Heuristics for Base‐Stock Levels in Multi‐Echelon Distribution Networks

We study inventory optimization for locally controlled, continuous‐review distribution systems with stochastic customer demands. Each node follows a base‐stock policy and a first‐come, first‐served allocation policy. We develop two heuristics, the recursive optimization (RO) heuristic and the decomposition‐aggregation (DA) heuristic, to approximate the optimal base‐stock levels of all the locations in the system. The RO heuristic applies a bottom‐up approach that sequentially solves single‐variable, convex problems for each location. The DA heuristic decomposes the distribution system into multiple serial systems, solves for the base‐stock levels of these systems using the newsvendor heuristic of Shang and Song (2003), and then aggregates the serial systems back into the distribution system using a procedure we call “backorder matching.” A key advantage of the DA heuristic is that it does not require any evaluation of the cost function (a computationally costly operation that requires numerical convolution). We show that, for both RO and DA, changing some of the parameters, such as leadtime, unit backordering cost, and demand rate, of a location has an impact only on its own local base‐stock level and its upstream locations’ local base‐stock levels. An extensive numerical study shows that both heuristics perform well, with the RO heuristic providing more accurate results and the DA heuristic consuming less computation time. We show that both RO and DA are asymptotically optimal along multiple dimensions for two‐echelon distribution systems. Finally, we show that, with minor changes, both RO and DA are applicable to the balanced allocation policy.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

Looking Upstream: Optimal Policies for a Class of Capacitated Multi‐Stage Inventory Systems

We consider a multi‐stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite‐horizon and infinite‐horizon, discounted‐cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order‐up‐to policy. We find the explicit functional form of the optimal order‐up‐to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single‐dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity‐constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three‐, four‐, and five‐stage capacitated systems over a range of model parameters, and discuss insights that emerge.     

A Hybrid Methodology for Modeling Risk of Adverse Events in Complex Health‐Care Settings

In spite of increased attention to quality and efforts to provide safe medical care, adverse events (AEs) are still frequent in clinical practice. Reports from various sources indicate that a substantial number of hospitalized patients suffer treatment‐caused injuries while in the hospital. While risk cannot be entirely eliminated from health‐care activities, an important goal is to develop effective and durable mitigation strategies to render the system “safer.” In order to do this, though, we must develop models that comprehensively and realistically characterize the risk. In the health‐care domain, this can be extremely challenging due to the wide variability in the way that health‐care processes and interventions are executed and also due to the dynamic nature of risk in this particular domain. In this study, we have developed a generic methodology for evaluating dynamic changes in AE risk in acute care hospitals as a function of organizational and nonorganizational factors, using a combination of modeling formalisms. First, a system dynamics (SD) framework is used to demonstrate how organizational‐level and policy‐level contributions to risk evolve over time, and how policies and decisions may affect the general system‐level contribution to AE risk. It also captures the feedback of organizational factors and decisions over time and the nonlinearities in these feedback effects. SD is a popular approach to understanding the behavior of complex social and economic systems. It is a simulation‐based, differential equation modeling tool that is widely used in situations where the formal model is complex and an analytical solution is very difficult to obtain. Second, a Bayesian belief network (BBN) framework is used to represent patient‐level factors and also physician‐level decisions and factors in the management of an individual patient, which contribute to the risk of hospital‐acquired AE. BBNs are networks of probabilities that can capture probabilistic relations between variables and contain historical information about their relationship, and are powerful tools for modeling causes and effects in many domains. The model is intended to support hospital decisions with regard to staffing, length of stay, and investments in safety, which evolve dynamically over time. The methodology has been applied in modeling the two types of common AEs: pressure ulcers and vascular‐catheter‐associated infection, and the models have been validated with eight years of clinical data and use of expert opinion.     

Competition and The Operational Performance of Hospitals: The Role of Hospital Objectives

We examine the effect of a hospital's objective (i.e., non‐profit vs. for‐profit) in hospital markets for elective care. Using game‐theoretic analysis and queueing models to capture the operational performance of hospitals, we compare the equilibrium behavior of three market settings in terms of such criteria as waiting times and patient costs from waiting and hospital payments. In the first setting, a monopoly, patients are served exclusively by a single non‐profit hospital; in the second, a homogeneous duopoly, patients are served by two competing non‐profit hospitals. In our third setting, a heterogeneous duopoly, the market is served by one non‐profit hospital and one for‐profit hospital. A non‐profit hospital provides free care to patients, although they may have to wait; for‐profit hospitals charge a fee to provide care with minimal waiting. A comparison between the monopolistic and each of the duopolistic settings reveals that the introduction of competition can hamper a hospital's ability to attain economies of scale and can also increase waiting times. Moreover, the presence of a for‐profit sector may be desirable only when the hospital market is sufficiently competitive. A comparison across the duopolistic settings indicates that the choice between homogeneous and heterogeneous competition depends on the patients' willingness to wait before receiving care and the reimbursement level of the non‐profit sector. When the public funder is not financially constrained, the presence of a for‐profit sector may allow the funder to lower both the financial costs of providing coverage and the total costs to patients. Finally, our analysis suggests that the public funder should exercise caution when using policy tools that support the for‐profit sector—for example, patient subsidies—because such tools may increase patient costs in the long run; it might be preferable to raise the non‐profit sector's level of reimbursement.     

Revenue Management in Order‐Driven Production Systems

This article investigates the effectiveness of a tactical demand‐capacity management policy to guide operational decisions in order‐driven production systems. The policy is implemented via a heuristic that attempts to maximize revenue by selectively accepting or rejecting customer orders for multiple product classes when demand exceeds capacity constantly over the short term. The performance of the heuristic is evaluated in terms of its ability to generate a higher profit compared to a first‐come‐first‐served (FCFS) policy. The policies are compared over a wide range of conditions characterized by variations in both internal (firm) and external (market) factors. The heuristic, when used with a Whole Lot order‐processing approach, produces higher profit compared to FCFS when profit margins of products are substantially different from each other and demand exceeds capacity by a large amount. In other cases it is better to use the heuristic in conjunction with the Split Lot order‐processing approach.     

Elective Patient Admission and Scheduling under Multiple Resource Constraints

We consider a patient admission problem to a hospital with multiple resource constraints (e.g., OR and beds) and a stochastic evolution of patient care requirements across multiple resources. There is a small but significant proportion of emergency patients who arrive randomly and have to be accepted at the hospital. However, the hospital needs to decide whether to accept, postpone, or even reject the admission from a random stream of non‐emergency elective patients. We formulate the control process as a Markov decision process to maximize expected contribution net of overbooking costs, develop bounds using approximate dynamic programming, and use them to construct heuristics. We test our methods on data from the Ronald Reagan UCLA Medical Center and find that our intuitive newsvendor‐based heuristic performs well across all scenarios.     

Capacity Sharing and Cost Allocation among Independent Firms with Congestion

We analyze the benefit of production/service capacity sharing for a set of independent firms. Firms have the choice of either operating their own production/service facilities or investing in a facility that is shared. Facilities are modeled as queueing systems with finite service rates. Firms decide on capacity levels (the service rate) to minimize delay costs and capacity investment costs possibly subject to service‐level constraints on delay. If firms decide to operate a shared facility they must also decide on a scheme for sharing the capacity cost. We formulate the problem as a cooperative game and identify settings under which capacity sharing is beneficial and there is a cost allocation that is in the core under either the first‐come, first‐served policy or an optimal priority policy. We show that capacity sharing may not be beneficial in settings where firms have heterogeneous work contents and service variabilities. In such cases, we specify conditions under which capacity sharing may still be beneficial for a subset of the firms.     

Appointment Scheduling with No‐Shows and Overbooking

We study an overbooking model for scheduling arrivals at a medical facility under no‐show behavior, with patients having different no‐show probabilities and different weights. The scheduler has to assign the patients to time slots in such a way that she minimizes the expected weighted sum of the patients' waiting times and the doctor's idle time and overtime. We first consider the static problem, where the set of patients to be scheduled and their characteristics are known in advance. We partially characterize the optimal schedule and introduce a new sequencing rule that schedules patients according to a single index that is a function of their characteristics. Then we apply our theoretical results and conclusions from numerical experiments to sequential scheduling procedures. We propose a heuristic solution to the sequential scheduling problem, where requests for appointments come in gradually over time and the scheduler has to assign each patient to one of the remaining slots that are available in the schedule for a given day. We find that the no‐show rate and patients' heterogeneity have a significant impact on the optimal schedule and should be taken under consideration.     

A reinforcement-learning approach for admission control in distributed network service systems

In the distributed network service systems such as streaming-media systems and resource-sharing systems with multiple service nodes, admission control (AC) technology is an essential way to enhance performance. Model-based optimization approaches are good ways to be applied to analyze and solve the optimal AC policy. However, due to “the curse of dimensionality”, computing such policy for practical systems is a rather difficult task. In this paper, we consider a general model of the distributed network service systems, and address the problem of designing an optimal AC policy. An analytical model is presented for the system with fixed parameters based on semi-Markov decision process (SMDP). We design an event-driven AC policy, and the stationary randomized policy is taken as the policy structure. To solve the SMDP, both the state aggregation approach and the reinforcement-learning (RL) method with online policy optimization algorithm are applied. Then, we extend the problem by considering the system with time-varying parameters, where the arrival rates of requests at each service node may change over time. In view of this situation, an AC policy switching mechanism is presented. This mechanism allows the system to decide whether to adjust its AC policy according to the policy switching rule. And in order to maximize the gain of system, that is, to obtain the optimal AC policy switching rule, another RL-based algorithm is applied. To assess the effectiveness of SMDP-based AC policy and policy switching mechanism for the system, numerical experiments are presented. We compare the performance of optimal policies obtained by the solutions of proposed methods with other classical AC policies. The simulation results illustrate that higher performance and computational efficiency could be achieved by using the SMDP model and RL-based algorithms proposed in this paper.     

Operational Impact of Service Innovations in Multi‐Step Service Systems

Service quality is an important attribute that is used to characterize many service systems. In this study, we examine a service system with two consecutive steps that have shared resources. The service process consists of a base service (first step in the process) followed by a second step that adds additional value. We first look at a social surplus maximizing service provider (SP) who decides the optimal service capacity and re‐optimizes in response to changes in the speed of service of the first step due to local innovations. Our main objective is to explore using simple and stylized models, the effect on the service system of local innovations in step 1 that decrease this step's service times. We find that the effect of such innovations can sometimes lead to the worsening of certain critical service quality measures when SPs are monopolists. Next, using a model of competition, we find that this effect continues to hold in settings where SPs compete for arrivals. Our results have interesting consequences for many service systems and may help explain some of the unintended effects of service innovations reported in the literature.     

A Framework for Facilitating Sourcing and Allocation Decisions for Make‐to‐Order Items

This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make‐to‐order items. We specifically address the buyer's vendor selection problem for make‐to‐order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume‐based discounts for bundles of items. The potential suppliers for make‐to‐order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%.     

An Analytical Framework for Designing Community‐Based Care for Chronic Diseases

In this study, we propose a methodological framework to provide a road map to clinicians and system planners in developing chronic disease management strategies, and designing community‐based care. We extend the analytical epidemiologic model by utilizing a patient flow approach, in order to model the multiple care‐provider visit patterns of patients with a specific chronic illness. The patterns of care received by a group of patients are represented in compact form by means of a Markov model that is based on a disease‐specific state space. Our framework also reflects the case‐mix biases as well as the care‐provider level clustering of the patients. By using this approach, we identify the patterns of care, determine the care provider and patient characteristics associated with optimal management of care, and estimate the potential influence of various interventions. The framework is applied to the data of 4000+ stroke patients discharged from the acute care hospitals of Quebec to their homes. Our findings provide a basis for designing community‐based care initiatives for stroke survivors in the province.     

A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints

We study a hybrid push–pull production system with a two‐stage manufacturing process, which builds and stocks tested components for just‐in‐time configuration of the final product when a specific customer order is received. The first production stage (fabrication) is a push process where parts are replenished, tested, and assembled into components according to product‐level build plans. The component inventory is kept in stock ready for the final assembly of the end products. The second production stage (fulfillment) is a pull‐based assemble‐to‐order process where the final assembly process is initiated when a customer order is received and no finished goods inventory is kept for end products. One important planning issue is to find the right trade‐off between capacity utilization and inventory cost reduction that strives to meet the quarter‐end peak demand. We present a nonlinear optimization model to minimize the total inventory cost subject to the service level constraints and the production capacity constraints. This results in a convex program with linear constraints. An efficient algorithm using decomposition is developed for solving the nonlinear optimization problem. Numerical results are presented to show the performance improvements achieved by the optimized solutions along with managerial insights provided.     

The Value of Quality Grading in Remanufacturing

In this paper we consider a tactical production‐planning problem for remanufacturing when returns have different quality levels. Remanufacturing cost increases as the quality level decreases, and any unused returns may be salvaged at a value that increases with their quality level. Decision variables include the amount to remanufacture each period for each return quality level and the amount of inventory to carry over for future periods for both returns (unremanufactured), and finished remanufactured products. Our model is grounded with data collected at Pitney‐Bowes from their mailing systems remanufacturing operations. We derive some analytic properties for the optimal solution in the general case, and provide a simple greedy heuristic to computing the optimal solution in the case of deterministic returns and demand. Under mild assumptions, we find that the firm always remanufactures the exact demand in each period. We also study the value of a nominal quality‐grading system in planning production. Based on common industry parameters, we analyze, via a numerical study, the increase in profits observed by the firm if it maintains separate inventories for each quality grade. The results show that a grading system increases profit by an average of 4% over a wide range of parameter values commonly found in the remanufacturing industry; this number increases as the returns volume increases. We also numerically explore the case where there are capacity constraints and find the average improvement of a grading system remains around 4%.     

Panel Size and Overbooking Decisions for Appointment‐Based Services under Patient No‐Shows

Many service systems that work with appointments, particularly those in healthcare, suffer from high no‐show rates. While there are many reasons why patients become no‐shows, empirical studies found that the probability of a patient being a no‐show typically increases with the patient's appointment delay, i.e., the time between the call for the appointment and the appointment date. This paper investigates how demand and capacity control decisions should be made while taking this relationship into account. We use stylized single server queueing models to model the appointments scheduled for a provider, and consider two different problems. In the first problem, the service capacity is fixed and the decision variable is the panel size; in the second problem, both the panel size and the service capacity (i.e., overbooking level) are decision variables. The objective in both cases is to maximize some net reward function, which reduces to system throughput for the first problem. We give partial or complete characterizations for the optimal decisions, and use these characterizations to provide insights into how optimal decisions depend on patient's no‐show behavior in regards to their appointment delay. These insights especially provide guidance to service providers who are already engaged in or considering interventions such as sending reminders in order to decrease no‐show probabilities. We find that in addition to the magnitudes of patient show‐up probabilities, patients' sensitivity to incremental delays is an important determinant of how demand and capacity decisions should be adjusted in response to anticipated changes in patients' no‐show behavior.     

Examining Links Between Sign-Out Reporting During Shift Changeovers and Patient Management Risks

This article reports on a qualitative study that investigated how various risk factors associated with the process of sign-out reporting across shifts in critical care hospital environments could lead to flawed communication and thus to increased risk of poor patient outcomes. The study was performed in two critical care hospital units: the pediatric intensive care unit (PICU) and the postanesthesia care unit (PACU). We collected data from observations of eight nurses and four resident physicians in the PICU and four nurses and four resident physicians in the PACU giving sign-out reports during their shift changes. In addition, we conducted semi-structured interviews with a separate sample of medical providers consisting of nurse managers, attending physicians, nurses, and residents from each of these two units. The issues that were addressed in these interviews included how various methods of conducting sign-outs and factors such as personality and experience could impact the effectiveness of communication during sign-out reporting. We also collected data from these medical providers on how failures in communication during sign-out reporting could lead to potentially adverse patient outcomes. The article concludes with the presentation of a modeling framework that demonstrates how the combined influences of risk factors can generate a particularly important type of failure mode in communication and how interventions can be targeted to serve as barriers to such events. A number of recommendations intended for reducing risks associated with the communication of sign-out reports are also presented.     

Life Is All about Timing: An Examination of Differences in Treatment Quality for Trauma Patients Based on Hospital Arrival Time

In health care, most quality transparency and improvement programs focus on the quality variation across hospitals, while we know much less about within‐hospital quality variation. This study examines one important factor that is associated with the fluctuation of quality of care in the same hospital—the timing of patient arrival. We analyze data from the National Trauma Data Bank and find that patients arriving at the hospital during off‐hours (6 PM–6 AM) receive significantly lower quality care than those who arrive during the daytime, as reflected in higher mortality rates, among other measures. More importantly, we try to uncover the mechanism for the quality variation. Interestingly, we find consistent evidence that the inferior care received during off‐hours is not likely due to unobserved heterogeneity, disruptions in circadian rhythms, or delays in receiving treatment. Instead, it is more likely due to the limited availability of high‐quality resources. This leads to a higher surgical complication rate, a higher likelihood of multiple surgeries, and longer patient length of stay in the intensive care unit. These findings have important implications for optimal resource allocation in hospitals to improve the quality‐of‐care delivery.     

Clinic Overbooking to Improve Patient Access and Increase Provider Productivity*

The problem of patient no‐shows (patients who do not arrive for scheduled appointments) is significant in many health care settings, where no‐show rates can vary widely. No‐shows reduce provider productivity and clinic efficiency, increase health care costs, and limit the ability of a clinic to serve its client population by reducing its effective capacity. In this article, we examine the problem of no‐shows and propose appointment overbooking as one means of reducing the negative impact of no‐shows. We find that patient access and provider productivity are significantly improved with overbooking, but that overbooking causes increases in both patient wait times and provider overtime. We develop a new clinic utility function to capture the trade‐offs between these benefits and costs, and we show that the relative values that a clinic assigns to serving additional patients, minimizing patient waiting times, and minimizing clinic overtime will determine whether overbooking is warranted. From the results of a series of simulation experiments, we determine that overbooking provides greater utility when clinics serve larger numbers of patients, no‐show rates are higher, and service variability is lower. Even with highly variable service times, many clinics will achieve positive net results with overbooking. Our analysis provides valuable guidance to clinic administrators about the use of appointment overbooking to improve patient access, provider productivity, and overall clinic performance.     

Design and Analysis of Hospital Admission Control for Operational Effectiveness

Variability in hospital occupancy negatively impacts the cost and quality of patient care delivery through increased emergency department (ED) congestion, emergency blockages and diversions, elective cancelations, backlogs in ancillary services, overstaffing, and understaffing. Controlling inpatient admissions can effectively reduce variability in hospital occupancy to mitigate these problems. Currently there are two major gateways for admission to a hospital: the ED and scheduled elective admission. Unfortunately, in highly utilized hospitals, excessive wait times make the scheduled gateway undesirable or infeasible for a subset of patients and doctors. As a result, this group often uses the ED gateway as a means to gain admission to the hospital. To better serve these patients and improve overall hospital functioning, we propose creating a third gateway: an expedited patient care queue. We first characterize an optimal admission threshold policy using controls on the scheduled and expedited gateways for a new Markov decision process model. We then present a practical policy based on insight from the analytical model that yields reduced emergency blockages, cancelations, and off‐unit census via simulation based on historical hospital data.