A note on first passage times in birth and death and nonnegative diffusion processes

Consider a birth and death process starting in state 0. Keilson has shown by analytical arguments that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR.     

A comparison of several estimates of availability

We compare several competing estimates of the availability of a system which alternates between two states, “up” and “down,” in accordance with an alternating renewal process. Both interval and point estimators are compared under several special but representative situations. The comparison reaffirms the validity and robustness of the log-logistic jackknifed estimates. However, when the point estimates are compared from the intrinsic criterion of probability of concentration, the uniformly minimum variance estimate obtained for the Markov model performs very well.     

On finding spanning eulerian subgraphs

In this article, we examine the problem of producing a spanning Eulerian subgraph in an undirected graph. After the ?-completeness of the general problem is established, we present polynomial-time algorithms for both the maximization and minimization versions where instances are defined on a restricted class of graphs referred to as series-parallel. Some novelties in the minimization case are discussed, as are heuristic ideas.     

The politics of population

This article suggests some of the principal factors behind the decisions by an increasing number of countries deciding that the achievement of their national objectives required a policy for population, and the way that they are likely to work out. By 1983, 35 developing countries had an official policy to reduce their population growth rate, and in 34 others, the government supported family planning activities--usually for reasons of health or as a human right. The number is remarkable given the many compelling reasons that governments have for not attempting anything so difficult as to modify demographic trends. The future results of population programs, in social and economic terms, are very difficult to quantify, thus defying cost-benefit analysis of the desirability of investing resources in this area, rather than in something else. There are also powerful political reasons why a government might well hesitate before embarking on a policy to reduce the nation's fertility. At the very least, it implies government interference in the most private and personal of human relations, an invasion of human rights, and a disturbance of the traditional patterns of society and behavior. For many countries that are pursuing a policy to limit population growth, the decision has been taken only after the grievous consequences of not having such a policy have already become manifest. The critical question is how soon a government will make the connection among political disobedience, economic and social distress, and the population explosion, and adopt a population policy. Although the number of developing countries that have officially proclaimed a strongly pro-natalist population policy is relatively small, many have Marxist governments. Overall, governments have several strategies at their disposal: 1) improving the accessability and the quality of the service; 2) promoting population education and family planning motivation (with the assistance of the media, folk art, and personal persuasion); and 3) applying a judicious mixture of incentives and disincentives.     

Book reviews

Red Banner: the Soviet Military System in Peace and War. By Christopher Donnelly. Jane's Information Group, Coulsdon, UK (1988), 288 pp., £35.00

Images of T. E. Lawrence. By S. E. Tabachnick and C. Matheson. Jonathan Cape, London (1988); The Letters of T. E. Lawrence. Edited by Malcolm Brown. Dent, London (1988); T. E. Lawrence. By J. Wilson. National Portrait Gallery Publications, London (1988); Lawrence and the Arab Revolts. By D. Nicolle. Osprey, London (1989)

Liddell Hart and the Weight of History. By John Mearsheimer. Brassey's, London (1989), £15.95

Science and Mythology in the Making of Defence Policy. Edited by Margaret Blunden and Owen Greene. Brassey's, London (1989), £27.50/$44.00

Warfare in the Twentieth Century. Edited by Colin McInnes and G. D. Sheffield. Unwin Hyman, London (1988), 239 pp., £25.00     

On the generation of deep disjunctive cutting planes

In this paper we address the question of deriving deep cuts for nonconvex disjunctive programs. These problems include logical constraints which restrict the variables to at least one of a finite number of constraint sets. Based on the works of Balas. Glover, and Jeroslow, we examine the set of valid inequalities or cuts which one may derive in this context, and defining reasonable criteria to measure depth of a cut we demonstrate how one may obtain the “deepest” cut. The analysis covers the case where each constraint set in the logical statement has only one constraint and is also extended for the case where each of these constraint sets may have more than one constraint.     

The bounded interval generalized assignment model

The bounded interval generalized assignment model is a “many-for-one” assignment model. Each task must be assigned to exactly one agent; however, each agent can be assigned multiple tasks as long as the agent resource consumed by performing the assigned tasks falls within a specified interval. The bounded interval generalized assignment model is formulated, and an algorithm for its solution is developed. Algorithms for the bounded interval versions of the semiassignment model and sources-to-uses transportation model are also discussed.