Order-preserving allocation of jobs to two machines

In this paper, we consider the problem of minimizing the mean flow time of jobs to be processed on two machines. The jobs have a predetermined order, perhaps reflecting the order of arrival, and each job has a known processing time. We wish to assign the jobs to machines so as to minimize the mean flow time, with the constraint that the original order must be preserved within the subset of jobs assigned to each machine. An efficient algorithm based on dynamic programming is developed.     

Toward optimal bidding strategies

In this paper we investigate a form of rational behavior in response to an oligopoly pricing problem where only one buyer is involved. We investigate the problem from the standpoint of the seller who wants to maximize his gain from the transaction. In particular, we deal with the problem of one seller's response to an invitation to submit a sealed (i. e., noncooperative) bid to a government or other dominant purchasing agency for supplying a specified bundle of goods and services for which either (1) no other demand exists, or (2) the terms or quantities involved cannot, at least in the short run, be obtained from another source. Although treated from a normative standpoint, i. e., what bid the supplier should make, the paper also has implications for the buyer's behavior and oligopoly-monopsony pricing in a more general sense.     

Determining the most vital link in a flow network

The most vital link in a single commodity flow network is that are whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an are to be the most vital link is established and is employed to decrease the number of ares which must be considered.     

A manpower planning/capital budgeting model (MAPCAB)

A deterministic resource allocation model is developed to optimize defense effectiveness subject to budget, manpower, and risk constraints. The model consists of two major submodels connected by a heuristic. The first is a mathematical program which optimizes the multiperiod weapon mix subject to the constraint set. The second is a manpower supply model based on a transition matrix in which individual transitions are functions of personnel related budgets and historical transition rates. The heuristic marries the submodels through an iterative process leading to improved solutions. An example is provided which demonstrates how systems are undercosted and overprocured if manpower supply is not properly reflected relative to manpower demand.     

Lower confidence limits for the impact probability within a circle in the normal case

Lower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.     

Alternate methods of project scheduling with limited resources

The applicability of critical path scheduling is limited by the inability of the algorithm to cope with conflicting resource demands. This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available. These heuristic rules are evaluated on their ability to solve a large multiproject scheduling problem.     

Multiproduct lot-size scheduling with proportional product demands

In this paper we consider the multiproduct, multiperiod production-scheduling model of Manne under the assumption that, across products, demands are interrelated over time. When demand requirements are proportional we show that the solution has a specific structure determined by the ratio of setup to production-run time of each product. This structure holds for any length horizon and may permit a substantial (time) savings for column generation solution procedures.     

Bayesian estimation and optimal designs in partially accelerated life testing

A method of life testing is proposed which combines both ordinary and accelerated life-testing procedures. It is assumed that an item can be tested either in a standard environment or under stress. The amount of stress is fixed in advance and is the same for all items to be tested However, the time x at which an item on lest is taken out of the standard environment and put under stress can be chosen by the experimenter subject to a given cost structure. When an item is put under stress its lifetime is changed by the factor α. Let the random variable T denote the lifetime of an item in the standard environment, and let γ denote its lifetime under the partially accelerated test procedure just described. Then Y = T if T ≦ x, and Y = x + α (T > x) if T > x. It is assumed that T has an exponential distribution with parameter θ. The estimation of θ and α and the optimal design of a partially accelerated life test are studied in the framework of Bayesian decision theory.     

A bibliography of search theory and reconnaissance theory literature

This bibliography consists of 75 items on search theory and reconnaissance theory found in periodicals and technical reports. Each entry includes a short summary or a quotation from the pertinent abstract. The items are classified into one or more of the following categories: (1) General Discussion of Problems; (2) Allocation of Effort; (3) Game Theory Formulations; (4) Geometric Search Patterns; (5) Measures of Performance and (6) Miscellaneous.