Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee

The paper presents a general method of designing constant-factor approximation algorithms for some discrete optimization problems with assignment-type constraints. The core of the method is a simple deterministic procedure of rounding of linear relaxations (referred to as pipage rounding). With the help of the method we design approximation algorithms with better performance guarantees for some well-known problems including MAXIMUM COVERAGE, MAX CUT with given sizes of parts and some of their generalizations.     

AN ANALYSIS OF THE DYNAMIC THEORY OF THE MULTI—PRODUCT FIRM USING THE CALCULUS OF VARIATIONS

The purpose of this paper is to present the theory of the multi-product firm in situations where the revenue function depends not only on the rate of output but also on changes in the rate of output, and, similarly, where the cost function depends on changes in the rate of factor utilization as well as the rate of their utilization. Since the analysis will utilize the calculus of variations, a general introduction to this technique is also presented. The model analyzed assumes perfect foresight and knowledge concerning the revenue, cost, and production functions, and the calculus of variations is used to derive the conditions for an extremum. The first section presents the mathematical model and the model of the firm, and the optimality conditions are discussed in the second section.     

METHODS FOR QUANTIFYING SUBJECTIVE PROBABILITIES AND MULTI-ATTRIBUTE UTILITIES*†

In many situations where normative decision-aiding techniques could be usefully applied, historical data are inadequate for estimating the required outcome probabilities, and economic methodologies are inadequate for estimating the aggregate utility derived from the several outcome attributes. In such cases it is often useful to obtain the required estimates in the form of expert judgments, i.e. to obtain subjective probabilities and multi-attribute utilities. Similarly, in many situations where behavioral decision processes are to be studied, it is necessary to scale the expectations and perceived values of the decision makers. This article describes the methods for eliciting subjective probabilities and multi-attribute utilities whose usefulness has been empirically studied and reported in the research literature. It also contains summary guidelines concerning the elicitation and use of such judgments.     

OPTIMIZING UNIVERSITY ADMISSIONS PLANNING

The crucial issues in the administration of higher education embody the very purpose, function, and concept of each institution. The institution's administrative policies are based on the combined philosophy of many conflicting interest groups such as taxpayers, donors, administrators, faculty, students, staff, and users of university services. A function performed by the university which is receiving increasing attention and outside pressure is the formulation of admissions policy for newly entering students. This paper investigates problems involved in the admissions planning and presents a goal programming model as an optimization tool for the problem.     

A HEURISTIC ALGORITHM FOR RESOURCE LEVELING IN MULTI-PROJECT,MULTI-RESOURCE SCHEDULING

The utility of conventional project management techniques, such as PERT and CPM, is hampered by significant and realistic network attributes and managerial considerations. There are many situations which involve more than one project and numerous resources. Of major concern in such situations is the reduction of the maximum quantity of each required resource. The algorithm presented here is capable of scheduling the individual activities in multiple projects with multiple resources and leveling the overall quantity of each resource which is required. The basis of the algorithm is a sequencing procedure for examining various combinations of activity start times. The measure of effectiveness for each combination is the sum of the squares of the required quantity of each resource in each time period.     

蒙古尔部族的组织

本文介绍了蒙古尔部族的组成、形成和发展,并对其族长、土司的特点和承继作了详尽的描述。本文介绍了蒙古尔部族的组成、形成和发展,并对其族长、土司的特点和承继作了详尽的描述。     

蒙古尔部族的组织(续二)

本文对蒙古尔部族的组成、形成和发展作了介绍,其中对族长、土司的特点和承继作了详尽的描述。     

Information theory and risk in capital markets

The present empirical study applies the methodology of information theory to the problem of assessing and separating capital market risk, which is separated into its systematic and unsystematic components. Monthly return relatives for all securities traded on the New York Stock Exchange are examined for the period 1926 to 1971, which is segmented into six 7-year subperiods. The securities are combined into portfolios of various sizes and ranked. It is concluded that although both systematic and unsystematic risks have increased over the 45-year interval—particularly between the pre-1940 and post-1940 periods—they have maintained their relative share of the total risk over the same period.     

Solving the part families problem in discrete-parts manufacture by simulated annealing

In the production planning and control of discrete-parts manufacture, aggregation of parts into families, on the basis of similarity, is carried out to ease both long-horizon planning and short-horizon scheduling. Additional advantages are related to those of group technology (GT), such as simplifying the flow of parts and tools and reducing both set-up and production costs. The problem of formally forming part families is presented and discussed. Previous work is reviewed and assessed. Two solution approaches, one based on a location model, the other on simulated annealing, are presented and compared along with test results. The location formulation, which results in an integer programming model solved by Lagrangian relaxation, proved capable of producing solutions of excellent quality, but only for relatively small problem instances. In contrast, simulated annealing, which is a general heuristic approach to combinatorial optimization, produced solutions of comparable quality and could handle realistically large problem instances. However, careful design of the simulated annealing algorithm is crucially important. An effective design is presented.     

The Assessment of Probability Distributions from Expert Opinions with an Application to Seismic Fragility Curves

A method is developed for estimating a probability distribution using estimates of its percentiles provided by experts. The analyst's judgment concerning the credibility of these expert opinions is quantified in the likelihood function of Bayes'Theorem. The model considers explicitly the random variability of each expert estimate, the dependencies among the estimates of each expert, the dependencies among experts, and potential systematic biases. The relation between the results of the formal methods of this paper and methods used in practice is explored. A series of sensitivity studies provides insights into the significance of the parameters of the model. The methodology is applied to the problem of estimation of seismic fragility curves (i.e., the conditional probability of equipment failure given a seismically induced stress).