Virtual Machine (VM) environments (e.g., VMware and Xen) are experiencing a resurgence of interest for diverse uses including server consolidation and shared hosting. An application's performance in a virtual machine environment can differ markedly from its performance in a nonvirtualized environment because of interactions with the underlying virtual machine monitor and other virtual machines. However, few tools are currently available to help debug performance problems in virtual machine environments.In this paper, we present Xenoprof, a system-wide statistical profiling toolkit implemented for the Xen virtual machine environment. The toolkit enables coordinated profiling of multiple VMs in a system to obtain the distribution of hardware events such as clock cycles and cache and TLB misses.We use our toolkit to analyze performance overheads incurred by networking applications running in Xen VMs. We focus on networking applications since virtualizing network I/O devices is relatively expensive. Our experimental results quantify Xen's performance overheads for network I/O device virtualization in uni-and multi-processor systems. Our results identify the main sources of this overhead which should be the focus of Xen optimization efforts. We also show how our profiling toolkit was used to uncover and resolve performance bugs that we encountered in our experiments which caused unexpected application behavior.

We study an inventory system under periodic review in the presence of two suppliers (or delivery modes). The emergency supplier has a shorter lead-time than the regular supplier, but the unit price he offers is higher. Excess demand is backlogged. We show that the classical "Lost Sales inventory problem" is a special case of this problem. Then, we generalize the recently studied class of Dual Index policies (Veeraraghavan and Scheller-Wolf (2007)) by proposing two classes of policies. The first class consists of policies that have an orderup-to structure for the emergency supplier. We provide analytical results that are useful for determining optimal or near-optimal policies within this class. This analysis and the policies that we propose leverage the connections we make between our problem and the lost sales problem. The second class consists of policies that have an order-up-to structure for the combined orders of the two suppliers. Here, we derive bounds on the optimal order quantity from the emergency supplier, in any period, and use these bounds for finding effective policies within this class. Finally, we undertake an elaborate computational investigation to compare the performance of the policies we propose with that of Dual Index policies. One of our policies provides an average cost-saving of 1.1 % over the Best Dual Index policy and has the same computational requirements. Another policy that we propose has a cost performance similar to the Best Dual Index policy but its computational requirements are lower.

We study a single-product single-location inventory system under periodic review, where excess demand is lost and the replenishment lead time is positive. The performance measure of interest is the long run average holding cost and lost sales penalty. For a large class of demand distributions, we show that when the lost sales penalty becomes large compared to the holding cost, the relative difference between the cost of the optimal policy and the best order-up-to policy converges to zero. For any given cost parameters, we establish a bound on this relative difference. Numerical experiments show that the best order-up-to policy performs well, yielding an average cost that is within 1.5% of the optimal cost even when the ratio between the lost sales penalty and the holding cost is just 100.

We study a stationary, single-stage inventory system, under periodic review, with fixed ordering costs and multiple sales levers (such as pricing, advertising, etc.). We show the optimality of s S-type policies in these settings under both the backordering and lost-sales assumptions. Our analysis is constructive and is based on a condition that we identify as being key to proving the s S structure. This condition is entirely based on the single-period profit function and the demand model. Our optimality results complement the existing results in this area.

We consider multiunit Vickrey auctions for procurement in supply chain settings. This is the first paper that incorporates transportation costs into auctions in a complex supply network. We first introduce an auction mechanism that makes simultaneous production and transportation decisions so that the total supply chain cost is minimized and induces truth telling from the suppliers. Numerical study shows that considerable supply chain cost savings can be achieved if production and transportation costs are considered simultaneously. However, the buyer's payments in such auctions can be high. We then develop a new Vickrey-type auction that incorporates the buyer's reservation price function into quantity allocation and payment decision. As a result, the buyer has some control over his payments at the expense of introducing uncertainty in the quantity acquired in the auction.mechanism design, VCG auctions, supply chain procurement

We study a model of a firm managing its inventory of a single product by sourcing supplies from two supply sources, a regular supplier who offers a lower unit cost and a longer lead time than a second, emergency, supplier. A practically implementable policy for such a firm is a Tailored Base-Surge (TBS) Policy (Allon and Van Mieghem, 2010) to manage its inventory: Under this policy, the firm procures a constant quantity from the regular supplier in every period and dynamically makes procurement decisions for the emergency supplier. Allon and Van Mieghem describe this practice as using the regular supplier to meet a base level of demand and the emergency supplier to manage demand surges, and they conjecture that this practice is most effective when the lead time difference between the two suppliers is large. We confirm these statements in two ways. First, we show the following analytical result: When demand is composed of a base demand random component plus a surge demand random component, which occurs with a certain small probability, the best TBS Policy is close to optimal (over all policies) in a well defined sense. Second, we also numerically investigate the cost-effectiveness of the best TBS policy on a test bed of problem instances. The emphasis of this investigation is the study of the effect of the lead time difference between the two suppliers. Our study reveals that the cost difference between the best TBS policy and the optimal policy decreases dramatically as the lead time of the regular supplier increases. On our test bed, this cost difference decreases from an average (over the test bed) of 21 % when the lead time from the regular supplier is two periods (the emergency supplier offers instant delivery) to 3.5 % when that lead time is seven periods.

We study a periodically reviewed, serial inventory system in which excess demand from external customers is lost. We derive elementary properties of the vector of optimal order quantities in this system. In particular, we derive bounds on the sensitivity (or, more mathematically, the derivative) of the optimal order quantity at each stage to the vector of the current inventory levels. Our analysis uses the concept of L-naturalconvexity, which was studied in discrete convex analysis (Murota (2003)) and recently used by Zipkin (2008) for studying single-stage inventory systems with lost sales. We also remark on how our analysis extends to models with capacity constraints and/or backordering.

In this paper, we describe the first computationally efficient policies for stochastic inventory models with lost sales and replenishment lead times that admit worst-case performance guarantees.In particular, we introduce dual-balancing policies for lost-sales models that are conceptually similar to dualbalancing policies recently introduced for a broad class of inventory models in which demand is backlogged rather than lost. That is, in each period, we balance two opposing costs: the expected marginal holding costs against the expected marginal lost-sales cost. Specifically, we show that the dual-balancing policies for the lost-sales models provide a worst-case performance guarantee of 2 under relatively general demand structures. In particular, the guarantee holds for independent (not necessarily identically distributed) demands and for models with correlated demands such as the AR(1) model and the multiplicative auto-regressive demand model. The policies and the worst-case guarantee extend to models with capacity constraints on the size of the order and stochastic lead times. Our analysis has several novel elements beyond the balancing ideas for backorder models.Key words: Inventory, Approximation ; Dual-Balancing ; Algorithms; Lost Sales MSC2000 Subject Classification: Primary: 90B05 , ; Secondary: 68W25 , OR/MS subject classification: Primary: inventory/production , approximation/heuristics ; Secondary: production/scheduling , approximation/heuristics 1. Introduction In this paper, we address one of the fundamental problems in stochastic inventory theory, the single-item, single location, periodic-review, stochastic inventory control problem with lost sales, which we refer to as the lost-sales problem. This problem has challenged researchers and practitioners for over five decades as very little is known about the structure of the optimal policy, and there are no known provably good heuristics even for the simplest settings. We build on ideas first proposed by Levi, Pál, Roundy and Shmoys [5]. They proposed what are called dual-balancing policies for a class of inventory models where unsatisfied demand is backlogged rather than lost. These policies have worst-case performance guarantees, that is, for each instance of the problem, the expected cost of the policy is guaranteed to be at most C times the optimal expected cost (for some constant C). In this paper, we discuss the implementation and the worst-case analysis of dual-balancing policies applied to inventory models with lost sales. These models have mathematical characteristics that are very different than the models in which excess demand is backlogged and thus require a fundamentally different and novel worst-case analysis. In particular, we shall describe the first computationally efficient policies for inventory models with lost sales that have a worst-case performance guarantee of 2. The analysis is based on several new ideas that we believe will contribute to future research in this domain.