Approximations of solutions to infinite–dimensional algebraic riccati equations with unbounded input operators

In this paper an approximation theory is provided for the solutions of infinite dimensional Algebraic Riccati Equations, which in particular includes convergence of the approximating Riccati operators as well as convergence of the approximating gain operators. The main features which distinguish this paper from other work existing in the literature of Riccati approximation theory are: (i) the original free system only generates a strongly continuous semigroup; (ii) the input (control) operator is generally unbounded; and (iii) no “smoothing” hypothesis on the observation operator is assumed. The abstract theory is illustrated by several examples arising in boundary control problems for wave and plate equations.     

Structure of subspaces of the compact operators having the Dunford-Pettis property

The structure of the subspaces having the Dunford-Pettis property (DPP) is studied, where is the space of all compact operators on and . The following conditions are shown to be equivalent: (i) M has the DPP, (ii) M is isomorphic to a subspace of (iii) the sets and are relatively compact for all and . The equivalence between (i) and (iii) was recently proven in the case of arbitrary Hilbert spaces by Brown and ülger. It is also shown that (i) and (ii) are equivalent for subspaces . This result is optimal in the sense that for there is a DPP-subspace that fails to be isomorphic to a subspace of . Received January 9, 1998; in final form October 1, 1998     

Strong polynomiality of resource constraint propagation

Constraint-based schedulers have been widely successful in tackling complex, disjunctive, and cumulative scheduling applications by combining tree search and constraint propagation. The constraint-propagation step is a fixpoint algorithm that applies pruning operators to tighten the release and due dates of activities using precedence or resource constraints. A variety of pruning operators for resource constraints have been proposed; they are based on edge finding or energetic reasoning and handle a single resource.

Complexity results in this area are only available for a single application of these pruning operators, which is problematic for at least two reasons. On the one hand, the operators are not idempotent, so a single application is rarely sufficient. On the other hand, the operators are not used in isolation but interact with each other. Existing results thus provide a very partial picture of the complexity of propagating resource constraints in constraint-based scheduling.

This paper aims at addressing these limitations. It studies the complexity of applying pruning operators for resource constraints to a fixpoint. In particular, it shows that: (1) the fixpoint of the edge finder for both release and due dates can be reached in strongly polynomial time for disjunctive scheduling; (2) the fixpoint can be reached in strongly polynomial time for updating the release dates or the due dates but not both for the cumulative scheduling; and (3) the fixpoint of “reasonable” energetic operators cannot be reached in strongly polynomial time, even for disjunctive scheduling and even when only the release dates or the due dates are considered.     

Schedule-an expert-like system for machine scheduling

The construction of an expert-like system for machine scheduling called SCHEDULE is presented. Essential parts of SCHEDULE were developed by students in a laboratory course Operations Research on Microcomputers at the University of Karlsruhe, Germany. SCHEDULE consists of the components data base, knowledge base, inference engine, explanation facility, dialog component, and knowledge acquisition component. The knowledge base contains an algorithm base for solving different types of scheduling problems. To establish the rules of the knowledge base the well-known three-field classification of deterministic machine scheduling problems and the concept of the reduction digraph are exploited. Experiences gained during building and demonstrating SCHEDULE are reported.     

Nicodemi sequences of operators between spaces of multilinear mappings

We obtain results on three aspects of Nicodemi extensions of multilinear mappings between Banach spaces: (i) subspace invariance, (ii) the norms of the extension operators, (iii) when Aron–Berner extensions are Nicodemi extensions.     

数学建模课内容和教学方法的探讨

拟就以下内容进行了探讨 .(i)该课程究竟应该讲什么内容、怎样讲 ,才能使学生在较短的时间内 ,掌握数学建模的基本知识和基本方法 ;(ii)该课程怎样与数学实验更好地结合起来 ,以培养学生的动手能力 ;(iii)该课程应采用什么样的教学手段和教学方法 ,才能加大课堂信息量 ,加强直观性和趣味性等 .我们的解决方法是 :(i)以介绍建立数学模型为主 ,按数学知识内容的不同来选取数学模型的典型案例 ,通过案例介绍 ,使学生学会怎样建立模型 .(ii)适当介绍数学软件包 ,让学生掌握运用软件包来求解模型能力 .(iii)做大作业 ,教员给出题目 ,学生自己收集资料、讨论、上机求解 ,最后写出报告 .(iv)开展多媒体教学 ,对主要的教学内容进行模块化教学 ,将建模分成 1 4个专题 ,做成 1 4个多媒体课件     

A global MILP model for FMS scheduling

Flexible manufacturing systems (FMS) require intelligent scheduling strategies to achieve their principal benefit — combining high flexibility with high productivity. A mixed-integer linear programming model (MILP) is presented here for FMS scheduling. The model takes a global view of the problem and specifically takes into account constraints on storage and transportation. Both of these constrained resources are critical for practical FMS scheduling problems and are difficult to model. The MILP model is explained and justified and its complexity is discussed. Two heuristic procedures are developed, based on an analysis of the global MILP model. Computational results are presented comparing the performance of the different solution strategies. The development of iterative global heuristics based on mathematical programming formulations is advocated for a wide class of FMS scheduling problems.     

Applications of resource assignment and scheduling with Petri Nets and heuristic search

This paper introduces a new Petri Net based approach for resource allocation and scheduling. The goals are (i) minimize the number of required resources given a set of jobs, (ii) find both an assignment for all jobs in the span of a predefined shift and (iii) the sequence in which such jobs are executed. The studied problem was inspired from a complex real life manufacturing shop as described in this document. The modeling of the processes and jobs is carried out with Petri Nets due to their capability of representing dynamic, concurrent discrete-event dynamic systems. The resource assignment starts with an initial feasible solution (initial number of resources) and then follows with a re-optimization process aimed to further reduce the resource requirements. The algorithm is based on a modified Heuristic Search method previously presented. The algorithm was tested first on a number of instances from the literature and then on the aforementioned system (a car seat cover manufacturer). The proposed approach shows not only good results in terms of performance but also shows the potential of Petri Nets for modeling and optimizing real-life systems. An implementation phase at the first stages of the process is underway at the time of writing.     

A DSS design framework for competitive strategy formulation

This paper discusses the design framework that is actually being used in a large corporation for building a special purpose decision support system for competitive strategy formulation. The main features of the design framework employed are its ability to provide (i) support for decision-making through management science/operations research, (ii) decision-making support to managers of different levels and functions, (iii) methods to evaluate the performances of managers of different levels as well as that of the firm, (iv) to integrate a variety of decision-making models into a competitive strategy formulation model, and (v) to increase the effectiveness through an evolutionary and participatory development process.     

R&D pipeline management: Task interdependencies and risk management

Maintaining a rich research and development (R&D) pipeline is the key to remaining competitive in many industrial sectors. Due to its nature, R&D activities are subject to multiple sources of uncertainty, the modeling of which is compounded by the ability of the decision maker to alter the underlying process. In this paper, we present a multi-stage stochastic programming framework for R&D pipeline management, which demonstrates how essential considerations can be modeled in an efficient manner including: (i) the selection and scheduling of R&D tasks with general precedence constraints under pass/fail uncertainty, and (ii) resource planning decisions (expansion/contraction and outsourcing) for multiple resource types. Furthermore, we study interdependencies between tasks in terms of probability of success, resource usage and market impact. Finally, we explore risk management approaches, including novel formulations for value at risk and conditional value at risk.     

Production Runs for Multiple Products: The Full-Capacity Heuristic

This paper presents the full-capacity heuristic, a procedure for determining run sizes for scheduling N products which must be produced on the same machine. First, the optimal solution for scheduling two products at full capacity is reviewed. Then a heuristic method is presented for solving the N product, full capacity problem. The method involves: (i) judgementally selecting the sequence of set-ups in the fundamental cycle; (ii) determining the relative durations of each run within the cycle by solving a system of linear equations; and (iii) computing the associated optimal cycle length and annual cost. Finally, there is discussion of how to apply the full capacity method in the more common situation when there is slack production capacity available.     

Sequential decision procedures for batching and balancing in FMSs

Batching and balancing constitute two of the several scheduling and resource allocation problems important over different time scales in FMS operations. The time scale for batching and balancing is of the order of days to weeks — which puts it between long-term planning and part selection, of the order of months to years, and real-time part entry and dispatching, of the order of minutes. All these scheduling and resource allocation problems have been addressed at the Charles Stark Draper Laboratoty by a common methodology. We have used a sequential decision algorithm, each decision based on optimization of a probabilistic performance criterion designed to trade off whatever and however many competing attributes may be important in the particular problem. This paper discusses the common methodology, and its application to FMS batching and balancing in particular. Our computer program BATCH/BAL which implements the algorithms given here has been the starting point for all the other sequential decision programs subsequently developed at our laboratory.This paper is based in part on work supported by the United States Army Tank Automotive Command under Contract DAAE07-83-C-R084 with the Charles Stark Draper Laboratory, Inc., and in part on work supported under Internal Research and Development at Draper.     

基于多Agent的车间任务招投标粗模糊集建模研究

首先通过相识集、招标集、投标集和任务集的概念 ,描述制造执行系统中的调度 Agent与资源 A-gent间任务招投标过程模型 ;基于任务的属性和资源 Agent完成任务的成本、质量、负荷和时间等属性 ,定义论域上的模糊集 ,将模糊集中的隶属度函数作为粗集的属性 ,在模糊集上作截集 ,从而获得系统的分类知识 ;收集样本数据 ,构造并分析决策表 ,进而获得调度 Agent调度决策知识 ;应用调度知识进行推理 ,从争取获得招标任务的若干个资源 Agent中 ,选出最适合招标任务的中标者 .     

On weak supercyclicity II

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbertspace operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly l-sequentially supercyclic, and (iii) weak l-sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators: (iv) the point spectrum of the normed-space adjoint of a power bounded supercyclic operator is either empty or is a singleton in the open unit disk, (v) weak l-sequential supercyclicity coincides with supercyclicity for compact operators, and (vi) every compact weakly l-sequentially supercyclic operator is quasinilpotent.     

Sequential Modelling of the Planning and Scheduling Problems of Flexible Manufacturing Systems

Research on the planning and scheduling issues of flexible manufacturing systems (FMS) has not been sparse. Most, if not all, studies, however, have focused on either developing the planning model or examining the performance of different scheduling rules. To date, the FMS planning and scheduling problems have not been studied together, though they are highly interrelated.This paper takes a first step to simultaneously address the planning and scheduling problems of flexible manufacturing systems. The problems are solved as a hierarchical process. We first integrate and formulate batching, loading, and routeing, three of the most important FMS planning problems, as a 0–1 mixed integer program. According to the optimal decisions provided by the integrated planning model, we then develop an off-line scheduling scheme that is capable of generating detail parts sequencing in the sequence independent environment (i.e. the operations are not constrained by a process sequence). Finally, we suggest several extensions and future research directions.     

Scheduling of plant maintenance personnel

Given (i) a set of maintenance jobs to be processed over a fixed time horizon, (ii) the breakdown of each job into finite time intervals in which the skills required are known, and (iii) the pool of available manpower for each skill type over the horizon, we formulate and solve the problem of scheduling personnel and jobs to minimize personnel idle time, by integer programming.     

A pattern-directed approach to FMS scheduling

Scheduling in flexible manufacturing systems (FMS) must take into account the shorter lead time, the multiprocessing environment, and the dynamically changing states. In this paper, a pattern-directed approach is presented which incorporates a nonlinear planning method developed in the artificial intelligence field. The scheduling system described here is knowledge-based and utilizes both forward-and backward-chaining for generating schedules (treated as state-space plans). The pattern-directed approach is dynamically adjustable and thus can handle scheduling requirements unique to the FMS environment, such as dynamic scheduling, failure-recovery scheduling, or prioritized scheduling for meeting deadlines.     

Orbital and spectral aspects of hypercyclic operators and semigroups

In connection with the theory of hypercyclicity of bounded linear operators and strongly continuous semigroups of operators on Banach spaces, we make several observations about the following three topics – (i) special types of orbits, (ii) the role of large subsets of $\mathbb{N}$, (iii) various spectral conditions – and thereby highlight some nuances of the theory.     

A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration

This paper addresses the integration of two emerging classes of scheduling problems which, for the most part, have evolved independently. These problem classes are (i) scheduling problems with time-dependent processing times and (ii) scheduling problems with rate-modifying activities (RMAs). The integration of these two concepts is motivated by human operators who experience fatigue while carrying out tasks and take rest breaks for recovery, but is also applicable to machines that experience performance degradation over time and require maintenance in order to sustain acceptable production rates. We explore a sequence-independent, single processor makespan problem with position-dependent processing times and prove that under certain conditions, the optimal policy is to schedule the RMA in the middle of the task sequence.     

Solving the AGV Problem via a Self-Organizing Neural Network

Automated Guided Vehicle (AGV)-based material handling systems (MHS) are used widely in Flexible Manufacturing Systems (FMS). The problem of AGV consists of the decisions and the operational control strategies of dispatching, routeing and scheduling of a set of AGVs under given system environments and operational objectives. One remaining challenge is to develop effective methods of AGV decisions for improved system productivity. This paper describes a prototype neural network approach for the AGV problem in an FMS environment. A group of neural network models are proposed to perform dispatching and routeing tasks for the AGV under conditions of single or multiple vehicles, and with or without time windows. The goal is to satisfy the transport requests in the shortest time and in a non-conflicting manner, subject to the global manufacturing objectives. Based on Kohonen's self-organizing feature maps, we have developed efficient algorithms for the AGVs decisions, and simulation results have been very encouraging.