Algorithms for Single-Item Lot-Sizing Problems with Constant Batch Size

• Published in: Mathematics of operations research Vol. 32; no. 3; pp. 594 - 613
• Main Author: Van Vyve, Mathieu
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.08.2007; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Analysis; capacitated lot-sizing; complexity; Dynamic programming; Economic lot size; Integers; Mathematical constants; Mathematical functions; Mathematical intervals; Mathematical vectors; Mathematics; Matrices; Operations research; Optimal solutions; Production costs; Production scheduling; Studies; United States
• ISSN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.1070.0257

The main result of this paper is an O ( n 3 ) algorithm for the single-item lot-sizing problem with constant batch size and backlogging. We consider a general number of installable batches, i.e., in each time period t we may produce up to m t batches, where the m t are given and time-dependent. This generalizes earlier results as we consider backlogging and a general number of maximum batches. We also give faster algorithms for three special cases of this general problem. When backlogging is not allowed and the costs satisfy the Wagner-Whitin property, the problem is solvable in O ( n 2 log n ) time. When the production in each period is required to be either zero or equal to the installed capacity, it is possible to solve the problem with and without backlogging in O ( n 2 ) and O ( n log n ) time, respectively.