The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct "BL"-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new "BL"-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views.

Breast cancer is the most common non-skin cancer affecting women in the United States, where every year more than 20 million mammograms are performed. Breast biopsy is commonly performed on the suspicious findings on mammograms to confirm the presence of cancer. Currently, 700,000 biopsies are performed annually in the U.S.; 55%-85% of these biopsies ultimately are found to be benign breast lesions, resulting in unnecessary treatments, patient anxiety, and expenditures. This paper addresses the decision problem faced by radiologists: When should a woman be sent for biopsy based on her mammographic features and demographic factors? This problem is formulated as a finite-horizon discrete-time Markov decision process. The optimal policy of our model shows that the decision to biopsy should take the age of patient into account; particularly, an older patient's risk threshold for biopsy should be higher than that of a younger patient. When applied to the clinical data, our model outperforms radiologists in the biopsy decision-making problem. This study also derives structural properties of the model, including sufficiency conditions that ensure the existence of a control-limit type policy and nondecreasing control-limits with age.

This paper considers the impact of congestion on the spatial distribution of customer utilization of service facilities in a stochastic-dynamic environment. Previous research has assumed that the rate of demand for service is independent of the attributes of the facilities. We consider the more general case in which facility utilization is determined both by individual facility choice (based on the stochastic disaggregate choice mechanism) and by the rate of demand for service. We develop generalized results for proving that equilibria exist and describe sufficient conditions for the uniqueness and global stability of these equilibria. These conditions depend upon the elasticity of demand with respect to the level of congestion at the facilities, and on whether customers are congestion-averse or are congestion-loving. Finally, we examine special cases when these conditions are satisfied.

We consider a time-dependent stopping problem and its application to the decision-making process associated with transplanting a live organ. "Offers" (e.g., kidneys for transplant) become available from time to time. The values of the offers constitute a sequence of independent identically distributed positive random variables. When an offer arrives, a decision is made whether to accept it. If it is accepted, the process terminates. Otherwise, the offer is lost and the process continues until the next arrival, or until a moment when the process terminates by itself. Self-termination depends on an underlying lifetime distribution (which in the application corresponds to that of the candidate for a transplant). When the underlying process has an increasing failure rate, and the arrivals form a renewal process, we show that the control-limit type policy that maximizes the expected reward is a nonincreasing function of time. For non-homogeneous Poisson arrivals, we derive a first-order differential equation for the control-limit function. This equation is explicitly solved for the case of discrete-valued offers, homogeneous Poisson arrivals, and Gamma distributed lifetime. We use the solution to analyze a detailed numerical example based on actual kidney transplant data.

This paper considers the multidimensional weighted minimax location problem, namely, finding a facility location that minimizes the maximal weighted distance to n points. General distance norms are used. An epsilon-approximate solution is obtained by applying a variant of the Russian method for the solution of Linear Programming. The algorithm has a time complexity of O(n log epsilon) for fixed dimensionality k. Computational results are presented.

After acute care services are no longer required, a patient in an acute care hospital often must remain there while he or she awaits the provision of extended care services by a nursing home, through social support services, or by a home health care service. This waiting period is often referred to as "administrative days" because the time is spent in the acute facility not for medical reasons, but rather for administrative reasons. In this paper we use a queueing-analytic approach to describe the process by which patients await placement. We model the situation using a state-dependent placement rate for patients backed up in the acute care facility. We compare our model results with data collected from a convenience sample of 7 hospitals in New York State. We conclude with a discussion of the policy implications of our models.

Antimicrobial resistance is a significant public health threat. In the U.S. alone, 2 million people are infected and 23,000 die each year from antibiotic resistant bacterial infections. In many cases, infections are resistant to all but a few remaining drugs. We examine the case where a single drug remains and solve for the optimal treatment policy for an SIS infectious disease model incorporating the effects of drug resistance. The problem is formulated as an optimal control problem with two continuous state variables, the disease prevalence and drug's "quality" (the fraction of infections that are drug-susceptible). The decision maker's objective is to minimize the discounted cost of the disease to society over an infinite horizon. We provide a new generalizable solution approach that allows us to thoroughly characterize the optimal treatment policy analytically. We prove that the optimal treatment policy is a bang-bang policy with a single switching time. The action/inaction regions can be described by a single boundary that is strictly increasing when viewed as a function of drug quality, indicating that when the disease transmission rate is constant, the policy of withholding treatment to preserve the drug for a potentially more serious future outbreak is not optimal. We show that the optimal value function and/or its derivatives are neither nor Lipschitz continuous suggesting that numerical approaches to this family of dynamic infectious disease models may not be computationally stable. Furthermore, we demonstrate that relaxing the standard assumption of constant disease transmission rate can fundamentally change the shape of the action region, add a singular arc to the optimal control, and make preserving the drug for a serious outbreak optimal. In addition, we apply our framework to the case of antibiotic resistant gonorrhea.

The classification of short-term hospitals into homogeneous groups has become an integral part of many systems designed to abate continuing cost inflation in the hospital industry. This paper describes one approach which was developed to identify homogeneous groups of short-term hospitals. The approach, based on hierarchical cluster analysis, defines an objective measure (called expected distinctiveness) to evaluate any group of hospitals identified by a hierarchical grouping structure or dendrogram. Using this measure, an efficient algorithm is developed which finds the hospital partition from the identified groups which maximizes total expected distinctiveness. A numerical example illustrates the application and extensions.

A general structural equation model for representing consumer response to innovation is derived and illustrated. The approach both complements and extends an earlier model proposed by Hauser and Urban. Among other benefits, the model is able to take measurement error into account explicitly, to estimate the intercorrelation among exogenous factors if these exist, to yield a unique solution in a statistical sense, and to test complex hypotheses (e.g., systems of relations, simultaneity, feedback) associated with the measurement of consumer responses and their impact on actual choice behavior. In addition, the procedures permit one to model environmental and managerially controllable stimuli as they constrain and influence consumer choice. Limitations of the procedures are discussed and related to existing approaches. Included in the discussion is a development of four generic response models designed to provide a framework for modeling how consumers behave and how managers might better approach the design of products, persuasive appeals, and other controllable factors in the marketing mix.

In this paper we present two iterative methods for solving a model to evaluate busy probabilities for Emergency Medical Service (EMS) vehicles. The model considers location dependent service times and is an alternative to the mean service calibration method; a procedure, used with the Hypercube Model, to accommodate travel times and location-dependent service times. We use monotonicity arguments to prove that one iterative method always converges to a solution. A large computational experiment suggests that both methods work satisfactorily in EMS systems with low ambulance busy probabilities and the method that always converges to a solution performs significantly better in EMS systems with high busy probabilities.

One measure of the effectiveness of institutional trauma and burn management based on collected patient data involves the computation of a standard normal Z statistic. A potential weakness of the measure arises from incomplete patient data. In this paper, we apply methods of fractional programming and global optimization to efficiently calculate bounds on the computed effectiveness of an institution. The measure of effectiveness (i.e., the trauma outcome function) is briefly described, the optimization problems associated with its upper and lower bounds are defined and characterized, and appropriate solution procedures are developed. We solve an example problem to illustrate the method.

This paper describes the development of a model for making project funding decisions at The National Cancer Institute (NCI). The American Stop Smoking Intervention Study (ASSIST) is a multiple-year, multiple-site demonstration project, aimed at reducing smoking prevalence. The initial request for ASSIST proposals was answered by about twice as many states as could be funded. Scientific peer review of the proposals was the primary criterion used for funding decisions. However, a modified Delphi process made explicit several criteria of secondary importance. A structured questionnaire identified the relative importance of these secondary criteria, some of which we incorporated into a composite preference function. We modeled the proposal funding decision as a zero-one program, and adjusted the preference function and available budget parametrically to generate many suitable outcomes. The actual funding decision, identified by our model, offers significant advantages over manually generated solutions found by experts at NCI.

A co-epidemic arises when the spread of one infectious disease stimulates the spread of another infectious disease. Recently, this has happened with human immunodeficiency virus (HIV) and tuberculosis (TB). We develop two variants of a co-epidemic model of two diseases. We calculate the basic reproduction number (R(0)), the disease-free equilibrium, and the quasi-disease-free equilibria, which we define as the existence of one disease along with the complete eradication of the other disease, and the co-infection equilibria for specific conditions. We determine stability criteria for the disease-free and quasi-disease-free equilibria. We present an illustrative numerical analysis of the HIV-TB co-epidemics in India that we use to explore the effects of hypothetical prevention and treatment scenarios. Our numerical analysis demonstrates that exclusively treating HIV or TB may reduce the targeted epidemic, but can subsequently exacerbate the other epidemic. Our analyses suggest that coordinated treatment efforts that include highly active antiretroviral therapy for HIV, latent TB prophylaxis, and active TB treatment may be necessary to slow the HIV-TB co-epidemic. However, treatment alone may not be sufficient to eradicate both diseases. Increased disease prevention efforts (for example, those that promote condom use) may also be needed to extinguish this co-epidemic. Our simple model of two synergistic infectious disease epidemics illustrates the importance of including the effects of each disease on the transmission and progression of the other disease.

The federal Medicare regulations reimburse hospitals on a pro rata share of the hospital's cost. Hence, to meet its financial requirements, a hospital is forced to shift more of the financial burdens onto its private patients. This procedure has contributed to double digit inflation in hospital prices and to proposed federal regulation to control the rate of increase in hospital revenues. In this regulatory environment, we develop nonlinear programming pricing and cost allocation models to aid hospital administrators in meeting their profit maximizing and profit satisfying goals. The model enables administrators to explore tactical issues such as: (i) studying the relationship between a voluntary or legislated cap on a hospital's total revenues and the hospital's profitability, (ii) identifying those departments within the hospital that are the most attractive candidates for cost reduction or cost containment efforts, and (iii) isolating those services that should be singled out by the hospital manager for renegotiation of the prospective or "customary and reasonable" cap. Finally the modeling approach is helpful in explaining the departmental cross subsidies observed in practice, and can be of aid to federal administrators in assessing the impacts of proposed changes in the Medicare reimbursement formula.

A work force includes workers of m types. The worker categories are ordered, with type-1 workers the most highly qualified, type-2 the next, and so on. If the need arises, a type-k worker is able to substitute for a worker of any type j greater than k (k = 1, ..., m - 1). For 7-day-a-week operation, daily requirements are for at least Dk workers of type-k or better, of which at least dk must be precisely type-k. Formulas are given to find the smallest number and most economical mix of workers, assuming that each worker must have 2 off-days per week and a given fraction of weekends off. Algorithms are presented which generate a feasible schedule, and provide work stretches between 2 and 5 days, and consecutive weekdays off when on duty for 2 weekends in a row, without additional staff.

This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.

The Confidence Profile Method is a Bayesian method for adjusting and combining pieces of evidence to estimate parameters, such as the effect of health technologies on health outcomes. The information in each piece of evidence is captured in a likelihood function that gives the likelihood of the observed results of the evidence as a function of possible values of the parameter. A posterior distribution is calculated from Bayes formula as the product of the likelihood function and a prior distribution. Multiple pieces of evidence are incorporated by successive applications of Bayes' formula. Pieces of evidence are adjusted for biases to internal or external validity by modeling the biases and deriving "adjusted" likelihood functions that incorporate the models. Likelihood functions have been derived for one-, two- and multi-arm prospective studies; 2 x 2, 2 x n and matched case-control studies, and cross-sectional studies. Biases that can be incorporated in likelihood functions include crossover in controlled trials, error in measurement outcomes, patient selection biases, differences in technologies, and differences in length of follow-up. Effect measures include differences of rates, ratios of rates, and odds ratios. The elements of the method are illustrated with an analysis of the effect of a thrombolytic agent on the difference in probability of 1-year survival after a heart attack.

We introduce a Markov chain model to represent a patient's path in terms of the number and type of infections s/he may have acquired during a hospitalization period. The model allows for categories of patient diagnosis, surgery, the four major types of nosocomial (hospital-acquired) infections, and discharge or death. Data from a national medical records survey including 58,647 patients enable us to estimate transition probabilities and, ultimately, perform statistical tests of fit, including a validation test. Novel parameterizations (functions of the transition matrix) are introduced to answer research questions on time-dependent infection rates, time to discharge or death as a function of patient diagnostic groups and conditional infection rates reflecting intervening variables (e.g., surgery).

In this paper, a simplified model describing the stochastic process underlying the etiology of contagious and noncontagious diseases with mass screening is developed. Typical examples might include screening of tuberculosis in urban ghetto areas, venereal diseases in the sexually active, or AIDS in high risk population groups. The model is addressed to diseases which have zero or negligible latent periods. In the model, it is assumed that the reliabilities of the screening tests are constant, and independent of how long the population unit has the disease. Both tests with perfect and imperfect reliabilities are considered. It is shown that most of the results of a 1978 study by W.P. Pierskalla and J.A. Voelker for noncontagious diseases can be generalized for contagious diseases. A mathematical program for computing the optimal test choice and screening periods is presented. It is shown that the optimal screening schedule is equally spaced for tests with perfect reliability. Other properties relating to the managerial problems of screening frequencies, test selection, and resource allocation are also presented.

Models estimating demand and need for emergency transportation services are developed. These models can provide reliable estimates which can be used for planning purposes, by complementing and/or substituting for historical data. The model estimating demand requires only four independent variables: population in the area, employment in the area, and two indicators of socioeconomic status which can be obtained from census data. The model can be used to estimate demand according to 4 operational categories and 11 clinical categories. The parameters of the model are calibrated with 1979 data from 82 ambulance services covering over 200 minor civil divisions in Southwestern Pennsylvania. This model was tested with data from another 55 minor civil divisions, also in Southwestern Pennsylvania, and it provided good estimates to total demand. The model to estimate need evolves from the demand model. It enables planners to estimate unmet need occurring in the region. The effect of emergency transportation service (ETS) provider characteristics on demand was also investigated. Statistical tests show that, for purposes of forecasting demand, when the sociodemographic factors are taken into account, provider characteristics are not significant.

The goal of a traditional Markov decision process (MDP) is to maximize expected cumulative reward over a defined horizon (possibly infinite). In many applications, however, a decision maker may be interested in optimizing a specific quantile of the cumulative reward instead of its expectation. In this paper we consider the problem of optimizing the quantiles of the cumulative rewards of a Markov decision process (MDP), which we refer to as a quantile Markov decision process (QMDP). We provide analytical results characterizing the optimal QMDP value function and present a dynamic programming-based algorithm to solve for the optimal policy. The algorithm also extends to the MDP problem with a conditional value-at-risk (CVaR) objective. We illustrate the practical relevance of our model by evaluating it on an HIV treatment initiation problem, where patients aim to balance the potential benefits and risks of the treatment.