The traveling salesman problem: An update of research

During the course of the last few years, attacks on the traveling salesman problem have resulted in a variety of often innovative and rather powerful computational procedures. In this article, we present a review of these results for problems defined on weighted and unweighted graphs. Some account of computational behavior for exact algorithms is provided; however, the primary coverage deals with the strategy of particular procedures. In addition, we include some aspects of nonexact algorithms with major interest confined to the establishment of worst-case bounds.     

Exact first and second order moments of order statistics from the truncated exponential distribution

Exact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–P of truncation is known in advance, are presented in this paper. Tables of expected values and variances-covariances are given for P = 0.5 (0.1) 0.9 and n = 1 (1) 10.     

Calculation of the cost of warranty policies as a function of estimated life distributions

Two types of warranties are analyzed. These are the free-replacement warranty, under which failed items are replaced free of charge until a specified total operating time has been achieved, and the pro rata warranty, under which items that fail prior to a specified time are replaced at pro rata cost to the buyer. Both the buyer's and seller's points of view are considered. The basis of the analysis is a comparison of warranted and unwarranted (otherwise identical) items with regard to long-run cost to the buyer and long-run profit to the seller. Application of the results requires knowledge of certain characteristics of the life distribution of the items in question. Parametric and nonparametric methods of estimation of these characteristics from incomplete data are discussed. Single and multiple failure-mode situations are considered. Some solutions to the problem are illustrated using incomplete data on failure times of an aircraft component.     

Optimal schedules for special structure flowshops

This paper considers the problem of scheduling a given number of jobs on a specified number of machines in a flowshop where the objective function is to minimize the total throughput time in which all jobs complete processing on all machines. Based on the combinatorial analysis of the problem, several simple algorithms are developed for solving special structure flowshop scheduling problems where the process times are not completely random, but bear a well-defined relationship to one another. The proposed algorithms are both simple and computationally efficient and can optimally solve large-sized problems even with manual computational devices.     

Upper and lower bounds for a pattern bombing problem

This paper includes two simple analytic formulas for kill probability that are applicable in circumstances where shots should be fired in a pattern. The two formulas bracket the maximum kill probability achievable with an optimal pattern. The upper bound corresponds to an optimal nonfeasible pattern, and the lower bound to a nonoptimal feasible pattern.     

On the evaluation of investment proposals having multiple attributes

A framework is developed for analyzing the likelihood of acceptance of an investment project proposal when objectives are uncertain. The foundation is a utility model of top management's choice process, modified if need be through a Bayesian approach which takes into account any apparent inconsistency in the history of past proposal acceptances and rejections.     

A proportional defense model

This paper considers the problem of defending a set of point targets of differing values. The defense is proportional in that it forces the offense to pay a price, in terms of reentry vehicles expended, that is proportional to the value of the target. The objective of the defense is to balance its resources so that no matter what attack is launched, the offense will have to pay a price greater than or equal to some fixed value for every unit of damage inflicted. The analysis determines which targets should be defended and determines the optimal firing doctrine for interceptors at defended targets. A numerical example is included showing the relationship between the total target damage and the size of the interceptor force for different values of p, the interceptor single shot kill probability. Some generalizations are discussed.     

Scheduling jobs,with exponentially distributed processing times,on two machines of a flow shop

This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.     

Numerical treatment of a class of semi-infinite programming problems

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.