Container Scheduling: Complexity and Algorithms

We consider the transport of containers through a fleet of ships. Each ship has a capacity constraint limiting the total number of containers it can carry and each ship visits a given set of ports following a predetermined route. Each container has a release date at its origination port, and a due date at its destination port. A container has a size 1 or size 2; size 1 represents a 1 TEU (20‐foot equivalent unit) and size 2 represents 2 TEUs. The delivery time of a container is defined as the time when the ship that carries the container arrives at its destination port. We consider the problem of minimizing the maximum tardiness over all containers. We consider three scenarios with regard to the routes of the ships, namely, the ships having (i) identical, (ii) nested, and (iii) arbitrary routes. For each scenario, we consider different settings for origination ports, release dates, sizes of containers, and number of ports; we determine the computational complexity of various cases. We also provide a simple heuristic for some cases, with its worst case analysis. Finally, we discuss the relationship of our problems with other scheduling problems that are known to be open.     

China's demographic dilemmas

The year 2000 marks the end of a tumultuous century in China's population history, which weathered the demographic effects of devastating famines, wars, and epidemics and population growth and change. This paper examines the effect of population policies on the demographic dilemmas of China. In the 1950s, China had seen the fastest demographic transition in history, with a dramatic decline in mortality rates, followed by a decrease in fertility rates. However, in the 1970s, revisions in population control measures, changes in age structure, and fluctuations in age at marriage resulted in lower fertility rates. The struggles encountered by China in regulating fertility are described; these include the different methods of birth control, gender preference, marriage, population aging, and minority populations. Population and development issues within the context of urbanization, employment, education, health care, economy, and environment are also discussed. Future implications of these findings indicate the need for a systematic, effective, and complete environmental clean-up, as well as fertility and population policies.     

Habitat stability and the larval mosquito community in treeholes and other containers on a temperate Island

The temporal fluctuation of water levels and the presence of mosquito larvae were investigated for four types of small container habitats (treeholes, bamboo stumps, cemetery stone vases, and cemetery stone vessels) on Kabeshima Island in Kyushu, southwestern Japan. The probability that containers held water was positively correlated with the quantity of the preceding rainfall and with the depth and volume of the containers. It was estimated that dehydration occurred more regularly in autumn and winter than in summer. The probability that mosquito larvae were present in each type of container was positively correlated with habitat stability in terms of the probability of the existence of standing water and the coefficient of variation of the water level. Twelve species of mosquito larvae, including two rare predators, were found. Species composition differed between the different types of container. Although 4 to 10 species used each type of container, the median number of species per container was two for treeholes and bamboo stumps, and one for the others. The dominant species wasTripteroides bambusa in treeholes and bamboo stumps,Aedes albopictus in stone vases, andA. japonicus in stone vessels. The larval mosquito community, which lacked major predators, possessed the following features that may facilitate the coexistence of many species: (1) niche segregation amongst species in terms of their selection of container types; (2) an aggregated distribution of the individual species among containers of the same type; (3) high intraspecific mean crowding (and hence probably intense intraspecific competition) in the dominant species in each type of container; (4) independent species associations within the same type of container; and (5) low interspecific mean crowding (and hence probablynot intense interspecific competition) between species in the same type of container.     

Teaching assertive skills to a passive homosexual adolescent: an illustrative case study

Social skills training was used to alter the socially inappropriate and ineffectual behavior of a 17-year old homosexual male. Target behaviors selected for treatment were the subject's effeminate mannerisms and lack of assertiveness in conflict situations, especially those involving other persons making derisive comments to him. A multiple baseline design was used to increase the patient's (a) eye contact, (b) rate of making appropriate requests for behavior change in others, and (c) general level of assertive affect. Six training and six generalization role-played interpersonal scenes were used. Results indicated significant improvement on trained social skills components with generalization to nontrained scenes as well. Implications of these findings are discussed, particularly with respect to social skills and assertion training for effeminate homosexuals.     

Maximum likelihood estimates for the parameters of a continuous time model for first conception

The duration of time between two successive births or between marriage and first birth is an indicator of the level of fertility of a couple. Potter and Parker (1964) and Singh (1961, 1967) have suggested the Type I Geometric as a distribution appropriate for representing the length of interval to first conception leading to a live birth. Potter and Parker estimated the parameters of this distribution with the help of the first two moments. Majumdar and Sheps (1970) pointed out the limitations of these moment estimates and gave a method to obtain maximum likelihood estimates, based on formulas which are too involved for solution without the help of a computer. Singh proposed a continuous probability distribution based on another set of assumptions for the above situation. He outlined a method to obtain best asymptotically normal estimates of the parameters. These estimates are obtained after several iterations starting from any set of consistent estimates. The objective of this paper is to show that it is relatively easier to obtain maximum likelihood estimates of the parameters of the continuous model, which describes the data on duration to first conception as well as does the discrete model. Simple expressions for the moment and maximum likelihood estimates with the corresponding covariance matrices are obtained. Application is made to three sets of data.     

Age at marriage and timing of the first birth

Summary An attempt has been made to measure the effect of age at marriage of brides on the timing of the first birth. In Australian vital statistics, first nuptial confinements have been tabulated by age of mothers and by single years of marriage duration in single months for the first two years and by single years for all other durations since 1916. A simple technique has been used to link such data with marriage cohorts. The study briefly reviews the prevailing patterns of the timing of first births by mothers' age at marriage and changes in this pattern since the marriages of the 1925/9 period. The analysis shows that after a period of relative stability of family formation patterns in the 1950s and early 1960s, women married in the late 1960s started postponing the first birth beyond the first two years of marriage. It is suggested that a fraction of the decline in total births recorded in Australia since 1972 can be attributed to the postponement of first nuptial confinements by women married in the late 1960s and early 1970s.     

Some demographic consequences of changing cohort fertility patterns: An investigation using the Gompertz function

Abstract In this paper are formulated some convenient summary measures of fertility patterns. These measures, which are based on the Gompertz function, are total lifetime fertility, median age of mothers at childbirth, and inter-quartile range of age of mothers at childbirth. Estimates of the parameters of Gompertz function, based on Canadian data, are used to derive, for each of the summary measures, values which reflect historical fertility experience, and thus give an impression about the range of realistic values for these measures. A simple model of demographic activity which includes the Gompertz function is also considered, and this model is used in computer simulation experiments to determine the macro-demographic effects of changes in each of the three summary measures.