Wiley

Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the “assignment problem” is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent in the work of two Hungarian mathematicians may be exploited to yield a new method of solving this problem.

Consider an experiment in which only record‐breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. We treat the problem of estimating the mean of an underlying exponential distribution, and we consider both fixed sample size problems and inverse sampling schemes. Under inverse sampling, we demonstrate certain global optimality properties of an estimator based on the “total time on test” statistic. Under random sampling, it is shown than an analogous estimator is consistent, but can be improved for any fixed sample size.

In recent papers by Kirkpatrick et al., an analogy between the statistical mechanics of large multivariate physical systems and combinatorial optimization has been presented and used to develop a general strategy for solving discrete optimization problems. The method relies on probabilistically accepting intermediate increases in the objective function through a set of user‐controlled parameters. It is argued that by taking such controlled uphill steps, from time to time, a high quality solution can eventually be found in a moderate amount of computer time. In this paper, we implement this idea, apply it to the traveling salesman problem and the p‐median location problem, and test the approach extensively.

A single machine is available to process a collection of stochastic jobs. There may be technological constraints on the job set. The machine sometimes breaks down. Costs are incurred and rewards are earned during processing. We seek strategies for processing the jobs which maximize the total expected reward earned.

A single machine scheduling problem in which both the processing times and due‐dates of the jobs awaiting servicing are random variables is analyzed. It is proved that the properties of the shortest processing time rule and the due‐date rule which are known for the deterministic situation also hold in the probabilistic environment when they are suitably, and reasonably, refined for this context.

Many optimization problems occur in both theory and practice when one has to optimize an objective function while an infinite number of constraints must be satisfied. The aim of this paper in to describe methods of handling such problems numerically in an effective manner. We also indicate a number of applications.