On the optimum capacity of capacity expansion problems

In this paper we consider problems of the following type: Let E = { e ₁, e ₂,..., e _n } be a finite set and be a family of subsets of E. For each element e _i in E, c _i is a given capacity and _i is the cost of increasing capacity c _i by one unit. It is assumed that we can expand the capacity of each element in E so that the capacity of family can be expanded to a level r. For each r, let f (r) be the efficient function with respect to the capacity r of family , and be the cost function for expanding the capacity of family to r. The goal is to find the optimum capacity value r ^* and the corresponding expansion strategy so that the pure efficency function is the largest. Firstly, we show that this problem can be solved efficiently by figuring out a series of bottleneck capacity expansion problem defined by paper (Yang and Chen, Acta Math Sci 22:207–212, 2002) if f (r) is a piecewise linear function. Then we consider two variations and prove that these problems can be solved in polynomial time under some conditions. Finally the optimum capacity for maximum flow expansion problem is discussed. We tackle it by constructing an auxiliary network and transforming the problem into a maximum cost circulation problem on the auxiliary network.     

Analysis of a finite capacity assembly system

Consider a finite capacity automatic assembly system consisting of a set of tandem work stations linked by a material handling system. Each work station consists of a set of machines and a local preprocessed inventory. The material handling system consists of a set of continuous line conveyors. Each conveyor has a beginning and an end with a specified length, velocity and capacity. The performance of the above manufacturing system is analyzed based on a mixed queuing network model, in the steady state. A methodology is presented for controlling blocking of the manufacturing system such that the probability of finding either a work station or a conveyor blocked will be sufficiently close to zero. Finally, numerical results are provided and the concluding remarks are discussed.     

On a capacity for modular spaces

The purpose of this article is to define a capacity on certain topological measure spaces X with respect to certain function spaces V consisting of measurable functions. In this general theory we will not fix the space V but we emphasize that V can be the classical Sobolev space W1,p(Ω), the classical Orlicz-Sobolev space W1,Φ(Ω), the Haj?asz-Sobolev space M1,p(Ω), the Musielak-Orlicz-Sobolev space (or generalized Orlicz-Sobolev space) and many other spaces. Of particular interest is the space given as the closure of in W1,p(Ω). In this case every function u∈V (a priori defined only on Ω) has a trace on the boundary ∂Ω which is unique up to a Capp,Ω-polar set.     

An analytical approach to calculate the capacity of a railway system

Railway capacity is a concept that is not easily defined or quantified. Difficulties include the numerous interrelated factors present in the already complex structure of the railway layout. In this paper capacity is defined as the maximum number of trains that can traverse the entire railway in a given period of time, subject to management constraints (such as junction capacity, track capacity, line capacity and interference probability between trains). The proposed method is based on defining and solving an optimization problem which aims at finding out the capacity value of a railway system. It is not based on timetables and moreover it can indirectly take into account priorities between trains and possible delays; it is able to give the time occupation percentage in each component for each train category. It has been applied to a real-life case study showing the range of its validity and the possibility of application for any generic railway scheme.     

On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-N system with wear-out

In this paper we consider a k-out-of-N system with identical, repairable components under a condition-based maintenance policy. Maintenance consists of replacing all failed and/or aged components. Next, the replaced components have to be repaired. The system availability can be controlled by the maintenance policy, the spare part inventory level, the repair capacity and repair job priority setting. We present two approximate methods to analyse the relation between these control variables and the system availability. Comparison with simulation results shows that we can generate accurate approximations using one of these models, depending on the system size.     

关于Shannon的容量问题

1.问题简历 这里要阐述的问题,最早是C.Shannon在1956年提出的,尔后,C.Berge在其1958年出版的书“图论及其应用”中,把它列为未解决的问题之一;O.Ore在其1962年出版的“图论”一书中,又专列一节论述这个问题。从此Shannon的这个问题广为传播,成为一个著名的图论难题。事隔25年后,C.Berye在其1973年英文版的“图与超图”一书中,再次专门提出了这个问题,更加提高了Shannon问题的知名度和挑战性。     

On the efficiency and capacity of computers

We address the problems of estimating the computer efficiency and the computer capacity. We define the computer efficiency and capacity and suggest a method for their estimation, based on the analysis of processor instructions and kinds of accessible memory. Obtained results can be of some interest for practical applications.     

An optimality criterion for a limited capacity queueing system

A single server, limited capacity queueing system with Poisson arrivals and exponential service is studied. The joint probability distribution of the number of times the system reaches its capacity in time interval (0t] and the number of customers in the system at time i has been obtained. From, the joint probability, the probability that the system has reached its capacity m times in time interval (0t] has been determined and the expectation and variance have been found explicitly. A criterion for the system to be optimum is established and is illustrated numerically.     

Joint demand and capacity management in a restaurant system

This paper studies the demand and capacity management problem in a restaurant system. A queueing-based optimization model with underlying quasi birth-and-death process and state-dependent functions is developed to address the dynamic and nonlinearity difficulties. In particular, our model explicitly captures the demand changes with respect to the system congestion state on a near real-time dynamic basis. With this framework, we empirically examine the relative performance of commonly used strategies for the case of a local restaurant. The study shows that a strategy that balances service quality and cost yields maximum profit. The result indicates that the traditional view of the conflict between service quality and cost can be overcome by using an interdisciplinary perspective of marketing and operations. Both perspectives should be embraced in academic research and industrial practice in capacity planning decisions for services.     

On asymmetry and capacity

This research was carried out while Professor Weitsman was visiting the University of York. He wishes to thank the SERC for its support and the Department of Mathematics of the University of York for its hospitality. Research supported in part by the N.S.F.     

On capacity characteristics of condensers

We introduce and study a one-parameter family of capacity characteristics of condensers in ? ^p ,p ≥ 3, that contains some known capacities as elements extremal with respect to the parameter. We establish new relations between the capacity characteristics of condensers and sets.     

On the optimality of a maintenance queueing system

We consider a finite single-server maintenance queue with multiple types of customers. The difference between customers' types is defined by the offered rewards. We show that the optimal admission control policy for maximizing the long-run average reward per unit time has a trunk reservation structure. Meanwhile, if the equipment is off, there exists a threshold of the queue length, above which the optimal repair speed is increasing in the queue length and below which the optimal repair speed is 0.     

On the symmetries of a Rikitake type system

A symplectic realization and some symmetries of a Rikitake type system are presented.