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Title:  Stochastic optimization for airport inventory management 
Authors:  Cesaro, Annalisa 
Tutor:  Pacciarelli, Dario 
Issue Date:  30Mar2010 
Publisher:  Università degli studi Roma Tre 
Abstract:  Effective supply chain management is currently recognized as a key determinant of competitiveness and success in manufacturing and services, because the
implementation of supply chain management has signiﬁcant impact on cost,
service and quality. Numerous strategies for achieving these targets have been
proposed.
The improvements in information technology coupled with the substantial reduction in the cost of processing, storing and analyzing data have made new
strategies more attractive. On such strategy allows movements of stock between locations at the same echelon level via lateral transshipment.
Despite the above technology improvements, the implementation of such transshipment strategy requires still great eﬃciency especially in real life problems,
because it suffers from computer memory limits and long computation times
when the number of warehouses gets large, or when the number of parallel items
to ba analyzed following an item approach gets large, too.In fact, a drawback
of the policy of interest is the state dependent nature of the reforwardings in
the systems.
Therefore an effective tactical planning requires joint contribution from various disciplines in order to be implemented eﬃciently, such as engineering,
mathematics, economics and computer science. New solution methods have to
be explored in order to effectively implementing new management strategies.
This thesis uses operations research techniques in order to study a single echelon, oneforone ordering policy with complete pooling, with a deterministic
rule for lateral transshipments.
Speciﬁcally we propose new evaluation and optimization methods thus handling real life problems within a reasonable amount of computation time. In
fact, we test all the proposed methods on the practical case study motivated
by the practical needs of an Italian logistics, supporting the activity of 38 civil
airports spread over the Italian territory. The company handles 17 warehouses
and manages the overall process of purchasing, holding, ensuring that the overall reliability of safety equipments is always within contractual limits. The aim
of the company is therefore to grant the prescribed quality of service at minimum cost.
The items to be managed in such a context are typically expensive ones and
with low demand, but we clearly recognize that there are many different types
of service parts and that they perform many different functions. Therefore, in
such a context also parts with a lower ratio between holding and transshipment
costs may be encountered and managed. Thus with all the uncertainties that
exist, a tactical plan should be created that will provide the ﬂexibility needed
to meet a wide range of scenarios, pointing the attention on the characteristics
of the majority of items. Common techniques models the management policy
with a Markov chain approach, thus evaluating such a policy given a spare
parts allocation. The optimal stock allocation problem is formulated as an
integer program with non linear objective function and non linear constraints.
Therefore total enumeration methods or approximation algorithms can be employed for optimally solve it.
Based on the needs summarized above, the following research objectives have
been achieved in this dissertation. We have focused on a single echelon oneforone ordering policy with complete pooling, with a deterministic rule for lateral
transshipments.
We have formalized mathematically the Spares Allocation Problem (SAP)
and have understood its mathematical structure for building an exact
algorithm for optimally allocating the spares. In fact, in literature to the
best of our knowledge no exact algorithm has been proposed for allocating
optimally the spares in a continuous review setting rather than a total
enumerative algorithm. By exploiting the above algorithm it is interesting
– Making insight in the SAP and underline which factors inﬂuence
inventories in such a context.
– Evaluating fast and accurate heuristics for SAP.
Efficient and accurate models for assessing the performance of a single
echelon replenishment policy have been proposed and evaluated especially
for large numbers of locations. A drawback of the policy of interest is the
state dependent nature of the reforwardings in the systems, it has been
therefore interesting.
– understanding the properties of the Markov chain associated to the
chosen policy.
– exploring, despite its state dependent nature, the possibility of expressing the state probabilities of the associated Markov chain model
exactly in product form
– developing fast and accurate approximate models for evaluating the
performance and costs in the system, since computing the state
probabilities is not practical as the number of states in the Markov
chain increases.
The achievement of the ﬁrst objective clearly required a strong connection
with the resolution of the second objective. In fact, the development of an
exact algorithm for allocating the spares may require in contexts with a large
number of warehouses and high rates approximate models for assessing the
performance and evaluating the costs.
Speciﬁcally, n this thesis by using a suitable optimization model we have shown
that the Markov chain cannot be decomposed exactly in product form. In fact,
the best product form approximation returns a positive accuracy error, which
implies that an exact product form does not exist.
Hence, we have adapted four approximation techniques to our model and evaluate their performance in terms of computational effort, memory requirement
and error with respect to the exact value. Three techniques approximate state
probabilities with others that can be expressed in product form, so that the
Markov chain can be decomposed. Speciﬁcally, we adapt a method by Alfredsson and Verrijdt, the Equivalent Random Traﬃc (ERT) method and the
Interrupted Poisson Process (IPP) method. The last two techniques have been
proposed for exploring the inﬂuence of peakedness in approximation models
with respect to the accuracy of performance estimation due to the state dependent nature of the reforwardings in the system.
The fourth technique is based on the multidimensional scaling down approach,
which studies an equivalent reduced Markov chain rather than decomposing the
original one. The scaling down method outperforms the decomposition techniques for small OA values (OA < 0.997), while the percentage error is similar
for larger OA values. Besides the better performance shown in ﬁgure, in our experiments the scaling down method provides OA values smaller than the exact
ones in more than 80% of the experiments while the decomposition methods
ﬁnd OA values always larger than the exact ones. The scaling down method
is therefore more conservative than the decomposition methods, and this is
an important feature when the method has to be used within an optimization
The formulation and solution of the Spares Allocation Problem (SAP) is one of
the main achievements of this thesis. The mathematical structure of the problem has been investigated to build an eﬃcient exact algorithm for optimally
allocating the spares. Two assumption on the cost structure of the problem
leads to prove properties of the cost function that in turns allow to design a new
efficient branch and bound procedure. The lower bound is obtained by solving
a reduced problem with convex objective function, solvable at optimally very
efficiently. A new fast heuristic algorithm is also developed to ﬁnd a feasible
allocation within small computation time.
Computational experiments demonstrate that the branch and bound technique
is able to optimally solve almost all tested instances within reasonable computation time. The heuristic algorithm ﬁnds quite good solutions within very
limited computation time, thus being a promising approach for ﬁnding feasible
solutions to difficult instances.
Moreover we have analyzed several cost structure scenarios and we have observed that the transshipment cost is often comparable with the holding cost
and therefore it cannot be neglected in the solution of the problem. ...more 
URI:  http://hdl.handle.net/2307/656 
Appears in Collections:  Dipartimento di Informatica e automazione T  Tesi di dottorato

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