Monotone Optimal Policies for a Transient Queueing Staffing Problem

We consider the problem of determining the optimal policy for staffing a queueing system over multiple periods, using a model that takes into account transient queueing effects. Formulating the problem in a dynamic programming setting, we show that the optimal policy follows a monotone optimal control by establishing the submodularity of the objective function with respect to the staffing level and initial queue size in a period. In particular, this requires proving that the system occupancy in a G/M/s queue is submodular in the number of servers and initial system occupancy

Essays on Skills-Based Routing

Service systems such as call centers and hospital inpatient wards typically feature multiple classes of customers and multiple types of servers. Not all customer-server pairs are compatible, and some types of servers may be more efficient at serving some classes of customers than others. In the queueing literature, the problem of matching customers and servers is known as skills-based routing. This thesis consists of two works I have done in this area. The first work, which is done jointly with Jing Dong and Pengyi Shi, considers the routing problem in the face of a demand surge such as a pandemic. It shows how future arrival rate information, which is often available through demand forecast models, can be used to route near-optimally, even when there may be prediction errors. The methods used involve fluid approximations and optimal control theory, and the policies obtained are intuitive and easy to implement. The second work, which is done jointly with Jing Dong, incorporates a staffing element in addition to routing. Asymptotically optimal staffing and scheduling policies are derived for an M-model, both with and without demand uncertainty. The methods used involve diffusion approximations and stochastic-fluid approximations

Optimal Pricing and Admission Control in a Queueing System with Periodically Varying Parameters

We consider congestion control in a nonstationary queueing system. Assuming that the arrival and service rates are bounded, periodic functions of time, a Markov decision process (MDP) formulation is developed. We show under the infinite horizon discounted and average reward optimality criteria, for each fixed time, optimal pricing and admission control strategies are nondecreasing in the number of customers in the system. This extends stationary results to the nonstationary setting. Despite this result, the problem still seems intractable. We propose an easily implementable pointwise stationary approximation (PSA) to approximate the optimal policies, suggest a heuristic to improve the implementation of the PSA and verify its usefulness via a numerical study.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47630/1/11134_2004_Article_5273757.pd

A Data-Driven Approach for Operational Improvement in Emergency Departments

Emergency departments (EDs) in the US are experiencing significant stress from crowding, of which one of the main contributors is the lengthy boarding process, which is the process of to-be-admit patients waiting in the ED for the hospital to ready beds for them. We explored ways to reduce crowding by initiating hospital bed request (BeRT) early on for likely to-be-admit patients. In Chapter 2, we modeled the ED patient flow as a Markov decision process. With the objective of balancing the tradeoff between waiting cost and the cost of false early BeRTs, we found the optimal early BeRT policy to be of threshold type, where the threshold is a function of census and patients probability of admission. Chapter 3 built a fluid model, where patients flow into the ED (a fluid tank) as continuous fluid flowing at a time-dependent deterministic rate. To control the number of false early BeRTs, we imposed a constraint on the length of time for the early BeRT option. The optimal policy that minimizes the fluid level (congestion level) in the ED dictates that when ED is under heavy traffic regime, one should BeRT early as early, and as long, as allowed. In chapter 4, we looked at several early BeRT heuristics that are inspired by the theoretical optimal policies found previously. We tested and compared their performances in terms of length-of-stay and waiting time using a simulation model built for the UNC ED based on 2012 patient data. We observed that as the admission probability distributions of the patient population became less variable, the heuristics that take more information into account performed better. Lastly, we offered a different perspective on ED crowding in Chapter 5, where we explored the association between ED cencus and providers’ triage and admission decisions. We found that the more crowded the ED was, the more conservative providers were, in that nurses tend to triage more patients as critical, and physicians tend to admit more patients into the hospital.Doctor of Philosoph

Data-driven System Design in Service Operations

The service industry has become an increasingly important component in the world's economy. Simultaneously, the data collected from service systems has grown rapidly in both size and complexity due to the rapid spread of information technology, providing new opportunities and challenges for operations management researchers. This dissertation aims to explore methodologies to extract information from data and provide powerful insights to guide the design of service delivery systems. To do this, we analyze three applications in the retail, healthcare, and IT service industries. In the first application, we conduct an empirical study to analyze how waiting in queue in the context of a retail store affects customers' purchasing behavior. The methodology combines a novel dataset collected via video recognition technology with traditional point-of-sales data. We find that waiting in queue has a nonlinear impact on purchase incidence and that customers appear to focus mostly on the length of the queue, without adjusting enough for the speed at which the line moves. We also find that customers' sensitivity to waiting is heterogeneous and negatively correlated with price sensitivity. These findings have important implications for queueing system design and pricing management under congestion. The second application focuses on disaster planning in healthcare. According to a U.S. government mandate, in a catastrophic event, the New York City metropolitan areas need to be capable of caring for 400 burn-injured patients during a catastrophe, which far exceeds the current burn bed capacity. We develop a new system for prioritizing patients for transfer to burn beds as they become available and demonstrate its superiority over several other triage methods. Based on data from previous burn catastrophes, we study the feasibility of being able to admit the required number of patients to burn beds within the critical three-to-five-day time frame. We find that this is unlikely and that the ability to do so is highly dependent on the type of event and the demographics of the patient population. This work has implications for how disaster plans in other metropolitan areas should be developed. In the third application, we study workers' productivity in a global IT service delivery system, where service requests from possibly globally distributed customers are managed centrally and served by agents. Based on a novel dataset which tracks the detailed time intervals an agent spends on all business related activities, we develop a methodology to study the variation of productivity over time motivated by econometric tools from survival analysis. This approach can be used to identify different mechanisms by which workload affects productivity. The findings provide important insights for the design of the workload allocation policies which account for agents' workload management behavior