Fluid Control Problem Research Articles

Dynamic Control of Service Systems with Returns: Application to Design of Postdischarge Hospital Readmission Prevention Programs

Dynamic Control of Service Systems with Returns Postdischarge interventions (e.g., follow-up phone calls, outpatient appointments) are commonly used to reduce unplanned hospital readmissions. Such interventions have been shown to be effective (to varying degrees) in reducing the probability of readmission (or return). The interventions are, however, costly, and hence, their benefits need to be carefully balanced with the costs. In “Dynamic Control of Service Systems with Returns: Application to Design of Postdischarge Hospital Readmission Prevention Programs,” Chan, Huang, and Sarhangian investigate how postservice interventions should be dynamically allocated, accounting for their costs as well as their benefits in terms of reducing returns and congestion costs. To this end, they study a transient queueing control problem and examine the structure of the optimal policy by analyzing associated fluid-control problems. The structural results motivate the design of intuitive surge protocols whereby different intensities of interventions are provided based on the congestion level of the system.

Ergodic Control of Bipartite Matching Queues with Class Change and Matching Failure

Motivated by transplant applications, we study a bipartite matching queue with multiclass customers and multitype resources. Customers may change their classes or abandon the system while waiting in queue, and they may decline the offered resource units which results in matching failure. We are interested in designing efficient instantaneous matching policies that allocate resources upon arrival to waiting customers. Our objective is bicriteria and formulated as a cost functional that linearly combines the long-run average expected reward due to successful matches and the long-run average expected cost from customer waiting and abandonment. We first develop a stability condition on the class change and abandonment rates, which requires at least one customer queue with abandonment and that any queue without abandonment have a class transition path to a queue with abandonment. Under this condition, we construct a simple linear program, referred to as the fluid control problem (FCP), which serves as a lower bound for the original stochastic control problem under any admissible policy. We then propose a randomized matching policy based on the solution of the FCP and show that the proposed policy is asymptotically optimal under both the long-run average and ergodic cost criteria. In addition, we apply our method to study two X matching models with two customer classes and two resource types to provide insights on how the class change and matching failure impact the optimal policies.

Utilizing partial flexibility to improve emergency department flow: Theory and implementation

AbstractEmergency departments (EDs) typically have multiple areas where patients of different acuity levels receive treatments. In practice, different areas often operate with fixed nurse staffing levels. When there are substantial imbalances in congestion among different areas, it could be beneficial to deviate from the original assignment and reassign nurses. However, reassignments typically are only feasible at the beginning of 8–12‐h shifts, providing partial flexibility in adjusting staffing levels. In this work, we propose a stochastic queueing network model of patient flow in the ED and study an associated fluid control problem to guide the reassignment decision for two types of nursing staff. We propose a heuristic solution approach and investigate its performance both analytically and using simulation. Analytical results and simulation experiments suggest a significant reduction of waiting times in parameter regimes relevant to the ED setting. We further implement the staffing approach at a large ED. This pilot study highlights several challenges of implementing operational interventions in the ED, including the difficulty of establishing a clean statistical environment in such setting. Despite these challenges, we find that guiding reassignment decisions using our approach is associated with significant improvements to patient flow including a reduction in average total ED length‐of‐stay of 1.7 h.

Asymptotically optimal idling in the GI/GI/N+GI queue

We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs with server utilization costs. To solve the control problem, we consider an asymptotic regime in which the arrival rate and the number of servers grow large. The solution to an associated fluid control problem motivates that non-idling service disciplines are not in general optimal, unless some arrivals are turned away. We propose an admission control policy designed to ensure that servers have sufficient idle time, which we show is asymptotically optimal.

Opaque selling of multiple substitutable products with finite inventories

AbstractOpaque selling, in which a seller offers opaque goods (OGs), in addition to physical goods, has been shown to be an effective strategy to segment a market and improve the seller's profit. This article studies opaque selling with stochastic demand and fixed initial inventories of multiple products, where the seller dynamically controls the product offers and determines the product assignment to fulfill the demand for OGs over time. The problem is formulated as a stochastic dynamic program. Due to the curse of dimensionality, we study the fluid control problem that gives a time‐based fluid policy and a stationary probabilistic fulfillment strategy. We show that the fluid policy is asymptotically optimal when the arrival rates and initial inventory level are scaled up linearly. Furthermore, we propose a decomposition heuristic based on the corresponding fluid solution. The decomposition heuristic is shown to provide a tighter upper bound than the fluid control problem. Numerical study on a set of test instances illustrates the performance and efficacy of opaque selling.

Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Motivated by production systems with nonstationary stochastic demand, we study a double-ended queueing model having back orders and customer abandonment. One side of our model stores back orders, and the other side represents inventory. We assume first-come-first-served instantaneous fulfillment discipline. Our goal is to determine the optimal (nonstationary) production rate over a finite time horizon to minimize the costs incurred by the system. In addition to the inventory-related (holding and perishment) and demand-related (waiting and abandonment) costs, we consider a cost that penalizes rapid fluctuations of production rates. We develop a deterministic fluid-control problem (FCP) that serves as a performance lower bound for the original queueing-control problem (QCP). We further consider a high-volume system for which an upper bound of the gap between the optimal values of the QCP and FCP is characterized and construct an asymptotically optimal production rate for the QCP, under which the FCP lower bound is achieved asymptotically. Demonstrated by numerical examples, the proposed asymptotically optimal production rate successfully captures the time variability of the nonstationary demand.

Opaque Selling of Multiple Substitutable Products with Finite Inventories

Opaque selling, in which a seller offers a menu of opaque products from a collection of physical products, has been shown to be an effective strategy to segment a market and improve the seller's profit. We study opaque selling with stochastic demand and fixed initial inventory, where we consider two scenarios. In the exogenous fulfillment scenario, the assignment of physical products to fulfill customer demand is based on pre-announced probabilities. In the endogenous fulfillment scenario, the assignment is dynamically determined by the seller. In both settings, the seller dynamically controls the offering of opaque products over time to maximize the total expected revenue. The existing literature has well studied the mechanism of opaque selling and its benefits over other selling strategies. However, much of the literature considers only a single opaque product. This paper contributes to the literature by considering multiple opaque products and focusing on the practice implementation of opaque selling. We formulate the seller's problem as a stochastic dynamic program. Due to the well-known curse of dimensionality, we study the fluid control problem and develop decomposition heuristic for both scenarios based on the corresponding fluid solution. We show that the fluid control problem can provide a time-based fluid policy that is asymptotically optimal. In particular, we show that adopting a stationary probabilistic fulfillment strategy for the endogenous fulfillment scenario is asymptotically optimal. The numerical study shows that offering multiple opaque products can substantially improve the seller's revenue under certain conditions. Our results provide guidance for sellers on how to implement the opaque selling practically when they have finite inventories of multiple substitutable products.

Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Motivated by production systems with nonstationary stochastic demand, we study a double-ended queueing model having backorders and customer abandonment. One side of our model stores backorders, and the other side represents inventory. We assume first-come- first-serve instantaneous ful fillment discipline. Our goal is to determine the optimal (nonstationary) production rate over a finite time horizon to minimize the costs incurred by the system. In addition to the inventory-related (holding, perishment) and demand-related (waiting, abandonment) costs, we consider a cost that penalizes rapid fluctuations of production rates. We develop a deterministic fluid control problem (FCP) that serves as a performance lower bound for the original queueing control problem (QCP). We further consider a high-volume system and construct an asymptotically optimal production rate for the QCP, under which the FCP lower bound is achieved asymptotically. Demonstrated by numerical examples, the proposed asymptotically optimal production rate successfully captures the time variability of the nonstationary demand.

Network Revenue Management with Cancellations and No‐Shows

Customer cancellations and no‐shows have an important impact on the performance of an airline's revenue management system. In this study, we study airline network revenue management problems with customer cancellations and no‐shows, considering two types of demand models: independent‐demand and choice‐based‐demand models. In independent‐demand models, the booking request rates for different products are independent of the assortment of products offered by the airline (exogenous), whereas in choice‐based‐demand models they depend on the airline's assortment (endogenous). The stochastic problems of optimizing the booking policies for the two demand models are not tractable because of the high‐dimensional state space. Therefore, for each model, we use the corresponding deterministic, continuous‐time, and continuous‐state model, known as the fluid model. A booking policy based on the fluid solution can be implemented for the original stochastic, discrete model. This fluid policy is shown to be asymptotically optimal when the arrival rates become high and the seat capacities become large. In the independent‐demand setting, an optimal fluid solution can be computed by solving a convex optimization problem for which efficient algorithms exist, whereas for some choice‐based‐demand models, the fluid control problems are known to be intractable. We also develop mixed fluid policies for the independent‐demand setting, taking advantage of the real‐time booking state, to improve the performance over the fluid policy. In a factorial experiment of 20 small‐sized single‐leg problems, the revenue loss under one of the mixed fluid policies is demonstrated to be less than 1% of the optimal value for all problems.

Opportunistic Scheduling of Randomly Coded Multicast Transmissions at Half-Duplex Relay Stations

We consider the multicast scheduling problem for the block transmission of packets in a heterogeneous network using a half-duplex relay station (RS). The RS uses random linear coding to efficiently transmit packets over time-varying multicast channels. Our goal is to minimize the average decoding delay. Because of the half-duplex operation, at each time slot, the RS must decide to either: 1) fetch a new packet for encoding from the base station or 2) multicast a coded packet to wireless users. Thus, optimal scheduling hinges on exploiting multicast opportunities while persistently supplying the encoder (at the RS) with new packets. We formulate an associated fluid control problem and show that the optimal policy incorporates opportunism across multicast channels, i.e., the RS performs a multicast transmission only if the collection of channel conditions is favorable; otherwise, it performs a fetch. Based on the fluid policy, we propose an online algorithm. We prove that our algorithm asymptotically incurs no more than 4/3 and 2 times the optimal delay, for two-user and arbitrary number of user system, respectively. Simulation results show that, in fact, our algorithm’s performance is very close to theoretical bounds.

Value management of diagnostic equipment with cancelation, no‐show, and emergency patients

Magnetic resonance imaging and other multifunctional diagnostic facilities, which are considered as scarce resources of hospitals, typically provide services to patients with different medical needs. This article examines the admission policies during the appointment management of such facilities. We consider two categories of patients: regular patients who are scheduled in advance through an appointment system and emergency patients with randomly generated demands during the workday that must be served as soon as possible. According to the actual medical needs of patients, regular patients are segmented into multiple classes with different cancelation rates, no‐show probabilities, unit value contributions, and average service times. Management makes admission decisions on whether or not to accept a service request from a regular patient during the booking horizon to improve the overall value that could be generated during the workday. The decisions should be made by considering the cancelation and no‐show behavior of booked patients as well as the emergency patients that would have to be served because any overtime service would lead to higher costs. We studied the optimal admission decision using a continuous‐time discrete‐state dynamic programming model. Identifying an optimal policy for this discrete model is analytically intractable and numerically inefficient because the state is multidimensional and infinite. We propose to study a deterministic counterpart of the problem (i.e., the fluid control problem) and to develop a time‐based fluid policy that is shown to be asymptotically optimal for large‐scale problems. Furthermore, we propose to adopt a mixed fluid policy that is developed based on the information obtained from the fluid control problem. Numerical experiments demonstrate that this improved policy works effectively for small‐scale problems. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 287–304, 2016

Meeting the Ultrahigh-Temperature/Ultrahigh-Pressure Fluid Challenge

Summary Ultrahigh-temperature/ultrahigh-pressure (uHT/uHP) conditions have a different definition, depending on the region, the operator, and the service company. In this paper, the definition used for uHT/uHP fluid performance is that the fluid be able to perform above 500°F and 30,000 psi. This paper describes the development of innovative drilling fluids that are specific to these well conditions. When bottomhole temperatures exceed 400°F, the design and engineering of drilling fluids can be challenging. Drilling fluids that destabilize can cause a variety of fluid-control problems that could lead to drilling and completion issues. With invert-emulsion fluids, the major challenges encountered with these conditions are related to the thermal degradation of the emulsifier and wetting package that can lead to gelation and syneresis. Another challenge is fluid loss that is related to the emulsion stability and to the degradation of the fluid-loss-control additives. Finally, efficient control of the rheological properties—critical to the success of any well—also can be challenging when effects from emulsion instability, filtration-control degradation, and rheology-control-additive degradation are coupled with increases in drilled solids, rapidly leading to rheological instability. This can manifest itself as high-fluctuating rheologies and gelation or the loss of rheological properties that can give rise to sag of weight material, both potentially leading to associated well-control problems. The paper describes the development of the new fluid system designed for such uHT/uHP environments (highlighting the chemical differences) and compares the test data of the system with more-conventional high-temperature/high-pressure (HT/HP) invert-emulsion fluids. Data are presented that show the stability and performance of the new fluid with extended exposure to temperature >500°F, demonstrating a tolerance to various contaminations and showing the rheological behavior and stability to 600°F and 40,000 psi.

Control of fluids [About This Issue

A large proportion of control problems involve the control of fluids, such as coaxing fluids to moving into desired spatial positions or acting as a medium for moving the positions of solid objects into desired spatial positions or orientations. Such fluid control problems are ubiquitous in a wide range of applications including in the process industries, nuclear reactors, biological systems, marine vehicles, and aeronautics. This issue of CSM is devoted to various kinds of fluid control problems.

Asymptotically Optimal Controls for Time-Inhomogeneous Networks

A framework is introduced for the identification of controls for single-class time-varying queueing networks that are asymptotically optimal in the so-called uniform acceleration regime. A related, but simpler, first-order (or fluid) control problem is first formulated. For a class of performance measures that satisfy a certain continuity property, it is then shown that any sequence of policies whose performances approach the infimum in the fluid control problem is asymptotically optimal for the original network problem. Examples of performance measures with this property are described, and simulations implementing asymptotically optimal policies are presented. The use of directional derivatives of the reflection map for solving fluid control problems is also illustrated. This work serves to complement a large body of literature on asymptotically optimal controls for time-homogeneous networks.

Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality

This paper describes a general approach for dynamic control of stochastic networks based on fluid model analysis, where in broad terms, the stochastic network is approximated by its fluid analog, an associated fluid control problem is solved and, finally, a scheduling rule for the original system is defined by interpreting the fluid control policy. The main contribution of this paper is to propose a general mechanism for translating the solution of the fluid optimal control problem into an implementable discrete-review policy that achieves asymptotically optimal performance under fluid scaling, and guarantees stability if the traffic intensity is less than one at each station. The proposed policy reviews system status at discrete points in time, and at each such point the controller formulates a processing plan for the next review period,based on the queue length vector observed, using the optimal control policy of the associated fluid optimization problem. Implementation of such a policy involves enforcement of certain safety stock requirements in order to facilitate the execution of the processing plans and to avoid unplanned server idleness. Finally, putting aside all considerations of system optimality, the following generalization is considered: every initial condition is associated with a feasible fluid trajectory that describes the desired system evolution starting at that point. A discrete-review policy is described that asymptotically tracks this target specification; that is, it achieves the appropriate target trajectory as its fluid limit.

Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies

This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r_k(q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.