Multiproduct dynamic lot-sizing model with coordinated replenishments

In this article we consider a multiproduct dynamic lot-sizing model. In addition to a separate setup cost for each product ordered, a joint setup cost is incurred when at least one product is ordered. We formulate the model as a concave minimization problem over a compact polyhedral set and present a finite branch and bound algorithm for finding an optimal ordering schedule. Superiority of the branch and bound algorithm to the existing exact procedures is demonstrated. We report computational experience with problems whose dimensions render the existing procedures computationally infeasible.     

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 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.     

On a large sample test for the traffic intensity in GI|G|s queue

A large sample test based on normal approximation for the traffic intensity parameter ρ in the cases of single and multiple-server queues has been proposed. The test procedure is developed without imposing steady-state assumptions and is applicable to queueing systems with general interarrival and service-time distributions.     

Minimizing mean absolute deviation of completion times about a common due date

We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.     

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.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.