Elodie Adida

A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders

In this paper, we present a robust optimization formulation for dealing with demand uncertainty in a dynamic pricing and inventory control problem for a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting. We introduce a demand-based fluid model where the demand is a linear function of the price, the inventory cost is linear, the production cost is an increasing strictly convex function of the production rate and all coefficients are time-dependent. A key part of the model is that no backorders are allowed. We show that the robust formulation is of the same order of complexity as the nominal problem and demonstrate how to adapt the nominal (deterministic) solution algorithm to the robust problem.

Supply Chain Competition with Multiple Manufacturers and Retailers

We study competition in a supply chain where multiple manufacturers compete in quantities to supply a set of products to multiple risk-averse retailers who compete in quantities to satisfy the uncertain consumer demand. For the symmetric supply chain, we give closed-form expressions for the unique equilibrium. We find that, provided there is a sufficiently large number of manufacturers and retailers, the supply chain efficiency (the ratio of the aggregate utility in the decentralized and centralized chains) can be raised to 1 by inducing the right degree of retailer differentiation. Also, risk aversion results in triple marginalization: retailers require a strictly positive margin to distribute even when they are perfectly competitive, because otherwise they are unwilling to undertake the risk associated with the uncertainty in demand. For the asymmetric supply chain, we show how numerical optimization can be used to compute the equilibria, and we find that the supply chain efficiency may drop sharply with the asymmetry of either manufacturers or retailers. We also find that the introduction of asymmetric product assortment reduces the degree of competition among retailers and thus has an effect similar to that of reducing the number of retailers. We show that, unlike in the symmetric chain, the asymmetric chain efficiency depends on product differentiation and risk aversion because of the interaction between these features and the asymmetry of manufacturers and retailers.

Dynamic Pricing and Inventory Control: Uncertainty and Competition

In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition (in particular a duopoly setting) together with the presence of demand uncertainty. We consider a dynamic setting where multiple products share production capacity. We introduce a demand-based fluid model where the demand is a linear function of the price of the supplier and of her competitor, the inventory and production costs are quadratic, and all coefficients are time dependent. A key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitors strategy. First, we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a Nash equilibrium in continuous time. We then discuss issues of uniqueness and address how to compute a particular Nash equilibrium, i.e., the normalized Nash equilibrium.

Consignment contracts with retail competition

Consignment contracts have been widely employed in many industries. Under such contracts, items are sold at a retailers but the supplier retains the full ownership of the inventory until purchased by consumers; the supplier collects payment from the retailer based on actual units sold. We investigate how competition among retailers influences the supply chain decisions and profits under different consignment arrangements, namely a consignment price contract and a consignment contract with revenue share. First, we investigate how these two consignment contracts and a price only contract compare from the perspective of each supply chain partner. We find that the retailers benefit more from a consignment price contract than from a consignment contract with revenue share or a price only contract, regardless of the level of retailer differentiation. The suppliers most beneficial contact, however, critically depends upon the level of retailer differentiation: a consignment contract with revenue share is preferable for the supplier if retailer differentiation is strong; otherwise a consignment price contract is preferable. Second, we study how retailer differentiation affects the profits of all supply chain partners. We find that less retailer differentiation improves the suppliers profit for both types of consignment contract. Moreover, less retailer differentiation improves profits of the retailers in a consignment price contract, but not necessarily in a consignment contract with revenue share.

Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study

In this paper, we consider a variety of models for dealing with demand uncertainty for a joint dynamic pricing and inventory control problem in a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting, where demand depends linearly on the price. Our goal is to address demand uncertainty using various robust and stochastic optimization approaches. For each of these approaches, we first introduce closed-loop formulations (adjustable robust and dynamic programming), where decisions for a given time period are made at the beginning of the time period, and uncertainty unfolds as time evolves. We then describe models in an open-loop setting, where decisions for the entire time horizon must be made at time zero. We conclude that the affine adjustable robust approach performs well (when compared to the other approaches such as dynamic programming, stochastic programming and robust open loop approaches) in terms of realized profits and protection against constraint violation while at the same time it is computationally tractable. Furthermore, we compare the complexity of these models and discuss some insights on a numerical example.

Operational issues and network effects in vaccine markets

Abstract 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.

Vaccine market coordination using subsidy

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.

Influenza infection risk and predominate exposure route: uncertainty analysis.

An effective nonpharmaceutical intervention for influenza interrupts an exposure route that contributes significantly to infection risk. Herein, we use uncertainty analysis (point-interval method) and Monte Carlo simulation to explore the magnitude of infection risk and predominant route of exposure. We utilized a previously published mathematical model of a susceptible person attending a bed-ridden infectious person. Infection risk is sensitive to the magnitude of virus emission and contact rates. The contribution of droplet spray exposure to infection risk increases with cough frequency, and decreases with virus concentration in cough particles. We consider two infectivity scenarios: greater infectivity of virus deposited in the upper respiratory tract than virus inhaled in respirable aerosols, based on human studies; and equal infectivity in the two locations, based on studies in guinea pigs. Given that virus have equal probability of infection throughout the respiratory tract, the mean overall infection risk is 9.8 × 10⁻² (95th percentile 0.78). However, when virus in the upper respiratory tract is less infectious than inhaled virus, the overall infection risk is several orders of magnitude lower. In this event, inhalation is a significant exposure route. Contact transmission is important in both infectivity scenarios. The presence of virus in only respirable particles increases the mean overall infection risk by 1-3 orders of magnitude, with inhalation contributing ≥ 99% of the infection risk. The analysis indicates that reduction of uncertainties in the concentration of virus in expiratory particles of different sizes, expiratory event frequency, and infectivity at different sites in the respiratory tract will clarify the predominate exposure routes for influenza.

Hospital stockpiling for disaster planning

In response to the increasing threat of terrorist attacks and natural disasters, governmental and private organizations worldwide have invested significant resources in disaster planning activities. This article addresses joint inventory stockpiling of medical supplies for groups of hospitals prior to a disaster. Specifically, the problem of determining the stockpile quantity of a medical item at several hospitals is considered. It is assumed that demand is uncertain and driven by the characteristics of a variety of disaster scenarios. Furthermore, it is assumed that hospitals have mutual aid agreements for inventory sharing in the event of a disaster. Each hospitals desire to minimize its stockpiling cost together with the potential to borrow from other stockpiles creates individual incentives well represented in a game-theoretic framework. This problem is modeled as a non-cooperative strategic game, the existence of a Nash equilibrium is proved, and the equilibrium solutions are analyzed. A centralized model of stockpile decision making where a central decision maker optimizes the entire system is also examined and the solutions obtained using this model are compared to those of the decentralized (game) model. The comparison provides some managerial insights and public health policy implications valuable for disaster planning.

Bundled Payment vs. Fee-for-Service: Impact of Payment Scheme on Performance

Healthcare reimbursements in the United States have been traditionally based on 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 patients 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 providers 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 providers 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. This paper was accepted by Serguei Netessine, operations management.