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Abstract
In this paper, concepts of linear programming-in particular the Simplex algorithm and the Dual Simplex algorithm-are used within a discrete renewal model for the development of a graded population, when the transfer rates between the various grades are given, and "wastage" is replaced by suitable recruiting.
The following questions are dealt with:
Which population structures (i.e. partitions into grades) can be attained from a given structure, after one or more steps?
From which structures can a given structure be attained in one or more steps?
If the present structure as well as a desired future structure are given, can the latter be attained from the former in one or more steps? If so, how?
The last problem is of special interest if the starting structure is identical with that to be attained and is called re-attaining after more than one step, or strictly maintaining after one step.
Examples are given to illustrate the procedure, and some attention is given to the possibility of alternative routes in cases (3) and (4). It is observed that if a structure is attainable (or re-attainable) after n steps, then it is not necessarily attainable (or re-attainable) after n + 1 steps.