A simple Markov model for the analysis of multiple air combat

It is proposed to describe multiple air-to-air combat having a moderate number of participants with the aid of a stochastic process based on end-game duels. A simple model describing the dominant features of air combat leads to a continuous time discrete-state Markov process. Solution of the forward Kolmogorov equations enables one to investigate the influence of initial force levels and performance parameters on the outcome probabilities of the multiple engagement. As is illustrated, such results may be useful in the decision-making process for aircraft and weapon system development planning. Some comparisons are made with Lanchester models as well as with a semi-Markov model.     

On fractional programming and equivalence

Under fairly general conditions, a nonlinear fractional program, where the function to be maximized has the form f(x)/g(x), is shown to be equivalent to a nonlinear program not involving fractions. The latter program is not generally a convex program, but there is often a convex program equivalent to it, to which the known algorithms for convex programming may be applied. An application to duality of a fractional program is discussed.     

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.     

Occupational structure in the military and civilian sectors of the economy

This paper focuses on trends in the occupational structure of the military and civilian sectors of the economy. Some implications of these trends for manpower policies for the all-volunteer military establishment are examined.     

Optimal flowshop schedules with no intermediate storage space

In this paper the problem of finding an optimal schedule for the n-job, M-machine flowshop scheduling problem is considered when there is no intermediate space to hold partially completed jobs and the objective function is to minimize the weighted sum of idle times on all machines. By assuming that jobs are processed as early as possible, the problem is modeled as a traveling salesman problem and solved by known solution techniques for the traveling salesman problem. A sample problem is solved and a special case, one involving only two machines, is discussed.     

A generalized recursive algorithm for a class of non-stationary regeneration (scheduling) problems

Recent efforts in the field of dynamic programming have explored the feasibility of solving certain classes of integer programming problems by recursive algorithms. Special recursive algorithms have been shown to be particularly effective for problems possessing a 0–1 attribute matrix displaying the “nesting property” studied by, Ignall and Veinott in inventory theory and by Glover in network flows. This paper extends the class of problem structures that has been shown amenable to recursive exploitation by providing an efficient dynamic programming approach for a general transportation scheduling problem. In particular, we provide alternative formulations lor the scheduling problem and show how the most general of these formulations can be readily solved vis a vis recursive techniques.     

Prediction with zero-one loss structure

This paper poses a prediction problem in which a linear model is assumed. With a “zero-one” loss structure as the loss from incorrect prediction, it is suggested that least squares may not be appropriate for estimating the parameters of the model. An alternate criterion is proposed and integer programming is used in order to find the estimates, given the proposed criterion.