A two-phase procedure for allotting geostationary orbital locations to communications satellites

We consider the problem of allotting locations in the geostationary orbit to communication satellites, subject to angle of elevation and electromagnetic interference constraints. An optimization framework is used as a means of finding feasible allotment plans. Specifically, we present a two-phase solution procedure for the satellite location problem (SLP). The objective in SLP is to allot geostationary orbital locations to satellites so as to minimize the sum of the absolute differences between the locations prescribed for the satellites and corresponding specified desired locations. We describe two heuristics, an ordering procedure and a k-permutation algorithm, that are used in tandem to find solutions to SLP. Solutions to a worldwide example problem with 183 satellites serving 208 service areas are summarized.     

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.     

Optimal control of price through restricted production

Consider a regulated monopolist whose current profits would be maximized if they could charge a price p?, where p? exceeds the current market price. By reducing production below current consumer demand the monopolist can create an illusion of a shortage and induce the regulator to allow a price increase. Conditions are given for which the production rate that maximizes the monopolist's expected discounted profits over an infinite horizon will have the property that the amount of unsatisfied consumer demand will be a non-increasing function of current market price.     

A linear programming approach to geometric programs

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.     

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.     

Some comparative & design aspects of fixed cycle production systems

A serial production line is defined wherein a unit is produced if, and only if, all machines are functioning. A single buffer stock with finite capacity is to be placed immediately after one of the first N-1 machines in the N machine line. When all machines have equal probability of failure it is shown that the optimal buffer position is exactly in the middle of the line. This result is synthesized with the earlier work of Koenigsberg and Buzacott including an analysis of the covariance between transition states. An alternative model formulation is presented and integrated with previous results. Finally, a sufficient condition and solution procedure is derived for the installation of a buffer where there is a possible trade-off between increasing the reliability of the line versus adding a buffer stock.     

Insurance type item provisioning guidelines

Policy decisions for insurance type items, where zero or one unit is maintained at the depot, are more difficult and more critical than decisions for common supply items. This report presents results of developing initial provisioning guidelines for insurance type items. The guidelines are based on examination of lifetime costs and benefits. Costs of stocking an item as compared with not stocking are developed through a sinking fund annual payment formulation. Benefits of stocking are developed as stationary reduction in time weighted backorders experienced. A resource allocation formulation yields an optimal policy for allocating a fixed budget. The guideline is presented with refinements based on a sample of items. A figure of merit is calculated for each item, and if it is large the item is stocked while if small it is not stocked. Empirical definitions for large and small are developed based on sample data. Estimation techniques are discussed for deriving all of an item's parameters needed to compute its figure of merit. A Bayes procedure is suggested based on family group Experienced Demand Replacement Factors. This and other techniques are discussed.     

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.