Knowledge that Transforms

Annual influenza outbreaks incur great expenses in both human and monetary terms, and billions of dollars are being allocated for influenza pandemic preparedness in an attempt to avert even greater potential losses. Vaccination is a primary weapon for fighting influenza outbreaks. The influenza vaccine supply chain has characteristics that resemble the newsvendor problem but possesses several characteristics that distinguish it from many other supply chains. Differences include a nonlinear value of sales (caused by the nonlinear health benefits of vaccination that are due to infection dynamics) and vaccine production yield issues. We show that production risks, taken currently by the vaccine manufacturer, lead to an insufficient supply of vaccine. Several supply contracts that coordinate buyer (governmental public health service) and supplier (vaccine manufacturer) incentives in many other industrial supply chains cannot fully coordinate the influenza vaccine supply chain. We design a variant of the cost-sharing contract and show that it provides incentives to both parties so that the supply chain achieves global optimization and hence improves the supply of vaccines.

We present a method to dynamically schedule patients with different priorities to a diagnostic facility in a public health-care setting. Rather than maximizing revenue, the challenge facing the resource manager is to dynamically allocate available capacity to incoming demand to achieve wait-time targets in a cost-effective manner. We model the scheduling process as a Markov decision process. Because the state space is too large for a direct solution, we solve the equivalent linear program through approximate dynamic programming. For a broad range of cost parameter values, we present analytical results that give the form of the optimal linear value function approximation and the resulting policy. We investigate the practical implications and the quality of the policy through simulation.

Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios. Yet, existing theoretical analysis of the optimal behavior of a trader subject to VaR limits has produced a negative view of VaR as a risk-control tool. In particular, VaR limits have been found to induce increased risk exposure in some states and an increased probability of extreme losses. However, these conclusions are based on models that are either static or dynamically inconsistent. In this paper, we formulate a dynamically consistent model of optimal portfolio choice subject to VaR limits and show that the concerns expressed in earlier papers do not apply if, consistently with common practice, the VaR limit is reevaluated dynamically. In particular, we find that the optimal risk exposure of a trader subject to a VaR limit is always lower than that of an unconstrained trader and that the probability of extreme losses is also lower. We also consider risk limits formulated in terms of tail conditional expectation (TCE), a coherent risk measure often advocated as an alternative to VaR, and show that in our dynamic setting it is always possible to transform a TCE limit into an equivalent VaR limit, and conversely.

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(ϵ) is reduced from O(ϵ−3) to O(ϵ−2 (log ϵ)2). The analysis is supported by numerical results showing significant computational savings.

A system consisting of two buffers, each with independent fluid sources, is considered in this paper. Due to ease of implementation, the output capacities for the two buffers depend on the workload of only one of the buffers that is measured. A threshold-based policy is considered to dynamically assign output capacities for both buffers. Marginal workload distributions for the two buffers need to be evaluated for this policy. The key contribution of this paper is the performance analysis to derive the workload distribution in the two buffers. In addition, the paper also provides some guidelines to choose the output capacities for the two buffers as well as a mathematical program to determine an optimal threshold to dynamically switch between output capacities. Further, various applications of such systems to computer-communication networks are discussed.

A DEA-based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one-sided inefficiency deviations as well as two-sided random noise. Conditions are identified under which a two-stage procedure consisting of DEA followed by ordinary least squares (OLS) regression analysis yields consistent estimators of the impact of contextual variables. Conditions are also identified under which DEA in the first stage followed by maximum likelihood estimation (MLE) in the second stage yields consistent estimators of the impact of contextual variables. This requires the contextual variables to be independent of the input variables, but the contextual variables may be correlated with each other. Monte Carlo simulations are carried out to compare the performance of our two-stage approach with one-stage and two-stage parametric approaches. Simulation results indicate that DEA-based procedures with OLS, maximum likelihood, or even Tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity. Simulation results also indicate that DEA-based procedures perform better than parametric methods in the estimation of individual decision-making unit (DMU) productivity. Overall, the results establish DEA as a nonparametric stochastic frontier estimation (SFE) methodology.

We consider the notoriously difficult discrete-time inventory model with stochastic demands, a constant lead time, and lost sales. We show that the effective state space is a relatively manageable compact set. Then, we test various plausible heuristics. We find that several perform reasonably well, although none is perfect. However, the standard base-stock policy (a direct analogue of the optimal policy for a backlog system) performs badly. We also show that the optimal cost is increasing in the lead time.

Many primary care offices and other medical practices regularly experience long backlogs for appointments. These backlogs are exacerbated by a significant level of last-minute cancellations or “no-shows,” which have the effect of wasting capacity. In this paper, we conceptualize such an appointment system as a single-server queueing system in which customers who are about to enter service have a state-dependent probability of not being served and may rejoin the queue. We derive stationary distributions of the queue size, assuming both deterministic as well as exponential service times, and compare the performance metrics to the results of a simulation of the appointment system. Our results demonstrate the usefulness of the queueing models in providing guidance on identifying patient panel sizes for medical practices that are trying to implement a policy of “advanced access.”

We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integrodifferential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time discretization schemes, where the differential (diffusion) term is treated implicitly, while the integral (jump) term is treated explicitly. In particular, the popular IMEX Euler scheme is first-order accurate in time. Second-order accuracy in time can be achieved by using the IMEX midpoint scheme. In contrast to the above approaches, we propose a new high-order time discretization scheme for the PIDE based on the extrapolation approach to the solution of ODEs that also treats the diffusion term implicitly and the jump term explicitly. The scheme is simple to implement, can be added to any PIDE solver based on the IMEX Euler scheme, and is remarkably fast and accurate. We demonstrate our approach on the examples of Merton's and Kou's jump-diffusion models, the diffusion-extended variance gamma model, as well as the two-dimensional Duffie-Pan-Singleton model with correlated and contemporaneous jumps in the stock price and its volatility. By way of example, pricing a one-year double-barrier option in Kou's jump-diffusion model, our scheme attains accuracy of 10−5 in 72 time steps (in 0.05 seconds). In contrast, it takes the first-order IMEX Euler scheme more than 1.3 million time steps (in 873 seconds) and the second-order IMEX midpoint scheme 768 time steps (in 0.49 seconds) to attain the same accuracy. Our scheme is also well suited for Bermudan options. Combining simplicity of implementation and remarkable gains in computational efficiency, we expect this method to be very attractive to financial engineering modelers.