A new approach for dealing with the startup problem in discrete event simulation

This article proposes a practical, data-based statistical procedure which can be used to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state means. We discuss results of experiments designed to choose good parameter values for this procedure, and present results of extensive testing of the procedure on a variety of stochastic models for which partial analytical results are available. The article closes with two illustrations of the application of the procedure to more complex statistical problems which are more representative of the kinds of purposes for which real-world steady-state simulation studies might be undertaken.     

Adjacent vertices on transportation polytopes

To solve linear fixed charge problems with Murty's vertex ranking algorithm, one uses a simplex algorithm and a procedure to determine the vertices adjacent to a given vertex. In solving fixed charge transportation problems, the simplex algorithm simplifies to the stepping-stone algorithm. To find adjacent vertices on transportation polytopes, we present a procedure which is a simplification of a more general procedure for arbitrary polytopes.     

A note on the optimal scheduling of two parallel processors

The problem of minimizing mean flow time of two parallel processors is discussed. Prior results are briefly reviewed. A dynamic programming algorithm is presented which minimizes mean flow time for a set of n preordered jobs on two nonequivalent parallel processors. The algorithm is illustrated with an example problem. The computational experience is presented which illustrates the efficiency of the algorithm.     

A theory of ideal linear weights for heterogeneous combat forces

Detailed combat simulations can produce effectiveness tables which measure the effectiveness of each weapon class on one side of an engagement, battle, or campaign to each weapon class on the other. Effectiveness tables may also be constructed in other ways This paper assumes that effectiveness tables are given and shows how to construct from them a system of weapon weights each of which is a weighted average of the effects of a given weapon against each of the enemy's weapons. These weights utilize the Perron- Frobenius theory of eigenvectors of nonnegative matrices. Methods of calculation are discussed and some interpretations are given for both the irreducible and reducible cases.     

Requirements of an “optimizer” for computer simulations

Computer simulation has many advantages. However, one major disadvantage is that, in all too many cases, the attempt to use computer simulation to find an optimum solution to a problem rapidly degenerates into a trial-and-error process. Techniques for overcoming this disadvantage, i. e., for making optimization and computer simulation more compatible, are applicable at two points in the development of the overall computer simulation. Techniques which are used within actual construction of the mathematical models comprising the simulation will be labeled as internal methods, while those which are used after the simulation has been completely developed will be termed external methods Because external methods appear to offer the largest potential payoff, discussion is restricted to these methods, which are essentially search techniques. In addition, the development of an “Optimizer” computer program based on these techniques is suggested Although drawbacks to the use of search techniques in the computer simulation framework exist, these techniques do offer potential for “optimization.” The modification of these techniques to satisfy the requirements of an “Optimizer” is discussed.     

An application of linear programming to contingency planning: A tactical airlift system analysis

A linear programming application for the selection of aircraft for a tactical airlift fleet is described.     

The fixed charge problem

The fixed charge problem is a nonlinear programming problem of practical interest in business and industry. Yet, until now no computationally feasible exact method of solution for large problems had been developed. In this paper an exact algorithm is presented which is computationally feasible for large problems. The algorithm is based upon a branch and bound approach, with the additional feature that the amount of computer storage required remains constant throughout (for a problem of any given size). Also presented are three suboptimal heuristic algorithms which are of interest because, although they do not guarantee that the true optimal solution will be found, they usually yield very good solutions and are extremely rapid techniques. Computational results are described for several of the heuristic methods and for the branch and bound algorithm.