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ABSTRACTCompanies in the service industry frequently depend on cyclic rosters to schedule their workforce. Such rosters offer a high degree of fairness and long-term predictability of days on and off, but they can hinder an organization’s ability to respond to changing demand. Motivated by the need for improving cyclic planning at an airport ground handling company, this article introduces the idea of flexible cyclic rostering as a means of accommodating limited weekly adjustments of employee schedules. The problem is first formulated as a multi-stage stochastic program; however, this turned out to be computationally intractable. To find solutions, two approximations were developed that involved reductions to a two-stage problem. In the computational study, the flexible and traditional cyclic rosters derived from these approximations are compared and metrics associated with the value of stochastic information are reported. In the testing, we considered seven different perturbations of the demand curve that incorporate the types of uncertainty that are common throughout the service industry. To the best of our knowledge, this is the first analysis of cyclic rostering that applies stochastic optimization. The results show that a reduction in undercoverage of more than 10% on average can be achieved with minimal computational effort. It was also observed that the new approach can overcome most of the limitations of traditional cyclic rostering while still providing most of its advantages.

ABSTRACTAnalysts predict impending shortages in the health care workforce, yet wages for health care workers already account for over half of U.S. health expenditures. It is thus increasingly important to adequately plan to meet health workforce demand at reasonable cost. Using infinite linear programming methodology, we propose an infinite-horizon model for health workforce planning in a large health system for a single worker class; e.g., nurses. We give a series of common-sense conditions that any system of this kind should satisfy and use them to prove the optimality of a natural lookahead policy. We then use real-world data to examine how such policies perform in more complex systems; in particular, our experiments show that a natural extension of the lookahead policy performs well when incorporating stochastic demand growth.

ABSTRACTThis research improves upon the monopsonist vaccine formulary design problem in the literature by incorporating several modeling enhancements and applying different methodologies to efficiently obtain solutions and derive insights. Our multi-objective formulation seeks to minimize the overall price to immunize a cohort of children, maximize the net profit shared among pediatric vaccine manufacturers, and minimize the average number of injections per child among the prescribed formularies. Accounting for Centers for Disease Control and Prevention (CDC) guidelines, we restrict vaccines utilized against a given disease within a given formulary to those produced by a single manufacturer. We also account for a circumstance in which one manufacturer's vaccine has a greater relative efficacy. For the resulting nonconvex mixed-integer nonlinear program, we bound the second and third objectives using optimal formulary designs for current public sector prices and utilize the ϵ -constraint method to solve an instance representative of contemporary immunization schedule requirements. Augmenting our formulation with symmetry reduction constraints to reduce the required computational effort, we identify a set of non-inferior solutions. Of practical interest to the CDC, our model enables the design of a pricing and purchasing policy, creating a sustainable and stable capital investment environment for the provision of pediatric vaccines.

ABSTRACTClosed-form likelihood expansion is an important method for econometric assessment of continuous-time models driven by stochastic differential equations based on discretely sampled data. However, practical applications for sophisticated models usually involve significant computational efforts in calculating high-order expansion terms in order to obtain the desirable level of accuracy. We provide new and efficient algorithms for symbolically implementing the closed-form expansion of the transition density. First, combinatorial analysis leads to an alternative expression of the closed-form formula for assembling expansion terms from that currently available in the literature. Second, as the most challenging task and central building block for constructing the expansions, a novel analytical formula for calculating the conditional expectation of iterated Stratonovich integrals is proposed and a new algorithm for converting the conditional expectation of the multiplication of iterated Stratonovich integrals to a linear combination of conditional expectation of iterated Stratonovich integrals is developed. In addition to a procedure for creating expansions for a nonaffine exponential Ornstein–Uhlenbeck stochastic volatility model, we illustrate the computational performance of our method.

ABSTRACTControlled trials are ubiquitously used to investigate the effect of a medical treatment. The trial outcome can be dependent on a set of patient covariates. Traditional approaches have relied primarily on randomized patient sampling and allocation to treatment and control groups. However, when covariate data for a large set of patients are available and the dependence of the outcome on the covariates is of interest, one can potentially design treatment/control groups that provide better estimates of the covariate-dependent effects of the treatment or provide similarly accurate estimates with a smaller trial cohort size. In this article, we develop an approach that uses optimal Design Of Experiments (DOE) concepts to select the patients for the treatment and control groups upfront, based on their covariate values, in a manner that optimizes the information content in the data. For the optimal treatment and control groups selection, we develop simple guidelines and an optimization algorithm that achieves much more accurate estimates of the covariate-dependent effects of the treatment than random sampling. We demonstrate the advantage of our method through both theoretical and numerical performance comparisons. The advantages are more pronounced when the trial cohort size is smaller, relative to the number of records in the database. Moreover, our approach causes no sampling bias in the estimated effects, for the same reason that DOE principles do not bias estimated effects. Although we focus on medical treatment assessment, the approach has applicability in many analytics application domains where one wants to conduct a controlled experimental study to identify the covariate-dependent effects of a factor (e.g., a marketing sales promotion), based on a sample of study subjects selected optimally from a large database of covariates.

ABSTRACTWe study the problem of capacity planning for long-term care services, which is important not only for the elderly and disabled who cannot adequately care for themselves but also for long-term care providers and health policymakers. Patients with long-term care needs usually have to transfer between different settings such as nursing homes and home- and community-based services. We model patient flows among these settings using an open migration network and formulate the planning of the capacity needed to provide long-term care with a newsvendor-type model. We explore the structural properties of the model and identify the most influential factors, such as the penalty cost for capacity shortage and transition rates between different care settings, in making capacity decisions. With the model developed, capacity decisions for long-term care service networks can be made more systematically with full consideration of different patient flow patterns and budget constraints. The research will be especially useful to long-term care policymakers in a state or nationwide given the worsening shortage of care providers and the escalating long-term care needs resulting from population aging.

ABSTRACTThis article examines the value of demand forecast updates in an assembly system where a single assembler must order components from independent suppliers with different lead times. By staggering each ordering time, the assembler can utilize the latest market information, as it is developed, to form a better forecast over time. The updated forecast can subsequently be used to decide the following procurement decision. The objective of this research is to understand the specific operating environment under which demand forecast updates are most beneficial. Using a uniform demand adjustment model, we are able to derive analytical results that allow us to quantify the impact of demand forecast updates. We show that forecast updates can drastically improve profitability by reducing the mismatch cost caused by demand uncertainty.

ABSTRACTCo-firing biomass is a strategy that leads to reduced greenhouse gas emissions in coal-fired power plants. Incentives such as the Production Tax Credit (PTC) are designed to help power plants overcome the financial challenges faced during the implementation phase. Decision makers at power plants face two big challenges. The first challenge is identifying whether the benefits from incentives such as PTC can overcome the costs associated with co-firing. The second challenge is identifying the extent to which a plant should co-fire in order to maximize profits. We present a novel mathematical model that integrates production and transportation decisions at power plants. Such a model enables decision makers to evaluate the impacts of co-firing on the system performance and the cost of generating renewable electricity. The model presented is a nonlinear mixed integer program that captures the loss in process efficiencies due to using biomass, a product that has lower heating value as compared with coal; the additional investment costs necessary to support biomass co-firing as well as savings due to PTC. In order to solve efficiently real-life instances of this problem we present a Lagrangean relaxation model that provides upper bounds and two linear approximations that provide lower bounds for the problem in hand. We use numerical analysis to evaluate the quality of these bounds. We develop a case study using data from nine states located in the southeast region of the United States. Via numerical experiments we observe that (i) incentives such as PTC do facilitate renewable energy production; (ii) the PTC should not be “one size fits all”; instead, tax credits could be a function of plant capacity or the amount of renewable electricity produced; (iii) there is a need for comprehensive tax credit schemes to encourage renewable electricity production and reduce GHG emissions.