Design models for unit load storage and retrieval systems using autonomous vehicle technology and resource conserving storage and dwell point policies

Computationally efficient design conceptualization models are proposed for automated unit load storage and retrieval systems based on autonomous vehicle technology. Vehicle and lift travel times and the probability distribution for 12 service scenarios occurring under realistic operating assumptions are formulated and used to generate expected transaction service times. Additional measures of system performance including transaction waiting time and vehicle utilization are formulated for systems using random storage and point-of-service-completion dwell point rules. The models provide a practical means of predicting key aspects of system performance based on five design variables that drive the majority of system costs. They are illustrated in the context of a conceptualization study adapted from an actual system installation.     

Travel time models for automated warehouses with aisle transferring storage and retrieval machine

This paper presents analytical travel time models for the computation of travel time for automated warehouses with the aisle transferring S/R machine (in continuation multi-aisle AS/RS). These models consider the operating characteristics of the storage and retrieval machine such as acceleration and deceleration and the maximum velocity. Assuming uniform distributed storage rack locations and pick aisles and using the probability theory, the expressions of the cumulative distribution functions with which the mean travel time is calculated, have been determined. The computational models enable the calculation of the mean travel time for the single and dual command cycles, from which the performance of multi-aisle AS/RS can be evaluated. A simulation model of multi-aisle AS/RS has been developed to compare the performances of the proposed analytical travel time models. The analyses show that regarding all examined types of multi-aisle AS/RS, the results of proposed analytical travel time models correlate with the results of simulation models of multi-aisle AS/RS.     

A storage model for data communication systems

We consider a storage model where the input and demand are modulated by an underlying Markov chain. Such models arise in data communication systems. The input is a Markov-compound Poisson process and the demand is a Markov linear process. The demand is satisfied if physically possible. We study the properties of the demand and its inverse, which may be viewed as transformed time clocks. We show that the unsatisfied demand is related to the infimum of the net input and that, under suitable conditions, it is an additive functional of the input process. The study of the storage level is based on a detailed analysis of the busy period, using techniques based on infinitesimal generators. The transform of the busy period is the unique solution of a certain matrix-functional equation. Steady state results are also obtained; these are not obvious generalizations of the results for simple storage models. In particular, a generalization of the Pollaczek-Khinchin formula brings new insight.Research supported by Grant BD/645/90-RM from Junta Nacional de Investigação Cientifica e Tecnológica.     

A survey of literature on automated storage and retrieval systems

Automated Storage and Retrieval Systems (AS/RSs) are warehousing systems that are used for the storage and retrieval of products in both distribution and production environments. This paper provides an overview of literature from the past 30 years. A comprehensive explanation of the current state of the art in AS/RS design is provided for a range of issues such as system configuration, travel time estimation, storage assignment, dwell-point location, and request sequencing. The majority of the reviewed models and solution methods are applicable to static scheduling and design problems only. Requirements for AS/RSs are, however, increasingly of a more dynamic nature for which new models will need to be developed to overcome large computation times and finite planning horizons, and to improve system performance. Several other avenues for future research in the design and control of AS/RSs are also specified.     

Some criteria for the existence of invariant measures and asymptotic stability for random dynamical systems on polish spaces

Tomasz Szarek presented interesting criteria for the existence of invariant measures and asymptotic stability of Markov operators on Polish spaces. Hans Crauel in his book presented the theory of random probabilistic measures on Polish spaces showing that notions of compactness and tightness for such measures are in one-to-one correspondence with such notions for non-random measures on Polish spaces, in addition to the criteria under which the space of random measures is itself a Polish space. This result allowed the transfer of results of Szarek to the case of random dynamical systems in the sense of Arnold. These criteria are interesting because they allow to use the existence of simple deterministic Lyapunov type function together with additional conditions to show the existence of invariant measures and asymptotic stability of random dynamical systems on general Polish spaces.     

A hybrid feedback control strategy for autonomous waypoint transitioning and loitering of unmanned aerial vehicles

We consider the problem of autonomously controlling a fixed-wing aerial vehicle to visit a neighborhood of a pre-defined waypoint, and when nearby it, loiter around it. To solve this problem, we propose a hybrid feedback control strategy that unites two state-feedback controllers: a transit controller capable of steering or transitioning the vehicle to nearby the waypoint and a loiter controller capable of steering the vehicle about a loitering radius. The aerial vehicle is modeled on a level flight plane with system performance characterized in terms of the aerodynamic, propulsion, and mass properties. Thrust and bank angle are the control inputs. Asymptotic stability properties of the individual control algorithms, which are designed using backstepping, as well as of the closed-loop system, which includes a hybrid algorithm uniting the two controllers, are established. In particular, for this application of hybrid feedback control, Lyapunov functions and hybrid systems theory are employed to establish stability properties of the set of points defining loitering. The analytical results are confirmed numerically by simulations.     

Symbolic models for infinite networks of control systems: A compositional approach

This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite network. The proposed approach is based on the notion of alternating simulation functions. This notion relates a concrete network to its symbolic model with guaranteed mismatch bounds between their output behaviors. We propose a compositional approach to construct a symbolic model for an infinite network, together with an alternating simulation function, by composing symbolic models and alternating simulation functions constructed for subsystems. Assuming that each subsystem is incrementally input-to-state stable and under some small-gain type conditions, we present an algorithm for orderly constructing local symbolic models with properly designed quantization parameters. In this way, the proposed compositional approach can provide us a guideline for constructing an overall symbolic model with any desired approximation accuracy. A compositional controller synthesis scheme is also provided to enforce safety properties on the infinite network in a decentralized fashion. The effectiveness of our result is illustrated through a road traffic network consisting of infinitely many road cells.     

A primogenitary linked quad tree approach for solution storage and retrieval in heuristic binary optimization

A data structure, called the primogenitary linked quad tree (PLQT), is used to store and retrieve solutions in heuristic solution procedures for binary optimization problems. Two ways are proposed to use integer vectors to represent solutions represented by binary vectors. One way is to encode binary vectors into integer vectors in a much lower dimension and the other is to use the sorted indices of binary variables with values equal to 0 or equal to 1. The integer vectors are used as composite keys to store and retrieve solutions in the PLQT. An algorithm processing trial solutions for insertion into or retrieval from the PLQT is developed. Examples are provided to demonstrate the way the algorithm works. Another algorithm traversing the PLQT is also developed. Computational results show that the PLQT approach takes only a very tiny portion of the CPU time taken by a linear list approach for the same purpose for any reasonable application. The CPU time taken by the PLQT managing trial solutions is negligible as compared to that taken by a heuristic procedure for any reasonably hard to solve binary optimization problem, as shown in a tabu search heuristic procedure for the capacitated facility location problem. Compared to the hashing approach, the PLQT approach takes the same or less amount of CPU time but much less memory space while completely eliminating collision.     

A geometric approach for reachability and observability of linear switched impulsive systems

This paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices. First some new concepts with respect to the reachability and unobservability are introduced. Especially, span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces. Then the geometric characterization of the span reachable and unobservable sets is presented. Moreover, the relations between the span reachable set, unobservable set and the invariant subspaces of such systems are discussed. Finally, corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed.     

A new algebraic approach to stabilization for boundary control systems of parabolic type

We study the stabilization problem of linear parabolic boundary control systems. While the control system is described by a pair of standard linear differential operators (L,τ), the corresponding semigroup generator generally admits no Riesz basis of eigenvectors. In the sense that very little information on the fractional powers of this generator is needed, our approach has enough generality as a prototype to be used for other types of parabolic systems. We propose in this paper a new algebraic approach to the stabilization, which gives—to the best of the author's knowledge—the simplest framework of the problem. The control system with the scheme of boundary observation/boundary feedback is turned into the differential equations with no boundary input in usual and standard L²-spaces in a readable manner.     

A mathematical model for Babesiosis disease in bovine and tick populations

In this paper, we analyze the Babesiosis transmission dynamics on bovine and tick populations. Ticks play a role of infectious agents and vector of the protozoan Babesia hemo‐parasite. In this sense, we set out a mathematical model with constant size population for the evolution of the infected bovines with Babesiosis and analyze its qualitative dynamics. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model varying the parameters show different scenarios about the spread of the disease. Copyright © 2011 John Wiley & Sons, Ltd.     

A partial adjustment valuation approach with stochastic and dynamic speeds of partial adjustment to measuring and evaluating the business value of information technology

This paper extends previous studies to develop a partial adjustment valuation (PAV) approach in which the speeds of partial adjustment are assumed to be stochastic and dynamic over time in measuring and evaluating the values of information technology and others (e.g., e-commerce or EC, brand name, etc.). A practical application is presented to demonstrate the application of the proposed PAV approach and it is compared to the other two existing PAV approaches.     

A multiscale Galerkin approach for a class of nonlinear coupled reaction-diffusion systems in complex media

A Galerkin approach for a class of multiscale reaction-diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented. This type of models are obtained e.g. by upscaling of processes in chemical engineering (particularly in catalysis), biochemistry, or geochemistry. Exploiting the special structure of the models, the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure. Uniform estimates for the finite dimensional approximations are proven. Based on these estimates, the convergence of the approximating sequence is shown. This approach can be used as a basis for the numerical computation of the solution.     

A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems

In this paper, by means of monotone iterative technique, a necessary and sufficient condition of the existence of positive solution for a class of nonlinear singular differential system is established, the results of the existence and uniqueness of the positive solution and the iterative sequence of solution are given. In the end, two classes extending boundary value differential systems are discussed and some further results are obtained.     

New stability criteria for a class of neutral systems with discrete and distributed time-delays: an LMI approach

In this paper, a problem of the asymptotic stability for a class of neutral systems with multiple discrete and distributed time-delays is considered. Lyapunov stability theory is applied to guarantee the stability for the systems. New discrete-delay-independent and discrete-delay-dependent stability conditions are derived in terms of the spectral radius and linear matrix inequality. By mathematical analysis, the stability criteria are proved to be less conservative than the ones reported in the current literatures. A numerical example is given to illustrate the availability of the proposed results.     

On modeling failure and repair times in stochastic models of manufacturing systems using generalized exponential distributions

Failures of machines have a significant effect on the behavior of manufacturing systems. As a result it is important to model this phenomenon. Many queueing models of manufacturing systems do incorporate the unreliability of the machines. Most models assume that the times to failure and the times to repair of each machine are exponentially distributed (or geometrically distributed in the case of discrete-time models). However, exponential distributions do not always accurately represent actual distributions encountered in real manufacturing systems. In this paper, we propose to model failure and repair time distributions bygeneralized exponential (GE) distributions (orgeneralized geometric distributions in the case of a discretetime model). The GE distribution can be used to approximate distributions with any coefficient of variation greater than one. The main contribution of the paper is to show that queueing models in which failure and repair times are represented by GE distributions can be analyzed with the same complexity as if these distributions were exponential. Indeed, we show that failures and repair times represented by GE distributions can (under certain assumptions) be equivalently represented by exponential distributions.This work was performed while the author was visiting the Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.     

A new multicriteria approach for the analysis of efficiency in the Spanish olive oil sector by modelling decision maker preferences

The efficiency in production is often analysed as technical efficiency using the production frontier function. Efficiency scores are usually based on distance computations to the frontier in an m + s-dimensional space, where m inputs produce s outputs. In addition, efficiency improvements consider the total consumption of each input. However, in many cases, the “consumption” of each input can be divided into input-consumption sections (ICSs), and trade-off among the ICSs is possible. This share framework can be used for computing efficiency. This analysis provides information about both the total optimal consumption of each input, as does data envelopment analysis, and the most efficient allocation of the “consumption” among the ICSs. This paper studies technical efficiency using this approach and applies it to the olive oil sector in Andalusia (Spain). A non-parametrical methodology is presented, and an input-oriented Multi-Criteria Linear Programming model (MLP) is proposed. The analysis is developed at global, input and ICSs levels, defining the extent of satisfaction achieved at all these levels for each company, in accordance with their own preferences. The companies’ preferences are modelled with their utility function and their set of weights. MLP offers more detailed information to assist decision makers than other models previously proposed in the literature. In addition to this application, it is concluded that there is room for improvement in the olive oil sector, particularly in the management of the skilled labour. Additionally, the solutions with two opposite scenarios indicate that the model is suitable for the intended decision making process.     

A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions

In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions

     

Adaptive stabilization and regulator design for distributed-parameter systems in the case of collocated actuators and sensors

In this paper, we consider adaptive stabilization and an adaptiveregulator design for collocated distributed-parameter systemsin the case of the input and output operators being unbounded.Adaptive stabilization is realized by the concept of high-gainoutput feedback. The adaptive regulator is constructed via theconcept of high-gain output feedback, using a mechanism to estimatethe unknown parameters of the bounded disturbances. The stateof the controlled system is shown to converge to zero.