On the relaxation of multi-level dynamic lot-sizing models

In this paper the multi level dynamic lot sizing problem is analyzed when setup and holding costs do not depend on time. A zero–one integer programming formulation and its linear relaxation are investigated. The paper shows that for certain classes of problems the relaxed models provide integer solution when the number of periods is below a certain threshold. A counter example shows that at least six periods are required to obtain a unique non-integer solution of the relaxed problem.