A Survey of Management Science Applications of the Deterministic Maximum Principle

Ever since the publication of Pontryagin's Maximum Principle, the number of its applications to management science problems has been steadily growing. This paper is an up-to-date survey of the applications of the deterministic maximum principle to the three functional areas of management: Finance, Production, and Marketing. The specific problems represented by these applications are cash balance problems, optimal financing problems, production and inventory problems, machine replacement problems, and optimal advertising problems. In addition, other selected management science applications are briefly described or simply listed. The survey concludes with suggestions for directions of future research