A Finite Renewal Algorithm for the Knapsack and Turnpike Models

The mathematical and algorithmic connections between the knapsack problem and a fundamental renewal-type problem are established. The renewal point of view leads to an efficient computational result and is based in part on an extension of a turnpike theorem shown by Gilmore and Gomory. The distribution of effort model is examined briefly by means of the renewal approach so as to add new insight to the mathematical structure of this problem.