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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]

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. Keywords: Overbooking, appointment scheduling, patient no-shows, outpatient clinics, 1. Introduction and literature review Between 80 and 90% of U.S. patient care is provided by approximately 200 000 non-psychiatric outpatient clinics (Bodenheimer and Grumback, 2002; United States Census, 2004). [...]

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. Keywords: Open access, appointment scheduling, patient no-shows, outpatient clinic operations, 1. Introduction Healthcare currently consumes 15% of the US Gross Domestic Product and is expected to reach 19% within the coming decade (Centers for Medicare and Office of the Actuary [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jedc.2006.04.005 Byline: Kumar Muthuraman Abstract: We consider the optimal investment - consumption strategy of an investor who can invest in a stock and a bank. We consider the case where proportional transaction costs are present and the objective is to maximize the discounted utility of consumption. We describe an efficient computational scheme that transforms the arising free-boundary problem to a sequence of fixed-boundary problems. We prove the convergence of the scheme and also show that the converged solution is the optimal value function. Finally, we compare and contrast the results obtained by our procedure with certain well-known results and approximations. The proposed scheme also lends itself to optimizing portfolios with multiple risky assets. Author Affiliation: School of Industrial Engineering, Purdue University, 315 N Grant St., West Lafayette, IN 47906, USA Article History: Received 15 March 2005; Accepted 5 April 2006

Abstract 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.

This paper studies the effects of bank credit availability, trade credit and the capital cost on inventory decisions. There are two competing theories on the effect of bank credit lines on investments. While one (Lins et al. 2010) suggests that the primary role played by undrawn credit is to finance new opportunities, the other (Acharya et al. 2014) suggests that undrawn credit serves primarily as a bank monitored liquidity insurance. We attempt to resolve these two conflict views in the context of inventory investments. Using empirical data, we show that the primary role of undrawn credit depends on the individual firm's financial status. When a firm is financially constrained, its inventory decisions are linked to the additional bank credit available to the firm—echoing the insurance nature of bank credits. On the other hand, when a firm is financially healthy, two other inventory financing factors play more significant roles than undrawn credits. For financially healthy firms, inventory investments are significantly negatively related to the financial cost of inventory and positively related to the credit offered by suppliers. Additionally, we study the financial crisis of 2007–2008 as a systematic shock in the credit market to identify the effects of a firm's financial credits. We show that during the financial crisis, the inventory turnover and working capital levels of US retailers were related to the availability of bank credit. However, immediately after the crisis, the evidence demonstrates the positive relationship between firms' inventory level and the trade credit they are offered. [ABSTRACT FROM AUTHOR]

Many parts of the healthcare system remain fragmented and outpatient surgical care is no exception. In this study, we develop a coordinated pre‐operative scheduling approach between Anesthesiology and Internal Medicine to optimize patients’ medical conditions prior to surgery. Coordinating these two services has conceptual appeal because any health issues discovered by the anesthesiologist can often be addressed by a general internist. We design a patient‐centered approach that allows the patient to see both providers, if necessary, on a single visit. This problem is modeled as a two‐station stochastic network, where each station (or clinic) may be staffed by multiple parallel providers and patients see the first available provider. To solve the scheduling problem, we formulate an optimization model to maximize the net benefit of scheduling patients. The objective balances benefits against patient waiting time and clinic overtime costs. We develop a scheduling method with a booking limit to create a balanced network schedule. Due to the complexity of this problem, the solution approach is myopic. In addition, we develop a hybrid method that combines analytical calculation and simulation‐based optimization. We demonstrate our approach on a healthcare network at The University of Texas Health Sciences Center in San Antonio. We compare our method against other policies and show that it yields high quality and robust results. Based on the level of generality of our model and results, the insights gained are not limited to the particular application, but can be applied to other patient‐centered models where scheduling coordination can be used. [ABSTRACT FROM AUTHOR]

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi-product stochastic inventory systems. The distinguishing feature of the multi-product inventory system that we analyze is the existence of correlated demand and joint-replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real-world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class ( s, c, d, S)-policies, and also develop an algorithm to compute good policies in this class, for large multi-product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective. [ABSTRACT FROM AUTHOR]

We consider the problem of finding optimal exercise policies for American options, both under constant and stochastic volatility settings. Rather than work with the usual equations that characterize the price exclusively, we derive and use boundary evolution equations that characterize the evolution of the optimal exercise boundary. Using these boundary evolution equations we show how one can construct very efficient computational methods for pricing American options that avoid common sources of error. First, we detail a methodology for standard static grids and then describe an improvement that defines a grid that evolves dynamically while solving the problem. When integral representations are available, as in the Black-Scholes setting, we also describe a modified integral method that leverages on the representation to solve the boundary evolution equations. Finally we compare runtime and accuracy to other popular numerical methods. The ideas and methodology presented herein can easily be extended to other optimal stopping problems. [ABSTRACT FROM AUTHOR]

We consider the instantaneous control of a diffusion process on the real line. Two types of costs are incurred. The holding cost rate, incurred at all times, is modeled by a convex function. Transactions costs have both fixed and proportional components, making it an impulse control problem. The objective is to minimize the expected infinite horizon discounted cost. The solution to a quasi-variational inequality, which takes the form of a free-boundary problem, can be shown to be the optimal solution. We develop a methodology that converts the free-boundary problem into a sequence of fixed boundary problems. We show that the arising sequence is monotonic and converges. Provided the converged solution is C¹, we show its optimality. We also provide an epsilon-optimality result. Finally, we illustrate a couple of popular applications of this model. [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]

We consider a portfolio optimization problem where the investor's objective is to maximize the long-term expected growth rate, in the presence of proportional transaction costs. This problem belongs to the class of stochastic control problems with singular controls, which are usually solved by computing solutions to related partial differential equations called the free-boundary Hamilton–Jacobi–Bellman (HJB) equations. The dimensionality of the HJB equals the number of stocks in the portfolio. The runtime of existing solution methods grow super-exponentially with dimension, making them unsuitable to compute optimal solutions to portfolio optimization problems with even four stocks. In this work we first present a boundary update procedure that converts the free boundary problem into a sequence of fixed boundary problems. Then by combining simulation with the boundary update procedure, we provide a computational scheme whose runtime, as shown by the numerical tests, scales polynomially in dimension. The results are compared and corroborated against existing methods that scale super-exponentially in dimension. The method presented herein enables the first ever computational solution to free-boundary problems in dimensions greater than three. [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.

We provide a computational study of the problem of optimally allocating wealth among multiple stocks and a bank account, to maximize the infinite horizon discounted utility of consumption. We consider the situation where the transfer of wealth from one asset to another involves transaction costs that are proportional to the amount of wealth transferred. Our model allows for correlation between the price processes, which in turn gives rise to interesting hedging strategies. This results in a stochastic control problem with both drift-rate and singular controls, which can be recast as a free boundary problem in partial differential equations. Adapting the finite element method and using an iterative procedure that converts the free boundary problem into a sequence of fixed boundary problems, we provide an efficient numerical method for solving this problem. We present computational results that describe the impact of volatility, risk aversion of the investor, level of transaction costs, and correlation among the risky assets on the structure of the optimal policy. Finally we suggest and quantify some heuristic approximations. [ABSTRACT FROM AUTHOR]