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comparison of the most used traditional forecasting As resulted by this brief and not exhaustive
methods has been made, also with application on literature analysis, many models have been
a real case study regarding aircraft spare parts. developed for the spare parts inventory
Another review of the past 50 years of the demand management. In this paper we want to analyze
forecasting literature on inventory management can two recent models, chosen for their simplicity and
be found in Syntetos, Boylan and Disney (2009). general validity, based on different approaches.
In the recent years, further models have been The studied policies are the (s, S) one with
developed to solve forecast problem in this delayed ordering, introduced by Teunter et al
particular industrial feld, using also new methods (2012) and policy based on binomial distribution
as (S) Arima Genetic Algorithm, Neural Networks and total cost function, developed by Persona et
and others (Gamberini et al, 2010; Gutierrez et al, al. (2006).
2008; Teunter et al, 2009). In the next section we briefy present these two
The second strategy regards these critical models and their assumptions and approaches.
questions: is it really necessary to store these
slow-moving items? How many pieces per code
is it better to stock? Where? 3. Methodology and compared
Inventory management models for spare parts models
are widely discussed in scientifc
The second strategy literature and many models Firstly a brief presentation of the compared models
regards these critical have been developed in the last is here reported, illustrating the main features
questions: is it really decades. and assumptions. For exhaustive discussion, see
Persona et al. (2006) and Teunter et al. (2012).
Typically, the base-stock policies
necessary to store these have been used to manage the Afterwards, these policies are applied in several
slow-moving items? How spare parts inventories for a long scenarios, defned by different number of spare
many pieces per code is time. parts requirements, unit cost, holding cost, stock-
it better to stock? Where? Williams (1982, 1984) proposed out cost, MTBF (Mean Time Between Failure),
Inventory management a continuous review model based Lead Time of supplying.
on (s, S) policy, considering
Generally, an exponential distribution has been
models for spare parts Gamma distribution for inter- used to model the demand of spare parts, that
are widely discussed in demand period for different kinds is the most critical situation for the second policy
scientifc literature and of demands. A periodic review (Teunter et al., 2012), and to evaluate the total cost
many models have been model was developed by Popovic of the two policies.
developed in the last in 1987. Petrovic et al. (1990) Then, for the frst policy the most preferable
introduced an expert system
number of spare parts has been estimated, for
decades for the spare parts inventory a given covering period T , while for the second
s
management with exponential distribution for one the more fexible delayed ordering has been
inter-demand process. Dekker, Kleijn and De calculated for every scenario.
Rooij (1998) developed a model with different For each policy, the total cost has been calculated
processing for demands named as critical and as the sum of holding and stock-out cost. After
non-critical. this phase, a sensitivity analysis has been carried
Jin and Liao (2009) developed a formulation for the out in order to analyze the impact of the variables
continuous review system (R, Q) where the spare on fnal total costs.
parts supplies the maintenance demand from a
growing set of products, minimizing the costs of
purchase, storage, failure, and revision of control 3.1. Model based on binomial
parameters at each time interval. The model distribution and total cost
assumes that the intervals between failures follow
an exponential distribution (constant failure rate). function (Persona et al. 2006)
Liao et al. (2008) developed a similar model, with
the assumption that the set of products grows at The aim of this model is to determine the
a constant rate and the interval between failures requirement N of replaceable parts in order to
follows Weibull distribution (therefore comprising minimize a total cost function defned by the sum
a wide range of failure models). of production losses costs C and storage costs
1
Lonardo et al. (2008) presented a method for the C .
2
determination of the desired levels of spare parts The model calculates the optimal number of
inventories, minimizing only the storage costs stocked spare parts as the sum of two terms. For a
subject to constraints of minimum service level fxed period T, the frst one covers the average
and assuming a normal distribution for demand. number of required spare parts using the MTBF
The proposed model was solved by probabilistic value, while the second one is used to satisfy
linear programming where the set of feasible the expected requirements in the rest period of
solutions is generated by Monte Carlo simulation. time .

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