Optimal lot-sizing algorithms for complex product structures
Operations Research
Integer and combinatorial optimization
Integer and combinatorial optimization
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
Facets and algorithms for capacitated lot sizing
Mathematical Programming: Series A and B
A strong cutting plane algorithm for production scheduling with changeover costs
Operations Research
A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Solving multi-item lot-sizing problems using strong cutting planes
Management Science
Analysis of relaxations for the multi-item capacitated lot-sizing problem
Annals of Operations Research
Some extensions of the discrete lotsizing and scheduling problem
Management Science
Economic lot sizing: an O(n log n) algorithm that runs in linear time in the Wagner-Whitin case
Operations Research - Supplement
Improved algorithms for economic lot size problems
Operations Research
A Lagrange relaxation approach for very-large-scale capacitated lot-sizing
Management Science
Lot-sizing with constant batches: formulation and valid inequalities
Mathematics of Operations Research
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
Lower Bounds in Lot-Sizing Models: a Polyhedral Study
Mathematics of Operations Research
Lot-Sizing with Start-Up Times
Management Science
Material Requirements Planning: The New Way of Life in Production and Inventory Management
Material Requirements Planning: The New Way of Life in Production and Inventory Management
Lotsizing with backlogging and start-ups: the case of Wagner-Whitin costs
Operations Research Letters
Workforce planning in a lotsizing mail processing problem
Computers and Operations Research
Fix and Relax Heuristic for a Stochastic Lot-Sizing Problem
Computational Optimization and Applications
Lot-sizing in a foundry using genetic algorithm and repair functions
EvoCOP'05 Proceedings of the 5th European conference on Evolutionary Computation in Combinatorial Optimization
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We study in this lecture the literature on mixed integer programming models and formulations for a specific problem class, namely deterministic production planning problems. The objective is to present the classical optimization approaches used, and the known models, for dealing with such management problems.We describe first production planning models in the general context of manufacturing planning and control systems, and explain in which sense most optimization solution approaches are based on the decomposition of the problem into single-item subproblems.Then we study in detail the reformulations for the core or simplest subproblem in production planning, the single-item uncapacitated lot-sizing problem, and some of its variants. Such reformulations are either obtained by adding variables - to obtain so called extended reformulations - or by adding constraints to the initial formulation. This typically allows one to obtain a linear description of the convexh ull of the feasible solutions of the subproblem. Such tight reformulations for the subproblems play an important role in solving the original planning problem to optimality.We then review two important classes of extensions for the production planning models, capacitated models and multi-stage or multi-level models. For each, we describe the classical modeling approaches used. Finally, we conclude by giving our personal view on some new directions to be investigated in modeling production planning problems. These include better models for capacity utilization and setup times, new models to represent the product structure - or recipes - in process industries, and the study of continuous time planning and scheduling models as opposed to the discrete time models studied in this review.