Unit:
Τομέας Στατιστικής και Επιχειρησιακής ΈρευναςLibrary of the School of Science
Author:
Καναβέτας Οδυσσέας
Dissertation committee:
Καθηγ. Απόστολος Μπουρνέτας
Original Title:
Βελτιστοποίηση Στοχαστικών Συστημάτων και Εφαρμογές
Translated title:
Optimization of Stochastic Systems and Applications
Summary:
The dissertation was focused on two research areas: (a) Adaptive sampling under
incomplete information and side constraints and (b) optimal ordering policies
in inventory systems with limited capacity and partial demand substitution.
The problems in the first part of the dissertation refer to adaptive sampling
in stochastic populations under partially known distributions, with the
objective of maximizing the long run expected average outcome per period under
an exogenous constraint on the average sampling cost. Two classes of adaptive
policies were developed: a class of feasible consistent policies, under which
the average outcome per period converges to the optimal under complete
information with probability one, and a class of efficient policies, under
which the rate of convergence of the average outcome is maximized according to
an asymptotic regret criterion.
The second part of the dissertation was focused on an inventory management
problem with two products under stochastic demand, limited storage capacity and
partial two-way substitution. The average profit per period was expressed as a
function of the order quantities. It was proved that the profit function is
submodular. Based on this property an efficient optimization algorithm was
developed for the maximization of the average profit.
Keywords:
Adaptive Optimization, Sequential Sampling, Efficient Policies, Inventory Management, Demand Substitution
