A note on “The economic lot sizing problem with inventory bounds”

In a recent paper, Liu [3] considers the lot-sizing problem with lower and upper bounds on the inventory levels. He proposes an O(n2)O(n2) algorithm for the general problem, and an O(n)O(n) algorithm for the special case with non-speculative motives. We show that neither of the algorithms provides an optimal solution in general. Furthermore, we propose a fix for the former algorithm that maintains the O(n2)O(n2) complexity.

► Algorithms by Liu for economic lot sizing with inventory bounds are not correct.
► We present numerical examples to illustrate this.
► We fix those algorithms and analyze the complexity of the new algorithms.