Two queueing systems sharing the same finite waiting room

In this paper, we consider the analysis of two M/G/1 queueing systems sharing the same finite waiting room. An exact analysis is given for several special cases, and then an algorithm is developed which approximates the system behavior for the general problem. Comparisons are made between the special cases and the algorithm.     

The search for an intelligent evader concealed in one of an arbitrary number of regions

This paper considers the search for an evader concealed in one of an arbitrary number of regions, each of which is characterized by its detection probability. We shall be concerned here with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move; his aim is to maximize the expected time to detection, while the searcher attempts to minimize it. The situation where two regions are involved has been studied previously and reported on recently. This paper represents a continuation of this analysis. It is normally true that as the number of regions increases, optimal strategies for both searcher and evader are progressively more difficult to determine precisely. However it will be shown that, generally, satisfactory approximations to each are almost as easily derived as in the two region problem, and that the accuracy of such approximations is essentially independent of the number of regions. This means that so far as the evader is concerned, characteristics of the two-region problem may be used to assess the accuracy of such approximate strategies for problems of more than two regions.     

Stochastic linear programs with simple recourse: The equivalent deterministic convex program for the normal,exponential, and erlang cases

We consider here stochastic linear programs with simple recourse when all the elements of the technology matrix and the resource vector have certain specific distributions. The distributions considered are the Normal, Exponential and Erlang. For the first two instances we extend the equivalent deterministic program to include the variance of the recourse. Finally, a simple example is given to illustrate the application of the formulas for the Erlang case.     

Spike swapping in basis reinversion

During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.     

Linear programming and the reliability of multicomponent systems

Several problems in the assignment of parallel redundant components to systems composed of elements subject to failure are considered. In each case the problem is to make an assignment which maximizes the system reliability subject to system constraints. Three distinct problems; are treated. The first is the classical problem of maximizing system reliability under total cost or weight constraints when components are subject to a single type of failure. The second problem deals with components which are subject to two types of failure and minimizes the probability of one mode of system failure subject to a constraint on the probability of the other mode of system failure. The third problem deals with components which may either fail to operate or may operate prematurely. System reliability is maximized subject to a constraint ori system safety. In each case the problem is formulated as an integer linear program. This has an advantage over alternative dynamic programming formulations in that standard algorithms may be employed to obtain numerical results.     

Impact of an all volunteer force upon the navy in the 1972-1973 timeframe

This paper develops estimates of true volunteer levels for 1972 and 1973, based on experience gained through 1970 draft lottery data. The paper also formulates estimates of the qualitative characteristics of a 1972-1973 Navy volunteer force, and establishes a relationship between rate of volunteerism and military pay. Utilizing estimates generated in the paper, Navy military personnel budget requirements for FY '72 and '73 are presented.     

Quadratic as parametric linear programming

This paper describes an approximate solution procedure for quadratic programming problems using parametric linear programming. Limited computational experience suggests that the approximation can be expected to be “good”.     

An informal survey of multi-echelon inventory theory

Contained herein is an informal nonmathematical survey of research in multi-echelon inventory theory covering published results through 1971. An introductory section defines the term, “multi-echelon,” and establishes the kinds of problems involving multi-echelon considerations. Subsequent sections provide surveys of research on deterministic and stochastic multi-echelon inventory control problems, allocation models, and multi-echelon planning and evaluation models. A final section discusses the present state of the art and suggests directions for future research. A bibliography of papers concerning multi-echelon inventory theory and applications is included.     

A finiteness proof for modified dantzig cuts in integer programming

Let be a basic solution to the linear programming problem subject to: where R is the index set associated with the nonbasic variables. If all of the variables are constrained to be nonnegative integers and x_u is not an integer in the basic solution, the linear constraint is implied. We prove that including these “cuts” in a specified way yields a finite dual simplex algorithm for the pure integer programming problem. The relation of these modified Dantzig cuts to Gomory cuts is discussed.     

Effective in battle: conceptualizing soldiers’ combat effectiveness*

How do we understand combat effectiveness – soldiers’ performance in battle? Despite the broad consensus that understanding combat effectiveness is important both for scholars and policymakers, there is widespread disagreement about what combat effectiveness is. More specifically, studies of effectiveness tend to focus on either the skill of soldiers in battle, or their will to fight. Yet both skill and will are essential components of an effective fighting force. This article argues that understanding combat effectiveness requires understanding both of these key components of effectiveness. In other words, combat effectiveness requires both the skill and will to engage the enemy in an organized manner. It then demonstrates the usefulness of this conceptualization by applying it to the cases of British, Indian, and Australian forces fighting the Japanese during the Second World War. Only when scholars are talking about the same concept will our understanding of the conditions under which militaries are effective in battle progress. By comparing different units fighting the same opponent under the same material conditions, I demonstrate that units vary both in their combat skill and their will to fight, and that understanding their effectiveness in battle requires analyzing both of these key factors.