Showing papers in "Naval Research Logistics Quarterly in 1962"

An approximative algorithm for the fixed‐charges transportation problem

Abstract: A computationally simple method for approximating the optimal solution to transportation problems is described. Also, a method to deal with fixed charges is proposed. The computational algorithms have been designed primarily to handle very large numbers of transportation problems each involving a small number of origins and destinations as is frequently the situation in the Navy supply system. The results of empirical tests of the effectiveness of the methods are summarized. INTMDUCTION In July of 1959 our research group was authorized to proceed on a research project for the Bureau of Supplies and Accounts of the United States Navy. The project was given the title "Modified Linear Programming." Specifications for the project, as prepared by the Bureau, read in part as follows: "This project task is directed toward development of more efficient rules for the distribution and redistribution of material in the Navy supply system, through modification of the techniques of solution of the transportation problem to represent adequately and minimize the total costs of alternative allocation and redistribution decision patterns for Navy material. In particular, the project seeks to discover feasible and workable approximating rules for distribution decisions where a fixed cost of shipment is postulated for each 'channel' in addition to the customary variable cost, linear with respect to quantity with fixed costs for a shipment approximately the same for all activities, with linear or piecewise linear variable costs based on distance and transportation rate data.. . ."

Multiship, multishop, workload‐smoothing progfum

Abstract: This paper describes a computer program that uses simple rules and applies them probabilistically to minimize manpower requirements in shops of a naval shipyard. Preliminary runs on a small fictitious problem show that this “multiship, multishop, workload-smoothing” program, called (MS)2, may be able to reduce the maximum number of men required on any one day by 30 to 60 percent. The program employs the critical path method of analyzing the jobs to be done on a given project (ship) and begins by assigning all jobs at their earliest possible start time. Then suitable jobs on peak workload days are selected at random and shifted to later days beyond the peak days until further shifting no longer reduces peak loads. The first segment of the program smooths the workloads on all shops simultaneously. After the first segment is completed the second segment performs further smoothing on individual shops, beginning with the most expensive shop. Although a limited amount of experience has been gained with this program, it appears likely that it can be developed further so that it can handle realistic-sized problems such as those encountered in a Naval Shipyard. Moreover, it can be applied on three levels: (1) smoothing shop workloads in a shipyard; (2) smoothing the workloads of individual shops; and (3) smoothing shipyard workloads.

An approximate method of solving Blotto games

Abstract: A Blotto game is a mathematical formulation of the problem of allocating forces in certain military situations, particularly when they are concerned with. an initial strike. In this paper an approximate method of solution is introduced. This is based on a new game involving the mean numbers of forces allocated to each battlefield in the original game.

Pure strategy solutions to blotto games in closed auction bidding

Abstract: This paper considers the problem of making simultaneous bids for two objects against competition by two competitors. A game-theoretic formulation of the problem is made and optimal pure strategies, when they exist, are derived.

Queuing problem with limited waiting space

Abstract: In this paper, the queuing problem characterised by Poisson arrivals and a wide class of service time distribution has been solved by applying the phase method under the condition of limited waiting space. This problem is already solved by Finch, but he gave only explicit solution for the case of exponential distribution. The phase method has an advantage of giving the solution in a form which is easily computable. Tables are presented for the operational parameters for exponential and 2-Erlang service time distributions.

Analytical study of a problem in air defense

Abstract: This paper deals with the analytical study of the encounter of fighter interceptors with the incoming formation of an air task force of enemy bombers. An attempt is made to frame a stochastic model of the situation and to determine the probabilities of hit under different conditions. It is indicated that with reasonable estimates of the operational parameters involved the various probabilities are capable of optimization.

Statistical properties of selected inventory models

Abstract: : In the study of inventory policies an interest is shown not only in the mean values of such important random variables as number of shortages per time period, but also in their variance and covariance properties. Such additional properties are of interest in interpreting the stability of an expected value, under assumed inventory policies and parameters, and in using stochastic or Monte Carlo models to calculate estimates of the expected values by sampling techniques. In this paper, comparatively simple inventory models are examined and the expected value, variance, and selected covariance and correlations of the random variables representing stock on hand, shortages per period, overages per period and reorder quantity are derived.

A triangulafuzation method for computations in linear programming

Abstract: This paper describes a method for computations in linear programming which is midway between methods such as the “stepping stone” procedure for the distribution model in which no inverses of bases are kept, and the modified simplex method in which one carries along the complete inverse of the basis at each stage. It is designed to avoid division by pivots until the optimum basis has been obtained. Thus a small pivot will not affect adversely all subsequent steps.

An AID to preliminary design of missile prelaunch checkout equipment

Abstract: The purpose of a missile prelaunch confidence checkout is to assure the commander that the weapon contains no undetected mission-failure-causing defects and, indeed, is ready to perform its assigned mission. If all the prelaunch tests that would be desirable cannot be scheduled because of the operational necessity to launch within a limited amount of time, then engineering and operational evaluations must be employed to determine the theoretically optimum content of the limited checkout and also the required capability of the checkout equipment. As an aid in preliminary design, perhaps as an objective point of departure for design compromises, this paper addresses the problem of making these design decisions from an operational viewpoint and, by use of reliability estimates as the basis for the analysis, develops (1) quantitative criteria for the value of inclusion of individual checks in the checkout, (2) an expression for the required efficiency of the checkout equipment, and (3) a mathematical method for determining the content of a theoretically optimum checkout. The latter result is for the case exemplified by ballistic missiles where, in general, all missile functions are energized prior to launch and where one operational constraint is dominant, namely, time allowed for checkout. The determination of the optimum checkout content can be done graphically, and the method developed can also be used to ascertain the launch confidence achieved by the checkout equipment of present missile systems.

A heuristic concept and an automatic computer program aid for operational simulation

Abstract: An operational simulation is a collection of interrelating events. In order to code a simulation more easily for an electronic computer the events should be isolated, i.e., free from immediate interactions. Logical aid is used to determine cause-effect relationships and eliminate impossible interactions from consideration. A timing model is set up, partitioning the events in time and space finely enough to insure their mutual exclusiveness. An automatic computer program is described that will compile mutually exclusive events, which may all be precoded as if occurring at one time and at one place. The program allows flexibility for adding, omitting, and replacing events or their parts, and for interrupting the simulation to allow human decisions to be incorporated.

A generalized problem in air defense

Abstract: In this paper a stochastic model for an air defense problem has been developed, in which it is assumed that the time during which the formation of enemy bombers is in free-state and in contact-state follows general distributions, and the probability of hits follows a Poisson process.