Solving multi-item capacitated lot-sizing problems using variable redefinition
Operations Research
Capacitated lot sizing with setup times
Management Science
Some extensions of the discrete lotsizing and scheduling problem
Management Science
The dynamic line allocation problem
Management Science
Lot-Sizing with Start-Up Times
Management Science
Constraint-Based Scheduling
Mixed Global Constraints and Inference in Hybrid CLP–IP Solvers
Annals of Mathematics and Artificial Intelligence
Constraint-Based Job Shop Scheduling with {\sc Ilog\ Scheduler}
Journal of Heuristics
Improving Branch and Bound for Jobshop Scheduling with Constraint Propagation
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Global Cut Framework for Removing Symmetries
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Integer Linear Programming and Constraint Programming Approaches to a Template Design Problem
INFORMS Journal on Computing
Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems
INFORMS Journal on Computing
Logic, Optimization, and Constraint Programming
INFORMS Journal on Computing
Constraint and Integer Programming in OPL
INFORMS Journal on Computing
Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs
Management Science
Improving Discrete Model Representations via Symmetry Considerations
Management Science
The Capacitated Lot-Sizing Problem with Linked Lot Sizes
Management Science
Enhanced Model Formulations for Optimal Facility Layout
Operations Research
Constraints
Computers and Operations Research
A Hybrid Method for the Planning and Scheduling
Constraints
Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Symmetric ILP: Coloring and small integers
Discrete Optimization
Improved lower bounds for the capacitated lot sizing problem with setup times
Operations Research Letters
Computers and Operations Research
Efficient symmetry breaking formulations for the job grouping problem
Computers and Operations Research
Computers and Industrial Engineering
| Hi-index | 0.01 |
Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lot-sizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper, we look at how to incorporate parallel machines in a mixed-integer programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lot-sizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry-breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving mixed-integer programming problems---specifically, the potential added value of symmetry-breaking constraints.