A Dynamic Model for Optimum Bonus Management: Computer Program and Mathematical Analysis.

摘要

This report describes the mathematics and the computer program for solving the problem of optimum bonus management formulated in 'A Dynamic Model for Optimum Bonus Management'. The problem of optimum bonus management is treated as a discrete linear control system with a quadratic cost function and solved by using Pontryagin's discrete maximum principle. The state of the system at discrete time is a vector of numbers of men in each of a set of year groups. The system evolves linearly in time under linear controls that are the bonuses paid to the men in a prescribed subset of the year groups. The program solves for the sequence of bonus values that drive a given initial state of year groups to a prescribed final state and minimize a sum of quadratic bonus and penalty costs. The program, which consists of a main program and 22 subroutines, is written in FORTRAN IV double precision for the IBM 370-158.