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We study the facility location problem with disruptions where the objective is to choose a set of locations that minimizes the sum of expected servicing and setup costs. Disruptions can affect multiple locations simultaneously and are caused by multiple factors like geography, supply chain characteristics, politics, and ownership. Accounting for the various factors when modeling disruptions is challenging due to a large number of required parameters, the lack of calibration methodologies, the sparsity of disruption data, and the number of scenarios to be considered in the optimization. Because of these reasons, existing models neglect dependence or prespecify the dependence structures. Using partially subordinated Markov chains, we present a comprehensive approach that starts from disruption data, models dependencies, calibrates the disruption model, and optimizes location choices. We construct a metric and a calibration algorithm that learns from the data the strength of dependence, the number of necessary factors (subordinators), and the locations each subordinator affects. We prove that our calibration approach yields consistent estimates of the model parameters. Then, we introduce a variant of the standard approach to the underlying optimization problem, which leverages partially subordinated Markov chains to solve it quickly and precisely. Finally, we demonstrate the efficacy of our approach using twelve different disruption data sets. Our calibrated parameters are robust, and our optimization algorithm performs better than the simulation-based algorithm. The solutions from our model for disruptions have lower costs than those from other disruption models. Our approach allows for better modeling of disruptions from historical data and can be adapted to other problems in logistics, like the hub location, capacitated facility location, and so on., with joint disruptions. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0103. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a sequential scheduling algorithm for consultation periods not divided into slots. Patients call a scheduler and request appointments with a specified provider. The scheduler provides the patient with an appointment time before the call terminates. In making the appointment, the scheduler cannot alter the appointments of previously scheduled patients. Service times are random and each scheduled patient has a probability of “no-showing” for the appointment. Each arriving patient generates a given amount of revenue, and costs are incurred from patient waiting and provider overtime. The scheduling method selects the calling patient's appointment time by minimizing the total expected cost. We prove that total expected cost is a convex function of appointment times and that the expected profit of the schedule is unimodal, which provides a unique stopping criterion for the scheduling algorithm. Computational studies compare this approach with no-show based sequential scheduling methods for out-patient clinics where a predefined slot structure is assumed. The new method yields higher expected profit and less overtime than when service periods are pre-divided into slots. Because slot scheduling is ingrained in healthcare, we use the model to design slot structures that account for no-show and service time variation. [Copyright &y& Elsevier]

A sequential clinical scheduling method for patients with general service time distributions is developed in this paper. Patients call a medical clinic to request an appointment with their physician. During the call, the scheduler assigns the patient to an available slot in the physician's schedule. This is communicated to the patient before the call terminates and, thus, the schedule is constructed sequentially. In practice, there is very limited opportunity to adjust the schedule once the complete set of patients is known. Scheduled patients might not attend, that is, they might “no-show,” and the service times of those attending are random. A myopic scheduling algorithm with an optimal stopping criteria for this problem assuming exponential service times already exists in the literature. This work relaxes this assumption and develops numerical techniques for general service time distributions. A special case in which service times are gamma distributed is considered and it is shown that computation is significantly reduced. Finally, exhaustive experimental results are provided along with discussions that provide insights into the practical aspects of the scheduling approach. [ABSTRACT FROM AUTHOR]

Background: Non-pharmaceutical interventions (NPI) are the first line of defense against pandemic influenza. These interventions dampen virus spread by reducing contact between infected and susceptible persons. Because they curtail essential societal activities, they must be applied judiciously. Optimal control theory is an approach for modeling and balancing competing objectives such as epidemic spread and NPI cost. Methods: We apply optimal control on an epidemiologic compartmental model to develop triggers for NPI implementation. The objective is to minimize expected person-days lost from influenza related deaths and NPI implementations for the model. We perform a multivariate sensitivity analysis based on Latin Hypercube Sampling to study the effects of input parameters on the optimal control policy. Additional studies investigated the effects of departures from the modeling assumptions, including exponential terminal time and linear NPI implementation cost. Results: An optimal policy is derived for the control model using a linear NPI implementation cost. Linear cost leads to a "bang-bang" policy in which NPIs are applied at maximum strength when certain state criteria are met. Multivariate sensitivity analyses are presented which indicate that NPI cost, death rate, and recovery rate are influential in determining the policy structure. Further death rate, basic reproductive number and recovery rate are the most influential in determining the expected cumulative death. When applying the NPI policy, the cumulative deaths under exponential and gamma terminal times are close, which implies that the outcome of applying the "bang-bang" policy is insensitive to the exponential assumption. Quadratic cost leads to a multi-level policy in which NPIs are applied at varying strength levels, again based on certain state criteria. Results indicate that linear cost leads to more costly implementation resulting in fewer deaths. Conclusions: The application of optimal control theory can provide valuable insight to developing effective control strategies for pandemic. Our findings highlight the importance of establishing a sensitive and timely surveillance system for pandemic preparedness. [ABSTRACT FROM AUTHOR]

Abstract: Recent changes in electricity markets have advocated the use of Local Marginal Prices (LMP) for congestion management and pricing. From the perspective of market participants, the LMPs pose a risk since they are not known before a transaction on the grid is made. Financial transmission rights (FTR) are instruments that help market participants hedge this risk and are issuable in two flavors—obligations and options. While pricing obligations are much easier, pricing FTR options pose a significant challenge. In this paper we develop a computational method for pricing FTR options. We also discuss the problem of designing financial instrument sets that assure revenue adequacy for the issuer. We point out the difficulty in assuring revenue adequacy when FTR options are present and propose a scheme for overcoming the difficulty. The proposed pricing method can be used to compute prices of options and obligations in the primary market or as a reliable pricing tool to compute option prices in the secondary market. Finally using a test network we present and discuss numerical results. [Copyright &y& Elsevier]

In this paper a stochastic overbooking model is formulated and an appointment scheduling policy is developed for outpatient clinics. The schedule is constructed for a single service period partitioned into time slots of equal length. A clinic scheduler assigns patients to slots through a sequential patient call-in process where the scheduler must provide each calling patient with an appointment time before the patient's call terminates. Once an appointment is added to the schedule, it cannot be changed. Each calling patient has a no-show probability, and overbooking is used to compensate for patient no-shows. The scheduling objective captures patient waiting time, staff overtime and patient revenue. Conditions under which the objective evolution is unimodal are derived and the behavior of the scheduling policy is investigated under a variety of conditions. Practical observations on the performance of the policy are presented. [ABSTRACT FROM AUTHOR]

Chapter 6 of the book "Foundations and Trends in Stochastic Systems" is presented. It demonstrates the possibility to overcome the challenges in higher dimensions, specially if one is willing to lower aspirations slightly. It focuses on a study of a variant of the portfolio optimization problems. It likewise discusses an appropriate policy space approximation that will facilitate efficient scaling and shows how a simulation based a variant of the boundary update procedure can be constructed.

Chapter 5 of the book "Foundations and Trends in Stochastic Systems" is presented. It recommends the use of the Finite Element Method (FEM) in resolving three issues found while solving PDE. It introduces one effective method of solving all the problems related to FEM. It likewise explains meshing, which can be accomplished easily using one of the many mesh generations routines that are widely available.

Chapter 4 of the book "Foundations and Trends in Stochastic Systems" is presented. It focuses on a problem where only the moving-boundary method has yielded results and is considered to be an excellent illustration of how to handle implicit boundary conditions. It demonstrates the impact of correlation between the two stock returns on the structure of optimal transaction policies. It likewise considers a variant of the portfolio optimization problems.

Chapter 3 of the book "Foundations and Trends in Stochastic Systems" is presented. It discusses the concept of option pricing. It explains how pricing the American call is no different from pricing the American put. It shares one effective method in which the price of an American call can be computed using American put pricing methods. It also cites a control problem where the boundary is a function.

Chapter 2 of the book "Foundations and Trends in Stochastic Systems" is presented. It considers the problem of computing the optical investment and consumption strategy of an investor who trades a single risky asset. It discusses several specific means for this investor to maximize its expected discounted utility of consumption. It explains the Merton's policy on transaction without costs, which states that an investor can make an infinite number of transactions in any finite time interval.

The article discusses various reports published within the issue, including one which explains various singular stochastic control problems and another which provides a simple illustration using a one-dimensional singular control problem.