Reorder Time Research Articles

Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

The Reverse Cuthill-McKee (RCM) algorithm is a well-known heuristicfor reordering sparse matrices. It is typically used to speed up the computation ofsparse linear systems of equations. This paper describes two parallel approachesfor the RCM algorithm as well as an optimized version of each one based on someproposed enhancements. The first one exploits a strategy for reducing lazy threads,while the second one makes use of a static bucket array as the main data structureand suppress some steps performed by the original algorithm. These related changesled to outstanding reordering time results and significant bandwidth reductions.The performance of two algorithms is compared with the respective implementationmade available by Boost library. The OpenMP framework is used for supportingthe parallelism and both versions of the algorithm are tested with large sparse andstructural symmetric matrices.

Parallel Implementations of RCM Algorithm for Bandwidth Reduction of Sparse Matrices

The Reverse Cuthill-McKee (RCM) algorithm is a well-known heuristic for reordering sparse matrices. It is typically used to speed up the computation of sparse linear systems of equations. This paper describes two parallel approaches for the RCM algorithm as well as an optimized version of each one based on some proposed enhancements. The first one exploits a strategy for reducing lazy threads, while the second one makes use of a static bucket array as the main data structure and suppress some steps performed by the original algorithm. These related changes led to outstanding reordering time results and significant bandwidth reductions. The performance of two algorithms is compared with the respective implementation made available by Boost library. The OpenMP framework is used for supporting the parallelism and both versions of the algorithm are tested with large sparse and structural symmetric matrices.

Evaluation of reordering time in a manufacturing inventory division

In this paper, a production process is considered which requires two kinds of raw materials as inputs to make a product. The two kinds of raw materials are stored separately. During the time of crisis like non-availability of the raw materials due to scarcity or delayed delivery or for some other reasons, the reserve stocks are utilised to continue the production process, as a result; the level of reserve stocks would come down and finally may go void. This may result into production halt. To avoid this situation, a reorder is made to maintain the level of reserve inventory as soon as the reserve level touches a particular level called the threshold level. Using the shock model and cumulative damage process technique, a stochastic model is derived to find the threshold level or the time of reordering, which helps the production system to eliminate the holding cost on excessive raw materials and also the loss arising from the shortage of raw materials. Numerical illustrations are provided.

Evaluation of reordering time in a manufacturing inventory division

In this paper, a production process is considered which requires two kinds of raw materials as inputs to make a product. The two kinds of raw materials are stored separately. During the time of crisis like non-availability of the raw materials due to scarcity or delayed delivery or for some other reasons, the reserve stocks are utilised to continue the production process, as a result; the level of reserve stocks would come down and finally may go void. This may result into production halt. To avoid this situation, a reorder is made to maintain the level of reserve inventory as soon as the reserve level touches a particular level called the threshold level. Using the shock model and cumulative damage process technique, a stochastic model is derived to find the threshold level or the time of reordering, which helps the production system to eliminate the holding cost on excessive raw materials and also the loss arising from the shortage of raw materials. Numerical illustrations are provided.

A Robust Reorder-Time/Order-Quantity Policy Under Invisible Stock Loss

Inventory record inaccuracy has significant negative impacts on the performance of inventory management. We investigate a robust replenishment problem for an inventory system under inventory record inaccuracy caused by invisible stock loss, with the objective of minimizing the sum of the inventory holding cost, the backorder cost, and the materials transportation cost. First, we develop a recursive algorithm to estimate the probability distribution of the physical inventory levels. Based on this probability distribution, a robust myopic reorder-time/order-quantity (RTQ) policy is designed, which determines the robust reorder time and the robust replenishment quantity. Theoretical analysis and numerical experiments reveal some managerial insights of the proposed RTQ policy and the classical ( ${r}$ , ${Q}$ ), ( ${s}$ , ${S}$ ), and ( ${R}$ , ${S}$ ) policies: 1) if there exist invisible stock loss and inaccurate inventory record, the inventory system will be trapped into the zero-service state (i.e., the inventory level becomes less than or equal to zero with probability one) in finite time under the classical policies and 2) if the probability distribution of inventory record error is known exactly, the RTQ policy prevents the inventory system from being trapped into the zero-service state and maintains a high service level, even if we do not make any audit of its physical inventory level.

Minimum information rate for observability of linear systems with stochastic time delay

ABSTRACTThis paper investigates the state estimation problem for linear time-invariant systems where sensors and controllers are geographically separated and connected via stationary memoryless uncertain digital communication channels with the information rate limitation. Such channels introduce data packet dropout, stochastic time delay, and data packet reordering. In the TCP/IP model, the transport layer provides a reliable service on top of an unreliable communication channel. However, the performance of such systems is still affected by packet reordering and stochastic time delay. In particular, we present an optimal encoding and decoding scheme to guarantee observability by employing the minimum information rate, and derive a necessary and sufficient condition on the delay distribution and information rate for observability. Illustrative examples are given to demonstrate the effectiveness of the proposed scheme.

A real-time inventory model to manage variance of demand for decreasing inventory holding cost

Variance of demand is one of the inevitable problems in the manufacturing environment. Market conditions and competition force companies reducing costs. Different approaches and methods have been developed to remedy these problems. Common points of these approaches are utilizing resources and responding in the shortest time possible. To achieve better inventory management, inventory-holding cost is tried to be decreased under the same service level. Re-order point is arranged dynamically regarding couple of factors in some studies. We try to arrange the re-order point in a time based manner by transforming the re-order point into re-order time, which eliminates the safety stock; and it makes the inventory model real-time.Recent production planning studies focus on real-time planning and dynamic scheduling to increase utilization and robustness. In these studies, real-time data is used for planning, but in most of them manufacturing systems and planning methodology are not transformed into a real-time system approach. The novel aspect of this study is the presentation of a model in which the manufacturing system has been designed as a real-time system that consists of real-time planning activities working with real-time data, and eliminating the safety stock.

Optimalisasi Sistem Persediaan Bahan Baku Karet Mentah (Lateks) dengan Metode Lot Sizing (Studi Kasus: PT Abaisiat Raya)

PT Abaisiat Raya is one of the manufacturers of rubber crumb (crumb rubber) in the city of Padang. Latex inventory management system at PT Abaisiat Kingdom basically signinfikan still need improvement. It is based on the planning activities in the warehouse inventory of raw materials firms irregular, thus causing excess stock (over stock) at a time and shortage of stock (stock out) at other times. Process optimization is done with latex inventory system involving factors such as demand forecasting production planning or latex needs during the period of next 12 (in 2012), the costs involved, the waiting time (lead time), the implementation of forecasting methods, determination of size lots (lot sizing), the determination of safety stock (safety stock), and re-ordering time (reorder point), so the output will get a number of requests are for 12 periods ahead, the size of each reservation period, the total cost is required, when re-ordering will be done , as well as how much inventory to latex in the warehouse. Based on these results, it was found that the optimal size of the book is the same as the demand for each period (reservation is made each period) due to a cyclical pattern of demand and decreases throughout the planning period. Value of the stock or safety stock is located in Kg 114,282.20, and re-ordering time (reorder point) to cope with fluctuations do when the stock has reached a level of 333,130.95 kg.Keywords: Forecasting, Time Wait, Lot Size, Safety Supplies, Reorder

Habeas Libris: For Books in Need of a Reprieve

Habeas Libris is a website (www.habeaslibris.com) dedicated to the salvation of books – old-fashioned, ink-on-paper books. The thinking behind the website is based on four simple observations about law libraries and law librarians: (1) they are reducing their print collections; (2) they are having a hard time finding buyers – or even takers – for the books they cannot keep; (3) they would rather give away than throw away their unwanted and unmarketable books; and (4) they lack a truly cheap and easy way to offer their unmarketable books to anyone who might want them. Habeas Libris aspires to be that cheap and easy way for law libraries to give away those surplus books. In addition, in this time of much re-ordering of priorities and re-tasking of facilities, and not so much re-shelving of books, Habeas Libris also aspires to provide book-loving librarians some small consolation that they have done everything they reasonably can before they consign any books to the dumpster – including offering their surplus books to the whole web-connected world for free. This article briefly puts the current circumstances of surplus law books in context, and then explains how Habeas Libris works.

Analyzing the Efficient Execution of In‐Store Logistics Processes in Grocery Retailing—The Case of Dairy Products

In this article, we examine in‐store logistics processes for handling dairy products, from the incoming dock to the shelves of supermarkets and hypermarkets. The efficient execution of the in‐store logistics related to such fast‐moving, sensitive, and essential items is challenging and crucial for grocery retailers' sales, profits, and image. In our empirical study, we survey in‐store logistics processes in 202 grocery supermarkets and hypermarkets belonging to a major retail chain in central Europe. Using a data envelopment analysis (DEA) and simulation, we facilitate process benchmarking. In particular, we identify ways of improving in‐store logistics processes by showing the performance impacts of different managerial strategies and tactics. The DEA results indicate different efficiency levels for different store formats; the hybrid store format of the small hypermarket exhibits a comparatively worse performance in the analyzed execution of in‐store logistics processes. The process simulation analysis reveals that the strategic and tactical design of in‐store logistics processes (such as store locations/layouts, capacity management, reorder time, order period, and safety stock factors) lead to substantial service performance improvements (such as higher on‐shelf availability combined with reduced inventory obsolescence costs). The results also show marginal improvements in the performance figures when delivery delays and damage to products are reduced.

Stock diffusion theory: a dynamic model for inventory control

This paper proposes a dynamic approach for inventory management, which can be used for a definitely non stationary demand whose rate evolves both in mean and in variance. Specifically, the stock consumption is modelled as a Markov process with a slow diffusion term and the Fokker Planck equation is used to derive the probability distribution of the stock consumption and that of the reorder time. The knowledge of these distributions makes it possible to manage the inventory in a dynamical way and to keep the safety stock to a minimum level. To test the model, some typical demand patterns are used: results demonstrate its ability to capture both the evolution of the mean and that of the variance of the demand.

Dynamic robust optimal reorder point with uncertain lead time and changeable demand distribution

In fixed order quantity systems, uncertainty in lead time is expressed as a set of scenarios with occurrence probabilities, and the mean and variance in demand distribution are supposed to be changeable according to a known pattern. A new concept of “dynamic robust optimal reorder point” is proposed in this paper and its value is calculated as a “robust optimal reorder point function with respect to reorder time”. Two approaches were employed in determining the dynamic optimal reorder point. The first is a shortage rate satisfaction approach and the second is a backorder cost minimization approach. The former aims at finding the minimum value of reorder point at each reorder time which satisfies the condition that the cumulative distribution function (CDF) of shortage rate under a given set of scenarios in lead time is greater than or equal to a basic CDF of shortage rate predetermined by a decision-maker. In the latter approach, the CDF of closeness of reorder point is defined at each reorder time to express how close to the optimal reorder points under the set of scenarios, and the dynamic optimal reorder point is defined according to stochastic ordering. Some numerical examples demonstrate the features of these dynamic robust optimal reorder points.

Multi-path transmission control scheme combining bandwidth aggregation and packet scheduling for real-time streaming in multi-path environment

These days, a wide variety of wireless interfaces are available to connect to Internet. When coverage area of these different technologies overlap, receiver equipped with multiple interfaces can use them simultaneously to improve the performance of its applications in terms of bandwidth rely on bandwidth aggregation. However, specific conditions such as bottleneck bandwidth and end-to-end delay need to be accounted for before using such techniques. If this problem of end-to-end delay and bottleneck bandwidth are not properly addressed, there may be many packets along multiple paths which can arrive late and can lead to a large number of out-of-order packets at the receiver, which can eventually cause serious degradation of video quality at the receiver. For this reason, in this study, the authors propose a multi-path transmission control scheme (MTCS) combining bandwidth aggregation and packet scheduling for real-time streaming in a multi-path environment. In a bandwidth aggregation scheme, the authors propose a mathematical model to find the transmission rate over each path in order to obtain the optimal total throughput. However, the end-to-end delay of each path is not the same. The out-of-order packets problem will become serious in a multi-path environment. Therefore the authors propose a packet scheduling scheme to arrange the transmission sequence in order to effectively minimise the impact of packet reordering at the receiver. Our proposed control scheme not only aggregates the available bandwidth of multiple paths, but also reduces the time of packet reordering at the receiver. Experimental results show with our proposed scheme, the authors not only obtain the optimal transmission throughput but also reduce packet reordering delays under varying drop and delay conditions caused by the underlying network.

‘The gloomy forebodings of this dread disease’, climate, famine and sleeping sickness in East Africa

Identifying the nature of the association between climate, environmental, socio‐economic and political context and disease remains a major challenge, yet a better comprehension of the linkages is imperative if predictive models to guide public health responses are to be devised. Our understanding of the relationships could be improved through investigations of historical epidemics. In this paper we draw on a range of published and unpublished documents to explore the complex relationship between climate, environmental change and epidemic disease (re)emergence in East Africa, and Uganda in particular. This is a region which has experienced climate variability at a range of temporal and spatial scales, but which also has a long history of episodic epidemic disease. We focus on the late nineteenth and early twentieth centuries – a time of social, economic and political reordering in East Africa associated with European colonial intervention, but also a period which witnessed a variety of climatic, ecological and disease events. It will be argued that these developments coalesced, creating a set of spatially distinctive social and environmental conditions which fostered the emergence and prolongation of one of the most deadly episodes of disease in East African history, the sleeping sickness epidemic of c.1900–20.

Magnetization dynamics and theMn3+d−dexcitation of hexagonalHoMnO3single crystals using wavelength-tunable time-resolved femtosecond spectroscopy

We analyze the photo-induced carrier and magnetization dynamics in antiferromagnetic (AFM) ${\text{HoMnO}}_{3}$ single crystals, delineated by wavelength-dependent femtosecond spectroscopy. The emergence of long-range and short-range magnetic order are unambiguously revealed in association with an abnormal blueshift of ${\text{Mn}}^{3+}$ $3d$ level around the N\'eel temperature and the slope variation in the temperature-dependent transient reflectivity change $(\ensuremath{\Delta}R/R)$ near the N\'eel transition, respectively. Furthermore, the disturbance (in ps time scale) of the AFM ordering and its reordering time (in a few 100 ps time scale) are clearly identified in the negative $\ensuremath{\Delta}R/R$.

EOQ model for non-instantaneous deteriorating items with time-varying demand and partial backlogging

In this study, an EOQ model is developed for non-instantaneous deteriorating items with demand rate as time-dependent. In the model, shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Analytical results indicate that the optimal re-order time of the proposed model is unique and independent of the form of demand rate. Results are illustrated with the help of numerical examples. Computational results show that a decrease in the backlogging parameter causes the lower average total cost per unit time.

A Note on EOQ Model for Items with Mixtures of Exponential Distribution Deterioration, Shortages and Time-varying Demand

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. In this paper, we derive the EOQ model for inventory of items that deteriorates at a mixtures of exponential distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal reorder time Further, we also find that the optimal procedure is independent of the form of the demand rate. Finally, we also assume that the holding cost is a continuous, nonnegative and non-decreasing function of time in order to generalize EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.

Optimal reorder decision utilizing centralized stock information in a two-echelon distribution system

The objective of this paper is to develop an optimal reorder policy for a two-echelon distribution system with one central warehouse and multiple retailers. We assume the warehouse has centralized stock information and each facility uses continuous-review batch ordering policy. Since echelon stock policies may show poor performance for distribution systems, we propose a new type of policy that utilizes the centralized stock information more effectively. We define the order risk policy, which decides reorder time based on the order risk which represents the relative cost increase due to immediate order compared to delayed order. We formulate the order risk and prove the optimality of the order risk policy under the system assumption that the warehouse guarantees delivery within the fixed lead time. The order risk is derived from the marginal analysis. Since exact calculation of the order risk is complex, an approximation method is provided. Computational experiment that compares our policy with existing policies shows that a significant cost savings is obtained. The concept of the order risk can be extended to the other models. Scope and purpose Due to the improvement of modern information technologies, many companies start tracking the real-time stock information of the supply chain members. Thus, the reorder policy based on the real-time centralized stock information becomes very important. In this paper, we consider the reorder policy for a continuous-review batch-ordering two-echelon distribution system, utilizing the centralized stock information. Existing reorder policies are classified into installation stock policies and echelon stock policies. Since installation stock policies consider only local stock information, echelon stock policies have been used when the centralized stock information is available. For serial and assembly systems, it has been known that the echelon stock policies are superior to the installation stock policies. However, for distribution systems, both policies may outperform each other in different situations. The purpose of this study is to develop the optimal reorder policy for a distribution system with one-warehouse and multiple retailers, where the real-time stock information is centralized at the warehouse. We define a new type of reorder policy of which the reorder decision is based on the ‘order risk’. The order risk is defined as the relative cost increase due to immediate order compared to delayed order. We formulate the order risk and prove the optimality. For computational simplicity, we provide an approximation method to calculate the order risk. Computational experiment shows that a significant cost savings is obtained.

Optimizing Inventory Replenishment of Retail Fashion Products

We consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution, and report results of the application of our procedure at a catalog retailer. Our procedure improves on the existing method by enough to double profits. In addition, our method can be used to choose the optimal reorder time, to quantify the benefit of leadtime reduction, and to choose the best replenishment contract.

An inventory model for deteriorating items with stock-dependent demand and shortages under inflation and time discounting

This paper develops a finite time-horizon deterministic economic order quantity (EOQ) inventory model for deteriorating items. The items deteriorating at a constant rate and the demand at any instant depends on the on-hand inventory (stock-level) at that instant, shortages are allowed and completely backordered and the effects of inflation and time-value of money are taken into consideration. The proposed model facilitates managers in determining the optimal number of replenishments and optimal reorder time point. The results are discussed with two numerical examples and a sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.