Billions of dollars are being allocated for influenza pandemic preparedness, and vaccination is a primary weapon for fighting influenza outbreaks. The influenza vaccine supply chain has characteristics that resemble the news vendor problem, but possesses several characteristics that distinguish it from typical supply chains. Differences include a nonlinear value of sales (caused by the nonlinear health benefits of vaccination due to infection dynamics) and vaccine production yield issues. We show that production risks, taken currently by the vaccine manufacturer, lead to insufficient supply of vaccine. Unfortunately, several supply contracts that coordinate buyer (governmental public health service) and supplier (vaccine manufacturer) incentives in industrial supply chains can not 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 gurantees sufficient supply of vaccine. Influenza is an acute respiratory illness that spreads rapidly in seasonal epidemics. Globally, annual influenza outbreaks result in 250,000 to 500,000 deaths. The World Health Organization reports that costs in terms of health care, lost days of work and education, and social disruption have been estimated to vary between $1 million and $6 million per 100,000 inhabitants yearly in industrialized countries. A moderate, new influenza pandemic could increase those losses by an order of magnitude (WHO, 2005).This paper provides background about influenza and vaccination, a key tool for controlling influenza outbreaks, then highlights some operational challenges for delivering those vaccines. One challenge is the design of contracts to coordinate the incentives of actors in a supply chain that crosses the boundary between the public sector (health care service systems) and private sector (vaccine manufacturers).Some experts suggest the U.S. government should promise to purchase a fixed amount of flu vaccine-despite the cost and the likelihood that some of the money would end up being wasted. Canada, for instance, has contracts with vaccine makers to cover most of its population. …That takes much of the risk out of the company's business, but still lets it manufacture additional doses for the private market… (WSJ, Wysocki and Lueck, 2006) I recently met with leaders of the vaccine industry. They assured me that they will work with the federal government to expand the vaccine industry, so that our country is better prepared for any pandemic. … I'm requesting a total of $7.1 billion in emergency funding from the United States Congress…(George W. Bush, 2005) We then present a model of a government's decision of purchase quantities of vaccines, which balances the public health benefits of vaccination and the cost of procuring and administering those vaccines, and a manufacturer's choice of production volume. We characterize the optimal decisions of each in both selfish and system...

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Healthcare reimbursements in the US have been traditionally based upon a fee-for-service (FFS) scheme, providing incentives for high volume of care, rather than efficient care. The new healthcare legislation tests new payment models that remove such incentives, such as the bundled payment (BP) system. We consider a population of patients (beneficiaries). The provider may reject patients based on the patient's cost profile, and selects the treatment intensity based on a risk-averse utility function. Treatment may result in success or failure, where failure means that unforeseen complications require further care. Our interest is in analyzing the effect of different payment schemes on outcomes such as the presence and extent of patient selection, the treatment intensity, the provider's utility and financial risk, and the total system payoff. Our results confirm that FFS provides incentives for excessive treatment intensity and results in suboptimal system payoff. We show that BP could lead to suboptimal patient selection and treatment levels that may be lower or higher than desirable for the system, with a high level of financial risk for the provider. We also find that the performance of BP is extremely sensitive to the bundled payment value and to the provider's risk aversion.The performance of both BP and FFS degrades when the provider becomes more risk averse. We design two payment systems, hybrid payment and stop-loss mechanisms, that alleviate the shortcomings of FFS and BP and may induce system optimum decisions in a complementary manner.

Influenza vaccination decisions in one country can influence the size of an outbreak in other countries due to interdependent risks from infectious disease transmission. This paper examines the inefficiency in the allocation of influenza vaccines that is due to interdependent risk of infection across borders and proposes a contractual mechanism to reduce such inefficiencies. The proposed contract is based on an epidemic model that accounts for intranational transmission and that from a source country where the dominant strain emerges. The contract reduces the overall financial burden of infection globally and improves the total number infected by seasonal influenza outbreaks. This is consistent with recent recommendations to improve pandemic preparedness. Numerical experiments demonstrate that the benefits of the contract can prevent millions of influenza cases and save tens of millions of dollars, and that the benefits are even greater when cross-border transmission is higher, even if cross-border transmission parameters have moderate estimation errors. This paper was accepted by Martin Lariviere, operations management.

We propose and analyze robust optimization models of an inventory management problem, where cumulative purchase, inventory, and shortage costs over n periods are minimized for correlated nonidentically distributed demand. We assume that the means and covariance matrix of stochastic demand are known; the distributions are not needed. We derive closed-form ordering quantities for both symmetric and asymmetric uncertainty sets, under capacitated inventory constraints, in both static and dynamic settings. The behaviors of our robust strategies differ qualitatively depending on the symmetry of the uncertainty set. For instance, considering our simplest static problem, (1) if the uncertainty set is symmetric, then there is positive ordering in all periods, whereas (2) if the set is asymmetric, then there is a set of periods in the middle of the planning horizon with zero orders. We also link the symmetry of the uncertainty set to the symmetry of the demand distribution. Finally, we present encouraging computational results where our solution compares favorably to previously studied, more complex robust solutions.

One of the most important concerns for managing public health is the prevention of infectious diseases. Although vaccines provide the most effective means for preventing infectious diseases, there are two main reasons why it is often difficult to reach a socially optimal level of vaccine coverage: (i) the emergence of operational issues (such as yield uncertainty) on the supply side, and (ii) the existence of negative network effects on the consumption side. In particular, uncertainties about production yield and vaccine imperfections often make manufacturing some vaccines a risky process and may lead the manufacturer to produce below the socially optimal level. At the same time, negative network effects provide incentives to potential consumers to free ride off the immunity of the vaccinated population. In this research, we consider how a central policy-maker can induce a socially optimal vaccine coverage through the use of incentives to both consumers and the vaccine manufacturer. We consider a monopoly market for an imperfect vaccine; we show that a fixed two-part subsidy is unable to coordinate the market, but derive a two-part menu of subsidies that leads to a socially efficient level of coverage.

Prevention of infectious diseases is an important concern for managing public health. Although vaccines are the most effective means for preventing infectious diseases, the existence of a negative network externality often makes it difficult for vaccine coverage to reach a level that is socially optimal. In this research, we consider how a subsidy program can induce a socially optimal vaccine coverage. We consider an oligopoly market with identical vaccine producers and derive a subsidy that leads to a socially efficient level of coverage. We also derive a tax-subsidy combination that is revenue neutral, but achieves the same effect. Overall, our results provide useful insights for governments and policy makers with respect to an important issue related to public health.

Gray markets, also known as parallel imports, have created fierce competition for manufacturers in many industries. We analyze the impact of parallel importation on a price‐setting manufacturer that serves two markets with uncertain demand, and characterize her policy against parallel importation. We show that ignoring demand uncertainty can take a significant toll on the manufacturer's profit, highlighting the value of making price and quantity decisions jointly. We find that adjusting prices is more effective in controlling gray market activity than reducing product availability, and that parallel importation forces the manufacturer to reduce her price gap while demand uncertainty forces her to lower prices. Furthermore, we explore the impact of market conditions (such as market base, price sensitivity, and demand uncertainty) and product characteristics (“fashion” vs. “commodity”) on the manufacturer's policy towards parallel importation. We also provide managerial insights about the value of strategic decision‐making by comparing the optimal policy to the uniform pricing policy that has been adopted by some companies to eliminate gray markets entirely. The comparison indicates that the value of making price and quantity decisions strategically is highest for moderately different market conditions and non‐commodity products.