An efficient algorithm for the capacitated single item dynamic lot size problem

A dynamic programming based algorithm is developed for the single item lot size problem with concave costs and arbitrary capacities. By making use of the extreme point properties of the problem, first the set of all feasible cumulative production levels that may occur in an optimal solution is generated. In the second stage, a dynamic programming procedure is carried out over this set. The worst case computational effort is equal to that of the standard dynamic programming approach but extensive computational tests with the algorithm indicate that for T periods problems the computational effort does not exceed O(T⁴). The performance of the algorithm is compared with the performance of the existing procedures in the literature for the general, the constant capacity, and the constant unit cost problems. The computational results demonstrate that the present algorithm is at least three times faster than the other procedures for all problem types considered.