We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one with linear costs 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 capacities explicitly and give exact separation algorithms. We also give a linear programming formulation of the problem when the order and inventory variable 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.
Operations Research 53, 711-730, 2005