Life-expectancy in a nonhomogeneous population

Mortality differentials exist even among people of the same age and environmental risks. These differences are due to individual frailty (risks due to biological or behavioural reasons) not considered in the computation of conventional life-tables (where populations are assumed to be homogeneous). This note seeks to show empirically that life-expectancies computed from homogeneous population models are overstated for ages less than the mean, and are understated for higher ages. It is also shown that life-expectancy curves for both homogeneous and nonhomogeneous populations intersect at the mean survival age (when the most frail would have all died off) and at the maximum age lived in the population (when the last members of the cohort would have died off).     

A critique of fractional age assumptions

Published mortality tables are usually calibrated to show the survival function of the age at death distribution at exact integer ages. Actuaries make fractional age assumptions when valuing payments that are not restricted to integer ages. A fractional age assumption is essentially an interpolation between integer age values which are accepted as given.Three fractional age assumptions have been widely used by actuaries. These are the uniform distribution of death (UDD) assumption, the constant force assumption and the hyperbolic or Balducci assumption. Under all three assumptions, the interpolated values of the survival function between two consecutive ages depend only on the survival function at those ages. While this has the advantage of simplicity, all three assumptions result in force of mortality and probability density functions with implausible discontinuities at integer ages.In this paper, we examine some families of fractional age assumptions that can be used to correct this problem. To help in choosing specific fractional age assumptions and in comparing different sets of assumptions, we present an optimality criterion based on the length of the probability density function over the range of the mortality table.     

Multi-Skilled Workforce Optimisation

This paper describes a problem faced by CS Energy's Swanbank Power Station in the Australian state of Queensland. It involved the personnel scheduling (rostering) of staff with multiple skill levels at the power station. Such a problem can be classified using the six stage construction process proposed by Ernst et al. We assume that the three processes of ‘demand modelling,’ ‘shift starting times’ and ‘task scheduling’ are specified. We are concerned with the essential processes of ‘day off scheduling,’ ‘line of work construction’ and ‘shift assignment to staff’ with requirements to maintain multiple skills. Several other authors have reported results for staff with hierarchical skills while the methods proposed in this paper are for non-hierarchical skill sets. The paper describes a set covering approach to the multi-skilled rostering problem. We propose a number of solution strategies for the set covering approach and give a comparison of the results.     

Does the chalkboard still hold its own against modern technology in teaching mathematics? A case study

The purpose of this case study is to explore the integration of technology into teaching at a mathematics department at a large South African University. Both quantitative and qualitative data were collected from staff teaching undergraduate mathematics. The study shows that many staff members feel that chalkboards are still more suitable than technology for teaching mathematics. This finding supports the idea of a strong subject culture. Age does not emerge as a determinant for preference of either technology or the chalkboard, although gender and academic qualifications do. Subject culture is strongly rooted under the male members of staff, while female staff members feel more positive towards the use of technology in teaching. Use of chalkboards has decreased significantly over the past 10 years, while the use of modern technologies has increased accordingly. Teaching of large groups has necessitated the use of technology in the classroom. Despite the strong subject culture, a shift in attitude towards technology use in teaching is noticed and there is a definite trend of moving towards using new technologies.     

On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem

In this paper a comparison is made between two decomposition techniques to solve a staff scheduling problem with column generation. In the first approach, decomposition takes place on the staff members, whereas in the second approach decomposition takes place on the activities that have to be performed by the staff members. The resulting master LP is respectively a set partitioning problem and a capacitated multi-commodity flow problem. Both approaches have been implemented in a branch-and-price algorithm. We show a trade-off between modeling power and computation times of both techniques.     

USE OF AGE‐ AND STAGE‐STRUCTURED MATRIX MODELS TO PREDICT LIFE HISTORY SCHEDULES FOR SEMELPAROUS POPULATIONS

Many studies of semelparous salmon populations use Leslie matrices that classify individuals on the basis of age alone and do not explicitly impose death upon reproduction. Although these models may suffice for studying long‐term population dynamics (like asymptotic growth rate), they do not accurately represent the diversity of individual life history outcomes in semelparous populations. Cohorts breeding at different ages have different life history traits (e.g., age at first reproduction and remaining life expectancy) that are obscured in Leslie models and this distorts our understanding of life history diversity and its importance for semelparous population dynamics. We present a simple transformation that uses age‐specific breeding probabilities to reconfigure Leslie matrices as explicitly semelparous models. Explicitly semelparous models conserve asymptotic measures like population growth rate, vital rate elasticities, life expectancy at birth, and generation time but also better predict life history schedules and reproductive values. Strictly age‐classified Leslie models underestimate ages at first reproduction and mean ages at death for older breeders but overestimate mean ages at death for early breeders. Leslie models also slightly overestimate variance in lifetime reproductive success, and underestimate entropy exhibited by life history outcomes.     

非整数年龄假设中的二次多项式死亡力研究

由于生命表只提供了整数年龄点上的生存函数值和死亡率值,所以在人口统计和寿险精算中计算非整数年龄处的生存函数值时,需要进行非整数年龄假设。传统的非整数年龄假设有死亡力函数和密度函数在整数年龄处有较大跳跃的缺点,而针对它们连续性的改进甚少,且没有针对死亡力函数二次多项式形式的研究。本文提出了死亡力的二次多项式形式,通过积分约束下的分段抛物插值方法给出了二次多项式死亡力形式对应的非整数年龄假设,并与前人已经提出的各种假设进行了比较,结果表明二次死亡力假设可以更精确地描述生存模型,从而使人口统计和保费、年金的计算更加精确。     

A comparative study of parametric mortality projection models

The relative merits of different parametric models for making life expectancy and annuity value predictions at both pensioner and adult ages are investigated. This study builds on current published research and considers recent model enhancements and the extent to which these enhancements address the deficiencies that have been identified of some of the models. The England & Wales male mortality experience is used to conduct detailed comparisons at pensioner ages, having first established a common basis for comparison across all models. The model comparison is then extended to include the England & Wales female experience and both the male and female USA mortality experiences over a wider age range, encompassing also the working ages.     

二阶段整群抽样的样本大小估计公式及其在医疗费用调查中的应用

本文利用哥西不等式原理及求极小值方法 ,在限定抽样误差的大小使调查花费最小及限定调查花费的大小使抽样误差最小两种情况下 ,对常用的二阶段整群抽样 ,推导出其最优样本大小计算公式 ,在中国铁路职工医疗费用的调查中取得了成功的应用。     

FOREST ROTATIONS AND STAND INTERDEPENDENCY: OWNERSHIP STRUCTURE AND TIMING OF DECISIONS

ABSTRACT. This paper extends the Hartman model to study the optimal rotation age of two interdependent stands at the steady state, when the rotation ages of the two stands are equal and the stream of amenities produced from the two stands may be complements or substitutes, both in space and over time. In the presence of stand interdependence both the ownership structure and the sequence of decision making matters. Rotation age choices are examined and compared under a variety of equilibria, including Nash, Stackelberg and sole owner cases. We show that the sole owner's rotation age is longer than the rotation age under both Nash and Stackelberg assumptions if the stands are spatial complements but shorter if they are spatial substitutes. The precise relationship between the Nash and Stackelberg rotation ages and the qualitative properties of rotation ages in terms of timber prices, regeneration costs and interest rates also depend on how spatial substitutability and complementarity between stands evolves through time.     

On a team control problem under obstacles

The paper deals with the problem of coordinated goal-oriented target control for a group of control systems that are to realize a joint movement towards a given target set under collision avoidance. The members of the group are obliged to lie inside a virtual ellipsoidal container, which realizes a reference motion while also avoiding external obstacles specified in advance. We describe a general solution scheme based on decomposing the main problem into auxiliary subproblems, for which we indicate solution methods as well as the necessity of coordinating these solutions at the final stage.     

The team orienteering problem

In the team orienteering problem, start and end points are specified along with other locations which have associated scores. Given a fixed amount of time for each of the M members of the team, the goal is to determine M paths from the start point to the end point through a subset of locations in order to maximize the total score. In this paper, a fast and effective heuristic is presented and tested on 353 problems ranging in size from 21 to 102 points. The computational results are presented in detail.     

Planning Annualised Hours with a Finite Set of Weekly Working Hours and Joint Holidays

The need to adjust productive capacity to seasonal demand and the increasing flexibility in the distribution of annual working hours has given rise to new problems with respect to the organisation of staff working time. This paper presents a problem of planning annual working hours, in which the number of weekly working hours for any worker must belong to a previously agreed finite set and holiday weeks are the same for all the staff members. The problem is modelled and solved as a mixed integer linear program.     

An Integer Goal Programming Model to Allocate Offices to Staff in an Academic Institution

This paper investigates the problem of allocating office space to members of staff in an academic institution. We identify several conflicting objectives and formulate an integer pre-emptive goal programming model to address them. Using data from a pilot site of the University of Westminster, UK, we then experiment with alternative rankings of the objectives. Finally, given the plans to consolidate the activities of this university into fewer sites and the resulting need to relocate some staff members, we discuss how this model can be used to ensure that this process is carried out with the least possible inconvenience.     

Composite alternatives in group decision support

Decision theory models of group decision processes usually assume a given set of alternatives, from which the group has to choose. In realistic group decision situations, however, alternatives are often not specified a priori, but are created during the group process from different components introduced by the group members. This paper develops methods for systematically creating such composite alternatives, also taking into account the necessity to keep both the computational effort and the cognitive load to group members within reasonable limits.Paper presented at the International Conference on Support Systems for Decision and Negotiation Processes DNS-92, Warsaw, 1992.     

Interactive group decision-making procedure using weak strength of preference

In the paper, we present an interactive decision procedure for aggregating group members’ preferences which are specified in incomplete ways. A group consensus under incomplete information is not usually reached at a single step since less-specific preferences on attribute weights and performance scores make a clear selection of best alternative more difficult. To circumvent these difficulties, a measure, indicating the strength of preference between alternatives, is derived to help each of decision makers change his/her preference structure. To make preference changes based on the measure effective, we present a solution method to convert an intractable nonlinear programme into a linear one.     

Finite Field Elements with Specified Order and Traces

Results of F. Özbudak on the existence of elements in a finite extension of a finite field with specified order and at which given rational functions have specified traces over the ground field are obtained by the method of character sums. There are significant applications to the construction of ordered arrays.AMS classification: 11T30, 11T24     

Explaining young mortality

Stochastic modeling of mortality rates focuses on fitting linear models to logarithmically adjusted mortality data from the middle or late ages. Whilst this modeling enables insurers to project mortality rates and hence price mortality products it does not provide good fit for younger aged mortality. Mortality rates below the early 20’s are important to model as they give an insight into estimates of the cohort effect for more recent years of birth. It is also important given the cumulative nature of life expectancy to be able to forecast mortality improvements at all ages. When we attempt to fit existing models to a wider age range, 5-89, rather than 20-89 or 50-89, their weaknesses are revealed as the results are not satisfactory. The linear innovations in existing models are not flexible enough to capture the non-linear profile of mortality rates that we see at the lower ages. In this paper, we modify an existing 4 factor model of mortality to enable better fitting to a wider age range, and using data from seven developed countries our empirical results show that the proposed model has a better fit to the actual data, is robust, and has good forecasting ability.     

Problems of maximizing the compliance of curvilinear rods

A number of problems of finding the shape of a thin curvilinear rod (the support element of an artificial lens) of constant cross-section and specified length with its ends at specified points and under specified loading conditions with maximum compliance for characteristic types of end restraint and loading are considered. It is shown that the boundary-value problem arising for the non-linear Euler equation may have a set (possibly denumerable) of solutions, one of which gives the absolute maximum compliance, and the others the local maxima. The problem is analysed in detail, analytical solutions are obtained and the corresponding shapes are constructed in a number of important cases.     

The value of cognitive foundations for dynamic social theory

It is possible to develop models of social behavior that are predicated on detailed mechanical models of cognition. Cognitively based social models are potentially unified theoretical frameworks that can be used to explain a wide variety of social phenomena. Moreover, if a knowledge representation scheme and a knowledge acquisition scheme are specified in the underlying cognitive model then it is possible to produce a dynamic social model. The resulting social model can thus be used to predict and explain not only conditions for specific behaviors but changes in those behaviors over time.

Constructuralism is a theory of social behavior that rests on a cognitive model. The cognitive model specified has a knowledge representation scheme, knowledge acquisition procedures, and control procedures for shifting cognitive attention. The resulting social model is a dynamic model that can be used to explain both conditions for the occurrence of a behavior and social and individual changes that accrue do to a series of behaviors. The explanatory breadth of the model is illustrated by looking at predictions about a variety of social phenomena including: development of shared knowledge, identical behavior by members of the society, foreign language acquisition, clique formation, civil disobedience, and diffusion of innovative information.