Search for: All records

Abstract This paper focuses on the assignment of attending physicians between the residents they supervise and their own responsibilities. Unlike prior work that assumes patient care can be interrupted at any time, we consider the more realistic and technically challenging situation when patient care is non-preemptive. Under the assumption that a holding cost is incurred when residents and patients wait for a conference with the attending physician and that rewards are earned whenever the attending physician completes a task (on his own or with his residents), we completely characterize the allocation of the attending physician that maximizes the long-run average profit. Furthermore, we show that the optimality conditions are simple thresholds on the holding cost. We also discuss how the optimal allocation of the attending physician differs from those in systems with preemptions. In particular, we show that the main difference occurs when the holding cost is high and there is no resident waiting for a conference. In this case, the attending physician waits for a resident to be ready for consultation in the non-preemptive case, whereas he works on his own responsibilities in the preemptive model. We conclude with a study of various extensions of our attending physician and residents interaction model and show that the structure of the optimal policy remains the same in these more general settings. 

We consider a Markovian queueing system with two types of customers (basic and advanced) and two types of servers (regular and specialist) in the presence of customer classification errors. We assume that there are always both types of customers waiting for service. When an advanced customer is misclassified as a basic customer, he needs to be served by a specialist after being served by a regular server. Our objective is to determine the dynamic assignment of the specialists between advanced and misclassified customers that maximizes the long-run average profit. We consider two versions of the problem that differ depending on whether the misclassified customers experience service continuity (the regular servers stay with misclassified customers while they wait for specialists, preventing the regular servers from serving other basic customers) or not (the regular servers continue serving other basic customers while misclassified customers wait for specialists). For both versions of the problem, we first characterize the optimal assignment of the specialists and then investigate how the optimal long-run average profit depends on the misclassification probability. We provide examples of systems where the optimal long-run average profit is not monotone in the misclassification probability, which is counter intuitive as one would expect misclassification to have a negative impact on system performance. We conclude our analysis by identifying under what conditions it is more profitable to serve customers with or without service continuity. 

We study optimal pricing in a single-server queueing system that can be observable or unobservable, depending on how customers receive information to estimate sojourn time. Our primary objective is to determine whether the service provider is better off making the system observable or unobservable under optimal pricing. We formulate the optimal pricing problem using Markov decision process (MDP) models for both observable and unobservable systems. For unobservable systems, the problem is studied using an MDP with a fixed-point equation as equilibrium constraints. We show that the MDPs for both observable and unobservable queues are special cases of a generalized arrivals-based MDP model, in which the optimal arrival rate (rather than price) is set in each state. Then, we show that the optimal policy that solves the generalized MDP exhibits a monotone structure in that the optimal arrival rate is non-increasing in the queue length, which allows for developing efficient algorithms to determine optimal pricing policies. Next, we show that if no customers overestimate sojourn time in the observable system, it is in the interest of the service provider to make the system observable. We also show that if all customers overestimate sojourn time, the service provider is better off making the system unobservable. Lastly, we learn from numerical results that when customers are heterogeneous in estimating their sojourn time, the service provider is expected to receive a higher gain by making the system observable if on average customers do not significantly overestimate sojourn time. 

Consider a Markovian tandem line with finite intermediate buffers and an equal number of stations and servers. Servers are flexible but noncollaborative, so that a job can be processed by at most one server at any time. When a job is being processed, it can be damaged and wasted depending on the proficiency of the server. We identify the dynamic server assignment policy that maximizes the long-run average throughput of the system with two stations and two servers. We find that the optimal policy is either a single or a double threshold policy on the number of jobs in the buffer, where the thresholds depend on the service rates and defect probabilities of the two servers at the two stations. For larger systems, we show that the optimal policy may involve server idling and that improving the service rate at any station is always beneficial. Finally, we propose heuristic server assignment policies motivated by experimentation for small systems with finite buffers and analysis of larger systems with infinite buffers. Numerical results suggest that our heuristics yield near-optimal performance. Funding: This research was supported by the National Science Foundation [Grants CMMI-1536990 and CMMI-2127778]. S. Andradóttir was also supported by the National Science Foundation [Grant CMMI-2348409]. 

This research investigates optimal pricing strategies in a service-providing queueing system where customers may renege before service completion. Prices are quoted upon customer arrivals and the incoming customers join the system if their willingness to pay exceeds the quoted price. While waiting in line or during service, customers may get impatient and leave without service, incurring an abandonment cost. There is also a per-unit time per-customer holding cost. Our objective is to maximize the long-run average profit through optimal pricing policies. We model the problem as a Markov decision process and identify the optimal pricing using policy iteration. We also study the structure of the optimal pricing policy. Furthermore, we show that under mild assumptions, the optimal price increases as the number of customers in the system increases. When those assumptions do not hold, optimal price decreases and then increases as the number of customers in the system grows. 

This research investigates optimal pricing strategies in a service-providing queueing system where customers may renege before service completion. Prices are quoted upon customer arrivals and the incoming customers join the system if their willingness to pay exceeds the quoted price. While waiting in line or during service, customers may get impatient and leave without service, incurring an abandonment cost. There is also a per-unit time per-customer holding cost. Our objective is to maximize the long-run average profit through optimal pricing policies. We model the problem as a Markov decision process and identify the optimal pricing using policy iteration. We also study the structure of the optimal pricing policy. Furthermore, we show that under mild assumptions, the optimal price increases as the number of customers in the system increases. When those assumptions do not hold, optimal price decreases and then increases as the number of customers in the system grows.