Lot sizing with inventory bounds and fixed costs: polyhedral study and computation

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 inventory bounds explicitly and give exact separation algorithms. We also describe a linear programming formulation of the problem when the order and inventory costs satisfy the Wagner–Whitin nonspeculative property. We present computational experiments that show the effectiveness of the results in tightening the linear programming relaxations of the lot-sizing problem with inventory bounds and fixed costs.