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In classical dynamic lot sizing problems with single level production, it has always been considered that production can start as early as the first period of the planning horizon. In this book, we show that usually, and naturally, this is not possible in several situations. Consider, for example the situation where raw materials arrive in different periods of the planning horizon with limited quantities. This imposes that production between two arrivals of raw material should exceed the available quantity between these periods. Thus some demands cannot be produced before a certain availability date.The book consists of the study of multi item lot sizing with time windows. After a review on capacitated multi-item lot sizing problems, we present several Lagrangian heuristics to solve the capacitated multi-item lot sizing problem with time windows. These heuristics are analyzed and compared. Numerical results showing the performance of each heuristic on different problem classes and data scenarios are presented. The results show that most of the presented Lagrangian heuristics are effective and robust.
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