A new bivariate negative binomial distribution

A new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.     

A theoretical and computational comparison of “equivalent” mixed-integer formulations

This paper provides a theoretical and computational comparison of alternative mixed integer programming formulations for optimization problems involving certain types of economy-of-scale functions. Such functions arise in a broad range of applications from such diverse areas as vendor selection and communications network design. A “nonstandard” problem formulation is shown to be superior in several respects to the traditional formulation of problems in this class.     

AN ALGORITHM FOR THE SEGREGATED STORAGE PROBLEM

The segregated storage problem involves the optimal distribution of products among compartments with the restriction that only one product may be stored in each compartment. The storage capacity of each compartment, the storage demand for each product, and the linear cost of storing one unit of a product in a given compartment are specified. The problem is reformulated as a large set-packing problem, and a column generation scheme is devised to solve the associated linear programming problem. In case of fractional solutions, a branch and bound procedure is utilized. Computational results are presented.     

Dynamic multiattribute models for mixed manpower systems

This paper reviews a wide variety of manpower and personnel models of the goal programming variety. This is done from a strategy-oriented point of view addressing the problems of interest for immediate implementation as well as basic problems of manpower model research development. Particular emphasis in this paper is concerned with how analytical models can be brought to bear on the problems of combining military and civilian manpower into one management system. This includes a discussion of the computer support arrangements necessary to implement the models. First, we discuss an extension of multilevel models to provide an integrated approach to program planning which includes the dynamics of the manpower requirements-inventory relationships of mixed military-civilian manpower systems. Then, focus is given to some of the potential Navy applications particularly in terms of ways the outputs from the global multilevel model might be interfaced with assignment models for operational planning. The paper concludes with a discussion of static and dynamic multiattribute assignment models which operate on the individual man-job matching level. It is at this level of detail that dynamic mixed manpower systems might be constructed for use in equal employment opportunity planning and for local organization design studies.     

A generalization of the entropy model for brand purchase behavior

Hemiter's entropy model for brand purchase behavior has been generalized for Renyi's measure of entropy which is a more general concept than Shannon's measure of entropy used by Herniter and which includes Shannon's measure as a limiting case. The generalized model considered here is more flexible than Herniter's model since it can give different marketing statistics for different products and it can give these statistics even when only some of the brands are considered.     

The one-period,N-location distribution problem

This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case.     

The bottleneck transportation problem

The bottleneck transportation problem can be stated as follows: A set of supplies and a set of demands are specified such that the total supply is equal to the total demand. There is a transportation time associated between each supply point and each demand point. It is required to find a feasible distribution (of the supplies) which minimizes the maximum transportaton time associated between a supply point and a demand point such that the distribution between the two points is positive. In addition, one may wish to find from among all optimal solutions to the bottleneck transportation problem, a solution which minimizes the total distribution that requires the maximum time Two algorithms are given for solving the above problems. One of them is a primal approach in the sense that improving fcasible solutions are obtained at each iteration. The other is a “threshold” algorithm which is found to be far superior computationally.     

Optimal scheduling of objects in circulating systems

A “circulating system” is a finite collection of objects, each of which is oscillaling between two states. The prototype system is that of ships on patrcl,each subject to a quasi-regular “duty-service” cycle. There are various restrictions on the time spent in either state by an object and on the number of objects in a state at any one time. Schedules are sought in which the total number in one state is as large and as constant as possible. The maximal average number in one state is calculated, and a necessary and sufficient condition is given for a schedule to achieve it. Procedures are developed for constructing a schedule which achieves the maximal average in the most constant manner.     

Landmarks in defense literature

The Weapons Acquisition Process: An Economic Analysis By M.J. Peck and F.M. Scherer Boston: Harvard University Press, (1962).