Search

Supply contracts are designed to minimize inventory costs or to hedge against undesirable events (e.g., shortages) in the face of demand or supply uncertainty. In particular, replenishment terms stipulated by supply contracts need to be optimized with respect to overall costs, profits, service levels, etc. In this paper, we shall be primarily interested in minimizing an inventory cost function with respect to a constant replenishment rate. Consider a single-product inventory system under continuous review with constant replenishment and compound Poisson demands subject to lost-sales. The system incurs inventory carrying costs and lost-sales penalties, where the carrying cost is a linear function of on-hand inventory and a lost-sales penalty is incurred per lost sale occurrence as a function of lost-sale size. We first derive an integro-differential equation for the expected cumulative cost until and including the first lost-sale occurrence. From this equation, we obtain a closed form expression for the time-average inventory cost, and provide an algorithm for a numerical computation of the optimal replenishment rate that minimizes the aforementioned time-average cost function. In particular, we consider two special cases of lost-sales penalty functions: constant penalty and loss-proportional penalty. We further consider special demand size distributions, such as constant, uniform and Gamma, and take advantage of their functional form to further simplify the optimization algorithm. In particular, for the special case of exponential demand sizes, we exhibit a closed form expression for the optimal replenishment rate and its corresponding cost. Finally, a numerical study is carried out to illustrate the results. [ABSTRACT FROM AUTHOR]

Over the past 30 years managers have increasingly focused on improving inventory management both within their own firms and across the supply chain. To this end, inventory turns metrics have been adopted as a popular tool for measuring flow velocity through the inventory and the efficiency of inventory-related asset utilization. There are multiple computational methods thereof currently used by practitioners, but each has some flaws. In particular, consensus is lacking as to (1) how to measure inventory flow and (2) how to measure the inventory level. Clearly, high-quality accounting information is essential for an accurate assessment of all inventory performance metrics. Unfortunately, when comparing efficiencies across firms or diagnosing and correcting intra-firm inefficiencies, choices of specific accounting rules and distortions between fair market values and corresponding accounting book values can lead to potentially misleading results. This paper presents finite-horizon versions of Little's Law and elucidates their connection to inventory turns and restricted sojourn times in inventory, defined as the portion of the full sojourn time that falls within a prescribed time period. In particular, it explains when the reciprocal of sample inventory turns coincides with the sample average of restricted sojourn times. As such, the paper provides a unified prescriptive model for correctly relating inventory turns to sojourn times through an inventory system, thereby facilitating more accurate intra-firm and cross-firm comparisons. [ABSTRACT FROM AUTHOR]

We study a new class of inventory control problems, the recruitment stocking problem (RSP), applicable to general recruitment systems and products with limited supplies. Recruitment stocking occurs routinely in many organizations with the goal of identifying qualified candidates rapidly and cost effectively. This activity may take place at multiple sites simultaneously to shorten the recruitment time. Examples include recruiting patients in clinical trials, enlisting personnel in the military, and recruiting customers for product sampling in market testing and promotion. RSP differs from the extant inventory management literature in that it stipulates a finite recruitment target, so that recruitment is terminated as soon as the total number of recruits across all locations reaches that prescribed target. This distinctive feature of RSP calls for the development of new stochastic models to evaluate and optimize system performance. Thus, we present a novel methodology of relaxation and decomposition to characterize the probability distribution of rejections in RSP (number of arrivals to an empty inventory). This method provides a basis for efficient and accurate evaluation of the Type 2 service level and expected recruitment time. We also leverage the attendant computational efficiency to develop optimization algorithms to compute the optimal stocking quantities. [ABSTRACT FROM AUTHOR]

We consider a limited-liability firm that owns a finite single-product inventory subject to periodic-review replenishment and a corporate treasury that mediates the firm’s financial transactions related to inventory operations. The firm may elect to borrow money to purchase product via a revolving line of credit, secured by a compensating balance which determines the credit limit. The line of credit is subject to rollover risk, namely, each period the funding entity may, with some probability, refuse to roll over the line of credit. In response, the firm can search for an alternate funding entity, but in so doing it may incur search costs, primarily in the form of lost sales. The firm optimizes inventory replenishment order sizes and decides whether it should declare bankruptcy, as function of its inventory and available capital. The recent credit crunch has rendered illiquidity a critical concern for funding and operating decisions in enterprises. This paper addresses optimal inventory management in the face of liquidity shocks and supply disruptions. We show that rollover risk and supply disruption are important considerations for firms that rely on external funding. Rollover risk alone results in optimal inventory replenishment policies that differ materially from those specified by traditional supply chain models; differences manifest as state-dependent precautionary replenishment or cash hoarding. Inventory management models which fail to take rollover risk and supply disruption risk into account can prescribe suboptimal replenishment policies. Such policies would generate suboptimal profits for firms that rely on short-term financing to fund their working capital. [ABSTRACT FROM AUTHOR]

Businesses nowadays often feel impelled to rush and implement Big Data and Artificial Intelligence initiatives in their organizations without clarity on their business problems, nor the appropriate methodologies for extracting actionable insights from the data. In contrast, this paper presents a process that starts with an articulated business problem instead of a "data rush". The presented process, dubbed the Business-Driven Data-Supported (BDDS) process, is rigorously anchored in concepts from Theory of Constraints and Information Theory. BDDS guides businesses in solving their problems by stating observed performance gaps, uncovering their underlying root cause, formulating the "right question", utilizing only the "right data", and choosing the "right methodology" to extract the "right information" from the data, leading to the "right actionable insights." Also provided is a prescriptive framework, dubbed the Data-to-Information-Extraction-Methodology (DIEM), for selecting the "right methodology", based on the understanding level of relevant system dependencies and the availability of relevant data. The BDDS process is illustrated by an example from the healthcare industry, and the efficacy and applicability of the DIEM framework are supported by eleven case studies from a broad range of industries. [ABSTRACT FROM AUTHOR]

Infinitesimal perturbation analysis (IPA) provides formulas for random gradients (derivatives) of performance measures with respect to parameters of interest, computed from sample paths of stochastic systems. In practice, IPA derivatives may be computed either from simulation runs or from empirical field data (when the formulas are nonparametric). Nonparametric IPA derivatives in fluid-flow queues have been recently derived for the loss volume and time average of buffer occupancy, with respect to buffer size, and arrival-rate or service-rate parameters. Additionally, these IPA derivatives have been shown to be unbiased in the sense that their expectation and differentiation operators commute, while their traditional discrete counterparts have long been known to be generally biased. Recent work has further shown how to map the computation of IPA derivatives from a fluid-flow queue to a compatible discrete counterpart without an appreciable loss of accuracy in performance measures. Thus, this work holds the promise of potential applications of IPA derivatives to gradient-based optimization of objective functions involving performance metrics parameterized by settable parameters in a queueing network context. This paper is an empirical study of IPA derivatives of individual queues within queueing systems which model telecommunications networks and some of their protocols. As a testbed, we used HNS (Hybrid Network Simulator) — a hybrid Java simulator of queueing networks with traffic streams subject to several telecommunications protocols. More specifically, the hybrid feature of HNS admits models with mixtures of discrete (packet) flows and continuous (fluid) flows, and collects detailed statistics and IPA derivatives for all flow types. The paper outlines the mapping of IPA derivatives from the fluid domain to the packet domain as implemented in HNS, and studies the accuracy of IPA derivatives in compatible fluid and packet queueing models, as well as the stabilization of their values in time. Our experimental results lend empirical support to the contention that IPA derivatives can be accurately computed from discrete versions by adopting a fluid-flow view. Furthermore, the long-run values of various IPA derivatives are empirically shown to stabilize quite fast. Finally, the results provide the basis and motivation for IPA applications to the optimization of telecommunications network design and to potential new open-loop protocols that take advantage of IPA information. [Copyright &y& Elsevier]

Manufacturing-related have traditionally made independence assumptions on associated stochastic processes in order to achieve tractability of analytical models and simplify Monte Carlo models. This paper aims to alert users to potential deleterious implications stemming from unfounded independence assumptions in traditional stochastic models of manufacturing systems. Specifically, it demonstrates the dramatic impact that appreciable autocorrelations can have on manufacturing performance measures through a preliminary study of prediction errors incurred in ignoring dependence. To this end, the study compared performance measures of common manufacturing models with renewal components to their autocorrelated counterparts, drawn From the TES (Transform-Expand-sample) class. TES models constitute a versatile class of stochastic processes, designed to capture empirical distributions and autocorrelation. simultaneously, and as such, are suitable for both Monte Carlo simulation and analytical modeling of autocorrelated time series. A brief overview of simple TES processes and their generation algorithms is also included. [ABSTRACT FROM AUTHOR]

Examines the idea of using a variable-speed processor (VSP) that can be operated at a high clock speed, and then slowed down to a lower speed before heat accumulation destroys an electronic circuit. Heat generation; Optimality of the bang-bang control policy; Stochastic modal for the VSP; Controlling the VSP with linear temperature gradients.

This paper studies the spectral properties of a class of stochastic sequences generated by basic TES (Transform-Expand-Sample) methods, as well as transformed TES sequences. A TES sequence is obtained as a marginally uniform process from an autoregressive scheme with modulo-1 reduction, followed by additional transformations. We derive formulas for the spectral density function and the spectral distribution function which are suitable for efficient numerical computation. A set of examples is calculated and exhibited for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context. [ABSTRACT FROM AUTHOR]

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d, uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient p, there is a IES method generating a uniform sequence with the 1-lag autocorrelation rho, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the "amplitude" and "frequency" of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. [ABSTRACT FROM AUTHOR]

The original version of this article was revised as some author corrections were overlooked by vendor. [ABSTRACT FROM AUTHOR]

A logical strategy to contain the Covid-19 pandemic is to completely isolate everyone for 2 weeks (the incubation period of the virus). However, such a strategy can have prohibitive economic and social costs and, therefore, will be difficult to implement. At the same time, the current situation is leading to an expanding humanitarian, health and economic crisis. Based on principles of the Theory of Constraints, we propose in this article the "Shutting-down Transmission Of Pandemic" (STOP Covid-19) plan that would reliably contain the pandemic, mitigate its economic consequences, and boost societal confidence. This plan requires the implementation of four strategies over 90 days: (a) stop all international, domestic passenger air and intercity bus/train travel; (b) create administrative zones of about 1 million people; (c) stop all non-emergency cross-zonal travel except for transportation of goods, and (d) deploy an information-driven service value chain to control the spread of the pandemic within a zone. [ABSTRACT FROM AUTHOR]

Temporal shaping of time series is the activity of deriving a time series model with a prescribed marginal distribution and some sample path characteristics. Starting with an empirical sample path, one often computes from it an empirical histogram (a step-function density) and empirical autocorrelation function. The corresponding cumulative distribution function is piecewise linear, and so is the inverse distribution function. The so-called inversion method uses the latter to generate the corresponding distribution from a uniform random variable on [0,1), histograms being a special case. This paper shows how to manipulate the inverse histogram and an underlying marginally uniform process, so as to “shape” the model sample paths in an attempt to match the qualitative nature of the empirical sample paths, while maintaining a guaranteed match of the empirical marginal distribution. It proposes a new approach to temporal shaping of time series and identifies a number of operations on a piecewise-linear inverse histogram function, which leave the marginal distribution invariant. For cyclical processes with a prescribed marginal distribution and a prescribed cycle profile, one can also use these transformations to generate sample paths which “conform” to the profile. This approach also improves the ability to approximate the empirical autocorrelation function. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of inventory penalty pricing under the risk-neutral valuation principle. The underlying production-inventory system has a constant replenishment rate and a compound renewal demand stream (i.e., iid demand interarrival times are independent of iid demand sizes), and is subject to underage and overage penalties. Our pricing approach treats the penalties as a series of perpetual American options, and constructs auxiliary martingale processes in term of the inventory process. We provide a necessary and sufficient martingale condition for general compound renewal demands. Explicit expressions of penalty functions for underage and overage are obtained for the case where demand arrivals follow a Poisson process. [ABSTRACT FROM AUTHOR]

Examines the effect of extrinsic motivation on user behavior in a collaborative information finding system. Evaluation on the free riding behavior of users; Development of the AntWorld system; Problem of getting users to provide information.