On compounded bivariate poisson distributions

A unified treatment is given for a class of discrete distributions derived by compounding a bivariate Poisson with a bivariate discrete or continuous distribution. Using generating functions a number of interesting results are obtained for probabilities, moments, cumulants, factorial moments, and factorial cumulants. Conditional distributions and regression functions are also examined. Five illustrative examples are presented in detail. © 1994 John Wiley & Sons, Inc.     

Nonpreemptive scheduling of independent tasks with prespecified processor allocations

In this article we study the problem of scheduling independent tasks, each of which requires the simultaneous availability of a set of prespecified processors, with the objective of minimizing the maximum completion time. We propose a graph-theoretical approach and identify a class of polynomial instances, corresponding to comparability graphs. We show that the scheduling problem is polynomially equivalent to the problem of extending a graph to a comparability graph whose maximum weighted clique has minimum weight. Using this formulation we show that in some cases it is possible to decompose the problem according to the canonical decomposition of the graph. Finally, a general solution procedure is given that includes a branch-and-bound algorithm for the solution of subproblems which can be neither decomposed nor solved in polynomial time. Some examples and computational results are presented. © 1994 John Wiley & Sons, Inc.     

A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

This article generalizes the model for the economic design of x̄-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.     

Use of a classifier in a knowledge-based simulation optimization system

This article defines and develops a simulation optimization system based upon response surface classification and the integration of multiple search strategies. Response surfaces are classified according to characteristics that indicate which search technique will be most successful. Typical surface characteristics include statistical measures and topological features, while search techniques encompass response surface methodology, simulated annealing, random search, etc. The classify-then-search process flow and a knowledge-based architecture are developed and then demonstrated with a detailed computer example. The system is useful not only as an approach to optimizing simulations, but also as a means for integrating search techniques and thereby providing the user with the most promising path toward an optimal solution. © 1995 John Wiley & Sons, Inc.     

An exact ceiling point algorithm for general integer linear programming

We present an algorithm called the exact ceiling point algorithm (XCPA) for solving the pure, general integer linear programming problem (P). A recent report by the authors demonstrates that, if the set of feasible integer solutions for (P) is nonempty and bounded, all optimal solutions for (P) are “feasible 1-ceiling points,” roughly, feasible integer solutions lying on or near the boundary of the feasible region for the LP-relaxation associated with (P). Consequently, the XCPA solves (P) by implicitly enumerating only feasible 1-ceiling points, making use of conditional bounds and “double backtracking.” We discuss the results of computational testing on a set of 48 problems taken from the literature.     

Initiatives in Africa

Since the 1st oil crisis in 1973, the economies of sub-Saharan Africa have barely kept pace with their burgeoning populations. Women in Sub-Saharan Africa give birth more often than women in any other region of the world, with an average of more than 6.5 live births each. The region's natural increase average 2.5% a year in the 1960s, 2.7% in the 1970s, and in the mid-1980s, it is 3.1% per annum--a rate that will double the regions population in 22 years. National leaders in Sub-Saharan Africa were slow to consider population policy as a key component of the social and economic development effort. The neglect of population issues is reflected in the limited scope of public or private family planning programs in the sub-continent. Donor countries and institutions play an important role in developing the information base by providing technical training to government staff, supporting research, and disseminating information to a broad spectrum of political actors. Some examples of policy reconsiderations in Nigeria, Zambia, Liberia, and Niger are given. These countries are starting to give active consideration to population policies to reduce fertility and high rates of population growth by expanding family planning services, raising the age of marriage, improving the status of women, providing family-life education, and incorporating economic incentives for smaller families into the provision of social services. The highly centralized nature of African governments dictates that the acquiescence of the governmental elite must be obtained before any policy can take hold. Overall, high population growth rates in combination with a stagnating social and economic development effort throughout the region have provided the catalyst for a new look at Sub-Saharan Africa population policy. The ability of African nations to implement policies that reduce fertility is more open to question; no African nation has as yet done so, and the socioeconomics factors contributing to high fertility remain strong.     

A new approach for dealing with the startup problem in discrete event simulation

This article proposes a practical, data-based statistical procedure which can be used to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state means. We discuss results of experiments designed to choose good parameter values for this procedure, and present results of extensive testing of the procedure on a variety of stochastic models for which partial analytical results are available. The article closes with two illustrations of the application of the procedure to more complex statistical problems which are more representative of the kinds of purposes for which real-world steady-state simulation studies might be undertaken.