An efficient approach for solving the lot-sizing problem with time-varying storage capacities

• Published in: European journal of operational research Vol. 189; no. 3; pp. 682 - 693
• Main Authors: Gutiérrez, J., Sedeño-Noda, A., Colebrook, M., Sicilia, J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.09.2008; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Capacity; Computational improvement; Cost structure; Dynamic programming; Inventory management; Inventory–production: policies; Lot-sizing; Problem solving; Studies; Inventory–production: policies; Lot-sizing; Computational improvement; Dynamic programming; Capacity
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2006.09.096

We address the dynamic lot size problem assuming time-varying storage capacities. The planning horizon is divided into T periods and stockouts are not allowed. Moreover, for each period, we consider a setup cost, a holding unit cost and a production/ordering unit cost, which can vary through the planning horizon. Although this model can be solved using O( T 3) algorithms already introduced in the specialized literature, we show that under this cost structure an optimal solution can be obtained in O( T log T) time. In addition, we show that when production/ordering unit costs are assumed to be constant (i.e., the Wagner–Whitin case), there exists an optimal plan satisfying the Zero Inventory Ordering (ZIO) property.