In a recent paper, Liu (2008) considers the lot-sizing problem with lower and upper bounds on the inventory levels. He proposes an O(n2) algorithm for the general problem, and an 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) complexity.
Efficient algorithms for the economic lot-sizing problem with storage capacity are proposed. On one hand, cost structure consisting of general linear holding and ordering costs fixed setup costs, an OT2 dynamic programming algorithm is introduced, where T number time periods. The
We study a two-level uncapacitated lot-sizing problem with inventory bounds that occurs in a supply chain composed of a supplier and a retailer. The first level with the demands is the retailer level and the second one is the supplier level. The aim is to minimize the cost of the
The costs of many economic activities such as production, purchasing, distribution, and inventory exhibit economies of scale under which the average unit cost decreases as the total volume of the activity increases. In this paper, we consider an economic lot-sizing problem with g
We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one with linear cost on inventory, the other with linear and fixed costs on inventory. For both models, we identify facet-defining inequalities that make use of the in
In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to th