Rounding off the optimal solution of the economic lot size problem

We consider the problem in which a facility periodically orders a product from another facility to face a constant demand. Orders are of equal size and the reorder interval is an integer number. The aim is to determine a policy that minimizes the sum of ordering cost and inventory cost over an infinite time horizon. This problem is a discretized version of the well-known economic lot size problem. We compare, from the worst-case point of view, the optimal cost of the discrete problem with the optimal cost of the economic lot size problem, both in the case in which in the discrete problem the reorder interval is restricted to be a power-of-two and in the more general case with integer reorder interval. Moreover, we prove that the well-known worst-case bound of about 1.06 between the optimal cost of the problem with power-of-two reorder interval and the optimal cost of the problem with integer reorder interval is tight. Finally, we evaluate the worst-case performance of procedures that round off the optimal reorder interval of the economic lot size problem to integer and to power-of-two values.