The diffusion process and residual stock in periodic review,coordinated control of families of items

Inventory control models which provide coordinated control ( or joint replenish ment) of families of items are very useful in practice. These models require expressions for the residual stock levels for each item in the family when a replenishment is placed. In this paper expressions are developed for the periodic review residual stock probability density function, when inventory position is modelled as a diffusion process, and heuristics are presented for quick calculation of these expressions. The importance of residual stock in setting inventory control model parameters is illustrated by showing how residual stock is taken into account in establishing item reorder points. The relationship of these residual stock pdf expressions to other components in a new class of coordinated control models is also discussed. This class of models has been shown to outperform existing models (IBM's IMPACT Inventory Control package).     

Accounting for residual stock in continuous review coordinated control of a family of items

Inventory models which permit coordinated control (or joint replenishment) of families of items are of considerable interest in practice. A major complexity in coordinated control is that, typically, one item triggers the family order and the other items have stock remaining above their reorder points. Account should be taken of this so-called residual stock when establishing the reorder points. In this paper, modelling the inventory position as a diffusion process permits us to develop expressions for the components of the residual stock probability density functions. Heuristics are presented for quick calculation of these expressions. Then we show how residual stock is taken into account in determining the reorder points of the individual items. The relationship of these residual stock pdf expressions to other components in a new class of coordinated control models is also discussed. This class of models has been shown to outperform existing models (IBM's IMPACT Inventory Control package(.     

A new class of parametric IRT models for dichotomous item scores

A new class of parametric IRT models for dichotomously scored items is presented. The new class of models is a subclass of both the class of models defined by the four-parameter logistic item response function and the nonparametric Double Monotonicity (DM) model. Three special cases of this new class of models are discussed. One of these special cases is shown to be the one-parameter logistic Rasch model. Both specific objectivity at the interval level of measurement and the sufficiency of the total score for the latent trait are shown to be measurement properties of the whole new class of models. For maximum likelihood estimation of the model parameters, both a joint and a conditional likelihood function are proposed.     

A survey of literature on reordering of stock items for production inventories

The problem of inventory control has received increasing attention over the last 16 to 20 years, which has resulted in a vast amount of literature. Two types of inventory can be distinguished: (1) manufacturing inventories, which contain dependent demand items and are most efficiently controlled by means of Material Requirements Planning (MRP), and (2) distribution inventories, which contain independent demand items and for which Statistical Inventory Control (SIC) techniques are usually employed.

This paper is a survey of the literature available on the management of production inventories. It deals with, and compares, MRP and SIC as both these techniques are used in industry.

For literature published before 1972 this survey has been based mainly on review articles, but for the period of 1972 to 1976 original books and papers are reviewed and listed as references.     

A control system for coordinated inventory replenishment*

There are frequent occasions where the coordination of replenishment orders for selected groups of items can lead to significant savings in the costs of replenishment. This paper is concerned with a practical procedure for selecting the order-up-to-levels, can-order points and must-order points of a particular coordinated control system. Demand is Foisson and a fixed non-zero replenishment lead time is assumed. Cost comparisons with the best independent control strategy indicate that substantial savings (averaging 18-8% over some 104 examples) are possible through coordination.     

Models and algorithms for the dynamic-demand joint replenishment problem

This paper considers the problem of coordinated ordering of items having deterministic but time-varying demands where there is a common ordering cost if one or more of these items are ordered in addition to individual items ordering costs. Two new integer linear-programming formulations are presented and compared with the classical formulation. Several well-known heuristics are described and a new improvement procedure is proposed. The relative performance of these heuristics is assessed. Results show the superiority of the new formulations and of the new improvement procedure.     

一种费用最小的非阻塞协同检查点算法

将协同检查点策略中采取的最小化同步信息以及检查点数量的策略与不阻塞进程的基本运行策略相结合,提出了一种只需最小数量的进程参与的非阻塞协同检查点算法。该算法利用计算检查点避免由于不阻塞进程的基本执行可能产生的孤儿消息。通过在广播确认消息中捎带哪些进程产生了新的检查点的信息,使每个进程的检查点序号在所有进程中是一致的。该算法在费用上优于已有的协同检查点算法。     

Reducing the item number to obtain same-length self-assessment scales: a systematic approach using result of graphical loglinear Rasch modeling

The Revised Danish Learning Styles Inventory (R-D-LSI) (Nielsen 2005), which is an adaptation of Sternberg-Wagner Thinking Styles Inventory (Sternberg, 1997), comprises 14 subscales, each measuring a separate learning style. Of these 14 subscales, 9 are eight items long and 5 are seven items long. For self-assessment, self-scoring and self-interpretational purposes it is deemed prudent that subscales measuring comparable constructs are of the same item length. Consequently, in order to obtain a self-assessment version of the R-D-LSI with an equal number of items in each subscale, a systematic approach to item reduction based on results of graphical loglinear Rasch modeling (GLLRM) was designed. This approach was then used to reduce the number of items in the subscales of the R-D-LSI which had an item-length of more than seven items, thereby obtaining the Danish Self-Assessment Learning Styles Inventory (D-SA-LSI) comprising 14 subscales each with an item length of seven. The systematic approach to item reduction based on results of GLLRM will be presented and exemplified by its application to the R-D-LSI.     

A bilinear programming model and a modified branch-and-bound algorithm for production planning in steel rolling mills with substitutable demand

In this paper, we address an instance of the dynamic capacitated multi-item lot-sizing problem (CMILSP) typically encountered in steel rolling mills. Production planning is carried out at the master production schedule level, where the various end items lot sizes are determined such that the total cost is minimised. Through incorporating the various technological constraints associated with the manufacturing process, the integrated production–inventory problem is formulated as a mixed integer bilinear program (MIBLP). Typically, such class of mathematical models is solved via linearisation techniques which transform the model to an equivalent MILP (mixed integer linear program) at the expense of increased model dimensionality. This paper presents an alternative branch-and-bound based algorithm that exploits the special structure of the mathematical model to minimise the number of branches and obtain the bound at each node. The performance of our algorithm is benchmarked against that of a classical linearisation technique for several problem instances and the obtained results are reported.     

一种基于蜜蜂进化选择算子的布局遗传算法

三维矩形布局问题属于NP难问题,对于三维矩形布局问题的求解大多依赖于各种启发式算法.该文以布局物体体积递减为定序规则,结合布局物体在布局空间中的几何可行域,以吸引子法为定位规则,利用蜜蜂进化型遗传算法优化吸引子函数中的参数来求解三维矩形布局问题（BEGA）,得到新型布局遗传算法.最后对不同的算例进行了计算,并与以标准比例选择作为选择算子的传统布局遗传算法（SPGA）等对比证明了该算法的有效性.     

Nonlinear control charts for jump detection

This paper presents a new class of nonlinear control charts which respond quickly to small shifts and jump patterns in tme series. The underlying disturbance models for the control charts are nonlinear extensions of the IMA(1,1) model. The Kalman filtering algorithm generates Bayesian estimates of the process level for the control chart plotting. The single-parameter chart is identical to the EWMA, while the two- and three-parameter designs are much more effective in detecting small shifts mixed with local trends. The nonlinear control charting scheme is also capable of detecting a mean shift in independent observation.     

A new approach to common cause failure

This paper presents a new approach to the problem of the quantification of common cause failure in systems. The basis of the new approach is the variability of a component's failure probability with ‘environment’, where the ‘environment’ means not just the obvious ambient conditions, but all the details which have a material effect on the component's performance. This variability is represented by a probability distribution for the failure probability. Different forms for this distribution describe a class of common cause failure models, which is shown to include the β-factor model and the Binomial Failure Rate model as special cases. It is also shown how this distribution can be estimated directly from data on multiple failures, so avoiding the use of any specific model. This direct procedure represents a novel way in which judgement is used to decide the relevance of particular data items to particular situations, and those considered relevant are used to construct the required probability distribution. The consequence of this direct use of data rather than fitting it to models, is a method that is general, simple, realistic rather than conservative, distinguishes between different levels of redundancy, and can be applied to ‘diffuse’ systems (i.e. those which rely on many or most of their components, such as control rod systems). Examples are given which show the ease with which the method can be applied, even using multiple failure data of poor quality.     

A data mining approach to optimise shelf space allocation in consideration of customer purchase and moving behaviours

A good shelf space allocation strategy can help customers easily find product items and dramatically increase store profit. Previous studies generally relied on the space elasticity formula to optimise space allocation models, but space elasticity requires estimates of many parameters, resulting in high costs and frequent errors in the mathematical models. In this study, a three-stage data mining method is proposed for solving the shelf space allocation problem with consideration of both customer purchase and moving behaviours. In the first stage, the customer’s purchasing behaviour is derived from records of previous transactions, while moving behaviour is collected through radio frequency identification systems. In the second stage, the A priori algorithm is applied to obtain frequent product association rules from purchase transactions. In addition, the UMSP_L algorithm is adopted to derive high-utility mobile sequential patterns from customer mobile transaction sequences. In the third stage, all product items are classified as either major, minor or trivial according to a set of criteria. A Location preference evaluation procedure is then developed to calculate location preference if a minor item is placed at a given section of the store. Based on the location preference matrix, minor items are reassigned to optimal shelves. The experimental results show the proposed method can reassign items to suitable shelves and dramatically increase cross-selling opportunities for major and minor items.     

Establishing reorder points in the (S,c,s) coordinated control system under compound Poisson demand

This paper is concerned with the coordinated control of a group of inventoried items in order to reduce the costs of replenishments. The specific control system considered is what is denoted as an (S,c,s) system. The very general case of compound Poisson demand is considered. In earlier work a procedure was developed for finding the order-up-to levels (i.e. the Ss) and the can-order points (i.e. the cs) for the case of a negligible lead time. Taking these quantities as input an algorithm is developed for finding the must-order points (i.e the.s values) so as to satisfy one of two types of service constraints specified item by item. The results of two numerical illustrations are also shown.     

A new inspection sampling plan under capacity constraints and multiple shifts

Various SPC models have been widely deployed in the quality control of different production systems. This paper considers a new design of SPC model with associated decision rules to control a process that produces items in finite lots and has a variance shift as well as a mean shift. Under both an inspection capacity constraint and a false alarm rate constraint, an inspection sampling plan that maximizes the yield of production is developed. Numerical examples are presented to illustrate and evaluate the approach. A semi-economic approach that computes the optimal quantity of inspection capacity is also presented.     

A New Microengineered Platform for 4D Tracking of Single Cells in a Stem-Cell-Based In Vitro Morphogenesis Model

Recently developed stem-cell-based in vitro models of morphogenesis can help shed light on the mechanisms involved in embryonic patterning. These models are showcased using traditional cell culture platforms and materials, which allow limited control over the biological system and usually do not support high-content imaging. In contrast, using advanced microengineered tools can help in microscale control, long-term culture, and real-time data acquisition from such biological models and aid in elucidating the underlying mechanisms. Here, a new culturing, manipulation and analysis platform is described to study in vitro morphogenesis using thin polycarbonate film-based microdevices. A pipeline consisting of open-source software to quantify 3D cell movement using 4D image acquisition is developed to analyze cell migration within the multicellular clusters. It is shown that the platform can be used to control and study morphogenesis in non-adherent cultures of the P19C5 mouse stem cell line and mouse embryonic stem cells (mESCs) that show symmetry breaking and axial elongation events similar to early embryonic development. Using the new platform, it is found that localized cell proliferation and coordinated cell migration result in elongation morphogenesis of the P19C5 aggregates. Further, it is found that polarization and elongation of mESC aggregates are dependent on directed cell migration.     

A general optimality criteria algorithm for a class of engineering optimization problems

An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.     

A note on evaluating the risk in continuous review inventory systems

This paper is an attempt to evaluate the long term risk of stock-out and obsolescence in continuous review inventory systems, typically of slow-moving but very critical items. Inventory decisions depend very much on the goodness of the estimates of the input parameters like the holding, ordering and stock-out costs. It is a well-known fact that stock-out cost is a very difficult parameter to estimate. The lower it is the lower the quality of service will be while the higher it is the higher the inventory cost would be and possibly higher obsolescence rate too. In this paper, we develop a framework to evaluate the risks, in the long term, of stock-out and obsolescence, especially for inventory of critical spares whose demand rate is not high. For this purpose, we propose the use of quasi-stationary distributions for continuous review (r, Q) inventory systems with the condition that the Laplace transforms of functions of interest are rational algebraic functions. We relate the quasi-stationary distribution to the conditional tail expectation which is a coherent risk measure used in finance and actuarial studies. Numerical illustration is also provided.     

Integrated optimisation on flow-shop production with cutting stock

This paper addresses the integrated scheduling optimisation on flow-shop production with one-dimensional cutting stock in make-to-order environments. The upstream cutting-stock process provides the items for the downstream production, while the flow-shop production can be executed only when the required items are released. The efficient schedules on cutting plan and the production sequence should be determined in a coordinated manner to improve the overall efficiency. This study aims to find an integrated schedule to minimise the makespan of the entire manufacturing process. We develop a hybrid algorithm by integrating a local search method and some efficient strategies under the nested partitions framework. Numerical experiments show that the proposed approach is capable of achieving high-quality solutions within a reasonable time.