Consider the problem of sequential sampling from m statistical populations to maximize the expected sum of outcomes in the long run. Under suitable assumptions on the unknown parameters g ⌰, it is shown that there exists a class C of R Ž. adaptive policies with the following properties: i The expected n horizon reward 0 n UF Policies in C are specified via easily computable indices, defined as unique R Ž. solutions to dual problems that arise naturally from the functional form of M. In addition, the assumptions are verified for populations specified by nonparametric discrete univariate distributions with finite support. In the case of normal populations with unknown means and variances, we leave as an open problem the verification of one assumption.

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In this paper we consider the problem of adaptive control for Markov Decision Processes. We give the explicit form for a class of adaptive policies that possess optimal increase rate properties for the total expected finite horizon reward, under sufficient assumptions of finite state-action spaces and irreducibility of the transition law. A main feature of the proposed policies is that the choice of actions, at each state and time period, is based on indices that are inflations of the right-hand side of the estimated average reward optimality equations.

We study the effects of disruption risk in a supply chain where one retailer deals with competing risky suppliers who may default during their production lead times. The suppliers, who compete for business with the retailer by setting wholesale prices, are leaders in a Stackelberg game with the retailer. The retailer, facing uncertain future demand, chooses order quantities while weighing the benefits of procuring from the cheapest supplier against the advantages of order diversification. For the model with two suppliers, we show that low supplier default correlations dampen competition among the suppliers, increasing the equilibrium wholesale prices. Therefore the retailer prefers suppliers with highly correlated default events, despite the loss of diversification benefits. In contrast, the suppliers and the channel prefer defaults that are negatively correlated. However, as the number of suppliers increases, our model predicts that the retailer may be able to take advantage of both competition and diversification.resilient supply chains, supply risk, supply disruptions, competition, procurement, default correlation, equilibrium pricing

We consider a single server Markovian queue with setup times. Whenever this system becomes empty, the server is turned off. Whenever a customer arrives to an empty system, the server begins an exponential setup time to start service again. We assume that arriving customers decide whether to enter the system or balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait.We examine customer behavior under various levels of information regarding the system state. Specifically, before making the decision, a customer may or may not know the state of the server and/or the number of present customers. We derive equilibrium strategies for the customers under the various levels of information and analyze the stationary behavior of the system under these strategies. We also illustrate further effects of the information level on the equilibrium behavior via numerical experiments.

This article investigates the role of option contracts in a supply chain when the demand curve is downward sloping. We consider call (put) options that provide the retailer with the right to reorder (return) goods at a fixed price. We show that the introduction of option contracts causes the wholesale price to increase and the volatility of the retail price to decrease. In general, options are not zero-sum games. Conditions are derived under which the manufacturer prefers to use options. When this happens the retailer is also better off, if the uncertainty in the demand curve is low. However, if the uncertainty is sufficiently high, then the introduction of option contracts alters the equilibrium prices in a way that hurts the retailer.real options, downward-sloping demand curve, Stackelberg games, supply chain contracts

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Distribution networks frequently contain multiple locations where product is held as inventory. These may be plants, warehouses, and retail outlets. Traditionally, inventory levels at these locations have been determined by optimizing the cost, demand, and customer service factors local to the particular inventory. With improvements in business information systems, it has become increasingly popular to treat multiple inventory locations as virtual inventories. That is, when customer demand cannot be served from the primary assigned location, other comparable inventory locations, usually more distant, may be used as backup stocking points for serving customer demand. Although delivery cost may be increased, customers actually receive fill rates approaching 100% even when the product in-stock probabilities for the individual stocking points are somewhat lower. While maintaining high fill rates for customers, stocking at low system-wide inventory levels is the appeal of filling customer orders from multiple inventories.In this article, a traditional inventory planning approach is compared with one that is based on filling customer demand from any one of several stocking locations. This provides insights into the impact of inventory control methods, item fill rates, demand dispersion among inventory locations, and relevant inventory costs on system inventory levels. Guidelines are provided for determining the items that should be handled in the traditional manner and those that should be managed as virtual inventories, thus creating a mixed control strategy for the inventoried items. TRADITIONAL INVENTORY PLANNINGCommon pull-type inventory control systems set stocking levels based on demand, costs, and service requirements associated with the defined demand territory of the inventory location. These territories are often determined from location analyses that make demand assignments among multiple facilities. The motivation for this localized control is that it leads to lower inventory levels in a stock location than from alternative control methods such as a push-type method. As shown in Figure 1, all demand is assumed to be served from its primary assigned location. Demand that JOURNAL OF BUSINESS LOGISTICS, Vol.24, No.2, 2003 65 cannot be filled immediately is either backordered or lost. Demand and inventory at other locations play no role in setting the stocking levels at any particular location.Pull-type stocking methods range from EOQ-based to stock-to-demand approaches. The EOQbased methods are commonly known as reorder point, periodic review, min-max, or their variants. On the other hand, stock-to-demand methods set inventory levels in direct proportion to demand. Targeting a certain number-of-weeks supply (inventory turnover) and using a multiple of the forecast are examples of this method.Product availability, or fill rate, is set at less than 100% to avoid excess carrying costs. Depending on the stocking method, product availability is determined statistically or through quantities added to forecasted re...