Queueing Systems with Random Volume Customers and their Performance Characteristics

In the paper, we consider non-classical queueing systems with non-homogeneous customers. The non-homogeneity we treat in the following sense: in systems under consideration, we characterize each customer by random capacity (volume) that can have an influence on his service time. We analyze a stochastic process having the sense of the total volume of all customers present in the system at given time instant. Such analysis for different queueing systems with unlimited or limited total volume can be used in designing of nodes of computer and communication networks while determining their buffer space capacity. We discuss basic problems of the theory of these systems and their performance characteristics. We also present some examples and results for systems with random volume customers

Integrated Multiresource Capacity Planning and Multitype Patient Scheduling

The joint optimization problem of multiresource capacity planning and multitype patient scheduling under uncertain demands and random capacity consumption poses a significant computational challenge. The common practice in solving this problem is to first identify capacity levels and then determine patient scheduling decisions separately, which typically leads to suboptimal decisions that often result in ineffective outcomes of care. In order to overcome these inefficiencies, in this paper, we propose a novel two-stage stochastic optimization model that integrates these two decisions, which can lower costs by exploring the coupling relationship between patient scheduling and capacity configuration. The patient scheduling problem is modeled as a Markov decision process. We first analyze the properties for the multitype patient case under specific assumptions and then establish structural properties of the optimal scheduling policy for the one-type patient case. Based on these findings, we propose optimal solution algorithms to solve the joint optimization problem for this special case. Because it is intractable to solve the original two-stage problem for a general multitype system with large state space, we propose a heuristic policy and a two-stage stochastic mixed-integer programming model solved by the Benders decomposition algorithm, which is further improved by combining an approximate linear program and the look-ahead strategy. To illustrate the efficiency of our approaches and draw managerial insights, we apply our solutions to a data set from the day surgery center of a large public hospital in Shanghai, China. The results show that the joint optimization of capacity planning and patient scheduling could significantly improve the performance. Furthermore, our model can be applied to a rolling-horizon framework to optimize dynamic patient scheduling decisions. Through extensive numerical analyses, we demonstrate that our approaches yield good performances, as measured by the gap against an upper bound, and that these approaches outperform several benchmark policies. Summary of Contribution: First, this paper investigates the joint optimization problem of multiresource capacity planning and multitype patient scheduling under uncertain demands and random capacity consumption, which poses a significant computational challenge. It belongs to the scope of computing and operations research. Second, this paper formulates a mathematical model, establishes optimality properties, proposes solution algorithms, and performs extensive numerical experiments using real-world data. This work includes aspects of dynamic stochastic control, computing algorithms, and experiments. Moreover, this paper is motivated by a practical problem (joint management of capacity planning and patient scheduling in the day surgery center) in our cooperative hospital, which is also key to numerous other applications, for example, the make-to-order manufacturing systems and computing facility systems. By using the optimality properties, solution algorithms, and management insights derived in this paper, the practitioners can be equipped with a decision support tool for efficient and effective operation decisions.

Data-Driven Models for Capacity Allocation of Inpatient Beds in a Chinese Public Hospital

Hospital beds are a critical but limited resource shared between distinct classes of elective patients. Urgent elective patients are more sensitive to delays and should be treated immediately, whereas regular patients can wait for an extended time. Public hospitals in countries like China need to maximize their revenue and at the same time equitably allocate their limited bed capacity between distinct patient classes. Consequently, hospital bed managers are under great pressure to optimally allocate the available bed capacity to all classes of patients, particularly considering random patient arrivals and the length of patient stay. To address the difficulties, we propose data-driven stochastic optimization models that can directly utilize historical observations and feature data of capacity and demand. First, we propose a single-period model assuming known capacity; since it recovers and improves the current decision-making process, it may be deployed immediately. We develop a nonparametric kernel optimization method and demonstrate that an optimal allocation can be effectively obtained with one year’s data. Next, we consider the dynamic transition of system state and extend the study to a multiperiod model that allows random capacity; this further brings in substantial improvement. Sensitivity analysis also offers interesting managerial insights. For example, it is optimal to allocate more beds to urgent patients on Mondays and Thursdays than on other weekdays; this is in sharp contrast to the current myopic practice.

Optimization of flexible production and supply systems

Η διδακτορική διατριβή εστιάζει σε προβλήματα στοχαστικής βελτιστοποίησης που σχετίζονται με το σχεδιασμό και τη λειτουργία ευέλικτων συστημάτων παραγωγής και εφοδιασμού. Συγκεκριμένα, η διατριβή αποτελείται από δύο ενότητες: (α) προβλήματα ανάθεσης πόρων σε σειριακά συστήματα ουρών, και (β) προβλήματα που αφορούν στη χρήση εφεδρικών προμηθευτών για την αντιμετώπιση των κινδύνων διατάραξης της ομαλής λειτουργίας εφοδιαστικών αλυσίδων.Στην πρώτη ενότητα μελετήθηκαν μαρκοβιανά συστήματα ουρών δύο σταδίων, σε καθένα από τα οποία έχει ανατεθεί ένας εξειδικευμένος εξυπηρετητής, ενώ υπάρχει και ένας ευέλικτος εξυπηρετητής που μπορεί να ανατεθεί και στα δύο στάδια. Μελετήθηκαν διάφορες παραλλαγές του μοντέλου που προέκυψαν από υποθέσεις σχετικά με το βαθμό συνεργασίας δύο εξυπηρετητών και τη δυνατότητα διακοπής μιας εργασίας πριν την περάτωσή της. Για όλες τις παραλλαγές εξήχθησαν ιδιότητες της πολιτικής ανάθεσης των εξυπηρετητών που ελαχιστοποιεί το αναμενόμενο κόστος αναμονής. Στη δεύτερη ενότητα μελετήθηκαν μοντέλα τύπου εφημεριδοπώλη (newsvendor) με προμηθευτές χαρακτηριζόμενους από αβεβαιότητα ως προς την παράδοση του συνόλου της παραγγελίας. Ως μέσο αντιμετώπισης της αβεβαιότητας αυτής μελετήθηκε η χρήση ενός αξιόπιστου εφεδρικού προμηθευτή από τον οποίο εξασφαλίζεται αρχικά μια ποσότητα έναντι κάποιου τιμήματος, με τη δυνατότητα αγοράς μέρους της ποσότητας αυτής μετά την παράδοση από τον αναξιόπιστο προμηθευτή. Για διάφορες παραλλαγές του μοντέλου ανάλογα με τον τύπο της αβεβαιότητας (random yield, random capacity) και το χρόνο άσκησης του δικαιώματος αγοράς από τον εφεδρικό προμηθευτή (πριν ή μετά τη γνωστοποίηση της ζήτησης), προσδιορίστηκαν ιδιότητες των βέλτιστων τιμών της παραγγελίας προς τον αναξιόπιστο προμηθευτή και της εξασφαλισμένης ποσότητας από τον εφεδρικό προμηθευτή.

RANDOM SPARSE SAMPLING IN A GIBBS WEIGHTED TREE AND PHASE TRANSITIONS

Let $\unicode[STIX]{x1D707}$ be the projection on $[0,1]$ of a Gibbs measure on $\unicode[STIX]{x1D6F4}=\{0,1\}^{\mathbb{N}}$ (or more generally a Gibbs capacity) associated with a Hölder potential. The thermodynamic and multifractal properties of $\unicode[STIX]{x1D707}$ are well known to be linked via the multifractal formalism. We study the impact of a random sampling procedure on this structure. More precisely, let $\{{I_{w}\}}_{w\in \unicode[STIX]{x1D6F4}^{\ast }}$ stand for the collection of dyadic subintervals of $[0,1]$ naturally indexed by the finite dyadic words. Fix $\unicode[STIX]{x1D702}\in (0,1)$, and a sequence $(p_{w})_{w\in \unicode[STIX]{x1D6F4}^{\ast }}$ of independent Bernoulli variables of parameters $2^{-|w|(1-\unicode[STIX]{x1D702})}$. We consider the (very sparse) remaining values $\widetilde{\unicode[STIX]{x1D707}}=\{\unicode[STIX]{x1D707}(I_{w}):w\in \unicode[STIX]{x1D6F4}^{\ast },p_{w}=1\}$. We study the geometric and statistical information associated with $\widetilde{\unicode[STIX]{x1D707}}$, and the relation between $\widetilde{\unicode[STIX]{x1D707}}$ and $\unicode[STIX]{x1D707}$. To do so, we construct a random capacity $\mathsf{M}_{\unicode[STIX]{x1D707}}$ from $\widetilde{\unicode[STIX]{x1D707}}$. This new object fulfills the multifractal formalism, and its free energy is closely related to that of $\unicode[STIX]{x1D707}$. Moreover, the free energy of $\mathsf{M}_{\unicode[STIX]{x1D707}}$ generically exhibits one first order and one second order phase transition, while that of $\unicode[STIX]{x1D707}$ is analytic. The geometry of $\mathsf{M}_{\unicode[STIX]{x1D707}}$ is deeply related to the combination of approximation by dyadic numbers with geometric properties of Gibbs measures. The possibility to reconstruct $\unicode[STIX]{x1D707}$ from $\widetilde{\unicode[STIX]{x1D707}}$ by using the almost multiplicativity of $\unicode[STIX]{x1D707}$ and concatenation of words is discussed as well.