolution of the installed base over
time, as well as a history of past part failures, and information on (past and future) preventive maintenance
interventions. As such, forecasting becomes the outcome of an inter-organizational process, where cooper-
ation and information sharing (for example on historical failures, maintenance actions, and product sales)
between different departments within the same company is needed. When the quality of the data is poor,
the method lacks its necessary inputs.
A second limitation of our method is that it does not consider the possibility of a part requiring mul-
tiple replacements within the same replenishment lead time, where the replaced part (either preventive or
corrective) fails again prior to its replenishment. This renders the model less accurate with very long lead
times (multiple months) in combination with short part lifetimes (failure within the month). In most set-
tings, including ours, the time to failure is typically much longer than the replenishment lead time. Heavy
equipment typically has an expected lifetime of several years, where the probability of the two replacements
within the same replenishment lead time is negligible.
For future work we suggest to investigate the impact of imperfect or missing information on the re-
sults, given the sensitivity of our method to good data quality. We could also extend the model with
inspection-based preventive maintenance, where the demand originating from preventive inspections is con-
sidered stochastic. Finally, whereas this paper optimises inventories for a given target service level, future
research could be devoted to a dynamic inventory model with cost-optimal service levels.
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... algorithm was presented in broad terms and could be applied to any probability distributions of crucial component failure times. d) The research in [13] developed a strategy for forecasting spare part demand that integrates data on the service maintenance procedures that drive demand for spare parts. Their approach is based on the premise that spare part demand is driven by part failures and equipment maintenance, which provides useful information for forecasting future demand. ...
Complex capital goods such as aircraft engines are stressed by the environment and actual operation. These influences, e.g. air pollution, lead to wear of the capital goods. Therefore, capital goods are maintained, repaired or overhauled (MRO). Regeneration is carried out by MRO service providers and enables an elongation of the utilization period within the product life cycle. Within the regeneration supply chain, spare parts demands arise for MRO service providers. However, at the beginning of the regeneration supply chain, the precise spare parts demand is uncertain in terms of the required type, quantity and quality of the spare parts. This kind of information is only available after the capital good has been inspected. Often long replenishment times for spare parts lead to the challenge of providing upcoming spare parts demand for assembly in time. This paper presents an approach to dimension spare parts inventory levels forecast- and model-based that addresses the underlying uncertainty related to aircraft spare parts demand. The forecasting model is based on historical data of past regeneration orders and takes relevant features into account. Based on this, a procedure is developed for the structured evaluation of procurement opportunities with regard to their logistical potential and financial risk. The approach addresses shortcomings of existing approaches related to repairable and serviceable aero engine components that can be stocked in pool levels. Consequently, the approach supports the achievement of short delivery times and high schedule reliability in the MRO industry. In addition to a literature review identifying shortcomings in existing approaches in this field, this paper includes a case study on forecasting spare parts demand focusing on the explorative data analysis to define forecasting model requirements.
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Configuring supply chains (SCs) is critical to spare parts retailers' success, entailing two key aspects: stock deployment into distribution centres (DCs) (i.e. inventory centralisation or decentralisation) and stock supply in each DC (how many spare parts to supply and how often). Given the unpre-dictability of spare parts demand, stock deployment and supply policies should be regularly reviewed, adapting to fluctuations in customer needs. A viable way to do this is to adopt a multi-criteria ABC criticality classification. However, the multi-criteria ABC criticality classification has often been used to plan stock supply policies in a single DC, but only once to plan spare parts deployment. Nevertheless, the available literature methodology presents major limitations, being not applicable in real companies. Therefore, this paper provides a novel methodology, called SP-LACE, which first reviews the configuration of spare parts SCs based on a multi-criteria criticality classification. Then, allows, for the first time, to evaluate the economic benefits of the reviewed SC configuration. SP-LACE was tested on two case studies and compared with the literature methodology. The results indicate that it provides economic benefits (in terms of total SC cost), overcoming the limitations of the literature methodology and ensuring high service levels.
Forecasting the demand of spare parts of vehicles in bus fleets is a vital issue. Vehicles must operate effectively and must have a high availability rate in the fleet. In maintenance operations, faulty parts or parts that complete their lifetime must be replaced with a new one. Spare parts needed must be in inventories with the required amount on time. In this sector, there are thousands of spare parts to manage. The maintenance and repair department must operate effectively. In order to accomplish this, accurate forecast of spare parts is required. In this study, demand forecasting was carried out with regression-based methods (multivariate linear regression, multivariate nonlinear regression, Gaussian process regression, additive regression, regression by discretion, support vector regression), rule-based methods (decision table, M5Rule), tree-based methods (random forest, M5P, Random tree, REPTree) and artificial neural networks. The forecasting model developed in this study includes critical variables such as the number of vehicles in the fleet, the number of breakdowns that cause parts to change, the number of periodic maintenance, mean time between failure and demand quantity in previous years. The application was carried out with real data of eight (2013–2020) years. 2013–2019 data was used for training and 2020 data was used for testing. In forecasts, support vector regression among regression-based methods, decision table among rule-based methods, M5P among tree-based methods gave the best results. It has been observed that the artificial neural network produced more accurate forecasts than all other methods. Artificial neural network forecasts give the highest forecast accuracy rate and the least deviation.
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In this era of trying to get more information from data, demand forecasting plays a very important role for companies. Companies implement many of their plans based on these forecasts. However, forecasting demand is not always easy. Demand is divided into many different classes depending on its structure. One of them is the problem of intermittent demand. Estimating intermittent demand is a more difficult problem than estimating series with low variability and no null demand. When working with intermittent demands, either a good demand forecast or a good inventory policy is required. Determining an efficient inventory policy is important in terms of meeting customer demand and customer satisfaction. In this study, an inventory lower bound and upper bound are calculated to balance the inventory cost of intermittent demand and the lost sale cost. For this purpose, 7 different test data with intermittent demand structure were studied. A mathematical model is proposed to calculate the cost with the upper and lower inventories under intermittent demand. A feasible solution could not be obtained with the proposed model, and a fitness function for the relevant model was proposed. This function was run on test data using genetic algorithm (GA) and particle swarm optimization (PSO). The results and solution times of GA and PSO were compared. In this way, the variability of demand and the difference between arrival times of demands were met with minimal cost.
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Purpose: To classify the type of product demand placed on the market by auto parts companies in Mexico focusing on the assembly and sale of auto parts at national and international level, which is the basis for the adequate provision of materials in the studied supply chain. Methodologyical design: From a total of 14,895 products, 326 components were selected through the ABC method to perform the demand pattern analysis which was carried out according to the average demand interval and the square coefficient of variation using the monthly demands of each product. Results: The probabilistic analysis of the demand for the 14,895 products shows smoothed (63.80%), erratic (19.94%), lumpy (11.35%) and intermittent (4.91%) demand patterns from which it is concluded that the demand patterns for these companies are mainly of the smoothed type. Research limitations: The probabilistic analysis conducted is based on the data provided by three autoparts companies in México, of which, after the ABC analysis, only the articles of category A were considered for the results obtained. Proposing a different technique other than ABC analysis is limited by the type of data provided by companies. Findings: Due to the number of factors involved in demand variability, it is vital to rely on tools that aid in reaching trustworthy demand forecasts, maintaining companies competitive in customer service quality. Further, the complexity of forecasting automotive spare parts is a challenge which the automotive industry is currently facing. The classification of demand patterns resulting from the study allows for the selection of an appropriate forecasting method for each pattern and improvement of supply conditions of the different companies. This type of study and data analysis permits better decision-making by those responsible for the supply components.
Previous studies on production scheduling have neglected the impact of the supply mode of inventory allocation on the arrangement of production resources and guiding significance of delivery information to the demand side. To fill these gaps, this study investigates a collaborative scheduling model of production resources and spare parts inventory to satisfy the spare parts requirements of demand-side distributed equipment, and we propose feedback guidance based on delivery information to reduce the negative impact of delayed spare parts. The feedback guidance adopts an optimal operating strategy to reduce the capacity loss of the equipment corresponding to the delayed spare parts. An optimization objective, referred to as the total capacity loss of all distributed equipment, is introduced to visually display the effect of the scheduling scheme on the demand side. Another objective is to minimize the total service cost of the service provider, including the inventory, transportation, and tardiness costs. A modified restarted iterated Pareto greedy algorithm is proposed to solve the model. Based on the problem characteristics, certain effective operators, including two problem-dependent local-search operators and a modified idle-time insertion method, are designed to improve the search performance. Extensive experiments are conducted to demonstrate the effectiveness of the algorithm, including the feedback guidance and proposed operators. Finally, the impact of different inventory levels on the service provider and demand side is analyzed, and the results indicate that the collaborative mode can effectively reduce inventory.
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The classical spare part demand forecasting literature studies methods for forecasting intermittent demand. However, the majority of these methods do not consider the underlying demand-generating factors. The demand for spare parts originates from the replacement of parts in the installed base of machines, either preventively or upon breakdown of the part. This information from service operations, which we refer to as installed base information, can be used to forecast the future demand for spare parts. This paper reviews the literature on the use of such installed base information for spare part demand forecasting in order to asses (1) what type of installed base information can be useful; (2) how this information can be used to derive forecasts; (3) the value of using installed base information to improve forecasting; and (4) the limits of the existing methods. This serves as motivation for future research.
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Capital assets, such as manufacturing equipment, require maintenance to remain functioning. Maintenance can be performed when a component breaks down and needs replacement (i.e., corrective maintenance), or the maintenance and part replacement can be performed preventively. Preventive maintenance can be planned on a periodic basis (periodic maintenance), or it can be triggered by a certain monitored condition (condition-based maintenance). Preventive maintenance policies are gaining traction in the business world, but for many companies it is unclear what their impact is on the resulting inventory requirements for the spare parts that are used for the maintenance interventions. We study the impact of the maintenance policy on the inventory requirements and the corresponding costs for a setting that is realistic at an OEM in the compressed air industry. Preventive policies increase the total demand for spare parts compared to corrective maintenance, since the former do not exploit the entire useful life of the components. This leads to higher inventory requirements. At the same time, the preventive policies inhibit advance demand information, as the interventions, and correspondingly the spare parts demands, are planned in advance. Using a simulation study, we show that by using this advance demand information in managing the spare part inventory, the increase in inventory requirements of preventive maintenance policies can to a large extent be offset; for condition-based maintenance, we find that inventories can even be lower compared to corrective maintenance, provided that the advance demand information is used correctly when managing inventories. Our analysis sheds light on the behaviour of the inventory related costs under various maintenance policies.
A completely revised and updated edition of a bestseller, Maintenance, Replacement, and Reliability: Theory and Applications, Second Edition supplies the tools needed for making data-driven physical asset management decisions. The well-received first edition quickly became a mainstay for professors, students, and professionals, with its clear presentation of concepts immediately applicable to real-life situations. However, research is ongoing and relentless-in only a few short years, much has changed. See What's New in the Second Edition: New Topics •The role of maintenance in sustainability issues •PAS 55, a framework for optimizing management assets •Data management issues, including cases where data are unavailable or sparse •How candidates for component replacement can be prioritized using the Jack-knife diagram New Appendices •Maximum Likelihood Estimated (MLE) •Markov chains and knowledge elicitation procedures based on a Bayesian approach to parameter estimation •E-learning materials now supplement two previous appendices (Statistics Primer and Weibull Analysis) •Updated the appendix List of Applications of Maintenance Decision Optimization Models Firmly based on the results of real-world research in physical asset management, the book focuses on data-driven tools for asset management decisions. It provides a solid theoretical foundation for various tools (mathematical models) that, in turn, can be used to optimize a variety of key maintenance/replacement/reliability decisions. It presents cases that illustrate the application of these tools in a variety of settings, such as food processing, petrochemical, steel and pharmaceutical industries, as well as the military, mining, and transportation (land and air) sectors. Based on the authors' experience, the second edition maintains the format that made the previous edition so popular. It covers theories and methodologies grounded in the real world. Simply stated, no other book available addresses the range of methodologies associated with, or focusing on, tools to ensure that asset management decisions are optimized over the product's life cycle. And then presents them in an easily digestable and immediately applicable way.
The (s, S) form of the periodic review inventory control system has been claimed theoretically to be the best for the management of items of low and intermittent demand. Various heuristic procedures have been put forward, usually justified on the basis of generated data with known properties. Some stock controllers also have other simple rules which they employ and which are rarely seen in the literature. Determining how to forecast future demands is also a major problem in the area. The research described in this paper compares various periodic inventory policies as well as some forecasting methods and attempts to determine which are best for low and intermittent demand items. It evaluates the alternative methods on some long series of daily demands for low demand items for a typical spare parts depot.
Purpose The purpose of this paper is to examine how installed base information could help servitizing original equipment manufacturers (OEMs) forecast and support their industrial service sales, and thus increase OEMs’ understanding regarding the dynamics of their customers lifetime values (CLVs). Design/methodology/approach This work constitutes a constructive research aiming to arrive at a practically relevant, yet scientific model. It involves a case study that employs statistical methods to analyze real-life quantitative data about sales and the global installed base. Findings The study introduces a forecasting model for industrial service sales, which considers the characteristics of the installed base and predicts the number of active customers and their yearly volume. The forecasting model performs well compared to other approaches (Croston’s method) suitable for similar data. However, reliable results require comprehensive, up-to-date information about the installed base. Research limitations/implications The study contributes to the servitization literature by introducing a new method for utilizing installed base information and, thus, a novel approach for improving business profitability. Practical implications OEMs can use the forecasting model to predict the demand for – and measure the performance of – their industrial services. To-the-point predictions can help OEMs organize field services and service production effectively and identify potential customers, thus managing their CLV accordingly. At the same time, the findings imply new requirements for managing the installed base information among the OEMs, to understand and realize the industrial service business potential. However, the results have their limitations concerning the design and use of the statistical model in comparison with alternative approaches. Originality/value The study presents a unique method for employing installed base information to manage the CLV and supplement the servitization literature.
Forecasts are often made at various levels of aggregation of individual products, which combine into groups at higher hierarchical levels. We provide an alternative to the traditional discussion of bottom-up versus top-down forecasting by examining how the hierarchy of products can be exploited when forecasts are generated. Instead of selecting series from parts of the hierarchy for forecasting, we explore the possibility of using all the series. Moreover, instead of using the hierarchy after the initial forecasts are generated, we consider the hierarchical structure as a defining feature of the data-generating process and use it to instantaneously generate forecasts for all levels of the hierarchy. This integrated approach uses a state space model and the Kalman filter to explicitly incorporate product dependencies, such as complementarity of products and product substitution, which are otherwise ignored. An empirical study shows the substantial gain in forecast and inventory performance of generalizing the bottom-up and top-down forecast approaches to an integrated approach. The integrated approach is applicable to hierarchical forecasting in general, and extends beyond the current application of demand forecasting for manufacturers.
System prognostics and health management (PHM) is a new health management methodology proposed for complex engineering systems to reduce maintenance costs, improve the system operating reliability and safety, and mitigate the failure risk [1, 2]
When stopping production, the manufacturer has to decide on the lot size in the final production run to cover spare part demand during the end-of-life phase. This decision can be supported by forecasting how much demand is expected in the future. Forecasts can be obtained from the installed base of the product, that is, the number of products still in use. This type of information is relatively easily available in case of B2B maintenance contracts, but it is more complicated in B2C spare parts supply management. Consumer decisions on whether or not to repair a malfunctioning product depend on the specific product and spare part. Further, consumers may differ in their decisions, for example, for products with fast innovations and changing social trends. Consumer behavior can be accounted for by using appropriate types of installed base, for example, lifetime installed base for essential spare parts of expensive products with ling lifecycle, and warranty installed base for products with short lifecycle. This paper proposes a set of installed base concepts with associated simple empirical forecasting methodologies that can be applied in practice for B2C spare parts supply management during the end-of-life phase of consumer products. The methodology is illustrated by case studies for eighteen spare parts of six products from a consumer electronics company. The research hypotheses on which installed base type performs best under which conditions are supported in the majority of cases, and forecasts obtained from installed base are substantially better than simple black box forecasts. Incorporating past sales via installed base therefore supports final production decisions to cover future consumer demand for spare parts.
High demand variability and uncertainty that is driven by different phases of a product’s and its critical components life-cycles make spare parts demand forecasting and safety inventory management a major challenge. Mainstream stochastic inventory management approaches for spare parts make use of distributional assumptions for demands. In reality, distributions and their parameters are hardly known and need to be estimated. In this paper we pursue a causal demand modeling approach that combines theoretical models from reliability and inventory theory to derive improved service parts demand forecasts. Based on a small simulation experiment we illustrate the benefits of this accurate but more complex approach over simple time series based forecasting techniques and forecast error driven safety stock approaches for different life-cycle patterns and different phases of a product life-cycle.