Heuristics for multilevel lot-sizing with a bottleneck
Management Science
Lot-size models with back-logging: strong reformulations and cutting planes
Mathematical Programming: Series A and B
Solving multi-item capacitated lot-sizing problems using variable redefinition
Operations Research
Capacitated lot sizing with setup times
Management Science
Solving multi-item lot-sizing problems using strong cutting planes
Management Science
Polyhedra for lot-sizing with Wagner-Whitin costs
Mathematical Programming: Series A and B
A cutting plane approach to capacitated lot-sizing with start-up costs
Mathematical Programming: Series A and B
Aggregation and Mixed Integer Rounding to Solve MIPs
Operations Research
Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs
Management Science
bc -- prod: A Specialized Branch-and-Cut System for Lot-Sizing Problems
Management Science
A study of the lot-sizing polytope
Mathematical Programming: Series A and B
A General Heuristic for Production Planning Problems
INFORMS Journal on Computing
Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)
Computational methods for big bucket production planning problems: feasible solutions and strong formulations
Uncapacitated lot sizing with backlogging: the convex hull
Mathematical Programming: Series A and B
Multi-item lot-sizing with joint set-up costs
Mathematical Programming: Series A and B
Mathematics of Operations Research
Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems
Operations Research
Improved lower bounds for the capacitated lot sizing problem with setup times
Operations Research Letters
Fixed-charge transportation on a path: linear programming formulations
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research.