Assignment

Abstract

Fractional task sizes may be allocated, starting at the president’s level in order to make full use of presidential capacity. Thus when

$$1<\text{Q}\le \text{s}$$

the president is assigned an amount x of operative work such that

$${\text{s(1 - x) = Q - x}}$$

operatives supervised = operatives hired

$$x=\frac{s-Q}{s-1}$$

Now let

$${{\text{s}}^{\text{R-1}}}\text{Q}\le {{\text{s}}^{\text{R}}}$$

One possible assignment is the following: Assign s^R−r persons to rank r, r = 1,..., R. Assign an amount x of operative work to first line supervisors of rank 1. The number of operatives in rank zero is then given by

$${{\text{n}}_{\text{0}}}\text{=Q-x=s(}{{\text{s}}^{\text{R-1}}}\text{-x)}$$

from which

$$\text{x=}\frac{{{\text{s}}^{\text{R}}}\text{-Q}}{\text{s-1}}$$

Generalizing (1). In either case operative work is handled at the lowest possible levels. Now turn to the problem of full-time, i.e., integer assignments.