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
Facets and algorithms for capacitated lot sizing
Mathematical Programming: Series A and B
Solving multi-item lot-sizing problems using strong cutting planes
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
Lot-sizing with constant batches: formulation and valid inequalities
Mathematics of Operations Research
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
Solving large-scale requirements planning problems with component substitution options
Computers and Industrial Engineering
Random Yield and Random Demand in a Production System with Downward Substitution
Operations Research
Single-Period Multiproduct Inventory Models with Substitution
Operations Research
Management of Multi-Item Retail Inventory Systems with Demand Substitution
Operations Research
Manufacturing & Service Operations Management
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
Tight Mip Formulation for Multi-Item Discrete Lot-Sizing Problems
Operations Research
A study of the lot-sizing polytope
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)
Uncapacitated lot sizing with backlogging: the convex hull
Mathematical Programming: Series A and B
On formulations of the stochastic uncapacitated lot-sizing problem
Operations Research Letters
Lot-sizing with fixed charges on stocks: the convex hull
Discrete Optimization
Lotsizing with backlogging and start-ups: the case of Wagner-Whitin costs
Operations Research Letters
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We consider a production planning problem for two items where the high quality item can substitute the demand for the low quality item. Given the number of periods, the demands, the production, inventory holding, setup and substitution costs, the problem is to find a minimum cost production and substitution plan. This problem generalizes the well-known uncapacitated lot-sizing problem. We study the projection of the feasible set onto the space of production and setup variables and derive a family of facet defining inequalities for the associated convex hull. We prove that these inequalities together with the trivial facet defining inequalities describe the convex hull of the projection if the number of periods is two. We present the results of a computational study and discuss the quality of the bounds given by the linear programming relaxation of the model strengthened with these facet defining inequalities for larger number of periods.