Optimal Dynamic Appointment Scheduling of Base and Surge Capacity

2021 ◽  
Author(s):  
Benjamin Grant ◽  
Itai Gurvich ◽  
R. Kannan Mutharasan ◽  
Jan A. Van Mieghem
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Capacity Utilization ◽  
Healthcare Setting ◽  
Appointment Scheduling ◽  
Problem Definition ◽  
Stochastic Dynamic ◽  
Surge Capacity ◽  
Trade Off ◽  
Dynamic Stochastic

Problem definition: We study dynamic stochastic appointment scheduling when delaying appointments increases the risk of incurring costly failures, such as readmissions in healthcare or engine failures in preventative maintenance. When near-term base appointment capacity is full, the scheduler faces a trade-off between delaying an appointment at the risk of costly failures versus the additional cost of scheduling the appointment sooner using surge capacity. Academic/practical relevance: Most appointment-scheduling literature in operations focuses on the trade-off between waiting times and utilization. In contrast, we analyze preventative appointment scheduling and its impact on the broader service-supply network when the firm is responsible for service and failure costs. Methodology: We adopt a stochastic dynamic programming (DP) formulation to characterize the optimal scheduling policy and evaluate heuristics. Results: We present sufficient conditions for the optimality of simple policies. When analytical solutions are intractable, we solve the DP numerically and present optimality gaps for several practical policies in a healthcare setting. Managerial implications: Intuitive appointment policies used in practice are robust under moderate capacity utilization, but their optimality gap can quadruple under high load.

scholarly journals Managing Shutdown Decisions in Merchant Commodity and Energy Production: A Social Commerce Perspective

2020 ◽  
Author(s):  
Alessio Trivella ◽  
Selvaprabu Nadarajah ◽  
Stein-Erik Fleten ◽  
Denis Mazieres ◽  
David Pisinger
Keyword(s):  
Energy Production ◽  
Local Community ◽  
Binary Classification ◽  
Problem Definition ◽  
Stochastic Dynamic ◽  
Anticipated Regret ◽  
Social Commerce ◽  
Asset Value ◽  
Plant Closures ◽  
Operating Policies

Problem definition: Merchant commodity and energy production assets operate in markets with volatile prices and exchange rates. Plant closures adversely affect societal entities beyond the specific plant being shut down, such as the parent company and the local community. Motivated by an aluminum producer, we study if mitigating these hard-to-assess broader impacts of a shutdown is financially viable using the plant’s operating flexibility. Academic/practical relevance: Our social commerce perspective toward managing shutdown decisions deviates from the commonly used asset value maximization objective in merchant operations. Identifying operating policies that delay or decrease the likelihood of a shutdown without incurring a significant asset value loss supports socially responsible plant shutdown decisions. Methodology: We formulate a constrained Markov decision process to manage shutdown decisions and limit the probability of future plant closures. We provide theoretical support for approximating this intractable model using unconstrained stochastic dynamic programs with modified shutdown costs and explore two classes of operating policies. Our first policy leverages anticipated regret theory, and the second policy generalizes, using machine learning, production-margin heuristics used in practice. We compute the former and latter policies using a least squares Monte Carlo method and combining this method with binary classification, respectively. Results: Anticipated-regret policies possess desirable asymptotic properties absent in classification-based policies. On instances created using real data, anticipated-regret and classification-based policies outperform practice-based production-margin strategies. Significant reductions in shutdown probability and delays in plant closures are possible while incurring small asset value losses. Managerial implications: A plant’s operating flexibility provides an effective lever to balance the social objective to reduce closures and the financial goal to maximize asset value. Adhering to both objectives requires combining short-term commitments with external stakeholders to avoid shutdown with longer-term internal efforts to reduce the probability of plant closures.

scholarly journals Integrating Dynamic Pricing and Inventory Control for Fresh Agriproduct under Multinomial Logit Choice

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Xiong-zhi Wang ◽  
Wenliang Zhou
Keyword(s):  
Dynamic Pricing ◽  
Programming Model ◽  
Choice Model ◽  
Multinomial Logit ◽  
Linear Ordering ◽  
Stochastic Dynamic ◽  
Inventory Problem ◽  
Numerical Illustration ◽  
Dynamic Stochastic ◽  
Joint Pricing

In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh agriproducts (FAPs) with two-period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period the retailer makes ordering decision for new FAP and sets regular and discount price for new and old inventories, respectively. After demand realization, the expired leftover is disposed and unexpired inventory is carried to the next period, continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximize the total expected discount profit over the whole planning horizon. We present a price-dependent, stochastic dynamic programming model taking into account zero lead time, linear ordering costs, inventory holding, and backlogging costs, as well as disposal cost. Considering the influence of the perishability, we integrate a Multinomial Logit (MNL) choice model to describe the consumer behavior on purchasing fresh or nonfresh product. By way of the inverse of the price vector, the original formulation can be transferred to be jointly concave and tractable. Finally we characterize the optimal policy and develop effective methods to solve the problem and conduct a simple numerical illustration.

On a tandem queueing model with identical service times at both counters, I

1979 ◽  
Vol 11 (3) ◽  
pp. 616-643 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Complete Analysis ◽  
Single Server ◽  
Stationary Distributions ◽  
In Series ◽  
Queues In Series ◽  
Service Times ◽  
Necessary And Sufficient ◽  
Insight Into

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process.Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue.In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

Dynamic Type Matching

2021 ◽  
Author(s):  
Ming Hu ◽  
Yun Zhou
Keyword(s):  
Sufficient Conditions ◽  
Sharing Economy ◽  
Problem Definition ◽  
Periodic Review ◽  
Optimal Matching ◽  
Demand And Supply ◽  
Holding Costs ◽  
Current Period ◽  
Dynamic Type ◽  
Managerial Implications

Problem definition: We consider an intermediary’s problem of dynamically matching demand and supply of heterogeneous types in a periodic-review fashion. Specifically, there are two disjoint sets of demand and supply types, and a reward for each possible matching of a demand type and a supply type. In each period, demand and supply of various types arrive in random quantities. The platform decides on the optimal matching policy to maximize the expected total discounted rewards, given that unmatched demand and supply may incur waiting or holding costs, and will be fully or partially carried over to the next period. Academic/practical relevance: The problem is crucial to many intermediaries who manage matchings centrally in a sharing economy. Methodology: We formulate the problem as a dynamic program. We explore the structural properties of the optimal policy and propose heuristic policies. Results: We provide sufficient conditions on matching rewards such that the optimal matching policy follows a priority hierarchy among possible matching pairs. We show that those conditions are satisfied by vertically and unidirectionally horizontally differentiated types, for which quality and distance determine priority, respectively. Managerial implications: The priority property simplifies the matching decision within a period, and the trade-off reduces to a choice between matching in the current period and that in the future. Then the optimal matching policy has a match-down-to structure when considering a specific pair of demand and supply types in the priority hierarchy.

A stability analysis on a smoking model with stochastic perturbation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anwar Zeb ◽  
Sunil Kumar ◽  
Almaz Tesfay ◽  
Anil Kumar
Keyword(s):  
Stochastic Model ◽  
Stochastic System ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Reproductive Number ◽  
Content Type ◽  
Model Form ◽  
The World ◽  
Dynamic Stochastic

Purpose The purpose of this paper is to investigate the effects of irregular unsettling on the smoking model in form of the stochastic model as in the deterministic model these effects are neglected for simplicity. Design/methodology/approach In this research, the authors investigate a stochastic smoking system in which the contact rate is perturbed by Lévy noise to control the trend of smoking. First, present the formulation of the stochastic model and study the dynamics of the deterministic model. Then the global positive solution of the stochastic system is discussed. Further, extinction and the persistence of the proposed system are presented on the base of the reproductive number. Findings The authors discuss the dynamics of the deterministic smoking model form and further present the existence and uniqueness of non-negative global solutions for the stochastic system. Some previous study’s mentioned in the Introduction can be improved with the help of obtaining results, graphically present in this manuscript. In this regard, the authors present the sufficient conditions for the extinction of smoking for reproductive number is less than 1. Research limitations/implications In this work, the authors investigated the dynamic stochastic smoking model with non-Gaussian noise. The authors discussed the dynamics of the deterministic smoking model form and further showed for the stochastic system the existence and uniqueness of the non-negative global solution. Some previous study’s mentioned in the Introduction can be improved with the help of obtained results, clearly shown graphically in this manuscript. In this regard, the authors presented the sufficient conditions for the extinction of smoking, if <1, which can help in the control of smoking. Motivated from this research soon, the authors will extent the results to propose new mathematical models for the smoking epidemic in the form of fractional stochastic modeling. Especially, will investigate the effective strategies for control smoking throughout the world. Originality/value This study is helpful in the control of smoking throughout the world.

Pricing and Matching with Forward-Looking Buyers and Sellers

2020 ◽  
Vol 22 (4) ◽  
pp. 717-734 ◽  
Author(s):  
Yiwei Chen ◽  
Ming Hu
Keyword(s):  
Operations Management ◽  
Sharing Economy ◽  
Problem Definition ◽  
Fixed Base ◽  
Managerial Implications ◽  
Dynamic Stochastic ◽  
Bid Prices ◽  
Supply Costs ◽  
Heuristic Policy ◽  
Forward Looking

Problem definition: We study a dynamic market over a finite horizon for a single product or service in which buyers with private valuations and sellers with private supply costs arrive following Poisson processes. A single market-making intermediary decides dynamically on the ask and bid prices that will be posted to buyers and sellers, respectively, and on the matching decisions after buyers and sellers agree to buy and sell. Buyers and sellers can wait strategically for better prices after they arrive. Academic/practical relevance: This problem is motivated by the emerging sharing economy and directly speaks to the core of operations management that is about matching supply with demand. Methodology: The dynamic, stochastic, and game-theoretic nature makes the problem intractable. We employ the mechanism-design methodology to establish a tractable upper bound on the optimal profit, which motivates a simple heuristic policy. Results: Our heuristic policy is: fixed ask and bid prices plus price adjustments as compensation for waiting costs, in conjunction with the greedy matching policy on a first-come-first-served basis. These fixed base prices balance demand and supply in expectation and can be computed efficiently. The waiting-compensated price processes are time-dependent and tend to have opposite trends at the beginning and end of the horizon. Under this heuristic policy, forward-looking buyers and sellers behave myopically. This policy is shown to be asymptotically optimal. Managerial implications: Our results suggest that the intermediary might not lose much optimality by maintaining stable prices unless the underlying market conditions have significantly changed, not to mention that frequent surge pricing may antagonize riders and induce riders and drivers to behave strategically in ways that are hard to account for with traditional pricing models.

Incentivized Actions in Freemium Games

2020 ◽  
Author(s):  
Lifei Sheng ◽  
Christopher Thomas Ryan ◽  
Mahesh Nagarajan ◽  
Yuan Cheng ◽  
Chunyang Tong
Keyword(s):  
Operations Management ◽  
Sufficient Conditions ◽  
Problem Definition ◽  
Data Set ◽  
New Class ◽  
Recent Innovation ◽  
Markov Decision ◽  
Managerial Implications ◽  
Operational Issues ◽  
Data Driven Decisions

Problem definition: Games are the fastest-growing sector of the entertainment industry. Freemium games are the fastest-growing segment within games. The concept behind freemium is to attract large pools of players, many of whom will never spend money on the game. When game publishers cannot earn directly from the pockets of consumers, they employ other revenue-generating content, such as advertising. Players can become irritated by revenue-generating content. A recent innovation is to offer incentives for players to interact with such content, such as clicking an ad or watching a video. These are termed incentivized (incented) actions. We study the optimal deployment of incented actions. Academic/practical relevance: Removing or adding incented actions can essentially be done in real-time. Accordingly, the deployment of incented actions is a tactical, operational question for game designers. Methodology: We model the deployment problem as a Markov decision process (MDP). We study the performance of simple policies, as well as the structure of optimal policies. We use a proprietary data set to calibrate our MDP and derive insights. Results: Cannibalization—the degree to which incented actions distract players from making in-app purchases—is the key parameter for determining how to deploy incented actions. If cannibalization is sufficiently high, it is never optimal to offer incented actions. If cannibalization is sufficiently low, it is always optimal to offer. We find sufficient conditions for the optimality of threshold strategies that offer incented actions to low-engagement users and later remove them once a player is sufficiently engaged. Managerial implications: This research introduces operations management academics to a new class of operational issues in the games industry. Managers in the games industry can gain insights into when incentivized actions can be more or less effective. Game designers can use our MDP model to make data-driven decisions for deploying incented actions.

Complements to heavy traffic limit theorems for the GI/G/1 queue

1972 ◽  
Vol 9 (1) ◽  
pp. 185-191 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Rate Of Convergence ◽  
Limit Theorems ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Sufficient Conditions ◽  
Critical Value ◽  
Traffic Intensity ◽  
Heavy Traffic Limit ◽  
Convergence Of Moments

A bound on the rate of convergence and sufficient conditions for the convergence of moments are obtained for the sequence of waiting times in the GI/G/1 queue when the traffic intensity is at the critical value ρ = 1.

scholarly journals Overbooked and Overlooked: Machine Learning and Racial Bias in Medical Appointment Scheduling

2021 ◽  
Author(s):  
Michele Samorani ◽  
Shannon L. Harris ◽  
Linda Goler Blount ◽  
Haibing Lu ◽  
Michael A. Santoro
Keyword(s):  
Machine Learning ◽  
Racial Disparities ◽  
Real World ◽  
Racial Disparity ◽  
Racial Bias ◽  
State Of The Art ◽  
Waiting Times ◽  
Appointment Scheduling ◽  
Racial Group ◽  
Black Patients

Problem definition: Machine learning is often employed in appointment scheduling to identify the patients with the greatest no-show risk, so as to schedule them into or right after overbooked slots. That scheduling decision maximizes the clinic performance, as measured by a weighted sum of all patients’ waiting time and the provider’s overtime and idle time. However, if a racial group is characterized by a higher no-show risk, then the patients belonging to that racial group will be scheduled into or right after overbooked slots disproportionately to the general population. Academic/Practical Relevance: That scheduling decision is problematic because patients scheduled in those slots tend to have a worse service experience than the other patients, as measured by the time they spend in the waiting room. Thus, the challenge becomes minimizing the schedule cost while avoiding racial disparities. Methodology: Motivated by the real-world case of a large specialty clinic whose black patients have a higher no-show probability than non-black patients, we analytically study racial disparity in this context. Then, we propose new objective functions that minimize both schedule cost and racial disparity and that can be readily adopted by researchers and practitioners. We develop a race-aware objective, which instead of minimizing the waiting times of all patients, minimizes the waiting times of the racial group expected to wait the longest. We also develop race-unaware methodologies that do not consider race explicitly. We validate our findings both on simulated and real-world data. Results: We demonstrate that state-of-the-art scheduling systems cause the black patients in our data set to wait about 30% longer than nonblack patients. Our race-aware methodology achieves both goals of eliminating racial disparity and obtaining a similar schedule cost as that obtained by the state-of-the-art scheduling method, whereas the race-unaware methodologies fail to obtain both efficiency and fairness. Managerial implications: Our work uncovers that the traditional objective of minimizing schedule cost may lead to unintended racial disparities. Both efficiency and fairness can be achieved by adopting a race-aware objective.

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