Stock Control Using the Stock Level Frequency Distribution

Stock level frequency distributions are derived for continuous review stock control policies in which the lead time demand is normally distributed. The percentage points of the distributions have been tabulated, and the table can be used to determine the reorder point that will meet a specified customer order quantity from stock with a specified probability. The results can also be used to determine the order up to point for a periodic review policy and the reorder point for a mixed policy.     

A Probabilistic Expert System for Automatic Musical Accompaniment

This article presents methodology that allows a computer to play the role of musical accompanist in a nonimprovised musical composition for soloist and accompaniment. The modeling of the accompaniment incorporates a number of distinct knowledge sources including timing information extracted in real-time from the soloist's acoustic signal, an understanding of the soloist's interpretation learned from rehearsals, and prior knowledge that guides the accompaniment toward musically plausible renditions. The solo and accompaniment parts are represented collectively as a large number of Gaussian random variables with a specified conditional independence structure—a Bayesian belief network. Within this framework a principled and computationally feasible method for generating real-time accompaniment is presented that incorporates the relevant knowledge sources. The EM algorithm is used to adapt the accompaniment to the soloist's interpretation through a series of rehearsals. A demonstration is provided from J.S. Bach's Cantata 12.     

灰色理论结合专家系统预测煤层气井压裂效果

煤层气井水力压裂效果受煤层条件、煤层气井条件、压裂施工参数等影响,压裂效果难以预测.通过对煤层气井压裂后累积增产量分析,从中确定出煤层厚度、煤层深度、煤层渗透率等26个影响煤层气井压裂效果的因素.运用灰色关联法筛选主要因素和次主要因素,并分别建立不同的隶属函数用于专家系统的知识库建立,形成一种灰色理论结合专家系统的煤层气井压裂效果预测方法.将方法运用与鄂尔多斯某区块,对200组测试数据进行计算,预测错误率仅为3.5%.计算结果表明,方法预测结果准确可靠,可为煤层气井压裂优化提供指导.     

Experiences in Developing an Expert System for MBA Admissions

An expert system to assist in admitting students onto a part-time postgraduate course has been developed through three phases, using an expert systems shell. The first phase was an unstructured approach, which demonstrated the feasibility of the system but led to difficulties in development. The second phase followed a simplified systems analysis and resulted in a more comprehensive and structured system. However, its operation was cumbersome and unfriendly. The third phase involved developing a mathematical model of the decision-maker's judgement and led to a simpler, more effective and easier to use system.     

A Problem-driven Approach to Expert System Development

Expert system technology can fairly be described as high profile at present. Yet its track record as a useful method for tackling problems is subject to widely differing views. This paper considers the domain of production planning and control, which has been described as a good application area for expert systems a domain where OR has had little success. The authors argue that mainstream expert system methodology is exploratory rather than problem-driven and thus is not suited to the domain. A problem-driven approach to expert system development is presented, an approach which makes use of soft systems methodology. The reasons for such an approach within production planning and control are discussed, and the use of soft systems methodology within the approach is reflected on.     

Technical Stability of an Automatic Control System with a Changing Structure in the Neutral Case

We obtain conditions for the technical stability, with respect to a given measure, of autonomous dynamical systems with a discontinuous control for all possible initial conditions ranging over a given region of admissible initial perturbations of the processes under consideration. The formulated criteria depend on properties of roots of the secular equation of a given quadratic form corresponding to the control system under investigation.     

An Interactive Stock Control System with a Strategic Management Role

This note describes the design, implementation and consequences of a stock control system employing interactive mini computers for a number of builders and plumbers merchants.The system enables the quantification of the strategic decisions of the company, for example the consequences of changing the total investment in stock, or the overall service level. The selected strategy determines the calculations used for the interactive buying routines, which consider items in groups. Other aspects and the results of the implementation are described together with the necessary theory and routines employed.     

Piecewise Polynomial Approximate Solutions of an Automatic Control Problem

This paper considers piecewise polynomial approximate solutionsof a variational problem in which boundary conditions dependon values on the solution at interior points. The approximatesolutions are shown to converge to the solution of the variationalproblem in the L² and uniform norms, and algorithms for findingthe approximate solutions are obtained. Numerical examples arealso given.     

A Nomogram for Stock Control

A well-known replenishment policy for an inventory subject to probabilistic demand gives rise to the problem of determining an order quantity and a reorder level which minimize the average cost of keeping inventory. If the problem can be expressed in terms of a simple approximative model which includes a restriction on back-orders and represents demand in the replenishment lead time as normally distributed, it is possible to construct a "set-square index" nomogram which accomplishes a major part of the necessary computations. The procedure for using the nomogram and the principles of its construction are described.     

Application of Dynamic Programming to the Control of Stock and to the Calculation of a Maximum Stock Capacity

At the beginning the problem, as expressed by the heads of the Company which posed it, was in essence to find out whether, within the framework of a limited and well-defined expansion to level off in 1961, the existing capacity for stocks at a port used for shipping overseas would or would not be sufficient (it was thought it would not be).If more warehouses were shown to be needed, the amount of this extra capacity was to be worked out.It was very quickly discovered by an examination of the situation that the real problem would be rather to advise rules of stock management so as to take the best advantage of the existing stock capacity, in this way reducing the investment in buildings and maintenance to a minimum.Study of the model confirmed that the new management rules would make it unnecessary to increase the existing stock capacity.The model has the following characteristics: non-stationary process (e.g. an ever-changing situation), and an absence of any hypothesis on even the type of decision as to the method of renewing stock.Dynamic Programming used for this set of circumstances has made it possible to arrive at optimum management rules, demonstrating, incidentally, the power of this method in the study of non-stationary processes.     

Problem of Stabilizing a Switching System Using a Piecewise-Linear Control System

The problem of stabilizing a mathematical hybrid system with switchings between the operating modes is solved. Each of these modes is associated with nonlinear differential equations that have control parameters. The switching instances (conditions) are control components. A stabilizer must be designed in positional form that allows the trajectory of the entire nonlinear system to reach the target set in the phase space for a (prescribed) finite time. To solve the problem, k]an apparatus of continuous piecewise-linear Lyapunov functions is used along with the corresponding piecewise-linear control functions. A theorem concerning the sufficient conditions for the stabilizability of a hybrid system in the considered class of controls is proved. An algorithm for constructing the Lyapunov functions and the stabilizer is given.

     

A Stock Control Policy for Important Spares in a Two Level Stores System

This paper describes the results of an investigation to determine correct re-order levels and order quantities. The problem had three important features:

1. i)
   a simple stock control system was required for about 15,000 items;
    
2. ii)
   run-out costs needed to be estimated;
    
3. iii)
   the solution required best stock levels and order quantities for a central store and for smaller stores supplied by it.
    

The problem arose because it was felt that production delays were being caused by the stores too frequently being unable to supply spares.Items were grouped by their importance and portability. Average run-out costs were estimated for each group. An approximate model of the two level stock holding problem was derived. An iterative process was required to obtain solutions.It was observed that the stock control rules were insensitive to run-out cost, and that items of equal run-out cost had widely differing run-out probabilities. This indicates that, in this case, it is invalid to group items by importance and to assign fixed run-out probabilities to each group.     

A Criterion for an Optimal Control System to have Finite Switchings

A simple criterion is suggested which determines whether ornot an optimal control system has a finite number of switches.The results are developed using as an example the simple system with performance criterion , but are shown to hold for the more general system where f(0, 0) = 0 (i.e. the uncontrolled system has the originas an equilibrium point) subject to a performance criterion where g(0, 0) 0. The cases where g(0, 0)and are zero for all are also discussed. In particular one obtains a very simpleproof of the result that all two dimensional time optimal controlsystems with a single linear control, whose objective set consistsof the (assumed) unique critical point of the uncontrolled system,have a finite number of switches.     

Development of an Expert System: Translating Higher-Level Decisions into Lower-Level Aircraft Flights

This note describes two phases in the development of an expert system that translates European-wide directives into individual flight orders. This expert system was built for a military computer simulation, but parts of the logic can apply — and many of the illustrations in the text have been tailored — to creating and organizing commercial flights. The first phase of the development — a proof of principle expert system — emulated the logical deductions of an air traffic control supervisor or a flight planner. The second phase of development led to a working prototype decision support system that employed more mathematical comparisons of aircraft attributes than logical deductions.     

Validating an Expert Support System for Tender Enquiry Evaluation: A Case Study

An expert system was developed as a support tool for a large electro-mechanical engineering company. The system was developed to assist in tender enquiry evaluation and the bid versus no bid decision. It was developed using repertory grid techniques based on the expertise of two senior managers. The importance of the system's validation is stressed and an appropriate formal validation framework developed. The results from the validation study suggest that the system provides an appropriate model of the organization's consensual business perspective regarding the bid versus no bid decision. Furthermore, the study drew attention to some dissenting views amongst the organization's senior management which the management believed to be helpful in clarifying their understanding of the issues affecting the bid versus no bid decision.     

The Application of the Negative Binomial Distribution to Stock Control Problems

Random demand and a gamma distribution of lead times results in a negative binomial distribution of the number of demands during a lead time. This fact, together with a rather surprising mathematical equality, enables one to use tables of the positive binomial distribution to determine reorder levels and also to calculate stocks of rotable components for aircraft.     

An Automatic User-Recognition Approach Within a Reputation System Using a Nonlinear Hausdorff-Derived Metric

In this paper, we provide an automatic unsupervised recognition technique for Web community user reputations that uses a special nonlinear metric. First we describe the general framework for reputation systems. Then, we propose a feature extraction approach for the reputation system users. The resulting feature vectors (reputations) are clustered with an unsupervised classification algorithm using a nonlinear distance, derived from the Hausdorff metric for sets.