This paper describes a method for obtaining numerical information concerning the time-dependent behavior of stochastic processes such as those arising in queuing theory. The method leads to an approximate inverse of the Laplace transform. Examples are given of applications to transforms with known inverses, and the evolution of expected waiting time at a simple single-server queue is illustrated, both when there is a stationary solution and in the saturated case.

This paper provides models for economic enterprises or projects whose returns vary randomly in time and which are subject to termination or “ruin” provided assets or net worth fall to a prescribed level. In particular, strategies for dealing with environmental changes, innovations, and catastrophe are considered.

We propose a new type of repairman model in which failures may require multiple repair operations, each done by a specialized repair crew. These repair operations may occur simultaneously. An analysis of the model is carried out using diffusion approximation techniques. The analysis predicts that the number of customers in service will have a steady state normal distribution with specified mean and covariance structure. Numerical studies are presented which substantiate this assertion in the infinite server case. An analysis for the multiple server case is also provided.

This paper attempts to coordinate at the macro level the research potential and the development capability of an organization in a competitive environment. New product ideas generate from various sources of research which are then processed (preliminary screening, market appraisal, technical development etc.) by the development section. In view of the randomness present in the above process, a backlog of ideas will normally be present awaiting development. The longer the delay in processing them, the greater are the chances of a competitor introducing the product in the meantime. Simple queueing models are set up which abstract the essence of the problem, and reveal the causal relationships of the underlying structure. The decision variable (relationship of the research rate to the development rate) is optimized, and its sensitivity to changes in the parameters describing the environment is examined. Generalizations of the approach using Monte-Carlo methods arc also indicated.

Some parts of the long-range planning problem have been widely discussed. Other parts have received less attention. Of the relatively neglected areas, one of special importance is manpower planning. Manpower planning includes a specification of the kinds and numbers of men an organization will need to accomplish its profit, growth, or service objectives; a forecast from current personnel inventories of how well it is now set to meet the projected needs; and by a comparison of needs with forecasted supply, the formulation of plans for recruiting, assigning, and developing personnel. This paper explores some issues in manpower planning. We review some of the kinds of approaches that have been tried and look in some detail at two approaches which seem especially promising.