Dynamic programming

INTRODUCTION

Dynamic programming is both an approach to problem solving and a decomposition technique that can be effectively applied to mathematically describable problems having a sequence of interrelated decisions. Such decision making problems are pervasive. Determining a route from an origin (e.g., your house) to a destination (e.g., your school or place of employment) on a network of roads requires a sequence of turns. Managing a retail store (e.g., that sells, say, televisions) requires a sequence of wholesale purchasing decisions.

Such problems also share common characteristics. Each is invariably associated with a criterion. We may wish to choose the shortest or most scenic route from home to our place of employment; the retail store manager purchases televisions with the intent of selling them to maximize expected profit. Each is such that a currently determined decision has impact on the future decision making environment. In going from home to work, the turn currently...