Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint

We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does not exceed an upper bound. The outcome distributions are not known. We construct a class of consistent adaptive policies, under which the average outcome converges with probability 1 to the true value under complete information for all distributions with finite means. We also compare the rate of convergence for various policies in this class using simulation

Optimization of Stochastic Systems and Applications

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.Στη διατριβή μελετήθηκαν προβλήματα σε δύο βασικές περιοχές: (α) Προσαρμοστική δειγματοληψία υπό ελλιπή πληροφόρηση και επιπλέον περιορισμούς και (β) Βέλτιστες πολιτικές παραγγελιών σε σύστημα αποθεμάτων με πεπερασμένη χωρητικότητα και μερική υποκατάσταση ζήτησης. Στο πρώτο μέρος μελετήθηκαν υποδείγματα προσαρμοστικού ελέγχου σε στοχαστικούς πληθυσμούς με μερικώς γνωστές κατανομές, στα οποία μεγιστοποιείται το αναμενόμενο μέσο αποτέλεσμα ανά βήμα κάτω από ένα εξωγενή περιορισμό ως προς το κόστος δειγματοληψίας ανά περίοδο. Στη διατριβή αναπτύχθηκαν δύο κατηγορίες προσαρμοστικών πολιτικών για αυτό το πρόβλημα. Μια κατηγορία συνεπών εφικτών πολιτικών, για τις οποίες το αναμενόμενο μέσο κέρδος ανά μονάδα χρόνου συγκλίνει με πιθανότητα 1 στην αντίστοιχη ποσότητα κάτω από πλήρη πληροφόρηση και μια κατηγορία αποδοτικών εφικτών πολιτικών, για τις οποίες ο ρυθμός σύγκλισης του μέσου κέρδους ανά περίοδο σε αυτό κάτω από πλήρη πληροφόρηση μεγιστοποιείται σύμφωνα με ασυμπτωτικό κριτήριο απώλειας. Στο δεύτερο μέρος της διατριβής μελετήθηκε ένα πρόβλημα διαχείρισης αποθεμάτων δύο προϊόντων για τα οποία χρησιμοποιείται κοινός αποθηκευτικός χώρος πεπερασμένης χωρητικότητας, και στα οποία υπάρχει μερική αμφίδρομη υποκατάσταση ζήτησης όταν δεν υπάρχει διαθεσιμότητα ενός προϊόντος. Αποδείχθηκε ότι το μέσο κέρδος ανά μονάδα χρόνου είναι submodular συνάρτηση ως προς τις ποσότητες παραγγελίας, γεγονός που επιτρέπει την ανάπτυξη αποδοτικών αλγορίθμων για την εύρεση των βέλτιστων ποσοτήτων

A dynamic prioritization policy for the callback option in a call center

In this paper, we study the M_n/M_n/c/(K_1+K_2)+M_n system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join the online or the offline/callback queue or simply balk. Customers waiting in the online queue are impatient and if their patience expires, they may choose to join the callback queue instead of abandoning the system for good. Customers in the callback queue are assumed to be patient. Customers are served following a threshold policy: when the number of customers in the callback queue surpasses a threshold level, the next customer to serve is picked from here. Otherwise, only after a predetermined number of agents are reserved for future arrivals, customers remaining in the callback queue can be served. We conduct an exact analysis of this system and obtain its steady-state performance measures. The times spent in both queues are expressed as Phase-type distributions. With numerical examples, we present how the policy responds when shorter callback times are promised or customer characteristics vary

A dynamic prioritization policy for the callback option in a call center

In this paper, we study the Mn/Mn/c/(K1+K2)+Mn system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join the online or the offline/callback queue or simply balk. Customers waiting in the online queue are impatient and if their patience expires, they may choose to join the callback queue instead of abandoning the system for good. Customers in the callback queue are assumed to be patient. Customers are served following a threshold policy: when the number of customers in the callback queue surpasses a threshold level, the next customer to serve is picked from here. Otherwise, only after a predetermined number of agents are reserved for future arrivals, customers remaining in the callback queue can be served. We conduct an exact analysis of this system and obtain its steady-state performance measures. The times spent in both queues are expressed as Phase-type distributions. With numerical examples, we present how the policy responds when shorter callback times are promised or customer characteristics vary

The "Sensitive" Markovian queueing system and its application for a call center problem

In this paper, we study the Mn/ Mn/ c/ K+ Mn queueing system where customers arrive according to a Poisson process with state-dependent rates. Moreover, the rates of the exponential service times and times to abandonment of the queued customers can also change whenever the system size changes. This implies that a customer may experience different service rates throughout the time she is being served. Similarly, a queued customer can change her patience time limits while waiting in the queue. Thus, we refer to the analyzed system as the “sensitive” Markovian queue. We conduct an exact analysis of this system and obtain its steady-state performance measures. The steady-state system size distribution yields itself via a birth–death process. The times spent in the queue by an arbitrary or an eventually served customer are represented as the times until absorption in two continuous-time Markov chains and follow Phase-type distributions with which the queueing time distributions and moments are obtained. Then, we demonstrate how the Mn/ Mn/ c/ K+ Mn queue can be employed to approximately yet accurately estimate the performance measures of the Mn/ GI/ c/ K+ GI type call center

The "sensitive" Markovian queueing system and its application for a call center problem

In this paper, we study the M_n/M_n/c/K+M_n queueing system where customers arrive according to a Poisson process with state-dependent rates. Moreover, the rates of the exponential service times and times-to-abandonment of the queued customers can also change whenever the system size changes. This implies that a customer may experience different service rates throughout the time she is being served. Similarly, a queued customer can change her patience time limits while waiting in the queue. Thus, we refer to the analyzed system as the ``sensitive" Markovian queue. We conduct an exact analysis of this system and obtain its steady-state performance measures. The steady-state system size distribution yields itself via a birth-death process. The times spent in the queue by an arbitrary or an eventually served customer are represented as the times until absorption in two continuous-time Markov chains and follow Phase-type distributions with which the queueing time distributions and moments are obtained. Then, we demonstrate how the M_n/M_n/c/K+M_n queue can be employed to approximately yet accurately estimate the performance measures of the M_n/GI/c/K+GI type call center