This paper presents two new solution procedures for a deterministic lot size problem, a matrix algorithm and a heuristic matrix method. The algorithm is based on the dual of a linear programming model formulation of the lot size problem, and it provides optimal solutions even in the general case of time-varying parameters. A comparison of the efficiency of the new solution procedures with well-known methods is developed. New applications of the techniques described within the fields of engineering (optimal design of a pump-pipe system) and economics (a model for import-planning) are referred to.